0.04/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : eprover --auto -s --tableau=1 [--tableau-equality=1] --tableau-depth=10 %s 0.13/0.33 % Computer : n004.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 960 0.13/0.33 % WCLimit : 120 0.13/0.33 % DateTime : Thu Jul 2 08:19:58 EDT 2020 0.13/0.33 % CPUTime : 0.20/0.46 % Running in FOF/CNF-non-UEQ mode 0.36/0.66 # No SInE strategy applied 0.36/0.66 # Auto-Mode selected heuristic G_E___200_C41_F1_AE_CS_SP_PI_S0Y 0.36/0.66 # and selection function SelectMaxLComplexAvoidPosPred. 0.36/0.66 # 0.36/0.66 # Number of axioms: 1709 Number of unprocessed: 1709 0.36/0.66 # Tableaux proof search. 0.36/0.66 # 1709 beginning clauses after preprocessing and clausification 0.36/0.66 # Creating start rules for all conjectures. 0.36/0.66 # 360 unit axioms, 1 start rules, and 1349 other extension candidates. 0.36/0.66 ## Beginning tableaux proof search with 1 start rule applications. 1.08/1.43 # Beginning deep saturation check 1.08/1.43 # Saturate returned empty clause 0x5877d20. 1.08/1.43 # Success 1.08/1.43 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p 1.08/1.43 # SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 1.08/1.43 # Begin clausification derivation 1.08/1.43 fof(fact_realpow__two__diff, axiom, ![X21, X14, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X14,X21)),c_Groups_Oplus__class_Oplus(X7,X14,X21))=c_Groups_Ominus__class_Ominus(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X21),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))<=class_Rings_Ocomm__ring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_realpow__two__diff)). 1.08/1.43 fof(fact_Suc__eq__plus1, axiom, ![X2]:c_Nat_OSuc(X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__eq__plus1)). 1.08/1.43 fof(fact_Suc__mult__less__cancel1, axiom, ![X19, X29, X26]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X26)),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X26)),X19))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__mult__less__cancel1)). 1.08/1.43 fof(fact_Suc__mult__le__cancel1, axiom, ![X19, X29, X26]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X26)),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X26)),X19))<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__mult__le__cancel1)). 1.08/1.43 fof(fact_reals__Archimedean4, axiom, ![X14, X21]:((?[X22]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X22))),X21))&c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X22)),X21),X14))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_reals__Archimedean4)). 1.08/1.43 fof(fact_lemma__NBseq__def2, axiom, ![X23, X72]:(class_RealVector_Oreal__normed__vector(X72)=>(?[X50]:![X22]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X72,hAPP(X23,X22)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X50)))<=>?[X36]:(![X22]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X72,hAPP(X23,X22)),X36)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_lemma__NBseq__def2)). 1.08/1.43 fof(fact_lemma__NBseq__def, axiom, ![X23, X72]:((?[X50]:![X22]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X72,hAPP(X23,X22)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X50)))<=>?[X36]:(![X22]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X72,hAPP(X23,X22)),X36)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)))<=class_RealVector_Oreal__normed__vector(X72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_lemma__NBseq__def)). 1.08/1.43 fof(conj_0, conjecture, c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_0)). 1.08/1.43 fof(fact_Bseq__iff1a, axiom, ![X23, X7]:((?[X50]:![X22]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(X23,X22)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X50)))<=>c_SEQ_OBseq(X7,X23))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Bseq__iff1a)). 1.08/1.43 fof(fact_Bseq__iff, axiom, ![X23, X7]:((c_SEQ_OBseq(X7,X23)<=>?[X50]:![X22]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(X23,X22)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X50))))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Bseq__iff)). 1.08/1.43 fof(fact_realpow__two__disj, axiom, ![X6, X5, X7]:(class_Rings_Oidom(X7)=>((X5=X6|c_Groups_Ouminus__class_Ouminus(X7,X6)=X5)<=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X5),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X7),X6),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_realpow__two__disj)). 1.08/1.43 fof(fact_power__le__imp__le__base, axiom, ![X12, X2, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),c_Nat_OSuc(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X12),c_Nat_OSuc(X2)))=>(c_Orderings_Oord__class_Oless__eq(X7,X13,X12)<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12)))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__le__imp__le__base)). 1.08/1.43 fof(fact_lemma__realpow__diff, axiom, ![X21, X2, X16, X7]:((hAPP(hAPP(c_Power_Opower__class_Opower(X7),X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),X16))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X16))),X21)<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X2))<=class_Groups_Omonoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_lemma__realpow__diff)). 1.08/1.43 fof(fact_power_Opower_Opower__Suc, axiom, ![X19, X8, X68, X69, X7]:hAPP(hAPP(c_Power_Opower_Opower(X7,X69,X68),X8),c_Nat_OSuc(X19))=hAPP(hAPP(X68,X8),hAPP(hAPP(c_Power_Opower_Opower(X7,X69,X68),X8),X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power_Opower_Opower__Suc)). 1.08/1.43 fof(fact_Suc__mult__cancel1, axiom, ![X19, X29, X26]:(X19=X29<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X26)),X19)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X26)),X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__mult__cancel1)). 1.08/1.43 fof(fact_one__less__mult, axiom, ![X3, X2]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_one__less__mult)). 1.08/1.43 fof(fact_one__le__mult__iff, axiom, ![X19, X29]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)&c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_one__le__mult__iff)). 1.08/1.43 fof(fact_diff__Suc__diff__eq2, axiom, ![X3, X30, X4]:(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X4)),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X30),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X3))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__Suc__diff__eq2)). 1.08/1.43 fof(fact_diff__Suc__diff__eq1, axiom, ![X3, X30, X4]:(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4),c_Nat_OSuc(X30))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X4)))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__Suc__diff__eq1)). 1.08/1.43 fof(fact_power__inject__base, axiom, ![X12, X2, X13, X7]:((hAPP(hAPP(c_Power_Opower__class_Opower(X7),X12),c_Nat_OSuc(X2))=hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),c_Nat_OSuc(X2))=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(X12=X13<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12))))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__inject__base)). 1.08/1.43 fof(fact_int__power__div__base, axiom, ![X4, X3]:((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),X3),X4)<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_int__power__div__base)). 1.08/1.43 fof(fact_nat__lt__two__imp__zero__or__one, axiom, ![X14]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__lt__two__imp__zero__or__one)). 1.08/1.43 fof(fact_n__less__n__mult__m, axiom, ![X3, X2]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_n__less__n__mult__m)). 1.08/1.43 fof(fact_n__less__m__mult__n, axiom, ![X3, X2]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_n__less__m__mult__n)). 1.08/1.43 fof(fact_Suc__diff__diff, axiom, ![X4, X2, X3]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),X4)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X2),c_Nat_OSuc(X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__diff__diff)). 1.08/1.43 fof(fact_power__Suc__less__one, axiom, ![X2, X13, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Oone__class_Oone(X7))=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),c_Nat_OSuc(X2)),c_Groups_Oone__class_Oone(X7))))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__Suc__less__one)). 1.08/1.43 fof(fact_realpow__Suc__le__self, axiom, ![X2, X47, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X47)=>(c_Orderings_Oord__class_Oless__eq(X7,X47,c_Groups_Oone__class_Oone(X7))=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X47),c_Nat_OSuc(X2)),X47)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_realpow__Suc__le__self)). 1.08/1.43 fof(fact_div__geq, axiom, ![X3, X2]:((~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2))=>c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),X2))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__geq)). 1.08/1.43 fof(fact_div__if, axiom, ![X3, X2]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=>((c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),X2))<=~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)))&(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__if)). 1.08/1.43 fof(fact_nat__one__le__power, axiom, ![X2, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__one__le__power)). 1.08/1.43 fof(fact_power__gt1, axiom, ![X2, X13, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),c_Nat_OSuc(X2)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X13))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__gt1)). 1.08/1.43 fof(fact_Suc__less__SucD, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3),c_Nat_OSuc(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__less__SucD)). 1.08/1.43 fof(fact_Suc__less__eq, axiom, ![X19, X29]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X29),c_Nat_OSuc(X19))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__less__eq)). 1.08/1.43 fof(fact_Suc__le__mono, axiom, ![X29, X19]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X29)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__le__mono)). 1.08/1.43 fof(fact_Suc__pred, axiom, ![X2]:(X2=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__pred)). 1.08/1.43 fof(fact_diff__Suc__less, axiom, ![X18, X2]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Nat_OSuc(X18)),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__Suc__less)). 1.08/1.43 fof(fact_add__eq__if, axiom, ![X2, X3]:((c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))<=X3!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3=>c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)=X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__eq__if)). 1.08/1.43 fof(fact_power__Suc2, axiom, ![X2, X13, X7]:(hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),c_Nat_OSuc(X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)),X13)<=class_Groups_Omonoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__Suc2)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, axiom, ![X15, X14, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),c_Nat_OSuc(X15))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X15)),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 1.08/1.43 fof(fact_reals__Archimedean6a, axiom, ![X47]:(?[X22]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X47,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X22)))&c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X22),X47))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_reals__Archimedean6a)). 1.08/1.43 fof(fact_mult__Suc, axiom, ![X2, X3]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__Suc)). 1.08/1.43 fof(fact_Suc__diff__le, axiom, ![X3, X2]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)=>c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X2)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__diff__le)). 1.08/1.43 fof(fact_less__add__Suc1, axiom, ![X3, X18]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__add__Suc1)). 1.08/1.43 fof(fact_less__add__Suc2, axiom, ![X3, X18]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__add__Suc2)). 1.08/1.43 fof(fact_le__Suc__eq, axiom, ![X19, X29]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,c_Nat_OSuc(X19))<=>(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)|c_Nat_OSuc(X19)=X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__Suc__eq)). 1.08/1.43 fof(fact_le__SucE, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Nat_OSuc(X2))=>(X3=c_Nat_OSuc(X2)<=~(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__SucE)). 1.08/1.43 fof(fact_Suc__mono, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3),c_Nat_OSuc(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__mono)). 1.08/1.43 fof(fact_less__Suc__eq__0__disj, axiom, ![X19, X29]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,c_Nat_OSuc(X19))<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X29|?[X70]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X70,X19)&X29=c_Nat_OSuc(X70)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__Suc__eq__0__disj)). 1.08/1.43 fof(fact_le__less__Suc__eq, axiom, ![X19, X29]:((X19=X29<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X29)))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__less__Suc__eq)). 1.08/1.43 fof(fact_not__less__eq__eq, axiom, ![X19, X29]:(~(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19))<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__less__eq__eq)). 1.08/1.43 fof(fact_not__less__eq, axiom, ![X19, X29]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X29))<=>~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__less__eq)). 1.08/1.43 fof(fact_power__Suc__0, axiom, ![X2]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__Suc__0)). 1.08/1.43 fof(fact_less__trans__Suc, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X30)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X18),X4)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__trans__Suc)). 1.08/1.43 fof(fact_diff__Suc__eq__diff__pred, axiom, ![X2, X3]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Nat_OSuc(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__Suc__eq__diff__pred)). 1.08/1.43 fof(fact_add__Suc__shift, axiom, ![X2, X3]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Nat_OSuc(X2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X3),X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__Suc__shift)). 1.08/1.43 fof(fact_diff__Suc__Suc, axiom, ![X2, X3]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),c_Nat_OSuc(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__Suc__Suc)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, axiom, ![X15, X14, X7]:(hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),c_Nat_OSuc(X15))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X15))<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, axiom, ![X15, X14, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),c_Nat_OSuc(X15))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J)). 1.08/1.43 fof(fact_power__Suc, axiom, ![X2, X13, X7]:(class_Power_Opower(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),c_Nat_OSuc(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__Suc)). 1.08/1.43 fof(fact_add__Suc, axiom, ![X2, X3]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X3),X2)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__Suc)). 1.08/1.43 fof(fact_add__Suc__right, axiom, ![X2, X3]:c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Nat_OSuc(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__Suc__right)). 1.08/1.43 fof(fact_less__Suc__eq, axiom, ![X19, X29]:((X19=X29|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,c_Nat_OSuc(X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__Suc__eq)). 1.08/1.43 fof(fact_less__SucE, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X2))=>(X2=X3<=~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__SucE)). 1.08/1.43 fof(fact_not__less__less__Suc__eq, axiom, ![X29, X19]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X29))<=>X29=X19)<=~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__less__less__Suc__eq)). 1.08/1.43 fof(fact_less__antisym, axiom, ![X3, X2]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X3))=>X3=X2)<=~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__antisym)). 1.08/1.43 fof(fact_Suc__lessD, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3),X2)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__lessD)). 1.08/1.43 fof(fact_Suc__le__lessD, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__le__lessD)). 1.08/1.43 fof(fact_Suc__le__eq, axiom, ![X19, X29]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X29),X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__le__eq)). 1.08/1.43 fof(fact_less__eq__Suc__le, axiom, ![X29, X19]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X29)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__eq__Suc__le)). 1.08/1.43 fof(fact_Suc__leD, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3),X2)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__leD)). 1.08/1.43 fof(fact_less__Suc__eq__le, axiom, ![X19, X29]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,c_Nat_OSuc(X19))<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__Suc__eq__le)). 1.08/1.43 fof(fact_less__iff__Suc__add, axiom, ![X19, X29]:(?[X24]:c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X24))=X19<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__iff__Suc__add)). 1.08/1.43 fof(fact_Suc__lessI, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)=>(c_Nat_OSuc(X3)!=X2=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__lessI)). 1.08/1.43 fof(fact_mult__Suc__right, axiom, ![X2, X3]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__Suc__right)). 1.08/1.43 fof(fact_real__of__nat__Suc__gt__zero, axiom, ![X2]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__Suc__gt__zero)). 1.08/1.43 fof(fact_one__is__add, axiom, ![X19, X29]:(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X19)<=>((X19=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X29)|(X29=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&X19=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_one__is__add)). 1.08/1.43 fof(fact_add__is__1, axiom, ![X19, X29]:(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X19)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X29&c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X19)|(X29=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&X19=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__is__1)). 1.08/1.43 fof(fact_mult__eq__1__iff, axiom, ![X19, X29]:((c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X19&X29=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X19)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__eq__1__iff)). 1.08/1.43 fof(fact_less__Suc0, axiom, ![X19]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X19<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__Suc0)). 1.08/1.43 fof(fact_diff__less__Suc, axiom, ![X2, X3]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Nat_OSuc(X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__less__Suc)). 1.08/1.43 fof(fact_Suc__n__not__le__n, axiom, ![X2]:~(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__n__not__le__n)). 1.08/1.43 fof(fact_Suc__pred_H, axiom, ![X2]:(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X2<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__pred_H)). 1.08/1.43 fof(fact_Suc__diff__1, axiom, ![X2]:(X2=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__diff__1)). 1.08/1.43 fof(fact_Suc__leI, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__leI)). 1.08/1.43 fof(fact_less__SucI, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X2))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__SucI)). 1.08/1.43 fof(fact_le__imp__less__Suc, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X2))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__imp__less__Suc)). 1.08/1.43 fof(fact_le__SucI, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Nat_OSuc(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__SucI)). 1.08/1.43 fof(fact_nat__power__eq__Suc__0__iff, axiom, ![X29, X5]:(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5),X29)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X29|X5=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__power__eq__Suc__0__iff)). 1.08/1.43 fof(fact_real__of__nat__Suc, axiom, ![X2]:c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X2))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__Suc)). 1.08/1.43 fof(fact_power__0__Suc, axiom, ![X2, X7]:((class_Rings_Osemiring__0(X7)&class_Power_Opower(X7))=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Ozero__class_Ozero(X7)),c_Nat_OSuc(X2))=c_Groups_Ozero__class_Ozero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__0__Suc)). 1.08/1.43 fof(fact_Suc__inject, axiom, ![X21, X14]:(c_Nat_OSuc(X14)=c_Nat_OSuc(X21)=>X21=X14), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__inject)). 1.08/1.43 fof(fact_nat_Oinject, axiom, ![X75, X76]:(c_Nat_OSuc(X75)=c_Nat_OSuc(X76)<=>X76=X75), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat_Oinject)). 1.08/1.43 fof(fact_div__1, axiom, ![X3]:X3=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__1)). 1.08/1.43 fof(fact_diff__Suc__1, axiom, ![X2]:X2=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__Suc__1)). 1.08/1.43 fof(fact_zero__less__Suc, axiom, ![X2]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__Suc)). 1.08/1.43 fof(fact_lessI, axiom, ![X2]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_lessI)). 1.08/1.43 fof(fact_gr0__conv__Suc, axiom, ![X19]:(?[X61]:c_Nat_OSuc(X61)=X19<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_gr0__conv__Suc)). 1.08/1.43 fof(fact_Suc__eq__plus1__left, axiom, ![X2]:c_Nat_OSuc(X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__eq__plus1__left)). 1.08/1.43 fof(fact_nat_Osimps_I3_J, axiom, ![X88]:c_Nat_OSuc(X88)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat_Osimps_I3_J)). 1.08/1.43 fof(fact_Suc__not__Zero, axiom, ![X3]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__not__Zero)). 1.08/1.43 fof(fact_Suc__neq__Zero, axiom, ![X3]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__neq__Zero)). 1.08/1.43 fof(fact_nat_Osimps_I2_J, axiom, ![X82]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X82), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat_Osimps_I2_J)). 1.08/1.43 fof(fact_Zero__neq__Suc, axiom, ![X3]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Zero__neq__Suc)). 1.08/1.43 fof(fact_Zero__not__Suc, axiom, ![X3]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Zero__not__Suc)). 1.08/1.43 fof(fact_n__not__Suc__n, axiom, ![X2]:X2!=c_Nat_OSuc(X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_n__not__Suc__n)). 1.08/1.43 fof(fact_Suc__n__not__n, axiom, ![X2]:X2!=c_Nat_OSuc(X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Suc__n__not__n)). 1.08/1.43 fof(fact_lemmaCauchy, axiom, ![X23, X94, X7, X72]:((![X22]:(c_Orderings_Oord__class_Oless__eq(X7,X94,X22)=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X72,hAPP(X23,X22)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X72,hAPP(X23,X94)))))<=![X22]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X72,c_Groups_Ominus__class_Ominus(X72,hAPP(X23,X94),hAPP(X23,X22))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))<=c_Orderings_Oord__class_Oless__eq(X7,X94,X22)))<=(class_Orderings_Oord(X7)&class_RealVector_Oreal__normed__vector(X72))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_lemmaCauchy)). 1.08/1.43 fof(fact_Bseq__iff3, axiom, ![X23, X7]:((c_SEQ_OBseq(X7,X23)<=>?[X24]:(?[X50]:![X22]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(X23,X22),c_Groups_Ouminus__class_Ouminus(X7,hAPP(X23,X50)))),X24)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Bseq__iff3)). 1.08/1.43 fof(fact_Bseq__iff2, axiom, ![X23, X7]:((?[X24]:(?[X25]:![X22]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(X23,X22),c_Groups_Ouminus__class_Ouminus(X7,X25))),X24)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24))<=>c_SEQ_OBseq(X7,X23))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Bseq__iff2)). 1.08/1.43 fof(fact_int__val__lemma, axiom, ![X26, X27, X19]:(![X28]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X27,X28))),c_Groups_Oone__class_Oone(tc_Int_Oint))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X19))=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26)=>(?