TSTP Solution File: SWW190+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWW190+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:44:27 EDT 2023
% Result : Theorem 76.47s 10.11s
% Output : CNFRefutation 77.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SWW190+1 : TPTP v8.1.2. Released v5.2.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 11:26:00 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.39 % Drodi V3.5.1
% 76.47/10.11 % Refutation found
% 76.47/10.11 % SZS status Theorem for theBenchmark: Theorem is valid
% 76.47/10.11 % SZS output start CNFRefutation for theBenchmark
% 76.47/10.11 fof(f7,axiom,(
% 76.47/10.11 (! [V_x] :( hBOOL(hAPP(v_P,V_x))=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,v_Y____) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f9,axiom,(
% 76.47/10.11 (! [V_Pa_2,T_a] : c_Set_OCollect(T_a,V_Pa_2) = V_Pa_2 )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f18,axiom,(
% 76.47/10.11 (! [V_xa_2,T_a] : c_member(T_a,V_xa_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f22,axiom,(
% 76.47/10.11 (! [V_A_2,V_xa_2,T_a] :( c_member(T_a,V_xa_2,V_A_2)<=> hBOOL(hAPP(V_A_2,V_xa_2)) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f42,axiom,(
% 76.47/10.11 (! [V_z,V_y,V_x,T_a] :( class_Orderings_Opreorder(T_a)=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f104,axiom,(
% 76.47/10.11 (! [V_y_2,V_xa_2,T_a] :( class_Orderings_Opreorder(T_a)=> ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_y_2)& ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_xa_2) ) ) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f125,axiom,(
% 76.47/10.11 (! [V_u_2,V_S_2,T_a] :( class_Orderings_Oord(T_a)=> ( (! [B_y] :( c_member(T_a,B_y,V_S_2)=> c_Orderings_Oord__class_Oless__eq(T_a,B_y,V_u_2) ))=> hBOOL(hAPP(c_Lubs_OisUb(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_u_2)) ) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f126,axiom,(
% 76.47/10.11 (! [V_y_2,V_xa_2] :( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)| V_xa_2 = V_y_2 ) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f127,axiom,(
% 76.47/10.11 (! [V_y_2,V_xa_2] :( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)& V_xa_2 != V_y_2 ) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f156,axiom,(
% 76.47/10.11 (! [V_w,V_z] :( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f184,axiom,(
% 76.47/10.11 (! [V_Pa_2,T_a] :( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Set_OCollect(T_a,V_Pa_2)<=> (! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) )) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f532,axiom,(
% 76.47/10.11 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f709,axiom,(
% 76.47/10.11 (! [V_y_2,V_xa_2,V_z_2] :( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2) ) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f710,axiom,(
% 76.47/10.11 (! [V_y_2,V_xa_2,V_z_2] :( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2) ) ) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1009,axiom,(
% 76.47/10.11 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1028,axiom,(
% 76.47/10.11 class_Rings_Olinordered__semidom(tc_Int_Oint) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1037,axiom,(
% 76.47/10.11 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1039,axiom,(
% 76.47/10.11 class_Rings_Olinordered__idom(tc_Int_Oint) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1040,axiom,(
% 76.47/10.11 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1045,axiom,(
% 76.47/10.11 class_Orderings_Opreorder(tc_Int_Oint) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1046,axiom,(
% 76.47/10.11 class_Orderings_Olinorder(tc_Int_Oint) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1048,axiom,(
% 76.47/10.11 class_Groups_Omonoid__add(tc_Int_Oint) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1054,axiom,(
% 76.47/10.11 class_Orderings_Oorder(tc_Int_Oint) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1065,axiom,(
% 76.47/10.11 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1077,axiom,(
% 76.47/10.11 class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1086,axiom,(
% 76.47/10.11 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1087,axiom,(
% 76.47/10.11 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1093,axiom,(
% 76.47/10.11 class_Groups_Omonoid__add(tc_Nat_Onat) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1094,axiom,(
% 76.47/10.11 class_Rings_Osemiring__1(tc_Nat_Onat) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1100,axiom,(
% 76.47/10.11 class_Orderings_Oord(tc_Nat_Onat) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1131,axiom,(
% 76.47/10.11 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1151,axiom,(
% 76.47/10.11 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1152,axiom,(
% 76.47/10.11 class_Lattices_Osemilattice__sup(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1153,axiom,(
% 76.47/10.11 class_Lattices_Osemilattice__inf(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1155,axiom,(
% 76.47/10.11 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1160,axiom,(
% 76.47/10.11 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1163,axiom,(
% 76.47/10.11 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1165,axiom,(
% 76.47/10.11 class_Groups_Oab__group__add(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1168,axiom,(
% 76.47/10.11 class_Orderings_Opreorder(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1169,axiom,(
% 76.47/10.11 class_Orderings_Olinorder(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1171,axiom,(
% 76.47/10.11 class_Groups_Omonoid__add(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1172,axiom,(
% 76.47/10.11 class_Rings_Osemiring__1(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1175,axiom,(
% 76.47/10.11 class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1177,axiom,(
% 76.47/10.11 class_Orderings_Oorder(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1180,axiom,(
% 76.47/10.11 class_Orderings_Oord(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1181,axiom,(
% 76.47/10.11 class_Rings_Oring__1(tc_RealDef_Oreal) ),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1189,conjecture,(
% 76.47/10.11 (? [B_x1] : hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P)),B_x1)) )),
% 76.47/10.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 76.47/10.11 fof(f1190,negated_conjecture,(
% 76.47/10.11 ~((? [B_x1] : hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P)),B_x1)) ))),
% 76.47/10.11 inference(negated_conjecture,[status(cth)],[f1189])).
% 76.47/10.11 fof(f1204,plain,(
% 76.47/10.11 ![V_x]: (~hBOOL(hAPP(v_P,V_x))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,v_Y____))),
% 76.47/10.11 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 76.47/10.11 fof(f1205,plain,(
% 76.47/10.11 ![X0]: (~hBOOL(hAPP(v_P,X0))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_Y____))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1204])).
% 76.47/10.11 fof(f1209,plain,(
% 76.47/10.11 ![X0,X1]: (c_Set_OCollect(X0,X1)=X1)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f9])).
% 76.47/10.11 fof(f1233,plain,(
% 76.47/10.11 ![X0,X1]: (c_member(X0,X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f18])).
% 76.47/10.11 fof(f1249,plain,(
% 76.47/10.11 ![V_A_2,V_xa_2,T_a]: ((~c_member(T_a,V_xa_2,V_A_2)|hBOOL(hAPP(V_A_2,V_xa_2)))&(c_member(T_a,V_xa_2,V_A_2)|~hBOOL(hAPP(V_A_2,V_xa_2))))),
% 76.47/10.11 inference(NNF_transformation,[status(esa)],[f22])).