[X28]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X19)&X26=hAPP(X27,X28))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,hAPP(X27,X19))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_int__val__lemma)). 1.08/1.43 fof(fact_nat0__intermed__int__val, axiom, ![X26, X27, X19]:(![X28]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X19)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X27,X28))),c_Groups_Oone__class_Oone(tc_Int_Oint)))=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26)=>(?[X28]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X19)&X26=hAPP(X27,X28))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,hAPP(X27,X19))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat0__intermed__int__val)). 1.08/1.43 fof(fact_decr__lemma, axiom, ![X10, X14, X39]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X10)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X39)),X10)<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_decr__lemma)). 1.08/1.43 fof(fact_incr__lemma, axiom, ![X14, X10, X39]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X10)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X39)))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_incr__lemma)). 1.08/1.43 fof(fact_le__fun__def, axiom, ![X71, X27, X7, X72]:(class_Orderings_Oord(X72)=>(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X72),X27,X71)<=>![X25]:c_Orderings_Oord__class_Oless__eq(X72,hAPP(X27,X25),hAPP(X71,X25)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__fun__def)). 1.08/1.43 fof(fact_BseqI2_H, axiom, ![X89, X23, X90, X7]:((c_SEQ_OBseq(X7,X23)<=![X22]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X90,X22)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(X23,X22)),X89)))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_BseqI2_H)). 1.08/1.43 fof(fact_mult_Oprod__diff__prod, axiom, ![X12, X13, X21, X14, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>c_Groups_Ominus__class_Ominus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))=c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X14,X13)),c_Groups_Ominus__class_Ominus(X7,X21,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X14,X13)),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Ominus__class_Ominus(X7,X21,X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Oprod__diff__prod)). 1.08/1.43 fof(fact_abs__sum__triangle__ineq, axiom, ![X3, X34, X21, X14]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,X21),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X34),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X34))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__sum__triangle__ineq)). 1.08/1.43 fof(fact_less__add__iff1, axiom, ![X52, X11, X53, X54, X8, X7]:(class_Rings_Oordered__ring(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X8,X11)),X54),X53),X52)<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X54),X53),c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X54),X52)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__add__iff1)). 1.08/1.43 fof(fact_le__add__iff1, axiom, ![X52, X11, X53, X54, X8, X7]:(class_Rings_Oordered__ring(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X54),X53),c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X54),X52))<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X8,X11)),X54),X53),X52))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__add__iff1)). 1.08/1.43 fof(fact_less__add__iff2, axiom, ![X52, X11, X53, X54, X8, X7]:(class_Rings_Oordered__ring(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X54),X53),c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X54),X52))<=>c_Orderings_Oord__class_Oless(X7,X53,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X11,X8)),X54),X52)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__add__iff2)). 1.08/1.43 fof(fact_le__add__iff2, axiom, ![X52, X11, X53, X54, X8, X7]:(class_Rings_Oordered__ring(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X54),X53),c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X54),X52))<=>c_Orderings_Oord__class_Oless__eq(X7,X53,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X11,X8)),X54),X52)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__add__iff2)). 1.08/1.43 fof(fact_nat__less__add__iff1, axiom, ![X19, X29, X73, X66, X74]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X74)),X73),X29),X19)<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X66),X73),X29),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X74),X73),X19)))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X74,X66)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__less__add__iff1)). 1.08/1.43 fof(fact_nat__le__add__iff1, axiom, ![X19, X29, X73, X66, X74]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X74,X66)=>(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X74)),X73),X29),X19)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X66),X73),X29),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X74),X73),X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__le__add__iff1)). 1.08/1.43 fof(fact_nat__less__add__iff2, axiom, ![X19, X29, X73, X74, X66]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X74)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X66),X73),X29),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X74),X73),X19))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X66)),X73),X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__less__add__iff2)). 1.08/1.43 fof(fact_nat__le__add__iff2, axiom, ![X19, X29, X73, X74, X66]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X66)),X73),X19))<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X66),X73),X29),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X74),X73),X19)))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X74)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__le__add__iff2)). 1.08/1.43 fof(fact_abs__diff__triangle__ineq, axiom, ![X39, X20, X12, X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),c_Groups_Oplus__class_Oplus(X7,X20,X39))),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X13,X20)),c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X12,X39))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__diff__triangle__ineq)). 1.08/1.43 fof(fact_norm__diff__triangle__ineq, axiom, ![X39, X20, X12, X13, X7]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),c_Groups_Oplus__class_Oplus(X7,X20,X39))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X13,X20)),c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X12,X39))))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__diff__triangle__ineq)). 1.08/1.43 fof(fact_nat__diff__add__eq1, axiom, ![X2, X3, X78, X18, X30]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X18)=>c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X78),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X78),X2))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X30)),X78),X3),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__diff__add__eq1)). 1.08/1.43 fof(fact_nat__diff__add__eq2, axiom, ![X2, X3, X78, X30, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X30)=>c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X18)),X78),X2))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X78),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X78),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__diff__add__eq2)). 1.08/1.43 fof(fact_decr__mult__lemma, axiom, ![X26, X62, X52]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X52)=>(![X25]:(hBOOL(hAPP(X62,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X25,X52)))<=hBOOL(hAPP(X62,X25)))=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)=>![X25]:(hBOOL(hAPP(X62,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X52))))<=hBOOL(hAPP(X62,X25)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_decr__mult__lemma)). 1.08/1.43 fof(fact_incr__mult__lemma, axiom, ![X26, X62, X52]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X52)=>(![X25]:(hBOOL(hAPP(X62,X25))=>hBOOL(hAPP(X62,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X52))))=>(![X25]:(hBOOL(hAPP(X62,X25))=>hBOOL(hAPP(X62,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X52)))))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_incr__mult__lemma)). 1.08/1.43 fof(fact_poly__rec__0, axiom, ![X7, X48, X27, X72]:((c_Polynomial_Opoly__rec(X7,X72,X48,X27,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X72)))=X48<=X48=hAPP(hAPP(hAPP(X27,c_Groups_Ozero__class_Ozero(X72)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X72))),X48))<=class_Groups_Ozero(X72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__rec__0)). 1.08/1.43 fof(fact_zdiv__mono2__neg__lemma, axiom, ![X79, X80, X35, X47, X15, X12]:(((c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,X12)=>((c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35)=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X80,X15)<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X12)))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X35),X80),X79),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X35),X80),X79)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X15),X47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__mono2__neg__lemma)). 1.08/1.43 fof(fact_zdiv__mono2__lemma, axiom, ![X79, X80, X35, X47, X15, X12]:(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X15),X47)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X35),X80),X79)=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X35),X80),X79))=>(c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X35)=>((c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35)=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X80)<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X12)))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__mono2__lemma)). 1.08/1.43 fof(fact_mult_Opos__bounded, axiom, ![X7]:(?[X36]:(![X37, X38]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X37),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X37)),c_RealVector_Onorm__class_Onorm(X7,X38))),X36))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36))<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Opos__bounded)). 1.08/1.43 fof(fact_mult_Obounded, axiom, ![X7]:(?[X36]:![X37, X38]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X37),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X37)),c_RealVector_Onorm__class_Onorm(X7,X38))),X36))<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Obounded)). 1.08/1.43 fof(fact_mult_Ononneg__bounded, axiom, ![X7]:(class_RealVector_Oreal__normed__algebra(X7)=>?[X36]:(![X37, X38]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X37),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X37)),c_RealVector_Onorm__class_Onorm(X7,X38))),X36))&c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Ononneg__bounded)). 1.08/1.43 fof(fact_unique__quotient__lemma, axiom, ![X47, X15, X79, X80, X12]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X80),X79),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X15),X47))=>(((c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,X12)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X80,X15))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X12))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_unique__quotient__lemma)). 1.08/1.43 fof(fact_unique__quotient__lemma__neg, axiom, ![X47, X15, X79, X80, X12]:((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X47,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=>((c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X79)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X80))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X47)))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X80),X79),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X15),X47))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_unique__quotient__lemma__neg)). 1.08/1.43 fof(fact_nat__eq__add__iff1, axiom, ![X19, X29, X73, X66, X74]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X74,X66)=>(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X74)),X73),X29)=X19<=>c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X66),X73),X29)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X74),X73),X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__eq__add__iff1)). 1.08/1.43 fof(fact_nat__eq__add__iff2, axiom, ![X19, X29, X73, X74, X66]:((c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X66),X73),X29)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X74),X73),X19)<=>X29=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X66)),X73),X19))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X74)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__eq__add__iff2)). 1.08/1.43 fof(fact_eq__add__iff2, axiom, ![X52, X11, X53, X54, X8, X7]:((c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X54),X52)=c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X54),X53)<=>c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X11,X8)),X54),X52)=X53)<=class_Rings_Oring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_eq__add__iff2)). 1.08/1.43 fof(fact_eq__add__iff1, axiom, ![X52, X11, X53, X54, X8, X7]:(class_Rings_Oring(X7)=>(c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X54),X52)=c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X54),X53)<=>X52=c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X8,X11)),X54),X53))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_eq__add__iff1)). 1.08/1.43 fof(fact_split__zdiv, axiom, ![X26, X19, X62]:(hBOOL(hAPP(X62,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X19,X26)))<=>(((c_Orderings_Oord__class_Oless(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=>![X28]:(hBOOL(hAPP(X62,X28))<=?[X70]:((c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X28),X70)=X19&c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X70,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&c_Orderings_Oord__class_Oless(tc_Int_Oint,X26,X70))))&(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)=>![X28]:(hBOOL(hAPP(X62,X28))<=?[X70]:((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X70)&c_Orderings_Oord__class_Oless(tc_Int_Oint,X70,X26))&c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X28),X70)=X19))))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X26=>hBOOL(hAPP(X62,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_split__zdiv)). 1.08/1.43 fof(fact_mult__diff__mult, axiom, ![X12, X13, X21, X14, X7]:(class_Rings_Oring(X7)=>c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),c_Groups_Ominus__class_Ominus(X7,X21,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X14,X13)),X12))=c_Groups_Ominus__class_Ominus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__diff__mult)). 1.08/1.43 fof(fact_LIMSEQ__inverse__realpow__zero__lemma, axiom, ![X2, X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),X14),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_LIMSEQ__inverse__realpow__zero__lemma)). 1.08/1.43 fof(fact_combine__common__factor, axiom, ![X20, X12, X93, X13, X7]:(c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X93),c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X93),X20))=c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X13,X12)),X93),X20)<=class_Rings_Osemiring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_combine__common__factor)). 1.08/1.43 fof(fact_convex__bound__lt, axiom, ![X77, X78, X21, X13, X14, X7]:(class_Rings_Olinordered__semiring__1__strict(X7)=>(c_Orderings_Oord__class_Oless(X7,X14,X13)=>(c_Orderings_Oord__class_Oless(X7,X21,X13)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X78)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X77)=>(c_Groups_Oone__class_Oone(X7)=c_Groups_Oplus__class_Oplus(X7,X78,X77)=>c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X78),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X77),X21)),X13))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_convex__bound__lt)). 1.08/1.43 fof(fact_convex__bound__le, axiom, ![X77, X78, X21, X13, X14, X7]:(class_Rings_Olinordered__semiring__1(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X14,X13)=>(c_Orderings_Oord__class_Oless__eq(X7,X21,X13)=>(((c_Groups_Oone__class_Oone(X7)=c_Groups_Oplus__class_Oplus(X7,X78,X77)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X78),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X77),X21)),X13))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X77))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X78))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_convex__bound__le)). 1.08/1.43 fof(fact_BseqI, axiom, ![X23, X89, X7]:(class_RealVector_Oreal__normed__vector(X7)=>((![X22]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(X23,X22)),X89)=>c_SEQ_OBseq(X7,X23))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X89))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_BseqI)). 1.08/1.43 fof(fact_Bseq__def, axiom, ![X23, X7]:((c_SEQ_OBseq(X7,X23)<=>?[X36]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)&![X22]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(X23,X22)),X36)))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Bseq__def)). 1.08/1.43 fof(fact_left__add__mult__distrib, axiom, ![X4, X30, X78, X18]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X78),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X78),X4))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X30)),X78),X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_left__add__mult__distrib)). 1.08/1.43 fof(fact_field__le__mult__one__interval, axiom, ![X21, X14, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X14,X21)<=![X67]:(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X67)=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X67),X14),X21)<=c_Orderings_Oord__class_Oless(X7,X67,c_Groups_Oone__class_Oone(X7)))))<=class_Fields_Olinordered__field__inverse__zero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_field__le__mult__one__interval)). 1.08/1.43 fof(fact_sum__squares__gt__zero__iff, axiom, ![X6, X5, X7]:(((X6!=c_Groups_Ozero__class_Ozero(X7)|X5!=c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X5),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6))))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sum__squares__gt__zero__iff)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, axiom, ![X86, X31, X32, X33, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X32)),X86))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X31),X86))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 1.08/1.43 fof(fact_sum__squares__le__zero__iff, axiom, ![X6, X5, X7]:(((X6=c_Groups_Ozero__class_Ozero(X7)&X5=c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X5),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6)),c_Groups_Ozero__class_Ozero(X7)))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sum__squares__le__zero__iff)). 1.08/1.43 fof(fact_not__sum__squares__lt__zero, axiom, ![X21, X14, X7]:(~(c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X21),X21)),c_Groups_Ozero__class_Ozero(X7)))<=class_Rings_Olinordered__ring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__sum__squares__lt__zero)). 1.08/1.43 fof(fact_realpow__minus__mult, axiom, ![X14, X2, X7]:((hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X14)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))<=class_Groups_Omonoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_realpow__minus__mult)). 1.08/1.43 fof(fact_lemma__interval__lt, axiom, ![X12, X14, X13]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X14)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,X12)=>?[X40]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X40)&![X41]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X41)),X40)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X41,X12)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X41)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_lemma__interval__lt)). 1.08/1.43 fof(fact_lemma__interval, axiom, ![X12, X14, X13]:((?[X40]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X40)&![X41]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X41,X12)&c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X41))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X41)),X40)))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,X12))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_lemma__interval)). 1.08/1.43 fof(fact_crossproduct__noteq, axiom, ![X52, X53, X11, X8, X7]:((c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X52))!=c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X53))<=>(X11!=X8&X52!=X53))<=class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_crossproduct__noteq)). 1.08/1.43 fof(fact_crossproduct__eq, axiom, ![X48, X5, X6, X49, X7]:(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)=>((X6=X48|X5=X49)<=>c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X49),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X5),X6))=c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X49),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X5),X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_crossproduct__eq)). 1.08/1.43 fof(fact_abs__diff__less__iff, axiom, ![X57, X8, X5, X7]:(class_Rings_Olinordered__idom(X7)=>((c_Orderings_Oord__class_Oless(X7,c_Groups_Ominus__class_Ominus(X7,X8,X57),X5)&c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Oplus__class_Oplus(X7,X8,X57)))<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X5,X8)),X57))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__diff__less__iff)). 1.08/1.43 fof(fact_power__minus, axiom, ![X2, X13, X7]:(class_Rings_Oring__1(X7)=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Ouminus__class_Ouminus(X7,X13)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7))),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__minus)). 1.08/1.43 fof(fact_q__neg__lemma, axiom, ![X79, X80, X35]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X35),X80),X79),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)=>(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X80,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_q__neg__lemma)). 1.08/1.43 fof(fact_q__pos__lemma, axiom, ![X79, X80, X35]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X35),X80),X79))=>((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X35))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_q__pos__lemma)). 1.08/1.43 fof(fact_split__div, axiom, ![X26, X19, X62]:(hBOOL(hAPP(X62,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X19,X26)))<=>((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X26=>![X28, X70]:((hBOOL(hAPP(X62,X28))<=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X28),X70)=X19)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X70,X26)))&(hBOOL(hAPP(X62,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X26))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_split__div)). 1.08/1.43 fof(fact_abs__triangle__ineq3, axiom, ![X12, X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oabs__class_Oabs(X7,X13),c_Groups_Oabs__class_Oabs(X7,X12))),c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__triangle__ineq3)). 1.08/1.43 fof(fact_norm__triangle__ineq3, axiom, ![X12, X13, X7]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X13),c_RealVector_Onorm__class_Onorm(X7,X12))),c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12)))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__triangle__ineq3)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, axiom, ![X86, X31, X32, X33, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X31),X86))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X32),X86))<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, axiom, ![X86, X31, X32, X33, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X31),X86))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X31),X86)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 1.08/1.43 fof(fact_complex__mod__triangle__ineq2, axiom, ![X13, X12]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X12,X13)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X12)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_complex__mod__triangle__ineq2)). 1.08/1.43 fof(fact_complex__mod__triangle__sub, axiom, ![X10, X43]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X43),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X43,X10)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X10))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_complex__mod__triangle__sub)). 1.08/1.43 fof(fact_mult__poly__add__left, axiom, ![X47, X15, X16, X7]:(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X16),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X15),X47))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),X16,X15)),X47)<=class_Rings_Ocomm__semiring__0(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__poly__add__left)). 1.08/1.43 fof(fact_nat__diff__split, axiom, ![X11, X8, X62]:((![X40]:(X8=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X40)=>hBOOL(hAPP(X62,X40)))&(hBOOL(hAPP(X62,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X11)))<=>hBOOL(hAPP(X62,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X8,X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__diff__split)). 1.08/1.43 fof(fact_nat__diff__split__asm, axiom, ![X11, X8, X62]:(~(((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X11)&~(hBOOL(hAPP(X62,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))|?[X40]:(~(hBOOL(hAPP(X62,X40)))&c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X40)=X8)))<=>hBOOL(hAPP(X62,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X8,X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__diff__split__asm)). 1.08/1.43 fof(fact_abs__mult__less, axiom, ![X39, X12, X20, X13, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,X13),X20)=>(c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oabs__class_Oabs(X7,X13)),c_Groups_Oabs__class_Oabs(X7,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X39))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,X12),X39)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__mult__less)). 1.08/1.43 fof(fact_power__Suc__less, axiom, ![X2, X13, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))<=c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Oone__class_Oone(X7))))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__Suc__less)). 1.08/1.43 fof(fact_odd__less__0, axiom, ![X48]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X48),X48),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_odd__less__0)). 1.08/1.43 fof(fact_norm__add__less, axiom, ![X46, X21, X47, X14, X7]:(((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oplus__class_Oplus(X7,X14,X21)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X47,X46))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X21),X46))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X14),X47))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__add__less)). 1.08/1.43 fof(fact_field__le__epsilon, axiom, ![X21, X14, X7]:(class_Fields_Olinordered__field(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X14,X21)<=![X55]:(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X55)=>c_Orderings_Oord__class_Oless__eq(X7,X14,c_Groups_Oplus__class_Oplus(X7,X21,X55))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_field__le__epsilon)). 1.08/1.43 fof(fact_poly__mult, axiom, ![X14, X15, X16, X7]:(class_Rings_Ocomm__semiring__0(X7)=>hAPP(c_Polynomial_Opoly(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X16),X15)),X14)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Polynomial_Opoly(X7,X16),X14)),hAPP(c_Polynomial_Opoly(X7,X15),X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__mult)). 1.08/1.43 fof(fact_mult__eq__if, axiom, ![X2, X3]:((c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)<=X3!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__eq__if)). 1.08/1.43 fof(fact_less__diff__iff, axiom, ![X19, X29, X26]:(((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X26),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X26)))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X19))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__diff__iff)). 1.08/1.43 fof(fact_le__diff__iff, axiom, ![X19, X29, X26]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X29)=>((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X26),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X26))<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__diff__iff)). 1.08/1.43 fof(fact_mult__strict__mono, axiom, ![X39, X20, X12, X13, X7]:((c_Orderings_Oord__class_Oless(X7,X13,X12)=>(((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X39)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X12))<=c_Orderings_Oord__class_Oless(X7,X20,X39)))<=class_Rings_Olinordered__semiring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__strict__mono)). 1.08/1.43 fof(fact_mult__strict__mono_H, axiom, ![X39, X20, X12, X13, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>(c_Orderings_Oord__class_Oless(X7,X13,X12)=>(c_Orderings_Oord__class_Oless(X7,X20,X39)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X39))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__strict__mono_H)). 1.08/1.43 fof(fact_mult__le__less__imp__less, axiom, ![X39, X20, X12, X13, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X13,X12)=>((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X39))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20)))<=c_Orderings_Oord__class_Oless(X7,X20,X39)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__le__less__imp__less)). 1.08/1.43 fof(fact_mult__less__le__imp__less, axiom, ![X39, X20, X12, X13, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,X20,X39)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X39)))))<=c_Orderings_Oord__class_Oless(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__le__imp__less)). 1.08/1.43 fof(fact_mult__mono_H, axiom, ![X39, X20, X12, X13, X7]:(class_Rings_Oordered__semiring(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,X20,X39)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X39))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20))))<=c_Orderings_Oord__class_Oless__eq(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__mono_H)). 1.08/1.43 fof(fact_mult__mono, axiom, ![X39, X20, X12, X13, X7]:(class_Rings_Oordered__semiring(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,X20,X39)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X39)))))<=c_Orderings_Oord__class_Oless__eq(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__mono)). 1.08/1.43 fof(fact_norm__mult__less, axiom, ![X46, X21, X47, X14, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X47),X46))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X21),X46))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X14),X47))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__mult__less)). 1.08/1.43 fof(fact_divmod__int__rel__div__eq, axiom, ![X83, X21, X84, X85]:((((c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X84)=>(c_Orderings_Oord__class_Oless(tc_Int_Oint,X83,X84)&c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X83)))&(~(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X84))=>(c_Orderings_Oord__class_Oless(tc_Int_Oint,X84,X83)&c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))=>(c_Divides_Odiv__class_Odiv(tc_Int_Oint,X85,X84)=X21<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X84))<=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X21),X83)=X85), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_divmod__int__rel__div__eq)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, axiom, ![X15, X21, X14, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X21),X15))=hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21)),X15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 1.08/1.43 fof(fact_power__mult__distrib, axiom, ![X2, X12, X13, X7]:(hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X12),X2))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__mult__distrib)). 1.08/1.43 fof(fact_sum__squares__ge__zero, axiom, ![X21, X14, X7]:(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X21),X21)))<=class_Rings_Olinordered__ring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sum__squares__ge__zero)). 1.08/1.43 fof(fact_real__squared__diff__one__factored, axiom, ![X14, X7]:(class_Rings_Oring__1(X7)=>c_Groups_Ominus__class_Ominus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X14),c_Groups_Oone__class_Oone(X7))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X14,c_Groups_Oone__class_Oone(X7))),c_Groups_Ominus__class_Ominus(X7,X14,c_Groups_Oone__class_Oone(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__squared__diff__one__factored)). 1.08/1.43 fof(fact_power__less__power__Suc, axiom, ![X2, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__less__power__Suc)). 1.08/1.43 fof(fact_mult__right__less__imp__less, axiom, ![X12, X20, X13, X7]:(class_Rings_Olinordered__semiring(X7)=>(c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20))=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>c_Orderings_Oord__class_Oless(X7,X13,X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right__less__imp__less)). 1.08/1.43 fof(fact_mult__less__imp__less__right, axiom, ![X12, X20, X13, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>((c_Orderings_Oord__class_Oless(X7,X13,X12)<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20))<=c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__imp__less__right)). 1.08/1.43 fof(fact_power__less__imp__less__base, axiom, ![X12, X2, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12)=>c_Orderings_Oord__class_Oless(X7,X13,X12))<=c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X12),X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__less__imp__less__base)). 1.08/1.43 fof(fact_mult__left__less__imp__less, axiom, ![X12, X13, X20, X7]:(((c_Orderings_Oord__class_Oless(X7,X13,X12)<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20))<=c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12)))<=class_Rings_Olinordered__semiring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left__less__imp__less)). 1.08/1.43 fof(fact_mult__less__cancel__left__pos, axiom, ![X11, X8, X53, X7]:(((c_Orderings_Oord__class_Oless(X7,X8,X11)<=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X11)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X53))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__cancel__left__pos)). 1.08/1.43 fof(fact_mult__less__imp__less__left, axiom, ![X12, X13, X20, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>((c_Orderings_Oord__class_Oless(X7,X13,X12)<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20))<=c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__imp__less__left)). 1.08/1.43 fof(fact_mult__right__le__imp__le, axiom, ![X12, X20, X13, X7]:(((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>c_Orderings_Oord__class_Oless__eq(X7,X13,X12))<=c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20)))<=class_Rings_Olinordered__semiring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right__le__imp__le)). 1.08/1.43 fof(fact_mult__le__cancel__left__pos, axiom, ![X11, X8, X53, X7]:(class_Rings_Olinordered__ring__strict(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,X8,X11)<=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X11)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X53))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__le__cancel__left__pos)). 1.08/1.43 fof(fact_mult__left__le__imp__le, axiom, ![X12, X13, X20, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12))=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>c_Orderings_Oord__class_Oless__eq(X7,X13,X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left__le__imp__le)). 1.08/1.43 fof(fact_mult__less__cancel__left__neg, axiom, ![X11, X8, X53, X7]:(class_Rings_Olinordered__ring__strict(X7)=>(c_Orderings_Oord__class_Oless(X7,X53,c_Groups_Ozero__class_Ozero(X7))=>(c_Orderings_Oord__class_Oless(X7,X11,X8)<=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X11))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__cancel__left__neg)). 1.08/1.43 fof(fact_mult__le__cancel__left__neg, axiom, ![X11, X8, X53, X7]:(class_Rings_Olinordered__ring__strict(X7)=>(c_Orderings_Oord__class_Oless(X7,X53,c_Groups_Ozero__class_Ozero(X7))=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X11))<=>c_Orderings_Oord__class_Oless__eq(X7,X11,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__le__cancel__left__neg)). 1.08/1.43 fof(fact_power__less__imp__less__exp, axiom, ![X2, X3, X13, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X13)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)<=c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__less__imp__less__exp)). 1.08/1.43 fof(fact_power__strict__increasing__iff, axiom, ![X6, X5, X11, X7]:(((c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X11),X6))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X6))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X11))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__strict__increasing__iff)). 1.08/1.43 fof(fact_power__le__imp__le__exp, axiom, ![X2, X3, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X13)=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__le__imp__le__exp)). 1.08/1.43 fof(fact_power__increasing__iff, axiom, ![X6, X5, X11, X7]:(((c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X11),X6))<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X6))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X11))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__increasing__iff)). 1.08/1.43 fof(fact_poly__power, axiom, ![X14, X2, X16, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(c_Polynomial_Opoly(X7,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X7)),X16),X2)),X14)=hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Polynomial_Opoly(X7,X16),X14)),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__power)). 1.08/1.43 fof(fact_le__mult__natfloor, axiom, ![X12, X13]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X13)),c_RComplete_Onatfloor(X12)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X12)))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__mult__natfloor)). 1.08/1.43 fof(fact_Deriv_Oadd__diff__add, axiom, ![X39, X12, X20, X13, X7]:(class_Groups_Oab__group__add(X7)=>c_Groups_Oplus__class_Oplus(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12),c_Groups_Ominus__class_Ominus(X7,X20,X39))=c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X39))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Deriv_Oadd__diff__add)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, axiom, ![X39, X20, X12, X13, X7]:(c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),c_Groups_Oplus__class_Oplus(X7,X20,X39))=c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X39))<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 1.08/1.43 fof(fact_power__strict__decreasing, axiom, ![X13, X45, X2, X7]:(class_Rings_Olinordered__semidom(X7)=>(((c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X45),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))<=c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Oone__class_Oone(X7)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X45))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__strict__decreasing)). 1.08/1.43 fof(fact_power__decreasing, axiom, ![X13, X45, X2, X7]:(((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X45),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))<=c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Oone__class_Oone(X7))))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X45))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__decreasing)). 1.08/1.43 fof(fact_div__mult__self2, axiom, ![X20, X13, X12, X7]:(class_Divides_Osemiring__div(X7)=>(c_Groups_Ozero__class_Ozero(X7)!=X12=>c_Groups_Oplus__class_Oplus(X7,X20,c_Divides_Odiv__class_Odiv(X7,X13,X12))=c_Divides_Odiv__class_Odiv(X7,c_Groups_Oplus__class_Oplus(X7,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20)),X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult__self2)). 1.08/1.43 fof(fact_div__mult__self1, axiom, ![X20, X13, X12, X7]:((c_Groups_Oplus__class_Oplus(X7,X20,c_Divides_Odiv__class_Odiv(X7,X13,X12))=c_Divides_Odiv__class_Odiv(X7,c_Groups_Oplus__class_Oplus(X7,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12)),X12)<=c_Groups_Ozero__class_Ozero(X7)!=X12)<=class_Divides_Osemiring__div(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult__self1)). 1.08/1.43 fof(fact_power__strict__mono, axiom, ![X2, X12, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless(X7,X13,X12)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X12),X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__strict__mono)). 1.08/1.43 fof(fact_mult__less__cancel__left__disj, axiom, ![X11, X8, X53, X7]:((c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X53),X11))<=>((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X53)&c_Orderings_Oord__class_Oless(X7,X8,X11))|(c_Orderings_Oord__class_Oless(X7,X53,c_Groups_Ozero__class_Ozero(X7))&c_Orderings_Oord__class_Oless(X7,X11,X8))))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__cancel__left__disj)). 1.08/1.43 fof(fact_mult__less__cancel__right__disj, axiom, ![X11, X53, X8, X7]:((c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X53))<=>((c_Orderings_Oord__class_Oless(X7,X8,X11)&c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X53))|(c_Orderings_Oord__class_Oless(X7,X53,c_Groups_Ozero__class_Ozero(X7))&c_Orderings_Oord__class_Oless(X7,X11,X8))))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__cancel__right__disj)). 1.08/1.43 fof(fact_mult__left_Obounded, axiom, ![X21, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>?[X36]:![X25]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X25)),X36))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left_Obounded)). 1.08/1.43 fof(fact_mult__left_Ononneg__bounded, axiom, ![X21, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>?[X36]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)&![X25]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X25)),X36)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left_Ononneg__bounded)). 1.08/1.43 fof(fact_mult__left_Opos__bounded, axiom, ![X21, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>?[X36]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)&![X25]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X25)),X36)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left_Opos__bounded)). 1.08/1.43 fof(fact_norm__mult__ineq, axiom, ![X21, X14, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X14)),c_RealVector_Onorm__class_Onorm(X7,X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__mult__ineq)). 1.08/1.43 fof(fact_mult__right_Ononneg__bounded, axiom, ![X14, X7]:(?[X36]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)&![X25]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X25)),X36)))<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right_Ononneg__bounded)). 1.08/1.43 fof(fact_mult__right_Opos__bounded, axiom, ![X14, X7]:(?[X36]:(![X25]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X25)),X36))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36))<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right_Opos__bounded)). 1.08/1.43 fof(fact_mult__right_Obounded, axiom, ![X14, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>?[X36]:![X25]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X25)),X36))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right_Obounded)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, axiom, ![X20, X12, X13, X7]:(c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X13,X12)),X20)<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 1.08/1.43 fof(fact_mult_Oadd__left, axiom, ![X12, X65, X13, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X65),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X13,X65)),X12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Oadd__left)). 1.08/1.43 fof(fact_mult_Odiff__left, axiom, ![X12, X65, X13, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X13,X65)),X12)=c_Groups_Ominus__class_Ominus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X65),X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Odiff__left)). 1.08/1.43 fof(fact_mult__left_Odiff, axiom, ![X81, X21, X14, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ominus__class_Ominus(X7,X14,X21)),X81)=c_Groups_Ominus__class_Ominus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X81),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X21),X81))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left_Odiff)). 1.08/1.43 fof(fact_comm__semiring__class_Odistrib, axiom, ![X20, X12, X13, X7]:(class_Rings_Ocomm__semiring(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X13,X12)),X20)=c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__class_Odistrib)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, axiom, ![X12, X3, X13, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X13,X12)),X3)=c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X3))<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 1.08/1.43 fof(fact_mult__left_Oadd, axiom, ![X81, X21, X14, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X14,X21)),X81)=c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X81),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X21),X81))<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left_Oadd)). 1.08/1.43 fof(fact_reals__Archimedean3, axiom, ![X14]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)=>![X41]:?[X22]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X41,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X22)),X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_reals__Archimedean3)). 1.08/1.43 fof(fact_zdiv__mono2, axiom, ![X12, X35, X13]:(((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X35))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X12))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__mono2)). 1.08/1.43 fof(fact_zdiv__mono2__neg, axiom, ![X12, X35, X13]:(((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X12)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X35),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12)))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__mono2__neg)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, axiom, ![X15, X16, X14, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X16)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X15))=hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15))<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 1.08/1.43 fof(fact_power__add, axiom, ![X2, X3, X13, X7]:(class_Groups_Omonoid__mult(X7)=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__add)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, axiom, ![X31, X32, X33, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X31)),X32)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X32)),X31)<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 1.08/1.43 fof(fact_abs__triangle__ineq2, axiom, ![X12, X13, X7]:(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oabs__class_Oabs(X7,X13),c_Groups_Oabs__class_Oabs(X7,X12)),c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12)))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__triangle__ineq2)). 1.08/1.43 fof(fact_abs__triangle__ineq2__sym, axiom, ![X12, X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oabs__class_Oabs(X7,X13),c_Groups_Oabs__class_Oabs(X7,X12)),c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X12,X13)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__triangle__ineq2__sym)). 1.08/1.43 fof(fact_abs__triangle__ineq4, axiom, ![X12, X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12)),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,X13),c_Groups_Oabs__class_Oabs(X7,X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__triangle__ineq4)). 1.08/1.43 fof(fact_abs__triangle__ineq, axiom, ![X12, X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12)),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,X13),c_Groups_Oabs__class_Oabs(X7,X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__triangle__ineq)). 