% 76.47/10.11 fof(f1250,plain,(
% 76.47/10.11 (![V_A_2,V_xa_2]: ((![T_a]: ~c_member(T_a,V_xa_2,V_A_2))|hBOOL(hAPP(V_A_2,V_xa_2))))&(![V_A_2,V_xa_2]: ((![T_a]: c_member(T_a,V_xa_2,V_A_2))|~hBOOL(hAPP(V_A_2,V_xa_2))))),
% 76.47/10.11 inference(miniscoping,[status(esa)],[f1249])).
% 76.47/10.11 fof(f1251,plain,(
% 76.47/10.11 ![X0,X1,X2]: (~c_member(X0,X1,X2)|hBOOL(hAPP(X2,X1)))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1250])).
% 76.47/10.11 fof(f1321,plain,(
% 76.47/10.11 ![V_z,V_y,V_x,T_a]: (~class_Orderings_Opreorder(T_a)|(~c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|(~c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))),
% 76.47/10.11 inference(pre_NNF_transformation,[status(esa)],[f42])).
% 76.47/10.11 fof(f1322,plain,(
% 76.47/10.11 ![T_a]: (~class_Orderings_Opreorder(T_a)|(![V_y,V_x]: (~c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|(![V_z]: (~c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))))),
% 76.47/10.11 inference(miniscoping,[status(esa)],[f1321])).
% 76.47/10.11 fof(f1323,plain,(
% 76.47/10.11 ![X0,X1,X2,X3]: (~class_Orderings_Opreorder(X0)|~c_Orderings_Oord__class_Oless(X0,X1,X2)|~c_Orderings_Oord__class_Oless(X0,X2,X3)|c_Orderings_Oord__class_Oless(X0,X1,X3))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1322])).
% 76.47/10.11 fof(f1524,plain,(
% 76.47/10.11 ![V_y_2,V_xa_2,T_a]: (~class_Orderings_Opreorder(T_a)|(c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)<=>(c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_y_2)&~c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_xa_2))))),
% 76.47/10.11 inference(pre_NNF_transformation,[status(esa)],[f104])).
% 76.47/10.11 fof(f1525,plain,(
% 76.47/10.11 ![V_y_2,V_xa_2,T_a]: (~class_Orderings_Opreorder(T_a)|((~c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|(c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_y_2)&~c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_xa_2)))&(c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|(~c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_xa_2)))))),
% 76.47/10.11 inference(NNF_transformation,[status(esa)],[f1524])).
% 76.47/10.11 fof(f1526,plain,(
% 76.47/10.11 ![T_a]: (~class_Orderings_Opreorder(T_a)|((![V_y_2,V_xa_2]: (~c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|(c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_y_2)&~c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_xa_2))))&(![V_y_2,V_xa_2]: (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|(~c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_xa_2))))))),
% 76.47/10.11 inference(miniscoping,[status(esa)],[f1525])).
% 76.47/10.11 fof(f1529,plain,(
% 76.47/10.11 ![X0,X1,X2]: (~class_Orderings_Opreorder(X0)|c_Orderings_Oord__class_Oless(X0,X1,X2)|~c_Orderings_Oord__class_Oless__eq(X0,X1,X2)|c_Orderings_Oord__class_Oless__eq(X0,X2,X1))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1526])).
% 76.47/10.11 fof(f1610,plain,(
% 76.47/10.11 ![V_u_2,V_S_2,T_a]: (~class_Orderings_Oord(T_a)|((?[B_y]: (c_member(T_a,B_y,V_S_2)&~c_Orderings_Oord__class_Oless__eq(T_a,B_y,V_u_2)))|hBOOL(hAPP(c_Lubs_OisUb(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_u_2))))),
% 76.47/10.11 inference(pre_NNF_transformation,[status(esa)],[f125])).
% 76.47/10.11 fof(f1611,plain,(
% 76.47/10.11 ![T_a]: (~class_Orderings_Oord(T_a)|(![V_u_2,V_S_2]: ((?[B_y]: (c_member(T_a,B_y,V_S_2)&~c_Orderings_Oord__class_Oless__eq(T_a,B_y,V_u_2)))|hBOOL(hAPP(c_Lubs_OisUb(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_u_2)))))),
% 76.47/10.11 inference(miniscoping,[status(esa)],[f1610])).
% 76.47/10.11 fof(f1612,plain,(
% 76.47/10.11 ![T_a]: (~class_Orderings_Oord(T_a)|(![V_u_2,V_S_2]: ((c_member(T_a,sk0_16(V_S_2,V_u_2,T_a),V_S_2)&~c_Orderings_Oord__class_Oless__eq(T_a,sk0_16(V_S_2,V_u_2,T_a),V_u_2))|hBOOL(hAPP(c_Lubs_OisUb(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_u_2)))))),
% 76.47/10.11 inference(skolemization,[status(esa)],[f1611])).
% 76.47/10.11 fof(f1613,plain,(
% 76.47/10.11 ![X0,X1,X2]: (~class_Orderings_Oord(X0)|c_member(X0,sk0_16(X1,X2,X0),X1)|hBOOL(hAPP(c_Lubs_OisUb(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1),X2)))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1612])).
% 76.47/10.11 fof(f1614,plain,(
% 76.47/10.11 ![X0,X1,X2]: (~class_Orderings_Oord(X0)|~c_Orderings_Oord__class_Oless__eq(X0,sk0_16(X1,X2,X0),X2)|hBOOL(hAPP(c_Lubs_OisUb(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1),X2)))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1612])).
% 76.47/10.11 fof(f1615,plain,(
% 76.47/10.11 ![V_y_2,V_xa_2]: ((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)|(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|V_xa_2=V_y_2))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)&~V_xa_2=V_y_2)))),
% 76.47/10.11 inference(NNF_transformation,[status(esa)],[f126])).
% 76.47/10.11 fof(f1616,plain,(
% 76.47/10.11 (![V_y_2,V_xa_2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)|(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|V_xa_2=V_y_2)))&(![V_y_2,V_xa_2]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)&~V_xa_2=V_y_2)))),
% 76.47/10.11 inference(miniscoping,[status(esa)],[f1615])).
% 76.47/10.11 fof(f1619,plain,(
% 76.47/10.11 ![X0,X1]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|~X0=X1)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1616])).
% 76.47/10.11 fof(f1620,plain,(
% 76.47/10.11 ![V_y_2,V_xa_2]: ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)&~V_xa_2=V_y_2))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)|V_xa_2=V_y_2)))),
% 76.47/10.11 inference(NNF_transformation,[status(esa)],[f127])).
% 76.47/10.11 fof(f1621,plain,(
% 76.47/10.11 (![V_y_2,V_xa_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)&~V_xa_2=V_y_2)))&(![V_y_2,V_xa_2]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)|V_xa_2=V_y_2)))),
% 76.47/10.11 inference(miniscoping,[status(esa)],[f1620])).
% 76.47/10.11 fof(f1623,plain,(
% 76.47/10.11 ![X0,X1]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|~X0=X1)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1621])).
% 76.47/10.11 fof(f1714,plain,(
% 76.47/10.11 ![X0,X1]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f156])).