1.08/1.43 fof(fact_add__scale__eq__noteq, axiom, ![X39, X20, X12, X13, X47, X7]:(((c_Groups_Oplus__class_Oplus(X7,X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X47),X39))!=c_Groups_Oplus__class_Oplus(X7,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X47),X20))<=(X13=X12&X20!=X39))<=c_Groups_Ozero__class_Ozero(X7)!=X47)<=class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__scale__eq__noteq)). 1.08/1.43 fof(fact_nat__power__less__imp__less, axiom, ![X2, X3, X18]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X2)))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__power__less__imp__less)). 1.08/1.43 fof(fact_nat__mult__less__cancel1, axiom, ![X19, X29, X26]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X19))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__less__cancel1)). 1.08/1.43 fof(fact_real__mult__less__iff1, axiom, ![X6, X5, X48]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X48))<=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,X6))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__less__iff1)). 1.08/1.43 fof(fact_mult__le__cancel2, axiom, ![X19, X26, X29]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X26))<=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__le__cancel2)). 1.08/1.43 fof(fact_mult__le__cancel1, axiom, ![X19, X29, X26]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19))<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__le__cancel1)). 1.08/1.43 fof(fact_nat__mult__le__cancel1, axiom, ![X19, X29, X26]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X19)))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__le__cancel1)). 1.08/1.43 fof(fact_real__mult__le__cancel__iff1, axiom, ![X6, X5, X48]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X48))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X6))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__le__cancel__iff1)). 1.08/1.43 fof(fact_real__mult__le__cancel__iff2, axiom, ![X6, X5, X48]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X48),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X48),X6))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X6))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__le__cancel__iff2)). 1.08/1.43 fof(fact_natceiling__eq, axiom, ![X14, X2]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=>c_RComplete_Onatceiling(X14)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__eq)). 1.08/1.43 fof(fact_norm__triangle__ineq2, axiom, ![X12, X13, X7]:(class_RealVector_Oreal__normed__vector(X7)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X13),c_RealVector_Onorm__class_Onorm(X7,X12)),c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__triangle__ineq2)). 1.08/1.43 fof(fact_norm__diff__ineq, axiom, ![X12, X13, X7]:(class_RealVector_Oreal__normed__vector(X7)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X13),c_RealVector_Onorm__class_Onorm(X7,X12)),c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__diff__ineq)). 1.08/1.43 fof(fact_norm__triangle__ineq4, axiom, ![X12, X13, X7]:(class_RealVector_Oreal__normed__vector(X7)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X13),c_RealVector_Onorm__class_Onorm(X7,X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__triangle__ineq4)). 1.08/1.43 fof(fact_norm__triangle__ineq, axiom, ![X21, X14, X7]:(class_RealVector_Oreal__normed__vector(X7)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oplus__class_Oplus(X7,X14,X21)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X14),c_RealVector_Onorm__class_Onorm(X7,X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__triangle__ineq)). 1.08/1.43 fof(fact_poly__add, axiom, ![X14, X15, X16, X7]:(class_Rings_Ocomm__semiring__0(X7)=>c_Groups_Oplus__class_Oplus(X7,hAPP(c_Polynomial_Opoly(X7,X16),X14),hAPP(c_Polynomial_Opoly(X7,X15),X14))=hAPP(c_Polynomial_Opoly(X7,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),X16,X15)),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__add)). 1.08/1.43 fof(fact_coeff__diff, axiom, ![X2, X15, X16, X7]:(hAPP(c_Polynomial_Ocoeff(X7,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X7),X16,X15)),X2)=c_Groups_Ominus__class_Ominus(X7,hAPP(c_Polynomial_Ocoeff(X7,X16),X2),hAPP(c_Polynomial_Ocoeff(X7,X15),X2))<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_coeff__diff)). 1.08/1.43 fof(fact_coeff__add, axiom, ![X2, X15, X16, X7]:(class_Groups_Ocomm__monoid__add(X7)=>hAPP(c_Polynomial_Ocoeff(X7,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),X16,X15)),X2)=c_Groups_Oplus__class_Oplus(X7,hAPP(c_Polynomial_Ocoeff(X7,X16),X2),hAPP(c_Polynomial_Ocoeff(X7,X15),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_coeff__add)). 1.08/1.43 fof(fact_poly__diff, axiom, ![X14, X15, X16, X7]:(class_Rings_Ocomm__ring(X7)=>hAPP(c_Polynomial_Opoly(X7,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X7),X16,X15)),X14)=c_Groups_Ominus__class_Ominus(X7,hAPP(c_Polynomial_Opoly(X7,X16),X14),hAPP(c_Polynomial_Opoly(X7,X15),X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__diff)). 1.08/1.43 fof(fact_le__diff__conv2, axiom, ![X66, X74, X26]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X74)=>(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X26),X74)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X26)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__diff__conv2)). 1.08/1.43 fof(fact_zdiff__zmult__distrib, axiom, ![X43, X59, X60]:c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X59),X43))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X60,X59)),X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiff__zmult__distrib)). 1.08/1.43 fof(fact_zadd__zmult__distrib, axiom, ![X43, X59, X60]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X59),X43))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X60,X59)),X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__zmult__distrib)). 1.08/1.43 fof(fact_real__add__mult__distrib, axiom, ![X43, X59, X60]:c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X59),X43))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X60,X59)),X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__add__mult__distrib)). 1.08/1.43 fof(fact_diff__mult__distrib, axiom, ![X4, X2, X3]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)),X4)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__mult__distrib)). 1.08/1.43 fof(fact_add__mult__distrib, axiom, ![X4, X2, X3]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)),X4)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__mult__distrib)). 1.08/1.43 fof(fact_norm__power__ineq, axiom, ![X2, X14, X7]:(class_RealVector_Oreal__normed__algebra__1(X7)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X14)),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__power__ineq)). 1.08/1.43 fof(fact_add__less__imp__less__right, axiom, ![X12, X20, X13, X7]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X7)=>(c_Orderings_Oord__class_Oless(X7,X13,X12)<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__less__imp__less__right)). 1.08/1.43 fof(fact_add__less__cancel__right, axiom, ![X11, X53, X8, X7]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X7)=>(c_Orderings_Oord__class_Oless(X7,X8,X11)<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X8,X53),c_Groups_Oplus__class_Oplus(X7,X11,X53)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__less__cancel__right)). 1.08/1.43 fof(fact_add__less__cancel__left, axiom, ![X11, X8, X53, X7]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X7)=>(c_Orderings_Oord__class_Oless(X7,X8,X11)<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X53,X8),c_Groups_Oplus__class_Oplus(X7,X53,X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__less__cancel__left)). 1.08/1.43 fof(fact_add__less__imp__less__left, axiom, ![X12, X13, X20, X7]:((c_Orderings_Oord__class_Oless(X7,X13,X12)<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X20,X13),c_Groups_Oplus__class_Oplus(X7,X20,X12)))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__less__imp__less__left)). 1.08/1.43 fof(fact_add__le__imp__le__right, axiom, ![X12, X20, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X13,X12)<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X20)))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__le__imp__le__right)). 1.08/1.43 fof(fact_add__le__cancel__right, axiom, ![X11, X53, X8, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X8,X11)<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X8,X53),c_Groups_Oplus__class_Oplus(X7,X11,X53)))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__le__cancel__right)). 1.08/1.43 fof(fact_add__le__imp__le__left, axiom, ![X12, X13, X20, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X20,X13),c_Groups_Oplus__class_Oplus(X7,X20,X12))=>c_Orderings_Oord__class_Oless__eq(X7,X13,X12))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__le__imp__le__left)). 1.08/1.43 fof(fact_add__le__cancel__left, axiom, ![X11, X8, X53, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X53,X8),c_Groups_Oplus__class_Oplus(X7,X53,X11))<=>c_Orderings_Oord__class_Oless__eq(X7,X8,X11))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__le__cancel__left)). 1.08/1.43 fof(fact_Nat_Odiff__diff__eq, axiom, ![X2, X3, X4]:((c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X4))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X2))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat_Odiff__diff__eq)). 1.08/1.43 fof(fact_expand__poly__eq, axiom, ![X87, X9, X7]:((X87=X9<=>![X22]:hAPP(c_Polynomial_Ocoeff(X7,X87),X22)=hAPP(c_Polynomial_Ocoeff(X7,X9),X22))<=class_Groups_Ozero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_expand__poly__eq)). 1.08/1.43 fof(fact_power__gt1__lemma, axiom, ![X2, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__gt1__lemma)). 1.08/1.43 fof(fact_zpower__zadd__distrib, axiom, ![X10, X21, X14]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X10))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X21)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zpower__zadd__distrib)). 1.08/1.43 fof(fact_nat__add__left__cancel__less, axiom, ![X19, X29, X26]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X29),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__add__left__cancel__less)). 1.08/1.43 fof(fact_nat__add__left__cancel__le, axiom, ![X19, X29, X26]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X29),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__add__left__cancel__le)). 1.08/1.43 fof(fact_self__quotient__aux2, axiom, ![X15, X47, X13]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)=>(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X47,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X15))=X13=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,c_Groups_Oone__class_Oone(tc_Int_Oint))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_self__quotient__aux2)). 1.08/1.43 fof(fact_self__quotient__aux1, axiom, ![X15, X47, X13]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)=>(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X47,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X15))=X13=>(c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,X13)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_self__quotient__aux1)). 1.08/1.43 fof(fact_power__eq__imp__eq__base, axiom, ![X12, X2, X13, X7]:((hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X7),X12),X2)=>(((X13=X12<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__eq__imp__eq__base)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, axiom, ![X3, X13, X7]:(class_Rings_Ocomm__semiring__1(X7)=>c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X3),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Oone__class_Oone(X7))),X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, axiom, ![X13, X3, X7]:(c_Groups_Oplus__class_Oplus(X7,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Oone__class_Oone(X7))),X3)<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 1.08/1.43 fof(fact_natfloor__eq, axiom, ![X14, X2]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),X14)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=>c_RComplete_Onatfloor(X14)=X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__eq)). 1.08/1.43 fof(fact_mult__right__le__one__le, axiom, ![X21, X14, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X14)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X21)=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21),X14)<=c_Orderings_Oord__class_Oless__eq(X7,X21,c_Groups_Oone__class_Oone(X7)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right__le__one__le)). 1.08/1.43 fof(fact_mult__left__le__one__le, axiom, ![X21, X14, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X14)=>((c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X21),X14),X14)<=c_Orderings_Oord__class_Oless__eq(X7,X21,c_Groups_Oone__class_Oone(X7)))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left__le__one__le)). 1.08/1.43 fof(fact_norm__ratiotest__lemma, axiom, ![X21, X14, X20, X7]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),c_RealVector_Onorm__class_Onorm(X7,X21)))=>c_Groups_Ozero__class_Ozero(X7)=X14))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__ratiotest__lemma)). 1.08/1.43 fof(fact_mult__strict__right__mono, axiom, ![X20, X12, X13, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>((c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X20))<=c_Orderings_Oord__class_Oless(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__strict__right__mono)). 1.08/1.43 fof(fact_comm__mult__strict__left__mono, axiom, ![X20, X12, X13, X7]:(((c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X20))<=c_Orderings_Oord__class_Oless(X7,X13,X12))<=class_Rings_Olinordered__comm__semiring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__mult__strict__left__mono)). 1.08/1.43 fof(fact_mult__strict__left__mono, axiom, ![X20, X12, X13, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12)))<=c_Orderings_Oord__class_Oless(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__strict__left__mono)). 1.08/1.43 fof(fact_power__mono, axiom, ![X2, X12, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X13,X12)=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X12),X2))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__mono)). 1.08/1.43 fof(fact_mult__right__mono, axiom, ![X20, X12, X13, X7]:(class_Rings_Oordered__semiring(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20)))<=c_Orderings_Oord__class_Oless__eq(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right__mono)). 1.08/1.43 fof(fact_comm__mult__left__mono, axiom, ![X20, X12, X13, X7]:(((c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20))<=c_Orderings_Oord__class_Oless__eq(X7,X13,X12))<=class_Rings_Oordered__comm__semiring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__mult__left__mono)). 1.08/1.43 fof(fact_mult__left__mono, axiom, ![X20, X12, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X13,X12)=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20)))<=class_Rings_Oordered__semiring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left__mono)). 1.08/1.43 fof(fact_mult__strict__right__mono__neg, axiom, ![X20, X13, X12, X7]:((c_Orderings_Oord__class_Oless(X7,X12,X13)=>(c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20))<=c_Orderings_Oord__class_Oless(X7,X20,c_Groups_Ozero__class_Ozero(X7))))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__strict__right__mono__neg)). 1.08/1.43 fof(fact_mult__strict__left__mono__neg, axiom, ![X20, X13, X12, X7]:(((c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12))<=c_Orderings_Oord__class_Oless(X7,X20,c_Groups_Ozero__class_Ozero(X7)))<=c_Orderings_Oord__class_Oless(X7,X12,X13))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__strict__left__mono__neg)). 1.08/1.43 fof(fact_mult__right__mono__neg, axiom, ![X20, X13, X12, X7]:(class_Rings_Oordered__ring(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X12,X13)=>(c_Orderings_Oord__class_Oless__eq(X7,X20,c_Groups_Ozero__class_Ozero(X7))=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right__mono__neg)). 1.08/1.43 fof(fact_mult__left__mono__neg, axiom, ![X20, X13, X12, X7]:(class_Rings_Oordered__ring(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X12,X13)=>(c_Orderings_Oord__class_Oless__eq(X7,X20,c_Groups_Ozero__class_Ozero(X7))=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left__mono__neg)). 1.08/1.43 fof(fact_le__add__diff, axiom, ![X3, X2, X4]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X4))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__add__diff)). 1.08/1.43 fof(fact_add__strict__mono, axiom, ![X39, X20, X12, X13, X7]:(class_Groups_Oordered__cancel__ab__semigroup__add(X7)=>(c_Orderings_Oord__class_Oless(X7,X13,X12)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X39))<=c_Orderings_Oord__class_Oless(X7,X20,X39)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__strict__mono)). 1.08/1.43 fof(fact_add__le__less__mono, axiom, ![X39, X20, X12, X13, X7]:(class_Groups_Oordered__cancel__ab__semigroup__add(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X13,X12)=>(c_Orderings_Oord__class_Oless(X7,X20,X39)=>c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X39))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__le__less__mono)). 1.08/1.43 fof(fact_add__less__le__mono, axiom, ![X39, X20, X12, X13, X7]:(class_Groups_Oordered__cancel__ab__semigroup__add(X7)=>((c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X39))<=c_Orderings_Oord__class_Oless__eq(X7,X20,X39))<=c_Orderings_Oord__class_Oless(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__less__le__mono)). 1.08/1.43 fof(fact_add__mono, axiom, ![X39, X20, X12, X13, X7]:(((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X39))<=c_Orderings_Oord__class_Oless__eq(X7,X20,X39))<=c_Orderings_Oord__class_Oless__eq(X7,X13,X12))<=class_Groups_Oordered__ab__semigroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__mono)). 1.08/1.43 fof(fact_power__strict__increasing, axiom, ![X13, X45, X2, X7]:(class_Rings_Olinordered__semidom(X7)=>((c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X45))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X13))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X45))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__strict__increasing)). 1.08/1.43 fof(fact_power__increasing, axiom, ![X13, X45, X2, X7]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X45)=>(c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X45))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oone__class_Oone(X7),X13)))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__increasing)). 1.08/1.43 fof(fact_abs__eq__mult, axiom, ![X12, X13, X7]:(class_Rings_Oordered__ring__abs(X7)=>(c_Groups_Oabs__class_Oabs(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oabs__class_Oabs(X7,X13)),c_Groups_Oabs__class_Oabs(X7,X12))<=((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)|c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Ozero__class_Ozero(X7)))&(c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Ozero__class_Ozero(X7))|c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__eq__mult)). 1.08/1.43 fof(fact_ex__least__nat__less, axiom, ![X19, X62]:(~(hBOOL(hAPP(X62,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=>(?[X24]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X19)&hBOOL(hAPP(X62,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))&![X28]:(~(hBOOL(hAPP(X62,X28)))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X24)))<=hBOOL(hAPP(X62,X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ex__least__nat__less)). 1.08/1.43 fof(fact_realpow__num__eq__if, axiom, ![X3, X2, X7]:(((hAPP(hAPP(c_Power_Opower__class_Opower(X7),X3),X2)=c_Groups_Oone__class_Oone(X7)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)&(hAPP(hAPP(c_Power_Opower__class_Opower(X7),X3),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))<=X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=class_Power_Opower(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_realpow__num__eq__if)). 1.08/1.43 fof(fact_zdiv__mono1, axiom, ![X12, X65, X13]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,X65)=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X65,X12))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__mono1)). 1.08/1.43 fof(fact_div__le__mono2, axiom, ![X4, X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)=>(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4,X2),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4,X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__le__mono2)). 1.08/1.43 fof(fact_zdiv__mono1__neg, axiom, ![X12, X65, X13]:((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X65,X12),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,X65)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__mono1__neg)). 1.08/1.43 fof(fact_zadd__zless__mono, axiom, ![X10, X42, X43, X44]:((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X42,X10)=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X44,X42),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X43,X10)))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,X44,X43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__zless__mono)). 1.08/1.43 fof(fact_diff__less__mono, axiom, ![X20, X12, X13]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X12)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X13,X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X20))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__less__mono)). 1.08/1.43 fof(fact_diff__less__mono2, axiom, ![X34, X2, X3]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X3))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X34))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__less__mono2)). 1.08/1.43 fof(fact_add__less__mono, axiom, ![X34, X4, X30, X18]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X34))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X34))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__less__mono)). 1.08/1.43 fof(fact_add__le__mono, axiom, ![X34, X4, X30, X18]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X34)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X34)))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__le__mono)). 1.08/1.43 fof(fact_sum__squares__eq__zero__iff, axiom, ![X6, X5, X7]:((c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X5),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6))=c_Groups_Ozero__class_Ozero(X7)<=>(c_Groups_Ozero__class_Ozero(X7)=X5&c_Groups_Ozero__class_Ozero(X7)=X6))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sum__squares__eq__zero__iff)). 1.08/1.43 fof(fact_rabs__ratiotest__lemma, axiom, ![X21, X14, X20]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X21)))=>X14=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_rabs__ratiotest__lemma)). 1.08/1.43 fof(fact_mult__right_Odiff, axiom, ![X21, X14, X17, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>c_Groups_Ominus__class_Ominus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X17),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X17),X21))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X17),c_Groups_Ominus__class_Ominus(X7,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right_Odiff)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, axiom, ![X10, X21, X14, X7]:(class_Rings_Ocomm__semiring__1(X7)=>c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X10))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),c_Groups_Oplus__class_Oplus(X7,X21,X10))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 1.08/1.43 fof(fact_mult_Oadd__right, axiom, ![X35, X12, X13, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X35))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Oplus__class_Oplus(X7,X12,X35))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Oadd__right)). 1.08/1.43 fof(fact_mult__right_Oadd, axiom, ![X21, X14, X17, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>c_Groups_Oplus__class_Oplus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X17),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X17),X21))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X17),c_Groups_Oplus__class_Oplus(X7,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right_Oadd)). 1.08/1.43 fof(fact_mult_Odiff__right, axiom, ![X35, X12, X13, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Ominus__class_Ominus(X7,X12,X35))=c_Groups_Ominus__class_Ominus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X35))<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Odiff__right)). 1.08/1.43 fof(fact_mult__less__cancel1, axiom, ![X19, X29, X26]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X19))<=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__cancel1)). 1.08/1.43 fof(fact_mult__less__cancel2, axiom, ![X19, X26, X29]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X26))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__cancel2)). 1.08/1.43 fof(fact_nonneg1__imp__zdiv__pos__iff, axiom, ![X11, X8]:(((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X8)&c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11))<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X11)))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nonneg1__imp__zdiv__pos__iff)). 1.08/1.43 fof(fact_zero__less__mult__pos2, axiom, ![X13, X12, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X12)<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X13)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__mult__pos2)). 1.08/1.43 fof(fact_zero__less__mult__pos, axiom, ![X12, X13, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__mult__pos)). 1.08/1.43 fof(fact_power__commutes, axiom, ![X2, X13, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)),X13)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))<=class_Groups_Omonoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__commutes)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, axiom, ![X86, X31, X33, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X31)),X86)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X31),X86))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, axiom, ![X31, X32, X33, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X32),X31))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X32)),X31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 1.08/1.43 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, ![X20, X12, X13, X7]:(class_Groups_Oab__semigroup__mult(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12)),X20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ab__semigroup__mult__class_Omult__ac_I1_J)). 1.08/1.43 fof(fact_nat__less__real__le, axiom, ![X29, X19]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X29)<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__less__real__le)). 1.08/1.43 fof(fact_nat__le__real__less, axiom, ![X29, X19]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X29)<=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X29),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__le__real__less)). 1.08/1.43 fof(fact_reals__Archimedean6, axiom, ![X47]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X47)=>?[X22]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X47)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X47,c_RealDef_Oreal(tc_Nat_Onat,X22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_reals__Archimedean6)). 1.08/1.43 fof(fact_power__mult, axiom, ![X2, X3, X13, X7]:(class_Groups_Omonoid__mult(X7)=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X3)),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__mult)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, axiom, ![X15, X16, X14, X7]:(hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X15))=hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X16)),X15)<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 1.08/1.43 fof(fact_zmult__zless__mono2, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X30)=>(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X30))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zmult__zless__mono2)). 1.08/1.43 fof(fact_mult__less__mono1, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X30)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X4))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__mono1)). 1.08/1.43 fof(fact_mult__less__mono2, axiom, ![X4, X30, X18]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X30)))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__less__mono2)). 1.08/1.43 fof(fact_real__mult__less__mono2, axiom, ![X21, X14, X10]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X10)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X21))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__less__mono2)). 1.08/1.43 fof(fact_power__eq__if, axiom, ![X16, X3]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3=>c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X16),X3))&(X3!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X16),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X16),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__eq__if)). 1.08/1.43 fof(fact_less__diff__conv, axiom, ![X26, X74, X66]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X66,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X26))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X26),X74)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__diff__conv)). 1.08/1.43 fof(fact_le__diff__conv, axiom, ![X66, X26, X74]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X26),X66)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X74,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X26))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__diff__conv)). 1.08/1.43 fof(fact_mult__le__mono, axiom, ![X34, X4, X30, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X30)=>(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X34)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X34)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__le__mono)). 1.08/1.43 fof(fact_poly__div__mult__right, axiom, ![X10, X21, X14, X7]:(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),X14,X21),X10)=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X21),X10))<=class_Fields_Ofield(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__div__mult__right)). 1.08/1.43 fof(fact_add__diff__assoc2, axiom, ![X18, X30, X4]:(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X4),X18)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X18),X4)<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__diff__assoc2)). 1.08/1.43 fof(fact_diff__add__assoc2, axiom, ![X18, X30, X4]:(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X18),X4)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X4),X18)<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__add__assoc2)). 1.08/1.43 fof(fact_diff__diff__right, axiom, ![X18, X30, X4]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X30)=>c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X4),X30)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__diff__right)). 1.08/1.43 fof(fact_add__diff__assoc, axiom, ![X18, X30, X4]:(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X30),X4)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X4))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__diff__assoc)). 1.08/1.43 fof(fact_diff__add__assoc, axiom, ![X18, X30, X4]:(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X30),X4)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X4))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__add__assoc)). 1.08/1.43 fof(fact_pos__imp__zdiv__nonneg__iff, axiom, ![X8, X11]:((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)<=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X11)))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_pos__imp__zdiv__nonneg__iff)). 1.08/1.43 fof(fact_neg__imp__zdiv__neg__iff, axiom, ![X8, X11]:((c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__imp__zdiv__neg__iff)). 1.08/1.43 fof(fact_pos__imp__zdiv__neg__iff, axiom, ![X8, X11]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)=>(c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_pos__imp__zdiv__neg__iff)). 1.08/1.43 fof(fact_neg__imp__zdiv__nonneg__iff, axiom, ![X8, X11]:((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X11)))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__imp__zdiv__nonneg__iff)). 1.08/1.43 fof(fact_pos__imp__zdiv__pos__iff, axiom, ![X66, X26]:((c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X66,X26))<=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X66))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_pos__imp__zdiv__pos__iff)). 1.08/1.43 fof(fact_zdiv__zmult2__eq, axiom, ![X12, X13, X20]:(c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),X20)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X20))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__zmult2__eq)). 1.08/1.43 fof(fact_mult__le__0__iff, axiom, ![X11, X8, X7]:((((c_Orderings_Oord__class_Oless__eq(X7,X11,c_Groups_Ozero__class_Ozero(X7))&c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X8))|(c_Orderings_Oord__class_Oless__eq(X7,X8,c_Groups_Ozero__class_Ozero(X7))&c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X11)))<=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X11),c_Groups_Ozero__class_Ozero(X7)))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__le__0__iff)). 1.08/1.43 fof(fact_zero__le__mult__iff, axiom, ![X11, X8, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X11))<=>((c_Orderings_Oord__class_Oless__eq(X7,X11,c_Groups_Ozero__class_Ozero(X7))&c_Orderings_Oord__class_Oless__eq(X7,X8,c_Groups_Ozero__class_Ozero(X7)))|(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X11)&c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X8))))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__le__mult__iff)). 1.08/1.43 fof(fact_zero__less__zpower__abs__iff, axiom, ![X19, X5]:((X19=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X5!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X5)),X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__zpower__abs__iff)). 1.08/1.43 fof(fact_zdiff__zmult__distrib2, axiom, ![X59, X60, X43]:c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),X59))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X60,X59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiff__zmult__distrib2)). 1.08/1.43 fof(fact_add__mult__distrib2, axiom, ![X2, X3, X4]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__mult__distrib2)). 1.08/1.43 fof(fact_zadd__zmult__distrib2, axiom, ![X59, X60, X43]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X60,X59))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),X59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__zmult__distrib2)). 1.08/1.43 fof(fact_diff__mult__distrib2, axiom, ![X2, X3, X4]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__mult__distrib2)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, axiom, ![X3, X7]:(c_Groups_Oplus__class_Oplus(X7,X3,X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Oone__class_Oone(X7))),X3)<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 1.08/1.43 fof(fact_nat__mult__div__cancel1, axiom, ![X2, X3, X4]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)=>c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__div__cancel1)). 1.08/1.43 fof(fact_real__two__squares__add__zero__iff, axiom, ![X6, X5]:(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X6))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<=>(X6=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__two__squares__add__zero__iff)). 1.08/1.43 fof(fact_ln__add__one__self__le__self, axiom, ![X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X14)),X14)<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__add__one__self__le__self)). 1.08/1.43 fof(fact_add__neg__neg, axiom, ![X12, X13, X7]:(class_Groups_Oordered__comm__monoid__add(X7)=>((c_Orderings_Oord__class_Oless(X7,X12,c_Groups_Ozero__class_Ozero(X7))=>c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),c_Groups_Ozero__class_Ozero(X7)))<=c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__neg__neg)). 1.08/1.43 fof(fact_add__nonpos__neg, axiom, ![X12, X13, X7]:(((c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),c_Groups_Ozero__class_Ozero(X7))<=c_Orderings_Oord__class_Oless(X7,X12,c_Groups_Ozero__class_Ozero(X7)))<=c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Ozero__class_Ozero(X7)))<=class_Groups_Oordered__comm__monoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__nonpos__neg)). 1.08/1.43 fof(fact_add__neg__nonpos, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Ozero__class_Ozero(X7))=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),c_Groups_Ozero__class_Ozero(X7))<=c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Ozero__class_Ozero(X7))))<=class_Groups_Oordered__comm__monoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__neg__nonpos)). 1.08/1.43 fof(fact_add__nonpos__nonpos, axiom, ![X12, X13, X7]:(((c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Ozero__class_Ozero(X7))=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),c_Groups_Ozero__class_Ozero(X7)))<=c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Ozero__class_Ozero(X7)))<=class_Groups_Oordered__comm__monoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__nonpos__nonpos)). 1.08/1.43 fof(fact_add__pos__pos, axiom, ![X12, X13, X7]:(class_Groups_Oordered__comm__monoid__add(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X13,X12))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__pos__pos)). 1.08/1.43 fof(fact_add__nonneg__pos, axiom, ![X12, X13, X7]:(class_Groups_Oordered__comm__monoid__add(X7)=>((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X13,X12))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X12))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__nonneg__pos)). 1.08/1.43 fof(fact_add__pos__nonneg, axiom, ![X12, X13, X7]:(class_Groups_Oordered__comm__monoid__add(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12)=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X13,X12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__pos__nonneg)). 1.08/1.43 fof(fact_add__nonneg__nonneg, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X13,X12))))<=class_Groups_Oordered__comm__monoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__nonneg__nonneg)). 1.08/1.43 fof(fact_add__gr__0, axiom, ![X19, X29]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X19))<=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__gr__0)). 1.08/1.43 fof(fact_zpower__zpower, axiom, ![X10, X21, X14]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X21)),X10)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zpower__zpower)). 1.08/1.43 fof(fact_real__mult__assoc, axiom, ![X64, X59, X60]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),X59)),X64)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X59),X64)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__assoc)). 1.08/1.43 fof(fact_zmult__assoc, axiom, ![X64, X59, X60]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X59),X64))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X59)),X64), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zmult__assoc)). 1.08/1.43 fof(fact_nat__mult__assoc, axiom, ![X4, X2, X3]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__assoc)). 1.08/1.43 fof(fact_mult__neg__pos, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Ozero__class_Ozero(X7))=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X12)=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),c_Groups_Ozero__class_Ozero(X7))))<=class_Rings_Olinordered__semiring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__neg__pos)). 1.08/1.43 fof(fact_mult__pos__neg, axiom, ![X12, X13, X7]:(class_Rings_Olinordered__semiring__strict(X7)=>((c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),c_Groups_Ozero__class_Ozero(X7))<=c_Orderings_Oord__class_Oless(X7,X12,c_Groups_Ozero__class_Ozero(X7)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__pos__neg)). 1.08/1.43 fof(fact_mult__pos__neg2, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless(X7,X12,c_Groups_Ozero__class_Ozero(X7))=>c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X13),c_Groups_Ozero__class_Ozero(X7))))<=class_Rings_Olinordered__semiring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__pos__neg2)). 1.08/1.43 fof(fact_split__mult__neg__le, axiom, ![X12, X13, X7]:(class_Rings_Oordered__cancel__semiring(X7)=>(((c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Ozero__class_Ozero(X7))&c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12))|(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)&c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Ozero__class_Ozero(X7))))=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_split__mult__neg__le)). 1.08/1.43 fof(fact_mult__nonpos__nonneg, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Ozero__class_Ozero(X7))=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12)=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),c_Groups_Ozero__class_Ozero(X7))))<=class_Rings_Oordered__cancel__semiring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__nonpos__nonneg)). 1.08/1.43 fof(fact_mult__nonneg__nonpos, axiom, ![X12, X13, X7]:(class_Rings_Oordered__cancel__semiring(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Ozero__class_Ozero(X7))=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),c_Groups_Ozero__class_Ozero(X7))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__nonneg__nonpos)). 1.08/1.43 fof(fact_mult__nonneg__nonpos2, axiom, ![X12, X13, X7]:(class_Rings_Oordered__cancel__semiring(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X13),c_Groups_Ozero__class_Ozero(X7))<=c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Ozero__class_Ozero(X7)))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__nonneg__nonpos2)). 1.08/1.43 fof(fact_less__1__mult, axiom, ![X2, X3, X7]:(((c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X3),X2))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X2))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X3))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__1__mult)). 1.08/1.43 fof(fact_mult__pos__pos, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X12)=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))))<=class_Rings_Olinordered__semiring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__pos__pos)). 1.08/1.43 fof(fact_mult__nonneg__nonneg, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))))<=class_Rings_Oordered__cancel__semiring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__nonneg__nonneg)). 1.08/1.43 fof(fact_split__mult__pos__le, axiom, ![X12, X13, X7]:((((c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Ozero__class_Ozero(X7))&c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Ozero__class_Ozero(X7)))|(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)&c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X12)))=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12)))<=class_Rings_Oordered__ring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_split__mult__pos__le)). 1.08/1.43 fof(fact_mult__neg__neg, axiom, ![X12, X13, X7]:(((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))<=c_Orderings_Oord__class_Oless(X7,X12,c_Groups_Ozero__class_Ozero(X7)))<=c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Ozero__class_Ozero(X7)))<=class_Rings_Olinordered__ring__strict(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__neg__neg)). 1.08/1.43 fof(fact_mult__nonpos__nonpos, axiom, ![X12, X13, X7]:(class_Rings_Oordered__ring(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Ozero__class_Ozero(X7))=>(c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Ozero__class_Ozero(X7))=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__nonpos__nonpos)). 1.08/1.43 fof(fact_add__strict__right__mono, axiom, ![X20, X12, X13, X7]:(class_Groups_Oordered__cancel__ab__semigroup__add(X7)=>(c_Orderings_Oord__class_Oless(X7,X13,X12)=>c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__strict__right__mono)). 1.08/1.43 fof(fact_add__strict__left__mono, axiom, ![X20, X12, X13, X7]:(class_Groups_Oordered__cancel__ab__semigroup__add(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X20,X13),c_Groups_Oplus__class_Oplus(X7,X20,X12))<=c_Orderings_Oord__class_Oless(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__strict__left__mono)). 1.08/1.43 fof(fact_add__right__mono, axiom, ![X20, X12, X13, X7]:(class_Groups_Oordered__ab__semigroup__add(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),c_Groups_Oplus__class_Oplus(X7,X12,X20))<=c_Orderings_Oord__class_Oless__eq(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__right__mono)). 1.08/1.43 fof(fact_add__left__mono, axiom, ![X20, X12, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X13,X12)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X20,X13),c_Groups_Oplus__class_Oplus(X7,X20,X12)))<=class_Groups_Oordered__ab__semigroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__left__mono)). 1.08/1.43 fof(fact_realpow__pos__nth__unique, axiom, ![X13, X2]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)=>?[X25]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25)&X13=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X25),X2))&![X41]:(X41=X25<=(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X41)&X13=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X41),X2)))))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_realpow__pos__nth__unique)). 1.08/1.43 fof(fact_one__less__power, axiom, ![X2, X13, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X13)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_one__less__power)). 1.08/1.43 fof(fact_incseq__def, axiom, ![X23, X7]:((c_SEQ_Oincseq(X7,X23)<=>![X61, X22]:(c_Orderings_Oord__class_Oless__eq(X7,hAPP(X23,X61),hAPP(X23,X22))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X61,X22)))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_incseq__def)). 1.08/1.43 fof(fact_decseq__def, axiom, ![X23, X7]:(class_Orderings_Oorder(X7)=>(![X61, X22]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X61,X22)=>c_Orderings_Oord__class_Oless__eq(X7,hAPP(X23,X22),hAPP(X23,X61)))<=>c_SEQ_Odecseq(X7,X23))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_decseq__def)). 1.08/1.43 fof(fact_ge__natfloor__plus__one__imp__gt, axiom, ![X2, X10]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,c_RealDef_Oreal(tc_Nat_Onat,X2))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ge__natfloor__plus__one__imp__gt)). 1.08/1.43 fof(fact_add__strict__increasing2, axiom, ![X20, X12, X13, X7]:(class_Groups_Oordered__comm__monoid__add(X7)=>((c_Orderings_Oord__class_Oless(X7,X12,X20)=>c_Orderings_Oord__class_Oless(X7,X12,c_Groups_Oplus__class_Oplus(X7,X13,X20)))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__strict__increasing2)). 1.08/1.43 fof(fact_add__strict__increasing, axiom, ![X20, X12, X13, X7]:(class_Groups_Oordered__comm__monoid__add(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,X12,X20)=>c_Orderings_Oord__class_Oless(X7,X12,c_Groups_Oplus__class_Oplus(X7,X13,X20)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__strict__increasing)). 1.08/1.43 fof(fact_pos__add__strict, axiom, ![X20, X12, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>((c_Orderings_Oord__class_Oless(X7,X12,X20)=>c_Orderings_Oord__class_Oless(X7,X12,c_Groups_Oplus__class_Oplus(X7,X13,X20)))<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_pos__add__strict)). 1.08/1.43 fof(fact_add__increasing, axiom, ![X20, X12, X13, X7]:(class_Groups_Oordered__comm__monoid__add(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>(c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Oplus__class_Oplus(X7,X13,X20))<=c_Orderings_Oord__class_Oless__eq(X7,X12,X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__increasing)). 1.08/1.43 fof(fact_add__increasing2, axiom, ![X13, X12, X20, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X20)=>(c_Orderings_Oord__class_Oless__eq(X7,X12,c_Groups_Oplus__class_Oplus(X7,X13,X20))<=c_Orderings_Oord__class_Oless__eq(X7,X12,X13)))<=class_Groups_Oordered__comm__monoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__increasing2)). 1.08/1.43 fof(fact_real__minus__mult__self__le, axiom, ![X14, X78]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X78),X78)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__minus__mult__self__le)). 