% 76.47/10.11 fof(f1800,plain,(
% 76.47/10.11 ![V_Pa_2,T_a]: ((~c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_OCollect(T_a,V_Pa_2)|(![B_x]: ~hBOOL(hAPP(V_Pa_2,B_x))))&(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_OCollect(T_a,V_Pa_2)|(?[B_x]: hBOOL(hAPP(V_Pa_2,B_x)))))),
% 76.47/10.11 inference(NNF_transformation,[status(esa)],[f184])).
% 76.47/10.11 fof(f1801,plain,(
% 76.47/10.11 (![V_Pa_2]: ((![T_a]: ~c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_OCollect(T_a,V_Pa_2))|(![B_x]: ~hBOOL(hAPP(V_Pa_2,B_x)))))&(![V_Pa_2]: ((![T_a]: c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_OCollect(T_a,V_Pa_2))|(?[B_x]: hBOOL(hAPP(V_Pa_2,B_x)))))),
% 76.47/10.11 inference(miniscoping,[status(esa)],[f1800])).
% 76.47/10.11 fof(f1802,plain,(
% 76.47/10.11 (![V_Pa_2]: ((![T_a]: ~c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_OCollect(T_a,V_Pa_2))|(![B_x]: ~hBOOL(hAPP(V_Pa_2,B_x)))))&(![V_Pa_2]: ((![T_a]: c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_OCollect(T_a,V_Pa_2))|hBOOL(hAPP(V_Pa_2,sk0_31(V_Pa_2)))))),
% 76.47/10.11 inference(skolemization,[status(esa)],[f1801])).
% 76.47/10.11 fof(f1803,plain,(
% 76.47/10.11 ![X0,X1,X2]: (~c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))=c_Set_OCollect(X0,X1)|~hBOOL(hAPP(X1,X2)))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1802])).
% 76.47/10.11 fof(f2766,plain,(
% 76.47/10.11 ~c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f532])).
% 76.47/10.11 fof(f3348,plain,(
% 76.47/10.11 ![V_y_2,V_xa_2,V_z_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)))),
% 76.47/10.11 inference(pre_NNF_transformation,[status(esa)],[f709])).
% 76.47/10.11 fof(f3349,plain,(
% 76.47/10.11 ![V_y_2,V_xa_2,V_z_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2))))),
% 76.47/10.11 inference(NNF_transformation,[status(esa)],[f3348])).
% 76.47/10.11 fof(f3350,plain,(
% 76.47/10.11 ![V_z_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|((![V_y_2,V_xa_2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)))&(![V_y_2,V_xa_2]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)))))),
% 76.47/10.11 inference(miniscoping,[status(esa)],[f3349])).
% 76.47/10.11 fof(f3351,plain,(
% 76.47/10.11 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f3350])).
% 76.47/10.11 fof(f3353,plain,(
% 76.47/10.11 ![V_y_2,V_xa_2,V_z_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)))),
% 76.47/10.11 inference(pre_NNF_transformation,[status(esa)],[f710])).
% 76.47/10.11 fof(f3354,plain,(
% 76.47/10.11 ![V_y_2,V_xa_2,V_z_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2))))),
% 76.47/10.11 inference(NNF_transformation,[status(esa)],[f3353])).
% 76.47/10.11 fof(f3355,plain,(
% 76.47/10.11 ![V_z_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|((![V_y_2,V_xa_2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)))&(![V_y_2,V_xa_2]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_y_2)))))),
% 76.47/10.11 inference(miniscoping,[status(esa)],[f3354])).
% 76.47/10.11 fof(f3356,plain,(
% 76.47/10.11 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f3355])).
% 76.47/10.11 fof(f4262,plain,(
% 76.47/10.11 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1009])).
% 76.47/10.11 fof(f4281,plain,(
% 76.47/10.11 class_Rings_Olinordered__semidom(tc_Int_Oint)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1028])).
% 76.47/10.11 fof(f4290,plain,(
% 76.47/10.11 class_Groups_Ocomm__monoid__add(tc_Int_Oint)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1037])).
% 76.47/10.11 fof(f4292,plain,(
% 76.47/10.11 class_Rings_Olinordered__idom(tc_Int_Oint)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1039])).
% 76.47/10.11 fof(f4293,plain,(
% 76.47/10.11 class_Rings_Ocomm__semiring__1(tc_Int_Oint)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1040])).
% 76.47/10.11 fof(f4298,plain,(
% 76.47/10.11 class_Orderings_Opreorder(tc_Int_Oint)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1045])).
% 76.47/10.11 fof(f4299,plain,(
% 76.47/10.11 class_Orderings_Olinorder(tc_Int_Oint)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1046])).
% 76.47/10.11 fof(f4301,plain,(
% 76.47/10.11 class_Groups_Omonoid__add(tc_Int_Oint)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1048])).
% 76.47/10.11 fof(f4307,plain,(
% 76.47/10.11 class_Orderings_Oorder(tc_Int_Oint)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1054])).
% 76.47/10.11 fof(f4318,plain,(
% 76.47/10.11 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1065])).
% 76.47/10.11 fof(f4330,plain,(
% 76.47/10.11 class_Rings_Olinordered__semidom(tc_Nat_Onat)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1077])).
% 76.47/10.11 fof(f4339,plain,(
% 76.47/10.11 class_Groups_Ocomm__monoid__add(tc_Nat_Onat)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1086])).
% 76.47/10.11 fof(f4340,plain,(
% 76.47/10.11 class_Rings_Ocomm__semiring__1(tc_Nat_Onat)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1087])).
% 76.47/10.11 fof(f4346,plain,(
% 76.47/10.11 class_Groups_Omonoid__add(tc_Nat_Onat)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1093])).
% 76.47/10.11 fof(f4347,plain,(
% 76.47/10.11 class_Rings_Osemiring__1(tc_Nat_Onat)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1094])).
% 76.47/10.11 fof(f4353,plain,(
% 76.47/10.11 class_Orderings_Oord(tc_Nat_Onat)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1100])).
% 76.47/10.11 fof(f4384,plain,(
% 76.47/10.11 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1131])).
% 76.47/10.11 fof(f4404,plain,(
% 76.47/10.11 class_Rings_Olinordered__semidom(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1151])).
% 76.47/10.11 fof(f4405,plain,(
% 76.47/10.11 class_Lattices_Osemilattice__sup(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1152])).
% 76.47/10.11 fof(f4406,plain,(
% 76.47/10.11 class_Lattices_Osemilattice__inf(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1153])).
% 76.47/10.11 fof(f4408,plain,(
% 76.47/10.11 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1155])).
% 76.47/10.11 fof(f4413,plain,(
% 76.47/10.11 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1160])).
% 76.47/10.11 fof(f4416,plain,(
% 76.47/10.11 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1163])).
% 76.47/10.11 fof(f4418,plain,(
% 76.47/10.11 class_Groups_Oab__group__add(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1165])).
% 76.47/10.11 fof(f4421,plain,(
% 76.47/10.11 class_Orderings_Opreorder(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1168])).
% 76.47/10.11 fof(f4422,plain,(
% 76.47/10.11 class_Orderings_Olinorder(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1169])).
% 76.47/10.11 fof(f4424,plain,(
% 76.47/10.11 class_Groups_Omonoid__add(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1171])).
% 76.47/10.11 fof(f4425,plain,(
% 76.47/10.11 class_Rings_Osemiring__1(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1172])).
% 76.47/10.11 fof(f4428,plain,(
% 76.47/10.11 class_Groups_Ogroup__add(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1175])).
% 76.47/10.11 fof(f4430,plain,(
% 76.47/10.11 class_Orderings_Oorder(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1177])).
% 76.47/10.11 fof(f4433,plain,(
% 76.47/10.11 class_Orderings_Oord(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1180])).
% 76.47/10.11 fof(f4434,plain,(
% 76.47/10.11 class_Rings_Oring__1(tc_RealDef_Oreal)),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f1181])).
% 76.47/10.11 fof(f4442,plain,(
% 76.47/10.11 (![B_x1]: ~hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P)),B_x1)))),
% 76.47/10.11 inference(pre_NNF_transformation,[status(esa)],[f1190])).
% 76.47/10.11 fof(f4443,plain,(
% 76.47/10.11 ![X0]: (~hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P)),X0)))),
% 76.47/10.11 inference(cnf_transformation,[status(esa)],[f4442])).
% 76.47/10.11 fof(f4491,plain,(
% 76.47/10.11 ![X0]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0))),
% 76.47/10.11 inference(destructive_equality_resolution,[status(esa)],[f1619])).
% 76.47/10.11 fof(f4492,plain,(
% 76.47/10.11 ![X0]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X0))),
% 76.47/10.11 inference(destructive_equality_resolution,[status(esa)],[f1623])).
% 76.47/10.11 fof(f4582,plain,(
% 76.47/10.11 ![X0]: (~hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),v_P),X0)))),
% 76.47/10.11 inference(backward_demodulation,[status(thm)],[f1209,f4443])).
% 76.47/10.11 fof(f4593,plain,(
% 76.47/10.11 ![X0,X1,X2]: (~c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))=X1|~hBOOL(hAPP(X1,X2)))),
% 76.47/10.11 inference(forward_demodulation,[status(thm)],[f1209,f1803])).
% 76.47/10.11 fof(f4594,plain,(
% 76.47/10.11 ![X0,X1]: (~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1)))),
% 76.47/10.11 inference(destructive_equality_resolution,[status(esa)],[f4593])).
% 76.47/10.11 fof(f4897,plain,(
% 76.47/10.11 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)))),
% 76.47/10.11 inference(resolution,[status(thm)],[f3351,f1714])).
% 76.47/10.11 fof(f4932,plain,(
% 76.47/10.11 spl0_13 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_Y____,v_Y____)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f4933,plain,(
% 76.47/10.11 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_Y____,v_Y____)|~spl0_13),
% 76.47/10.11 inference(component_clause,[status(thm)],[f4932])).
% 76.47/10.11 fof(f4951,plain,(
% 76.47/10.11 spl0_15 <=> class_Orderings_Oord(tc_RealDef_Oreal)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f4953,plain,(
% 76.47/10.11 ~class_Orderings_Oord(tc_RealDef_Oreal)|spl0_15),
% 76.47/10.11 inference(component_clause,[status(thm)],[f4951])).
% 76.47/10.11 fof(f4966,plain,(
% 76.47/10.11 $false|spl0_15),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f4953,f4433])).
% 76.47/10.11 fof(f4967,plain,(
% 76.47/10.11 spl0_15),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f4966])).
% 76.47/10.11 fof(f5370,plain,(
% 76.47/10.11 spl0_26 <=> ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f5434,plain,(
% 76.47/10.11 spl0_30 <=> class_Orderings_Opreorder(tc_RealDef_Oreal)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f5436,plain,(
% 76.47/10.11 ~class_Orderings_Opreorder(tc_RealDef_Oreal)|spl0_30),
% 76.47/10.11 inference(component_clause,[status(thm)],[f5434])).
% 76.47/10.11 fof(f5494,plain,(
% 76.47/10.11 spl0_40 <=> class_Orderings_Oorder(tc_RealDef_Oreal)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f5496,plain,(
% 76.47/10.11 ~class_Orderings_Oorder(tc_RealDef_Oreal)|spl0_40),
% 76.47/10.11 inference(component_clause,[status(thm)],[f5494])).
% 76.47/10.11 fof(f5658,plain,(
% 76.47/10.11 spl0_67 <=> class_Orderings_Olinorder(tc_RealDef_Oreal)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f5660,plain,(
% 76.47/10.11 ~class_Orderings_Olinorder(tc_RealDef_Oreal)|spl0_67),
% 76.47/10.11 inference(component_clause,[status(thm)],[f5658])).
% 76.47/10.11 fof(f8511,plain,(
% 76.47/10.11 spl0_403 <=> ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f8512,plain,(
% 76.47/10.11 ![X0,X1]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)|~spl0_403)),
% 76.47/10.11 inference(component_clause,[status(thm)],[f8511])).
% 76.47/10.11 fof(f8514,plain,(
% 76.47/10.11 ![X0,X1]: (~class_Orderings_Opreorder(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0))),
% 76.47/10.11 inference(resolution,[status(thm)],[f1323,f4492])).
% 76.47/10.11 fof(f8515,plain,(
% 76.47/10.11 ~spl0_30|spl0_403),
% 76.47/10.11 inference(split_clause,[status(thm)],[f8514,f5434,f8511])).
% 76.47/10.11 fof(f9421,plain,(
% 76.47/10.11 ![X0]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_Y____,X0)|~hBOOL(hAPP(v_P,X0))|~spl0_403)),
% 76.47/10.11 inference(resolution,[status(thm)],[f8512,f1205])).
% 76.47/10.11 fof(f9817,plain,(
% 76.47/10.11 $false|spl0_30),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f4421,f5436])).
% 76.47/10.11 fof(f9818,plain,(
% 76.47/10.11 spl0_30),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f9817])).
% 76.47/10.11 fof(f9824,plain,(
% 76.47/10.11 $false|spl0_67),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f4422,f5660])).
% 76.47/10.11 fof(f9825,plain,(
% 76.47/10.11 spl0_67),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f9824])).
% 76.47/10.11 fof(f10887,plain,(
% 76.47/10.11 $false|spl0_40),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f4430,f5496])).
% 76.47/10.11 fof(f10888,plain,(
% 76.47/10.11 spl0_40),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f10887])).
% 76.47/10.11 fof(f10911,plain,(
% 76.47/10.11 spl0_508 <=> class_Orderings_Oord(tc_Nat_Onat)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f10913,plain,(
% 76.47/10.11 ~class_Orderings_Oord(tc_Nat_Onat)|spl0_508),
% 76.47/10.11 inference(component_clause,[status(thm)],[f10911])).