1.08/1.43 fof(fact_zadd__strict__right__mono, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X30)=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__strict__right__mono)). 1.08/1.43 fof(fact_add__less__mono1, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X30)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__less__mono1)). 1.08/1.43 fof(fact_zadd__left__mono, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X30)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X18),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X30))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__left__mono)). 1.08/1.43 fof(fact_div__le__mono, axiom, ![X4, X2, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X4),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__le__mono)). 1.08/1.43 fof(fact_diff__le__mono, axiom, ![X34, X2, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X34),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X34))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__le__mono)). 1.08/1.43 fof(fact_diff__le__mono2, axiom, ![X34, X2, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X3))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__le__mono2)). 1.08/1.43 fof(fact_add__le__mono1, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X4))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__le__mono1)). 1.08/1.43 fof(fact_real__add__left__mono, axiom, ![X10, X21, X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X14),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X21))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__add__left__mono)). 1.08/1.43 fof(fact_abs__power__minus, axiom, ![X2, X13, X7]:(class_Rings_Olinordered__idom(X7)=>c_Groups_Oabs__class_Oabs(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Ouminus__class_Ouminus(X7,X13)),X2))=c_Groups_Oabs__class_Oabs(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__power__minus)). 1.08/1.43 fof(fact_div__add__self1, axiom, ![X13, X12, X7]:((c_Groups_Oplus__class_Oplus(X7,c_Divides_Odiv__class_Odiv(X7,X13,X12),c_Groups_Oone__class_Oone(X7))=c_Divides_Odiv__class_Odiv(X7,c_Groups_Oplus__class_Oplus(X7,X12,X13),X12)<=X12!=c_Groups_Ozero__class_Ozero(X7))<=class_Divides_Osemiring__div(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__add__self1)). 1.08/1.43 fof(fact_div__add__self2, axiom, ![X13, X12, X7]:((X12!=c_Groups_Ozero__class_Ozero(X7)=>c_Groups_Oplus__class_Oplus(X7,c_Divides_Odiv__class_Odiv(X7,X13,X12),c_Groups_Oone__class_Oone(X7))=c_Divides_Odiv__class_Odiv(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),X12))<=class_Divides_Osemiring__div(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__add__self2)). 1.08/1.43 fof(fact_abs__add__abs, axiom, ![X12, X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Groups_Oabs__class_Oabs(X7,c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,X13),c_Groups_Oabs__class_Oabs(X7,X12)))=c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,X13),c_Groups_Oabs__class_Oabs(X7,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__add__abs)). 1.08/1.43 fof(fact_div__neg__pos__less0, axiom, ![X12, X13]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=>(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__neg__pos__less0)). 1.08/1.43 fof(fact_div__nonneg__neg__le0, axiom, ![X12, X13]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__nonneg__neg__le0)). 1.08/1.43 fof(fact_div__nonpos__pos__le0, axiom, ![X12, X13]:((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__nonpos__pos__le0)). 1.08/1.43 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J, axiom, ![X21, X14]:((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X14,X21))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Divides_Otransfer__nat__int__function__closures_I1_J)). 1.08/1.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, axiom, ![X21, X14]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J)). 1.08/1.43 fof(fact_ln__mult, axiom, ![X21, X14]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)=>c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X21))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(X14),c_Transcendental_Oln(X21)))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__mult)). 1.08/1.43 fof(fact_eq__diff__iff, axiom, ![X19, X29, X26]:(((X19=X29<=>c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X26)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X26))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X19))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_eq__diff__iff)). 1.08/1.43 fof(fact_int__div__less__self, axiom, ![X4, X14]:((c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4)=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X14,X4),X14))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_int__div__less__self)). 1.08/1.43 fof(fact_div__less__dividend, axiom, ![X3, X2]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2),X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__less__dividend)). 1.08/1.43 fof(fact_diff__less, axiom, ![X3, X2]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),X3)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__less)). 1.08/1.43 fof(fact_ln__less__cancel__iff, axiom, ![X6, X5]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,X6)<=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X5),c_Transcendental_Oln(X6))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__less__cancel__iff)). 1.08/1.43 fof(fact_ln__le__cancel__iff, axiom, ![X6, X5]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X6)<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X5),c_Transcendental_Oln(X6))))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__le__cancel__iff)). 1.08/1.43 fof(fact_natfloor__subtract, axiom, ![X14, X13]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X13),X14)=>c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,c_RealDef_Oreal(tc_Nat_Onat,X13)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X14),X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__subtract)). 1.08/1.43 fof(fact_natceiling__subtract, axiom, ![X14, X13]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X13),X14)=>c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X14),X13)=c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,c_RealDef_Oreal(tc_Nat_Onat,X13)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__subtract)). 1.08/1.43 fof(fact_zero__less__double__add__iff__zero__less__single__add, axiom, ![X8, X7]:(class_Groups_Olinordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X8,X8))<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X8))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__double__add__iff__zero__less__single__add)). 1.08/1.43 fof(fact_zero__le__double__add__iff__zero__le__single__add, axiom, ![X8, X7]:(class_Groups_Olinordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X8)<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X8,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__le__double__add__iff__zero__le__single__add)). 1.08/1.43 fof(fact_double__add__less__zero__iff__single__add__less__zero, axiom, ![X8, X7]:(class_Groups_Olinordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X8,X8),c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_double__add__less__zero__iff__single__add__less__zero)). 1.08/1.43 fof(fact_even__less__0__iff, axiom, ![X8, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X8,X8),c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_even__less__0__iff)). 1.08/1.43 fof(fact_double__add__le__zero__iff__single__add__le__zero, axiom, ![X8, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X8,X8),c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless__eq(X7,X8,c_Groups_Ozero__class_Ozero(X7)))<=class_Groups_Olinordered__ab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_double__add__le__zero__iff__single__add__le__zero)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, axiom, ![X20, X12, X13, X7]:(c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),X20)=c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),X12)<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 1.08/1.43 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, ![X20, X12, X13, X7]:(c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Oplus__class_Oplus(X7,X12,X20))=c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),X20)<=class_Groups_Oab__semigroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ab__semigroup__add__class_Oadd__ac_I1_J)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, axiom, ![X39, X20, X13, X7]:(c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Oplus__class_Oplus(X7,X20,X39))=c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X20),X39)<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, axiom, ![X20, X12, X13, X7]:(class_Rings_Ocomm__semiring__1(X7)=>c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Oplus__class_Oplus(X7,X12,X20))=c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),X20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, axiom, ![X39, X20, X13, X7]:(c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Oplus__class_Oplus(X7,X20,X39))=c_Groups_Oplus__class_Oplus(X7,X20,c_Groups_Oplus__class_Oplus(X7,X13,X39))<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 1.08/1.43 fof(fact_abs__add__one__not__less__self, axiom, ![X14]:~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X14),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__add__one__not__less__self)). 1.08/1.43 fof(fact_real__0__less__add__iff, axiom, ![X6, X5]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X6))<=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5),X6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__0__less__add__iff)). 1.08/1.43 fof(fact_real__0__le__add__iff, axiom, ![X6, X5]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X6))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5),X6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__0__le__add__iff)). 1.08/1.43 fof(fact_real__add__less__0__iff, axiom, ![X6, X5]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X6),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__add__less__0__iff)). 1.08/1.43 fof(fact_real__add__le__0__iff, axiom, ![X6, X5]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X6),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__add__le__0__iff)). 1.08/1.43 fof(fact_div__mult__mult2, axiom, ![X12, X13, X20, X7]:((c_Groups_Ozero__class_Ozero(X7)!=X20=>c_Divides_Odiv__class_Odiv(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X20))=c_Divides_Odiv__class_Odiv(X7,X13,X12))<=class_Divides_Osemiring__div(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult__mult2)). 1.08/1.43 fof(fact_div__mult__mult1, axiom, ![X12, X13, X20, X7]:(class_Divides_Osemiring__div(X7)=>(X20!=c_Groups_Ozero__class_Ozero(X7)=>c_Divides_Odiv__class_Odiv(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12))=c_Divides_Odiv__class_Odiv(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult__mult1)). 1.08/1.43 fof(fact_div__mult__mult1__if, axiom, ![X12, X13, X20, X7]:(((X20=c_Groups_Ozero__class_Ozero(X7)=>c_Divides_Odiv__class_Odiv(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12))=c_Groups_Ozero__class_Ozero(X7))&(X20!=c_Groups_Ozero__class_Ozero(X7)=>c_Divides_Odiv__class_Odiv(X7,X13,X12)=c_Divides_Odiv__class_Odiv(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X20),X12))))<=class_Divides_Osemiring__div(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult__mult1__if)). 1.08/1.43 fof(fact_less__iff__diff__less__0, axiom, ![X11, X8, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ominus__class_Ominus(X7,X8,X11),c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless(X7,X8,X11))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__iff__diff__less__0)). 1.08/1.43 fof(fact_le__iff__diff__le__0, axiom, ![X11, X8, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X8,X11)<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ominus__class_Ominus(X7,X8,X11),c_Groups_Ozero__class_Ozero(X7)))<=class_Groups_Oordered__ab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__iff__diff__le__0)). 1.08/1.43 fof(fact_abs__minus__add__cancel, axiom, ![X21, X14]:c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21)))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__minus__add__cancel)). 1.08/1.43 fof(fact_nat__0__less__mult__iff, axiom, ![X19, X29]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X19))<=>(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__0__less__mult__iff)). 1.08/1.43 fof(fact_real__mult__order, axiom, ![X21, X14]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X21))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__order)). 1.08/1.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, axiom, ![X21, X14]:((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X21)))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)). 1.08/1.43 fof(fact_abs__mult__pos, axiom, ![X21, X14, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Groups_Oabs__class_Oabs(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X21),X14))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oabs__class_Oabs(X7,X21)),X14)<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__mult__pos)). 1.08/1.43 fof(fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, axiom, ~(![X61]:~(![X67]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X67)),X61)<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X67),v_r)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)). 1.08/1.43 fof(fact_pCons, axiom, ?[X61]:(![X67]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X67),v_r)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X67)),X61))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_pCons)). 1.08/1.43 fof(fact_m, axiom, ![X67]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X67)),v_m____)<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X67),v_r)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_m)). 1.08/1.43 fof(fact_le__cube, axiom, ![X3]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__cube)). 1.08/1.43 fof(fact_diff__eq__diff__less, axiom, ![X52, X53, X11, X8, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Groups_Ominus__class_Ominus(X7,X53,X52)=c_Groups_Ominus__class_Ominus(X7,X8,X11)=>(c_Orderings_Oord__class_Oless(X7,X8,X11)<=>c_Orderings_Oord__class_Oless(X7,X53,X52)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__eq__diff__less)). 1.08/1.43 fof(fact_diff__eq__diff__less__eq, axiom, ![X52, X53, X11, X8, X7]:((c_Groups_Ominus__class_Ominus(X7,X8,X11)=c_Groups_Ominus__class_Ominus(X7,X53,X52)=>(c_Orderings_Oord__class_Oless__eq(X7,X53,X52)<=>c_Orderings_Oord__class_Oless__eq(X7,X8,X11)))<=class_Groups_Oordered__ab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__eq__diff__less__eq)). 1.08/1.43 fof(fact_mult__le__mono1, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X4))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__le__mono1)). 1.08/1.43 fof(fact_mult__le__mono2, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X30)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X30))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__le__mono2)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, axiom, ![X86, X31, X33, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),X86))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X31),X86))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 1.08/1.43 fof(fact_diff__cancel, axiom, ![X2, X3, X4]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__cancel)). 1.08/1.43 fof(fact_diff__cancel2, axiom, ![X2, X4, X3]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__cancel2)). 1.08/1.43 fof(fact_diff__commute, axiom, ![X4, X30, X18]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X30),X4)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X4),X30), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__commute)). 1.08/1.43 fof(fact_zadd__assoc, axiom, ![X64, X59, X60]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X60,X59),X64)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X60,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X59,X64)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__assoc)). 1.08/1.43 fof(fact_nat__add__assoc, axiom, ![X4, X2, X3]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X4)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__add__assoc)). 1.08/1.43 fof(fact_diff__diff__left, axiom, ![X4, X30, X18]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X4))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X30),X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__diff__left)). 1.08/1.43 fof(fact_zadd__left__commute, axiom, ![X10, X21, X14]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X10))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__left__commute)). 1.08/1.43 fof(fact_nat__add__left__commute, axiom, ![X10, X21, X14]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X10))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__add__left__commute)). 1.08/1.43 fof(fact_zless__add1__eq, axiom, ![X48, X49]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint)))<=>(c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,X48)|X48=X49)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zless__add1__eq)). 1.08/1.43 fof(fact_add1__zle__eq, axiom, ![X48, X49]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint)),X48)<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,X48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add1__zle__eq)). 1.08/1.43 fof(fact_zle__diff1__eq, axiom, ![X48, X49]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint)))<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,X48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zle__diff1__eq)). 1.08/1.43 fof(fact_zle__add1__eq__le, axiom, ![X48, X49]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,X48)<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zle__add1__eq__le)). 1.08/1.43 fof(fact_less__bin__lemma, axiom, ![X51, X26]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X26,X51)<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,X51),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__bin__lemma)). 1.08/1.43 fof(fact_real__le__eq__diff, axiom, ![X6, X5]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X6)<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5,X6),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__le__eq__diff)). 1.08/1.43 fof(fact_zero__less__diff, axiom, ![X29, X19]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__diff)). 1.08/1.43 fof(fact_less__add__eq__less, axiom, ![X2, X3, X34, X4]:((c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X34)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__add__eq__less)). 1.08/1.43 fof(fact_natfloor__add, axiom, ![X13, X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)=>c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_RealDef_Oreal(tc_Nat_Onat,X13)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X14),X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__add)). 1.08/1.43 fof(fact_natceiling__add, axiom, ![X13, X14]:(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_RealDef_Oreal(tc_Nat_Onat,X13)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X14),X13)<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__add)). 1.08/1.43 fof(fact_abs__less__iff, axiom, ![X11, X8, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,X8),X11)<=>(c_Orderings_Oord__class_Oless(X7,X8,X11)&c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X8),X11)))<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__less__iff)). 1.08/1.43 fof(fact_abs__le__iff, axiom, ![X11, X8, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,X8,X11)&c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X8),X11))<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X8),X11))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__le__iff)). 1.08/1.43 fof(fact_abs__leI, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X13,X12)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X13),X12)<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X13),X12)))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__leI)). 1.08/1.43 fof(fact_add__lessD1, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X30),X4)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__lessD1)). 1.08/1.43 fof(fact_add__leE, axiom, ![X2, X4, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4),X2)=>~((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)=>~(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__leE)). 1.08/1.43 fof(fact_add__leD1, axiom, ![X2, X4, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__leD1)). 1.08/1.43 fof(fact_add__leD2, axiom, ![X2, X4, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X2)<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__leD2)). 1.08/1.43 fof(fact_div__mult2__eq, axiom, ![X20, X12, X13]:c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X13,X12),X20)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult2__eq)). 1.08/1.43 fof(fact_real__of__nat__diff, axiom, ![X3, X2]:(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3),c_RealDef_Oreal(tc_Nat_Onat,X2))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__diff)). 1.08/1.43 fof(fact_add__nonneg__eq__0__iff, axiom, ![X6, X5, X7]:(((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)=>(c_Groups_Oplus__class_Oplus(X7,X5,X6)=c_Groups_Ozero__class_Ozero(X7)<=>(X6=c_Groups_Ozero__class_Ozero(X7)&c_Groups_Ozero__class_Ozero(X7)=X5)))<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X5))<=class_Groups_Oordered__comm__monoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__nonneg__eq__0__iff)). 1.08/1.43 fof(fact_less__fun__def, axiom, ![X71, X27, X7, X72]:(((c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X72),X27,X71)&~(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X72),X71,X27)))<=>c_Orderings_Oord__class_Oless(tc_fun(X7,X72),X27,X71))<=class_Orderings_Oord(X72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__fun__def)). 1.08/1.43 fof(fact_nat__zero__less__power__iff, axiom, ![X19, X5]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X19)<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5),X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__zero__less__power__iff)). 1.08/1.43 fof(fact_zero__less__power__nat__eq, axiom, ![X19, X5]:((X19=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5),X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__power__nat__eq)). 1.08/1.43 fof(fact_nat__mult__div__cancel__disj, axiom, ![X2, X3, X4]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X4=>c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__div__cancel__disj)). 1.08/1.43 fof(fact_minus__apply, axiom, ![X5, X91, X92, X72, X7]:(c_Groups_Ominus__class_Ominus(X7,hAPP(X92,X5),hAPP(X91,X5))=hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X72,X7),X92,X91),X5)<=class_Groups_Ominus(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__apply)). 1.08/1.43 fof(fact_ln__realpow, axiom, ![X2, X14]:(c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X14),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Transcendental_Oln(X14))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__realpow)). 1.08/1.43 fof(fact_abs__le__interval__iff, axiom, ![X57, X5]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),X57)<=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X57)&c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X57),X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__le__interval__iff)). 1.08/1.43 fof(fact_less__poly__def, axiom, ![X6, X5, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),X5,X6)<=>c_Polynomial_Opos__poly(X7,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X7),X6,X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__poly__def)). 1.08/1.43 fof(fact_less__eq__poly__def, axiom, ![X6, X5, X7]:((c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X7),X5,X6)<=>(c_Polynomial_Opos__poly(X7,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X7),X6,X5))|X6=X5))<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__eq__poly__def)). 1.08/1.43 fof(fact_realpow__pos__nth, axiom, ![X13, X2]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)=>?