% 76.47/10.11 fof(f10919,plain,(
% 76.47/10.11 $false|spl0_508),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f10913,f4353])).
% 76.47/10.11 fof(f10920,plain,(
% 76.47/10.11 spl0_508),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f10919])).
% 76.47/10.11 fof(f10924,plain,(
% 76.47/10.11 spl0_511 <=> class_Orderings_Olinorder(tc_Int_Oint)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f10926,plain,(
% 76.47/10.11 ~class_Orderings_Olinorder(tc_Int_Oint)|spl0_511),
% 76.47/10.11 inference(component_clause,[status(thm)],[f10924])).
% 76.47/10.11 fof(f10937,plain,(
% 76.47/10.11 spl0_514 <=> class_Rings_Olinordered__idom(tc_Int_Oint)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f10939,plain,(
% 76.47/10.11 ~class_Rings_Olinordered__idom(tc_Int_Oint)|spl0_514),
% 76.47/10.11 inference(component_clause,[status(thm)],[f10937])).
% 76.47/10.11 fof(f10942,plain,(
% 76.47/10.11 spl0_515 <=> class_Orderings_Oorder(tc_Int_Oint)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f10944,plain,(
% 76.47/10.11 ~class_Orderings_Oorder(tc_Int_Oint)|spl0_515),
% 76.47/10.11 inference(component_clause,[status(thm)],[f10942])).
% 76.47/10.11 fof(f10950,plain,(
% 76.47/10.11 spl0_517 <=> class_Orderings_Opreorder(tc_Int_Oint)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f10952,plain,(
% 76.47/10.11 ~class_Orderings_Opreorder(tc_Int_Oint)|spl0_517),
% 76.47/10.11 inference(component_clause,[status(thm)],[f10950])).
% 76.47/10.11 fof(f10955,plain,(
% 76.47/10.11 $false|spl0_517),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f10952,f4298])).
% 76.47/10.11 fof(f10956,plain,(
% 76.47/10.11 spl0_517),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f10955])).
% 76.47/10.11 fof(f10957,plain,(
% 76.47/10.11 $false|spl0_515),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f10944,f4307])).
% 76.47/10.11 fof(f10958,plain,(
% 76.47/10.11 spl0_515),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f10957])).
% 76.47/10.11 fof(f10959,plain,(
% 76.47/10.11 $false|spl0_514),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f10939,f4292])).
% 76.47/10.11 fof(f10960,plain,(
% 76.47/10.11 spl0_514),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f10959])).
% 76.47/10.11 fof(f10961,plain,(
% 76.47/10.11 $false|spl0_511),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f10926,f4299])).
% 76.47/10.11 fof(f10962,plain,(
% 76.47/10.11 spl0_511),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f10961])).
% 76.47/10.11 fof(f12062,plain,(
% 76.47/10.11 spl0_611 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sk0_2,sk0_2)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f12064,plain,(
% 76.47/10.11 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sk0_2,sk0_2)|spl0_611),
% 76.47/10.11 inference(component_clause,[status(thm)],[f12062])).
% 76.47/10.11 fof(f14257,plain,(
% 76.47/10.11 $false|spl0_611),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f12064,f4491])).
% 76.47/10.11 fof(f14258,plain,(
% 76.47/10.11 spl0_611),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f14257])).
% 76.47/10.11 fof(f15513,plain,(
% 76.47/10.11 spl0_856 <=> class_Groups_Omonoid__add(tc_Int_Oint)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f15515,plain,(
% 76.47/10.11 ~class_Groups_Omonoid__add(tc_Int_Oint)|spl0_856),
% 76.47/10.11 inference(component_clause,[status(thm)],[f15513])).
% 76.47/10.11 fof(f15523,plain,(
% 76.47/10.11 spl0_858 <=> class_Groups_Omonoid__add(tc_Nat_Onat)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f15525,plain,(
% 76.47/10.11 ~class_Groups_Omonoid__add(tc_Nat_Onat)|spl0_858),
% 76.47/10.11 inference(component_clause,[status(thm)],[f15523])).
% 76.47/10.11 fof(f15533,plain,(
% 76.47/10.11 $false|spl0_858),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f15525,f4346])).
% 76.47/10.11 fof(f15534,plain,(
% 76.47/10.11 spl0_858),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f15533])).
% 76.47/10.11 fof(f15535,plain,(
% 76.47/10.11 $false|spl0_856),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f15515,f4301])).
% 76.47/10.11 fof(f15536,plain,(
% 76.47/10.11 spl0_856),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f15535])).
% 76.47/10.11 fof(f15537,plain,(
% 76.47/10.11 spl0_860 <=> class_Groups_Ocomm__monoid__add(tc_Int_Oint)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f15539,plain,(
% 76.47/10.11 ~class_Groups_Ocomm__monoid__add(tc_Int_Oint)|spl0_860),
% 76.47/10.11 inference(component_clause,[status(thm)],[f15537])).
% 76.47/10.11 fof(f15544,plain,(
% 76.47/10.11 spl0_861 <=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f15546,plain,(
% 76.47/10.11 ~class_Groups_Ocomm__monoid__add(tc_Nat_Onat)|spl0_861),
% 76.47/10.11 inference(component_clause,[status(thm)],[f15544])).
% 76.47/10.11 fof(f15551,plain,(
% 76.47/10.11 $false|spl0_861),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f15546,f4339])).
% 76.47/10.11 fof(f15552,plain,(
% 76.47/10.11 spl0_861),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f15551])).
% 76.47/10.11 fof(f15553,plain,(
% 76.47/10.11 $false|spl0_860),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f15539,f4290])).
% 76.47/10.11 fof(f15554,plain,(
% 76.47/10.11 spl0_860),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f15553])).
% 76.47/10.11 fof(f15706,plain,(
% 76.47/10.11 spl0_883 <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f15708,plain,(
% 76.47/10.11 ~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint)|spl0_883),
% 76.47/10.11 inference(component_clause,[status(thm)],[f15706])).
% 76.47/10.11 fof(f15713,plain,(
% 76.47/10.11 spl0_884 <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f15715,plain,(
% 76.47/10.11 ~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat)|spl0_884),
% 76.47/10.11 inference(component_clause,[status(thm)],[f15713])).
% 76.47/10.11 fof(f15720,plain,(
% 76.47/10.11 $false|spl0_884),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f15715,f4318])).
% 76.47/10.11 fof(f15721,plain,(
% 76.47/10.11 spl0_884),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f15720])).
% 76.47/10.11 fof(f15722,plain,(
% 76.47/10.11 $false|spl0_883),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f15708,f4262])).
% 76.47/10.11 fof(f15723,plain,(
% 76.47/10.11 spl0_883),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f15722])).
% 76.47/10.11 fof(f15724,plain,(
% 76.47/10.11 spl0_885 <=> class_Rings_Ocomm__semiring__1(tc_Int_Oint)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f15726,plain,(
% 76.47/10.11 ~class_Rings_Ocomm__semiring__1(tc_Int_Oint)|spl0_885),
% 76.47/10.11 inference(component_clause,[status(thm)],[f15724])).
% 76.47/10.11 fof(f15731,plain,(
% 76.47/10.11 spl0_886 <=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f15733,plain,(
% 76.47/10.11 ~class_Rings_Ocomm__semiring__1(tc_Nat_Onat)|spl0_886),
% 76.47/10.11 inference(component_clause,[status(thm)],[f15731])).
% 76.47/10.11 fof(f15738,plain,(
% 76.47/10.11 $false|spl0_886),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f15733,f4340])).
% 76.47/10.11 fof(f15739,plain,(
% 76.47/10.11 spl0_886),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f15738])).
% 76.47/10.11 fof(f15740,plain,(
% 76.47/10.11 $false|spl0_885),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f15726,f4293])).
% 76.47/10.11 fof(f15741,plain,(
% 76.47/10.11 spl0_885),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f15740])).
% 76.47/10.11 fof(f15750,plain,(
% 76.47/10.11 spl0_887 <=> class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f15752,plain,(
% 76.47/10.11 ~class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal)|spl0_887),
% 76.47/10.11 inference(component_clause,[status(thm)],[f15750])).
% 76.47/10.11 fof(f15765,plain,(
% 76.47/10.11 $false|spl0_887),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f15752,f4408])).
% 76.47/10.11 fof(f15766,plain,(
% 76.47/10.11 spl0_887),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f15765])).
% 76.47/10.11 fof(f16177,plain,(
% 76.47/10.11 spl0_922 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f16178,plain,(
% 76.47/10.11 ![X0,X1]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)|~spl0_922)),
% 76.47/10.11 inference(component_clause,[status(thm)],[f16177])).
% 76.47/10.11 fof(f16180,plain,(
% 76.47/10.11 ![X0,X1]: (~class_Orderings_Opreorder(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0))),
% 76.47/10.11 inference(resolution,[status(thm)],[f1529,f1714])).
% 76.47/10.11 fof(f16181,plain,(
% 76.47/10.11 ~spl0_30|spl0_922),
% 76.47/10.11 inference(split_clause,[status(thm)],[f16180,f5434,f16177])).
% 76.47/10.11 fof(f16296,plain,(
% 76.47/10.11 ![X0,X1]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)|~spl0_922)),
% 76.47/10.11 inference(duplicate_literals_removal,[status(esa)],[f16178])).
% 76.47/10.11 fof(f17193,plain,(
% 76.47/10.11 $false|~spl0_13),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f4933,f4492])).
% 76.47/10.11 fof(f17194,plain,(
% 76.47/10.11 ~spl0_13),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f17193])).
% 76.47/10.11 fof(f17208,plain,(
% 76.47/10.11 spl0_1002 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f17210,plain,(
% 76.47/10.11 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|spl0_1002),
% 76.47/10.11 inference(component_clause,[status(thm)],[f17208])).
% 76.47/10.11 fof(f17456,plain,(
% 76.47/10.11 $false|spl0_1002),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f17210,f4491])).
% 76.47/10.11 fof(f17457,plain,(
% 76.47/10.11 spl0_1002),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f17456])).
% 76.47/10.11 fof(f19074,plain,(
% 76.47/10.11 ![X0,X1]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0))),
% 76.47/10.11 inference(resolution,[status(thm)],[f4897,f3356])).
% 76.47/10.11 fof(f19075,plain,(
% 76.47/10.11 spl0_26),
% 76.47/10.11 inference(split_clause,[status(thm)],[f19074,f5370])).
% 76.47/10.11 fof(f20112,plain,(
% 76.47/10.11 spl0_1210 <=> hBOOL(hAPP(X3,c_Orderings_Obot__class_Obot(tc_Nat_Onat)))),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f20113,plain,(
% 76.47/10.11 ![X0]: (hBOOL(hAPP(X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat)))|~spl0_1210)),
% 76.47/10.11 inference(component_clause,[status(thm)],[f20112])).
% 76.47/10.11 fof(f20179,plain,(
% 76.47/10.11 $false|~spl0_1210),
% 76.47/10.11 inference(resolution,[status(thm)],[f20113,f4594])).
% 76.47/10.11 fof(f20180,plain,(
% 76.47/10.11 ~spl0_1210),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f20179])).
% 76.47/10.11 fof(f20539,plain,(
% 76.47/10.11 spl0_1261 <=> class_Lattices_Osemilattice__sup(tc_RealDef_Oreal)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f20541,plain,(
% 76.47/10.11 ~class_Lattices_Osemilattice__sup(tc_RealDef_Oreal)|spl0_1261),
% 76.47/10.11 inference(component_clause,[status(thm)],[f20539])).
% 76.47/10.11 fof(f20598,plain,(
% 76.47/10.11 $false|spl0_1261),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f20541,f4405])).
% 76.47/10.11 fof(f20599,plain,(
% 76.47/10.11 spl0_1261),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f20598])).
% 76.47/10.11 fof(f20822,plain,(
% 76.47/10.11 spl0_1287 <=> class_Lattices_Osemilattice__inf(tc_RealDef_Oreal)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f20824,plain,(
% 76.47/10.11 ~class_Lattices_Osemilattice__inf(tc_RealDef_Oreal)|spl0_1287),
% 76.47/10.11 inference(component_clause,[status(thm)],[f20822])).
% 76.47/10.11 fof(f20875,plain,(
% 76.47/10.11 $false|spl0_1287),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f20824,f4406])).
% 76.47/10.11 fof(f20876,plain,(
% 76.47/10.11 spl0_1287),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f20875])).
% 76.47/10.11 fof(f21071,plain,(
% 76.47/10.11 spl0_1308 <=> class_Rings_Olinordered__semidom(tc_Nat_Onat)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f21073,plain,(
% 76.47/10.11 ~class_Rings_Olinordered__semidom(tc_Nat_Onat)|spl0_1308),
% 76.47/10.11 inference(component_clause,[status(thm)],[f21071])).
% 76.47/10.11 fof(f21086,plain,(
% 76.47/10.11 spl0_1311 <=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f21088,plain,(
% 76.47/10.11 ~class_Rings_Olinordered__semidom(tc_RealDef_Oreal)|spl0_1311),
% 76.47/10.11 inference(component_clause,[status(thm)],[f21086])).
% 76.47/10.11 fof(f21114,plain,(
% 76.47/10.11 spl0_1317 <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f21115,plain,(
% 76.47/10.11 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~spl0_1317),
% 76.47/10.11 inference(component_clause,[status(thm)],[f21114])).
% 76.47/10.11 fof(f21167,plain,(
% 76.47/10.11 $false|spl0_1308),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f21073,f4330])).
% 76.47/10.11 fof(f21168,plain,(
% 76.47/10.11 spl0_1308),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f21167])).