[X63]:(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X63),X2)=X13&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X63)))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_realpow__pos__nth)). 1.08/1.43 fof(fact_zero__le__power__abs, axiom, ![X2, X13, X7]:(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Oabs__class_Oabs(X7,X13)),X2))<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__le__power__abs)). 1.08/1.43 fof(fact_power__inject__exp, axiom, ![X19, X29, X8, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X8)=>(X29=X19<=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X8),X19)=hAPP(hAPP(c_Power_Opower__class_Opower(X7),X8),X29)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__inject__exp)). 1.08/1.43 fof(fact_less__natfloor, axiom, ![X2, X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,c_RealDef_Oreal(tc_Nat_Onat,X2))=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X14),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__natfloor)). 1.08/1.43 fof(fact_natceiling__le__eq, axiom, ![X8, X5]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)=>(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5),X8)<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,c_RealDef_Oreal(tc_Nat_Onat,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__le__eq)). 1.08/1.43 fof(fact_le__natfloor__eq, axiom, ![X8, X5]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,c_RComplete_Onatfloor(X5))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X8),X5))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__natfloor__eq)). 1.08/1.43 fof(fact_zero__less__power, axiom, ![X2, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__power)). 1.08/1.43 fof(fact_one__le__power, axiom, ![X2, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oone__class_Oone(X7),X13)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oone__class_Oone(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_one__le__power)). 1.08/1.43 fof(fact_zero__le__power, axiom, ![X2, X13, X7]:(class_Rings_Olinordered__semidom(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__le__power)). 1.08/1.43 fof(fact_natfloor__add__one, axiom, ![X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)=>c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X14),c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__add__one)). 1.08/1.43 fof(fact_natceiling__add__one, axiom, ![X14]:(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X14),c_Groups_Oone__class_Oone(tc_Nat_Onat))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__add__one)). 1.08/1.43 fof(fact_not__square__less__zero, axiom, ![X13, X7]:(class_Rings_Olinordered__ring(X7)=>~(c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X13),c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__square__less__zero)). 1.08/1.43 fof(fact_odd__nonzero, axiom, ![X10]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10),X10), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_odd__nonzero)). 1.08/1.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, axiom, ![X21, X14]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X14,X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J)). 1.08/1.43 fof(fact_power_Opower_Opower__0, axiom, ![X8, X68, X69, X7]:hAPP(hAPP(c_Power_Opower_Opower(X7,X69,X68),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X69, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power_Opower_Opower__0)). 1.08/1.43 fof(fact_le__imp__0__less, axiom, ![X10]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__imp__0__less)). 1.08/1.43 fof(fact_abs__mult, axiom, ![X12, X13, X7]:(class_Rings_Olinordered__idom(X7)=>c_Groups_Oabs__class_Oabs(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oabs__class_Oabs(X7,X13)),c_Groups_Oabs__class_Oabs(X7,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__mult)). 1.08/1.43 fof(fact_sgn__mult, axiom, ![X21, X14, X7]:(c_Groups_Osgn__class_Osgn(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Osgn__class_Osgn(X7,X14)),c_Groups_Osgn__class_Osgn(X7,X21))<=class_RealVector_Oreal__normed__div__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__mult)). 1.08/1.43 fof(fact_sgn__times, axiom, ![X12, X13, X7]:(class_Rings_Olinordered__idom(X7)=>c_Groups_Osgn__class_Osgn(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Osgn__class_Osgn(X7,X13)),c_Groups_Osgn__class_Osgn(X7,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__times)). 1.08/1.43 fof(fact_abs__minus__commute, axiom, ![X12, X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X12,X13))=c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__minus__commute)). 1.08/1.43 fof(fact_norm__minus__commute, axiom, ![X12, X13, X7]:(class_RealVector_Oreal__normed__vector(X7)=>c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12))=c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X12,X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__minus__commute)). 1.08/1.43 fof(fact_norm__mult, axiom, ![X21, X14, X7]:(class_RealVector_Oreal__normed__div__algebra(X7)=>c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X14)),c_RealVector_Onorm__class_Onorm(X7,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__mult)). 1.08/1.43 fof(fact_zless__imp__add1__zle, axiom, ![X10, X43]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X43,X10)=>c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X43,c_Groups_Oone__class_Oone(tc_Int_Oint)),X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zless__imp__add1__zle)). 1.08/1.43 fof(fact_not__add__less1, axiom, ![X30, X18]:~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X30),X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__add__less1)). 1.08/1.43 fof(fact_not__add__less2, axiom, ![X18, X30]:~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X18),X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__add__less2)). 1.08/1.43 fof(fact_poly__div__minus__left, axiom, ![X21, X14, X7]:(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X14),X21)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),X14,X21))<=class_Fields_Ofield(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__div__minus__left)). 1.08/1.43 fof(fact_poly__div__minus__right, axiom, ![X21, X14, X7]:(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),X14,X21))=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),X14,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X21))<=class_Fields_Ofield(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__div__minus__right)). 1.08/1.43 fof(fact_ln__gt__zero__iff, axiom, ![X5]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X5))<=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__gt__zero__iff)). 1.08/1.43 fof(fact_ln__gt__zero__imp__gt__one, axiom, ![X14]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X14))=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__gt__zero__imp__gt__one)). 1.08/1.43 fof(fact_ln__ge__zero__imp__ge__one, axiom, ![X14]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X14)<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__ge__zero__imp__ge__one)). 1.08/1.43 fof(fact_ln__ge__zero__iff, axiom, ![X5]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5)<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__ge__zero__iff)). 1.08/1.43 fof(fact_ln__less__zero__iff, axiom, ![X5]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))<=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X5),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__less__zero__iff)). 1.08/1.43 fof(fact_le__add__diff__inverse2, axiom, ![X3, X2]:(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),X2)=X3<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__add__diff__inverse2)). 1.08/1.43 fof(fact_diff__diff__cancel, axiom, ![X2, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X2)=>c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X18))=X18), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__diff__cancel)). 1.08/1.43 fof(fact_le__add__diff__inverse, axiom, ![X3, X2]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)=>X3=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__add__diff__inverse)). 1.08/1.43 fof(fact_le__funD, axiom, ![X5, X71, X27, X7, X72]:(class_Orderings_Oord(X72)=>(c_Orderings_Oord__class_Oless__eq(X72,hAPP(X27,X5),hAPP(X71,X5))<=c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X72),X27,X71))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__funD)). 1.08/1.43 fof(fact_le__funE, axiom, ![X5, X71, X27, X7, X72]:(class_Orderings_Oord(X72)=>(c_Orderings_Oord__class_Oless__eq(X72,hAPP(X27,X5),hAPP(X71,X5))<=c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X72),X27,X71))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__funE)). 1.08/1.43 fof(fact_less__imp__diff__less, axiom, ![X2, X4, X30]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X2),X4)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__imp__diff__less)). 1.08/1.43 fof(fact_termination__basic__simps_I1_J, axiom, ![X10, X21, X14]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X21)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X10))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_termination__basic__simps_I1_J)). 1.08/1.43 fof(fact_trans__less__add1, axiom, ![X3, X30, X18]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X30)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_trans__less__add1)). 1.08/1.43 fof(fact_trans__less__add2, axiom, ![X3, X30, X18]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X30)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X30))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_trans__less__add2)). 1.08/1.43 fof(fact_termination__basic__simps_I2_J, axiom, ![X21, X10, X14]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X10)=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X10))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_termination__basic__simps_I2_J)). 1.08/1.43 fof(fact_trans__le__add1, axiom, ![X3, X30, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X3))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_trans__le__add1)). 1.08/1.43 fof(fact_termination__basic__simps_I3_J, axiom, ![X10, X21, X14]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X21)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X10))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_termination__basic__simps_I3_J)). 1.08/1.43 fof(fact_termination__basic__simps_I4_J, axiom, ![X21, X10, X14]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X10))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_termination__basic__simps_I4_J)). 1.08/1.43 fof(fact_trans__le__add2, axiom, ![X3, X30, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X30))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_trans__le__add2)). 1.08/1.43 fof(fact_ln__less__zero, axiom, ![X14]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__less__zero)). 1.08/1.43 fof(fact_zero__le__zpower__abs, axiom, ![X2, X14]:c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X14)),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__le__zpower__abs)). 1.08/1.43 fof(fact_not__real__square__gt__zero, axiom, ![X5]:(~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X5)))<=>c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X5), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__real__square__gt__zero)). 1.08/1.43 fof(fact_nat__mult__eq__cancel1, axiom, ![X19, X29, X26]:((X19=X29<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X19))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__eq__cancel1)). 1.08/1.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, axiom, ![X2, X14]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X2))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J)). 1.08/1.43 fof(fact_order__less__trans, axiom, ![X10, X21, X14, X7]:(class_Orderings_Opreorder(X7)=>((c_Orderings_Oord__class_Oless(X7,X14,X10)<=c_Orderings_Oord__class_Oless(X7,X21,X10))<=c_Orderings_Oord__class_Oless(X7,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__trans)). 1.08/1.43 fof(fact_order__le__less__trans, axiom, ![X10, X21, X14, X7]:(((c_Orderings_Oord__class_Oless(X7,X14,X10)<=c_Orderings_Oord__class_Oless(X7,X21,X10))<=c_Orderings_Oord__class_Oless__eq(X7,X14,X21))<=class_Orderings_Opreorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__le__less__trans)). 1.08/1.43 fof(fact_order__less__le__trans, axiom, ![X10, X21, X14, X7]:(((c_Orderings_Oord__class_Oless(X7,X14,X10)<=c_Orderings_Oord__class_Oless__eq(X7,X21,X10))<=c_Orderings_Oord__class_Oless(X7,X14,X21))<=class_Orderings_Opreorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__le__trans)). 1.08/1.43 fof(fact_xt1_I10_J, axiom, ![X10, X14, X21, X7]:(class_Orderings_Oorder(X7)=>((c_Orderings_Oord__class_Oless(X7,X10,X14)<=c_Orderings_Oord__class_Oless(X7,X10,X21))<=c_Orderings_Oord__class_Oless(X7,X21,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_xt1_I10_J)). 1.08/1.43 fof(fact_xt1_I8_J, axiom, ![X10, X14, X21, X7]:(class_Orderings_Oorder(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X21,X14)=>(c_Orderings_Oord__class_Oless(X7,X10,X14)<=c_Orderings_Oord__class_Oless(X7,X10,X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_xt1_I8_J)). 1.08/1.43 fof(fact_xt1_I7_J, axiom, ![X10, X14, X21, X7]:(class_Orderings_Oorder(X7)=>(c_Orderings_Oord__class_Oless(X7,X21,X14)=>(c_Orderings_Oord__class_Oless(X7,X10,X14)<=c_Orderings_Oord__class_Oless__eq(X7,X10,X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_xt1_I7_J)). 1.08/1.43 fof(fact_order__trans, axiom, ![X10, X21, X14, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X14,X21)=>(c_Orderings_Oord__class_Oless__eq(X7,X14,X10)<=c_Orderings_Oord__class_Oless__eq(X7,X21,X10)))<=class_Orderings_Opreorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__trans)). 1.08/1.43 fof(fact_xt1_I6_J, axiom, ![X10, X14, X21, X7]:(class_Orderings_Oorder(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X21,X14)=>(c_Orderings_Oord__class_Oless__eq(X7,X10,X21)=>c_Orderings_Oord__class_Oless__eq(X7,X10,X14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_xt1_I6_J)). 1.08/1.43 fof(fact_Limits_Ominus__diff__minus, axiom, ![X12, X13, X7]:(class_Groups_Oab__group__add(X7)=>c_Groups_Ominus__class_Ominus(X7,c_Groups_Ouminus__class_Ouminus(X7,X13),c_Groups_Ouminus__class_Ouminus(X7,X12))=c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Limits_Ominus__diff__minus)). 1.08/1.43 fof(fact_minus__add, axiom, ![X12, X13, X7]:(class_Groups_Ogroup__add(X7)=>c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X12),c_Groups_Ouminus__class_Ouminus(X7,X13))=c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__add)). 1.08/1.43 fof(fact_minus__add__distrib, axiom, ![X12, X13, X7]:(class_Groups_Oab__group__add(X7)=>c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12))=c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X13),c_Groups_Ouminus__class_Ouminus(X7,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__add__distrib)). 1.08/1.43 fof(fact_real__natfloor__add__one__gt, axiom, ![X14]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X14)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__natfloor__add__one__gt)). 1.08/1.43 fof(fact_div__mult__self1__is__m, axiom, ![X3, X2]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=>c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X2)=X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult__self1__is__m)). 1.08/1.43 fof(fact_div__mult__self__is__m, axiom, ![X3, X2]:(X3=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X2)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult__self__is__m)). 1.08/1.43 fof(fact_z3div__def, axiom, ![X4, X34]:((c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X34)=c_SMT_Oz3div(X4,X34)<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34))&(~(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34))=>c_SMT_Oz3div(X4,X34)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X34))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_z3div__def)). 1.08/1.43 fof(fact_neg__less__iff__less, axiom, ![X8, X11, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless(X7,X8,X11)<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X11),c_Groups_Ouminus__class_Ouminus(X7,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__less__iff__less)). 1.08/1.43 fof(fact_compl__le__compl__iff, axiom, ![X6, X5, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X5),c_Groups_Ouminus__class_Ouminus(X7,X6))<=>c_Orderings_Oord__class_Oless__eq(X7,X6,X5))<=class_Lattices_Oboolean__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_compl__le__compl__iff)). 1.08/1.43 fof(fact_neg__le__iff__le, axiom, ![X8, X11, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X8,X11)<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X11),c_Groups_Ouminus__class_Ouminus(X7,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__le__iff__le)). 1.08/1.43 fof(fact_zdiv__eq__0__iff, axiom, ![X26, X66]:(((c_Orderings_Oord__class_Oless(tc_Int_Oint,X26,X66)&c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X66,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X66)&c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,X26))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X26)<=>c_Divides_Odiv__class_Odiv(tc_Int_Oint,X66,X26)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__eq__0__iff)). 1.08/1.43 fof(fact_div__neg__neg__trivial, axiom, ![X12, X13]:((c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X13)=>c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__neg__neg__trivial)). 1.08/1.43 fof(fact_div__pos__pos__trivial, axiom, ![X12, X13]:((c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,X12)=>c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12))<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__pos__pos__trivial)). 1.08/1.43 fof(fact_mult__left_Ominus, axiom, ![X21, X14, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ouminus__class_Ouminus(X7,X14)),X21)=c_Groups_Ouminus__class_Ouminus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left_Ominus)). 1.08/1.43 fof(fact_power__abs, axiom, ![X2, X13, X7]:(class_Rings_Olinordered__idom(X7)=>c_Groups_Oabs__class_Oabs(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Oabs__class_Oabs(X7,X13)),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__abs)). 1.08/1.43 fof(fact_minus__mult__left, axiom, ![X12, X13, X7]:(c_Groups_Ouminus__class_Ouminus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ouminus__class_Ouminus(X7,X13)),X12)<=class_Rings_Oring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__mult__left)). 1.08/1.43 fof(fact_mult_Ominus__left, axiom, ![X12, X13, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>c_Groups_Ouminus__class_Ouminus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ouminus__class_Ouminus(X7,X13)),X12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Ominus__left)). 1.08/1.43 fof(fact_le__imp__diff__is__add, axiom, ![X26, X74, X66]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X74)=>(X74=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X66)<=>c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X66)=X26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__imp__diff__is__add)). 1.08/1.43 fof(fact_norm__power, axiom, ![X2, X14, X7]:(class_RealVector_Oreal__normed__div__algebra(X7)=>c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X14)),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__power)). 1.08/1.43 fof(fact_add__minus__cancel, axiom, ![X12, X13, X7]:(X12=c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X13),X12))<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__minus__cancel)). 1.08/1.43 fof(fact_zle__trans, axiom, ![X4, X30, X18]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X30)=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X4)<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X30,X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zle__trans)). 1.08/1.43 fof(fact_le__trans, axiom, ![X4, X30, X18]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X4)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X4))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__trans)). 1.08/1.43 fof(fact_real__le__trans, axiom, ![X4, X30, X18]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X4)<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X30,X4))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__le__trans)). 1.08/1.43 fof(fact_pos__poly__mult, axiom, ![X15, X16, X7]:((c_Polynomial_Opos__poly(X7,X16)=>(c_Polynomial_Opos__poly(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X16),X15))<=c_Polynomial_Opos__poly(X7,X15)))<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_pos__poly__mult)). 1.08/1.43 fof(fact_real__of__nat__mult, axiom, ![X2, X3]:c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3)),c_RealDef_Oreal(tc_Nat_Onat,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__mult)). 1.08/1.43 fof(fact_coeff__minus, axiom, ![X2, X16, X7]:(hAPP(c_Polynomial_Ocoeff(X7,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X16)),X2)=c_Groups_Ouminus__class_Ouminus(X7,hAPP(c_Polynomial_Ocoeff(X7,X16),X2))<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_coeff__minus)). 1.08/1.43 fof(fact_poly__minus, axiom, ![X14, X16, X7]:(hAPP(c_Polynomial_Opoly(X7,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X16)),X14)=c_Groups_Ouminus__class_Ouminus(X7,hAPP(c_Polynomial_Opoly(X7,X16),X14))<=class_Rings_Ocomm__ring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__minus)). 1.08/1.43 fof(fact_minus__less__iff, axiom, ![X11, X8, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X8),X11)<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X11),X8))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__less__iff)). 1.08/1.43 fof(fact_abs__le__D2, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X13),X12)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X13),X12))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__le__D2)). 1.08/1.43 fof(fact_minus__le__iff, axiom, ![X11, X8, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X11),X8)<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X8),X11))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__le__iff)). 1.08/1.43 fof(fact_less__minus__iff, axiom, ![X11, X8, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Ouminus__class_Ouminus(X7,X11))<=>c_Orderings_Oord__class_Oless(X7,X11,c_Groups_Ouminus__class_Ouminus(X7,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__minus__iff)). 1.08/1.43 fof(fact_le__minus__iff, axiom, ![X11, X8, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X8,c_Groups_Ouminus__class_Ouminus(X7,X11))<=>c_Orderings_Oord__class_Oless__eq(X7,X11,c_Groups_Ouminus__class_Ouminus(X7,X8)))<=class_Groups_Oordered__ab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__minus__iff)). 1.08/1.43 fof(fact_real__of__nat__add, axiom, ![X2, X3]:c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3),c_RealDef_Oreal(tc_Nat_Onat,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__add)). 1.08/1.43 fof(fact_zminus__zadd__distrib, axiom, ![X43, X10]:c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X43))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X10),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zminus__zadd__distrib)). 1.08/1.43 fof(fact_mult__left__idem, axiom, ![X12, X13, X7]:(class_Lattices_Oab__semigroup__idem__mult(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left__idem)). 1.08/1.43 fof(fact_abs__add__one__gt__zero, axiom, ![X14]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__add__one__gt__zero)). 1.08/1.43 fof(fact_add__diff__inverse, axiom, ![X2, X3]:(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))=X3<=~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__diff__inverse)). 1.08/1.43 fof(fact_real__of__nat__less__iff, axiom, ![X29, X19]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_RealDef_Oreal(tc_Nat_Onat,X29))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__less__iff)). 1.08/1.43 fof(fact_real__of__nat__le__iff, axiom, ![X29, X19]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X29)<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_RealDef_Oreal(tc_Nat_Onat,X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__le__iff)). 