% 76.47/10.11 fof(f21169,plain,(
% 76.47/10.11 $false|spl0_1311),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f21088,f4404])).
% 76.47/10.11 fof(f21170,plain,(
% 76.47/10.11 spl0_1311),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f21169])).
% 76.47/10.11 fof(f21172,plain,(
% 76.47/10.11 $false|~spl0_1317),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f21115,f2766])).
% 76.47/10.11 fof(f21173,plain,(
% 76.47/10.11 ~spl0_1317),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f21172])).
% 76.47/10.11 fof(f21262,plain,(
% 76.47/10.11 spl0_1333 <=> class_Rings_Osemiring__1(tc_Nat_Onat)),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f21264,plain,(
% 76.47/10.11 ~class_Rings_Osemiring__1(tc_Nat_Onat)|spl0_1333),
% 76.47/10.11 inference(component_clause,[status(thm)],[f21262])).
% 76.47/10.11 fof(f21270,plain,(
% 76.47/10.11 $false|spl0_1333),
% 76.47/10.11 inference(forward_subsumption_resolution,[status(thm)],[f21264,f4347])).
% 76.47/10.11 fof(f21271,plain,(
% 76.47/10.11 spl0_1333),
% 76.47/10.11 inference(contradiction_clause,[status(thm)],[f21270])).
% 76.47/10.11 fof(f21291,plain,(
% 76.47/10.11 spl0_1335 <=> ~X0=X0),
% 76.47/10.11 introduced(split_symbol_definition)).
% 76.47/10.11 fof(f21292,plain,(
% 76.47/10.11 ![X0]: (~X0=X0|~spl0_1335)),
% 76.47/10.11 inference(component_clause,[status(thm)],[f21291])).
% 76.47/10.11 fof(f21299,plain,(
% 76.47/10.11 $false|~spl0_1335),
% 76.47/10.11 inference(trivial_equality_resolution,[status(esa)],[f21292])).
% 76.47/10.12 fof(f21300,plain,(
% 76.47/10.12 ~spl0_1335),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f21299])).
% 76.47/10.12 fof(f21420,plain,(
% 76.47/10.12 spl0_1343 <=> class_Rings_Olinordered__semidom(tc_Int_Oint)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f21422,plain,(
% 76.47/10.12 ~class_Rings_Olinordered__semidom(tc_Int_Oint)|spl0_1343),
% 76.47/10.12 inference(component_clause,[status(thm)],[f21420])).
% 76.47/10.12 fof(f21517,plain,(
% 76.47/10.12 $false|spl0_1343),
% 76.47/10.12 inference(forward_subsumption_resolution,[status(thm)],[f21422,f4281])).
% 76.47/10.12 fof(f21518,plain,(
% 76.47/10.12 spl0_1343),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f21517])).
% 76.47/10.12 fof(f22001,plain,(
% 76.47/10.12 spl0_1427 <=> c_member(tc_RealDef_Oreal,sk0_16(v_P,X0,tc_RealDef_Oreal),v_P)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f22002,plain,(
% 76.47/10.12 ![X0]: (c_member(tc_RealDef_Oreal,sk0_16(v_P,X0,tc_RealDef_Oreal),v_P)|~spl0_1427)),
% 76.47/10.12 inference(component_clause,[status(thm)],[f22001])).
% 76.47/10.12 fof(f22004,plain,(
% 76.47/10.12 ![X0]: (~class_Orderings_Oord(tc_RealDef_Oreal)|c_member(tc_RealDef_Oreal,sk0_16(v_P,X0,tc_RealDef_Oreal),v_P))),
% 76.47/10.12 inference(resolution,[status(thm)],[f1613,f4582])).
% 76.47/10.12 fof(f22005,plain,(
% 76.47/10.12 ~spl0_15|spl0_1427),
% 76.47/10.12 inference(split_clause,[status(thm)],[f22004,f4951,f22001])).
% 76.47/10.12 fof(f22028,plain,(
% 76.47/10.12 ![X0]: (hBOOL(hAPP(v_P,sk0_16(v_P,X0,tc_RealDef_Oreal)))|~spl0_1427)),
% 76.47/10.12 inference(resolution,[status(thm)],[f22002,f1251])).
% 76.47/10.12 fof(f23364,plain,(
% 76.47/10.12 spl0_1546 <=> class_Rings_Oring__1(tc_RealDef_Oreal)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f23366,plain,(
% 76.47/10.12 ~class_Rings_Oring__1(tc_RealDef_Oreal)|spl0_1546),
% 76.47/10.12 inference(component_clause,[status(thm)],[f23364])).
% 76.47/10.12 fof(f23372,plain,(
% 76.47/10.12 spl0_1548 <=> class_Rings_Osemiring__1(tc_RealDef_Oreal)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f23374,plain,(
% 76.47/10.12 ~class_Rings_Osemiring__1(tc_RealDef_Oreal)|spl0_1548),
% 76.47/10.12 inference(component_clause,[status(thm)],[f23372])).
% 76.47/10.12 fof(f23410,plain,(
% 76.47/10.12 spl0_1556 <=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f23412,plain,(
% 76.47/10.12 ~class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)|spl0_1556),
% 76.47/10.12 inference(component_clause,[status(thm)],[f23410])).
% 76.47/10.12 fof(f23423,plain,(
% 76.47/10.12 spl0_1559 <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f23425,plain,(
% 76.47/10.12 ~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)|spl0_1559),
% 76.47/10.12 inference(component_clause,[status(thm)],[f23423])).
% 76.47/10.12 fof(f23428,plain,(
% 76.47/10.12 spl0_1560 <=> class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f23430,plain,(
% 76.47/10.12 ~class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal)|spl0_1560),
% 76.47/10.12 inference(component_clause,[status(thm)],[f23428])).
% 76.47/10.12 fof(f23433,plain,(
% 76.47/10.12 spl0_1561 <=> class_Groups_Omonoid__add(tc_RealDef_Oreal)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f23435,plain,(
% 76.47/10.12 ~class_Groups_Omonoid__add(tc_RealDef_Oreal)|spl0_1561),
% 76.47/10.12 inference(component_clause,[status(thm)],[f23433])).
% 76.47/10.12 fof(f23442,plain,(
% 76.47/10.12 spl0_1562 <=> class_Groups_Ogroup__add(tc_RealDef_Oreal)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f23444,plain,(
% 76.47/10.12 ~class_Groups_Ogroup__add(tc_RealDef_Oreal)|spl0_1562),
% 76.47/10.12 inference(component_clause,[status(thm)],[f23442])).
% 76.47/10.12 fof(f23450,plain,(
% 76.47/10.12 $false|spl0_1559),
% 76.47/10.12 inference(forward_subsumption_resolution,[status(thm)],[f23425,f4384])).
% 76.47/10.12 fof(f23451,plain,(
% 76.47/10.12 spl0_1559),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f23450])).
% 76.47/10.12 fof(f23452,plain,(
% 76.47/10.12 $false|spl0_1562),
% 76.47/10.12 inference(forward_subsumption_resolution,[status(thm)],[f23444,f4428])).
% 76.47/10.12 fof(f23453,plain,(
% 76.47/10.12 spl0_1562),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f23452])).
% 76.47/10.12 fof(f23454,plain,(
% 76.47/10.12 $false|spl0_1546),
% 76.47/10.12 inference(forward_subsumption_resolution,[status(thm)],[f23366,f4434])).
% 76.47/10.12 fof(f23455,plain,(
% 76.47/10.12 spl0_1546),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f23454])).
% 76.47/10.12 fof(f23456,plain,(
% 76.47/10.12 $false|spl0_1548),
% 76.47/10.12 inference(forward_subsumption_resolution,[status(thm)],[f23374,f4425])).
% 76.47/10.12 fof(f23457,plain,(
% 76.47/10.12 spl0_1548),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f23456])).
% 76.47/10.12 fof(f23458,plain,(
% 76.47/10.12 $false|spl0_1556),
% 76.47/10.12 inference(forward_subsumption_resolution,[status(thm)],[f23412,f4416])).
% 76.47/10.12 fof(f23459,plain,(
% 76.47/10.12 spl0_1556),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f23458])).
% 76.47/10.12 fof(f23469,plain,(
% 76.47/10.12 spl0_1564 <=> class_Groups_Oab__group__add(tc_RealDef_Oreal)),
% 76.47/10.12 introduced(split_symbol_definition)).
% 76.47/10.12 fof(f23471,plain,(
% 76.47/10.12 ~class_Groups_Oab__group__add(tc_RealDef_Oreal)|spl0_1564),
% 76.47/10.12 inference(component_clause,[status(thm)],[f23469])).
% 76.47/10.12 fof(f23546,plain,(
% 76.47/10.12 $false|spl0_1564),
% 76.47/10.12 inference(forward_subsumption_resolution,[status(thm)],[f23471,f4418])).
% 76.47/10.12 fof(f23547,plain,(
% 76.47/10.12 spl0_1564),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f23546])).
% 76.47/10.12 fof(f23548,plain,(
% 76.47/10.12 $false|spl0_1561),
% 76.47/10.12 inference(forward_subsumption_resolution,[status(thm)],[f23435,f4424])).
% 76.47/10.12 fof(f23549,plain,(
% 76.47/10.12 spl0_1561),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f23548])).
% 76.47/10.12 fof(f23550,plain,(
% 76.47/10.12 $false|spl0_1560),
% 76.47/10.12 inference(forward_subsumption_resolution,[status(thm)],[f23430,f4413])).
% 76.47/10.12 fof(f23551,plain,(
% 76.47/10.12 spl0_1560),
% 76.47/10.12 inference(contradiction_clause,[status(thm)],[f23550])).
% 76.47/10.12 fof(f23849,plain,(
% 76.47/10.12 spl0_1586 <=> c_member(tc_RealDef_Oreal,c_Orderings_Obot__class_Obot(tc_RealDef_Oreal),c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)))),
% 77.18/10.19 introduced(split_symbol_definition)).
% 77.18/10.19 fof(f23851,plain,(
% 77.18/10.19 ~c_member(tc_RealDef_Oreal,c_Orderings_Obot__class_Obot(tc_RealDef_Oreal),c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)))|spl0_1586),
% 77.18/10.19 inference(component_clause,[status(thm)],[f23849])).
% 77.18/10.19 fof(f23863,plain,(
% 77.18/10.19 $false|spl0_1586),
% 77.18/10.19 inference(forward_subsumption_resolution,[status(thm)],[f23851,f1233])).
% 77.18/10.19 fof(f23864,plain,(
% 77.18/10.19 spl0_1586),
% 77.18/10.19 inference(contradiction_clause,[status(thm)],[f23863])).
% 77.18/10.19 fof(f24078,plain,(
% 77.18/10.19 spl0_1598 <=> ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sk0_16(v_P,X0,tc_RealDef_Oreal),X0)),
% 77.18/10.19 introduced(split_symbol_definition)).
% 77.18/10.19 fof(f24079,plain,(
% 77.18/10.19 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sk0_16(v_P,X0,tc_RealDef_Oreal),X0)|~spl0_1598)),
% 77.18/10.19 inference(component_clause,[status(thm)],[f24078])).
% 77.18/10.19 fof(f24081,plain,(
% 77.18/10.19 ![X0]: (~class_Orderings_Oord(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sk0_16(v_P,X0,tc_RealDef_Oreal),X0))),
% 77.18/10.19 inference(resolution,[status(thm)],[f1614,f4582])).
% 77.18/10.19 fof(f24082,plain,(
% 77.18/10.19 ~spl0_15|spl0_1598),
% 77.18/10.19 inference(split_clause,[status(thm)],[f24081,f4951,f24078])).
% 77.18/10.19 fof(f24465,plain,(
% 77.18/10.19 ![X0]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sk0_16(v_P,X0,tc_RealDef_Oreal))|~spl0_1598|~spl0_922)),
% 77.18/10.19 inference(resolution,[status(thm)],[f24079,f16296])).
% 77.18/10.19 fof(f24526,plain,(
% 77.18/10.19 ~hBOOL(hAPP(v_P,sk0_16(v_P,v_Y____,tc_RealDef_Oreal)))|~spl0_1598|~spl0_922|~spl0_403),
% 77.18/10.19 inference(resolution,[status(thm)],[f24465,f9421])).
% 77.18/10.19 fof(f24527,plain,(
% 77.18/10.19 $false|~spl0_1427|~spl0_1598|~spl0_922|~spl0_403),
% 77.18/10.19 inference(forward_subsumption_resolution,[status(thm)],[f24526,f22028])).
% 77.18/10.19 fof(f24528,plain,(
% 77.18/10.19 ~spl0_1427|~spl0_1598|~spl0_922|~spl0_403),
% 77.18/10.19 inference(contradiction_clause,[status(thm)],[f24527])).
% 77.18/10.19 fof(f24529,plain,(
% 77.18/10.19 $false),
% 77.18/10.19 inference(sat_refutation,[status(thm)],[f4967,f8515,f9818,f9825,f10888,f10920,f10956,f10958,f10960,f10962,f14258,f15534,f15536,f15552,f15554,f15721,f15723,f15739,f15741,f15766,f16181,f17194,f17457,f19075,f20180,f20599,f20876,f21168,f21170,f21173,f21271,f21300,f21518,f22005,f23451,f23453,f23455,f23457,f23459,f23547,f23549,f23551,f23864,f24082,f24528])).
% 77.18/10.19 % SZS output end CNFRefutation for theBenchmark.p
% 77.42/10.26 % Elapsed time: 9.918639 seconds
% 77.42/10.26 % CPU time: 77.240353 seconds
% 77.42/10.26 % Memory used: 401.786 MB
%------------------------------------------------------------------------------