1.08/1.43 fof(fact_neg__less__0__iff__less, axiom, ![X8, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X8)<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X8),c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__less__0__iff__less)). 1.08/1.43 fof(fact_neg__le__0__iff__le, axiom, ![X8, X7]:((c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X8),c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X8))<=class_Groups_Oordered__ab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__le__0__iff__le)). 1.08/1.43 fof(fact_sgn__greater, axiom, ![X8, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X8)<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Osgn__class_Osgn(X7,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__greater)). 1.08/1.43 fof(fact_sgn__less, axiom, ![X8, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Osgn__class_Osgn(X7,X8),c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Ozero__class_Ozero(X7)))<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__less)). 1.08/1.43 fof(fact_neg__0__less__iff__less, axiom, ![X8, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Ouminus__class_Ouminus(X7,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__0__less__iff__less)). 1.08/1.43 fof(fact_neg__0__le__iff__le, axiom, ![X8, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X8,c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Ouminus__class_Ouminus(X7,X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__0__le__iff__le)). 1.08/1.43 fof(fact_less__le__not__le, axiom, ![X6, X5, X7]:(class_Orderings_Opreorder(X7)=>((~(c_Orderings_Oord__class_Oless__eq(X7,X6,X5))&c_Orderings_Oord__class_Oless__eq(X7,X5,X6))<=>c_Orderings_Oord__class_Oless(X7,X5,X6))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__le__not__le)). 1.08/1.43 fof(fact_minus__mult__right, axiom, ![X12, X13, X7]:(class_Rings_Oring(X7)=>c_Groups_Ouminus__class_Ouminus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Ouminus__class_Ouminus(X7,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__mult__right)). 1.08/1.43 fof(fact_mult_Ominus__right, axiom, ![X12, X13, X7]:(class_RealVector_Oreal__normed__algebra(X7)=>c_Groups_Ouminus__class_Ouminus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Ouminus__class_Ouminus(X7,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Ominus__right)). 1.08/1.43 fof(fact_mult__right_Ominus, axiom, ![X14, X17, X7]:(c_Groups_Ouminus__class_Ouminus(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X17),X14))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X17),c_Groups_Ouminus__class_Ouminus(X7,X14))<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right_Ominus)). 1.08/1.43 fof(fact_compl__mono, axiom, ![X21, X14, X7]:(class_Lattices_Oboolean__algebra(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X21),c_Groups_Ouminus__class_Ouminus(X7,X14))<=c_Orderings_Oord__class_Oless__eq(X7,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_compl__mono)). 1.08/1.43 fof(fact_le__imp__neg__le, axiom, ![X12, X13, X7]:(class_Groups_Oordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X12),c_Groups_Ouminus__class_Ouminus(X7,X13))<=c_Orderings_Oord__class_Oless__eq(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__imp__neg__le)). 1.08/1.43 fof(fact_zero__less__two, axiom, ![X7]:(class_Rings_Olinordered__semidom(X7)=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Oone__class_Oone(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__two)). 1.08/1.43 fof(fact_real__natfloor__gt__diff__one, axiom, ![X14]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__natfloor__gt__diff__one)). 1.08/1.43 fof(fact_minus__add__cancel, axiom, ![X12, X13, X7]:(X12=c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X13),c_Groups_Oplus__class_Oplus(X7,X13,X12))<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__add__cancel)). 1.08/1.43 fof(fact_neg__less__nonneg, axiom, ![X8, X7]:(class_Groups_Olinordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X8),X8)<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X8))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__less__nonneg)). 1.08/1.43 fof(fact_minus__le__self__iff, axiom, ![X8, X7]:(class_Groups_Olinordered__ab__group__add(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X8),X8)<=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X8))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__le__self__iff)). 1.08/1.43 fof(fact_less__minus__self__iff, axiom, ![X8, X7]:((c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Ouminus__class_Ouminus(X7,X8))<=>c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Ozero__class_Ozero(X7)))<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__minus__self__iff)). 1.08/1.43 fof(fact_le__minus__self__iff, axiom, ![X8, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X8,c_Groups_Ozero__class_Ozero(X7))<=>c_Orderings_Oord__class_Oless__eq(X7,X8,c_Groups_Ouminus__class_Ouminus(X7,X8)))<=class_Groups_Olinordered__ab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__minus__self__iff)). 1.08/1.43 fof(fact_power__real__of__nat, axiom, ![X2, X3]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3)),X2)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__real__of__nat)). 1.08/1.43 fof(fact_real__of__nat__power, axiom, ![X2, X3]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3)),X2)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__power)). 1.08/1.43 fof(fact_zmult__zminus, axiom, ![X43, X10]:c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10),X43))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X10)),X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zmult__zminus)). 1.08/1.43 fof(fact_ln__inj__iff, axiom, ![X6, X5]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)=>(X5=X6<=>c_Transcendental_Oln(X5)=c_Transcendental_Oln(X6)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__inj__iff)). 1.08/1.43 fof(fact_nat__less__cases, axiom, ![X62, X19, X29]:((hBOOL(hAPP(hAPP(X62,X19),X29))<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19))=>((hBOOL(hAPP(hAPP(X62,X19),X29))<=X29=X19)=>(hBOOL(hAPP(hAPP(X62,X19),X29))<=(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X29)=>hBOOL(hAPP(hAPP(X62,X19),X29)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__less__cases)). 1.08/1.43 fof(fact_abs__mult__self, axiom, ![X13, X7]:(class_Rings_Olinordered__idom(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oabs__class_Oabs(X7,X13)),c_Groups_Oabs__class_Oabs(X7,X13))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__mult__self)). 1.08/1.43 fof(fact_minus__mult__commute, axiom, ![X12, X13, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Ouminus__class_Ouminus(X7,X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ouminus__class_Ouminus(X7,X13)),X12)<=class_Rings_Oring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__mult__commute)). 1.08/1.43 fof(fact_minus__mult__minus, axiom, ![X12, X13, X7]:(class_Rings_Oring(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ouminus__class_Ouminus(X7,X13)),c_Groups_Ouminus__class_Ouminus(X7,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__mult__minus)). 1.08/1.43 fof(fact_abs__le__D1, axiom, ![X12, X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X13,X12)<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X13),X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__le__D1)). 1.08/1.43 fof(fact_square__eq__iff, axiom, ![X11, X8, X7]:(class_Rings_Oidom(X7)=>((X8=c_Groups_Ouminus__class_Ouminus(X7,X11)|X11=X8)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X8)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),X11))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_square__eq__iff)). 1.08/1.43 fof(fact_BseqD, axiom, ![X23, X7]:(class_RealVector_Oreal__normed__vector(X7)=>(?[X36]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)&![X22]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,hAPP(X23,X22)),X36))<=c_SEQ_OBseq(X7,X23))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_BseqD)). 1.08/1.43 fof(fact_pos__poly__add, axiom, ![X15, X16, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Polynomial_Opos__poly(X7,X16)=>(c_Polynomial_Opos__poly(X7,X15)=>c_Polynomial_Opos__poly(X7,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),X16,X15))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_pos__poly__add)). 1.08/1.43 fof(fact_diff__eq__diff__eq, axiom, ![X52, X53, X11, X8, X7]:(((X52=X53<=>X8=X11)<=c_Groups_Ominus__class_Ominus(X7,X53,X52)=c_Groups_Ominus__class_Ominus(X7,X8,X11))<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__eq__diff__eq)). 1.08/1.43 fof(fact_natfloor__power, axiom, ![X2, X14]:(X14=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X14))=>c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X14),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X14)),X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__power)). 1.08/1.43 fof(fact_linorder__antisym__conv2, axiom, ![X6, X5, X7]:(class_Orderings_Olinorder(X7)=>((X6=X5<=>~(c_Orderings_Oord__class_Oless(X7,X5,X6)))<=c_Orderings_Oord__class_Oless__eq(X7,X5,X6))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__antisym__conv2)). 1.08/1.43 fof(fact_minus__diff__eq, axiom, ![X12, X13, X7]:(c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12))=c_Groups_Ominus__class_Ominus(X7,X12,X13)<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__diff__eq)). 1.08/1.43 fof(fact_order__eq__iff, axiom, ![X6, X5, X7]:(class_Orderings_Oorder(X7)=>((c_Orderings_Oord__class_Oless__eq(X7,X6,X5)&c_Orderings_Oord__class_Oless__eq(X7,X5,X6))<=>X6=X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__eq__iff)). 1.08/1.43 fof(fact_order__antisym, axiom, ![X21, X14, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X14,X21)=>(X21=X14<=c_Orderings_Oord__class_Oless__eq(X7,X21,X14)))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__antisym)). 1.08/1.43 fof(fact_xt1_I5_J, axiom, ![X14, X21, X7]:(class_Orderings_Oorder(X7)=>((X21=X14<=c_Orderings_Oord__class_Oless__eq(X7,X14,X21))<=c_Orderings_Oord__class_Oless__eq(X7,X21,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_xt1_I5_J)). 1.08/1.43 fof(fact_order__antisym__conv, axiom, ![X5, X6, X7]:(((c_Orderings_Oord__class_Oless__eq(X7,X5,X6)<=>X5=X6)<=c_Orderings_Oord__class_Oless__eq(X7,X6,X5))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__antisym__conv)). 1.08/1.43 fof(fact_real__of__nat__gt__zero__cancel__iff, axiom, ![X19]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X19))<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__gt__zero__cancel__iff)). 1.08/1.43 fof(fact_less__add__one, axiom, ![X13, X7]:(c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Oone__class_Oone(X7)))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__add__one)). 1.08/1.43 fof(fact_add__right__cancel, axiom, ![X53, X8, X11, X7]:((c_Groups_Oplus__class_Oplus(X7,X11,X8)=c_Groups_Oplus__class_Oplus(X7,X53,X8)<=>X53=X11)<=class_Groups_Ocancel__semigroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__right__cancel)). 1.08/1.43 fof(fact_add__right__imp__eq, axiom, ![X20, X13, X12, X7]:((c_Groups_Oplus__class_Oplus(X7,X20,X13)=c_Groups_Oplus__class_Oplus(X7,X12,X13)=>X12=X20)<=class_Groups_Ocancel__semigroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__right__imp__eq)). 1.08/1.43 fof(fact_add__left__cancel, axiom, ![X53, X11, X8, X7]:((c_Groups_Oplus__class_Oplus(X7,X8,X11)=c_Groups_Oplus__class_Oplus(X7,X8,X53)<=>X11=X53)<=class_Groups_Ocancel__semigroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__left__cancel)). 1.08/1.43 fof(fact_add__left__imp__eq, axiom, ![X20, X12, X13, X7]:((c_Groups_Oplus__class_Oplus(X7,X13,X20)=c_Groups_Oplus__class_Oplus(X7,X13,X12)=>X12=X20)<=class_Groups_Ocancel__semigroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__left__imp__eq)). 1.08/1.43 fof(fact_add__imp__eq, axiom, ![X20, X12, X13, X7]:((X12=X20<=c_Groups_Oplus__class_Oplus(X7,X13,X20)=c_Groups_Oplus__class_Oplus(X7,X13,X12))<=class_Groups_Ocancel__ab__semigroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__imp__eq)). 1.08/1.43 fof(fact_abs__zmult__eq__1, axiom, ![X2, X3]:(c_Groups_Oabs__class_Oabs(tc_Int_Oint,X3)=c_Groups_Oone__class_Oone(tc_Int_Oint)<=c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__zmult__eq__1)). 1.08/1.43 fof(fact_not__less__iff__gr__or__eq, axiom, ![X6, X5, X7]:((~(c_Orderings_Oord__class_Oless(X7,X5,X6))<=>(X5=X6|c_Orderings_Oord__class_Oless(X7,X6,X5)))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__less__iff__gr__or__eq)). 1.08/1.43 fof(fact_linorder__not__less, axiom, ![X6, X5, X7]:(class_Orderings_Olinorder(X7)=>(~(c_Orderings_Oord__class_Oless(X7,X5,X6))<=>c_Orderings_Oord__class_Oless__eq(X7,X6,X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__not__less)). 1.08/1.43 fof(fact_leD, axiom, ![X14, X21, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X21,X14)=>~(c_Orderings_Oord__class_Oless(X7,X14,X21)))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_leD)). 1.08/1.43 fof(fact_linorder__not__le, axiom, ![X6, X5, X7]:(class_Orderings_Olinorder(X7)=>(c_Orderings_Oord__class_Oless(X7,X6,X5)<=>~(c_Orderings_Oord__class_Oless__eq(X7,X5,X6)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__not__le)). 1.08/1.43 fof(fact_order__less__asym, axiom, ![X21, X14, X7]:((~(c_Orderings_Oord__class_Oless(X7,X21,X14))<=c_Orderings_Oord__class_Oless(X7,X14,X21))<=class_Orderings_Opreorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__asym)). 1.08/1.43 fof(fact_order__less__imp__not__less, axiom, ![X21, X14, X7]:(class_Orderings_Opreorder(X7)=>(~(c_Orderings_Oord__class_Oless(X7,X21,X14))<=c_Orderings_Oord__class_Oless(X7,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__imp__not__less)). 1.08/1.43 fof(fact_order__less__not__sym, axiom, ![X21, X14, X7]:(class_Orderings_Opreorder(X7)=>(~(c_Orderings_Oord__class_Oless(X7,X21,X14))<=c_Orderings_Oord__class_Oless(X7,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__not__sym)). 1.08/1.43 fof(fact_order__less__asym_H, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless(X7,X13,X12)=>~(c_Orderings_Oord__class_Oless(X7,X12,X13)))<=class_Orderings_Opreorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__asym_H)). 1.08/1.43 fof(fact_xt1_I9_J, axiom, ![X13, X12, X7]:((c_Orderings_Oord__class_Oless(X7,X12,X13)=>~(c_Orderings_Oord__class_Oless(X7,X13,X12)))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_xt1_I9_J)). 1.08/1.43 fof(fact_natceiling__le, axiom, ![X13, X14]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X14),X13)<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,c_RealDef_Oreal(tc_Nat_Onat,X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__le)). 1.08/1.43 fof(fact_le__natfloor, axiom, ![X13, X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),X13)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_RComplete_Onatfloor(X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__natfloor)). 1.08/1.43 fof(fact_order__root, axiom, ![X8, X9, X7]:(class_Rings_Oidom(X7)=>(c_Groups_Ozero__class_Ozero(X7)=hAPP(c_Polynomial_Opoly(X7,X9),X8)<=>(c_Polynomial_Oorder(X7,X8,X9)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))=X9))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__root)). 1.08/1.43 fof(fact_diffs0__imp__equal, axiom, ![X2, X3]:((c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>X3=X2)<=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diffs0__imp__equal)). 1.08/1.43 fof(fact_real__natfloor__le, axiom, ![X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X14)),X14)<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__natfloor__le)). 1.08/1.43 fof(fact_sgn__poly__def, axiom, ![X14, X7]:(class_Rings_Olinordered__idom(X7)=>((c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X7),X14)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))<=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))=X14)&(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))!=X14=>((c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7))=c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X7),X14)<=c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X14))&(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7)))=c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X7),X14)<=~(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X14))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__poly__def)). 1.08/1.43 fof(fact_abs__poly__def, axiom, ![X14, X7]:(class_Rings_Olinordered__idom(X7)=>((X14=c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X7),X14)<=~(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),X14,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))))&(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),X14,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))=>c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X14)=c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X7),X14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__poly__def)). 1.08/1.43 fof(fact_div__mult__self1__is__id, axiom, ![X13, X12, X7]:(class_Divides_Osemiring__div(X7)=>(X13=c_Divides_Odiv__class_Odiv(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X13),X12)<=c_Groups_Ozero__class_Ozero(X7)!=X12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult__self1__is__id)). 1.08/1.43 fof(fact_div__mult__self2__is__id, axiom, ![X13, X12, X7]:(class_Divides_Osemiring__div(X7)=>(X12!=c_Groups_Ozero__class_Ozero(X7)=>X13=c_Divides_Odiv__class_Odiv(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12),X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__mult__self2__is__id)). 1.08/1.43 fof(fact_zero__le__square, axiom, ![X13, X7]:(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X13))<=class_Rings_Olinordered__ring(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__le__square)). 1.08/1.43 fof(fact_zle__antisym, axiom, ![X43, X10]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X43)=>(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X43,X10)=>X43=X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zle__antisym)). 1.08/1.43 fof(fact_le__antisym, axiom, ![X2, X3]:((X3=X2<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3))<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__antisym)). 1.08/1.43 fof(fact_real__le__antisym, axiom, ![X43, X10]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X43)=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X43,X10)=>X10=X43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__le__antisym)). 1.08/1.43 fof(fact_add__diff__cancel, axiom, ![X12, X13, X7]:(class_Groups_Ogroup__add(X7)=>X13=c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X13,X12),X12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__diff__cancel)). 1.08/1.43 fof(fact_diff__add__cancel, axiom, ![X12, X13, X7]:(X13=c_Groups_Oplus__class_Oplus(X7,c_Groups_Ominus__class_Ominus(X7,X13,X12),X12)<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__add__cancel)). 1.08/1.43 fof(fact_pos__zmult__eq__1__iff, axiom, ![X19, X29]:((c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X19)<=>(X19=c_Groups_Oone__class_Oone(tc_Int_Oint)&c_Groups_Oone__class_Oone(tc_Int_Oint)=X29))<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_pos__zmult__eq__1__iff)). 1.08/1.43 fof(fact_nat__add__right__cancel, axiom, ![X19, X26, X29]:(X19=X29<=>c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X26)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__add__right__cancel)). 1.08/1.43 fof(fact_nat__add__left__cancel, axiom, ![X19, X29, X26]:(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X19)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X29)<=>X29=X19), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__add__left__cancel)). 1.08/1.43 fof(fact_le__iff__add, axiom, ![X19, X29]:(?[X24]:X19=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X24)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__iff__add)). 1.08/1.43 fof(fact_le__Suc__ex__iff, axiom, ![X51, X26]:(?[X22]:X51=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X22)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X51)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__Suc__ex__iff)). 1.08/1.43 fof(fact_diff__add__0, axiom, ![X3, X2]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__add__0)). 1.08/1.43 fof(fact_diff__add__inverse, axiom, ![X3, X2]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X2)=X3, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__add__inverse)). 1.08/1.43 fof(fact_diff__add__inverse2, axiom, ![X2, X3]:X3=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__add__inverse2)). 1.08/1.43 fof(fact_div__le__dividend, axiom, ![X2, X3]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2),X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__le__dividend)). 1.08/1.43 fof(fact_diff__le__self, axiom, ![X2, X3]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__le__self)). 1.08/1.43 fof(fact_le__add1, axiom, ![X3, X2]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__add1)). 1.08/1.43 fof(fact_le__add2, axiom, ![X3, X2]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__add2)). 1.08/1.43 fof(fact_le__natfloor__eq__one, axiom, ![X5]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__natfloor__eq__one)). 1.08/1.43 fof(fact_natceiling__le__eq__one, axiom, ![X5]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__le__eq__one)). 1.08/1.43 fof(fact_zero__less__abs__iff, axiom, ![X8, X7]:((c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oabs__class_Oabs(X7,X8))<=>X8!=c_Groups_Ozero__class_Ozero(X7))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__abs__iff)). 1.08/1.43 fof(fact_zdiv__zminus2, axiom, ![X12, X13]:c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X12))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X13),X12), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__zminus2)). 1.08/1.43 fof(fact_zdiv__zminus__zminus, axiom, ![X12, X13]:c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X13),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__zminus__zminus)). 1.08/1.43 fof(fact_ln__gt__zero, axiom, ![X14]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X14)=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__gt__zero)). 1.08/1.43 fof(fact_ln__ge__zero, axiom, ![X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X14)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__ge__zero)). 1.08/1.43 fof(fact_mult__cancel1, axiom, ![X19, X29, X26]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X19)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X29)<=>(X19=X29|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__cancel1)). 1.08/1.43 fof(fact_nat__mult__eq__cancel__disj, axiom, ![X19, X29, X26]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X19)<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X26|X29=X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__eq__cancel__disj)). 1.08/1.43 fof(fact_mult__cancel2, axiom, ![X19, X26, X29]:((X26=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X19=X29)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__cancel2)). 1.08/1.43 fof(fact_real__mult__right__cancel, axiom, ![X11, X8, X53]:((X8=X11<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X8),X53)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X53))<=X53!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__right__cancel)). 1.08/1.43 fof(fact_real__mult__left__cancel, axiom, ![X11, X8, X53]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X53),X8)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X53),X11)<=>X8=X11)<=X53!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__left__cancel)). 1.08/1.43 fof(fact_tsub__def, axiom, ![X14, X21]:((c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X21)=c_Nat__Transfer_Otsub(X14,X21)<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X14))&(~(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X14))=>c_Nat__Transfer_Otsub(X14,X21)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_tsub__def)). 1.08/1.43 fof(fact_tsub__eq, axiom, ![X14, X21]:(c_Nat__Transfer_Otsub(X14,X21)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X21)<=c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_tsub__eq)). 1.08/1.43 fof(fact_order__less__le, axiom, ![X6, X5, X7]:((c_Orderings_Oord__class_Oless(X7,X5,X6)<=>(X5!=X6&c_Orderings_Oord__class_Oless__eq(X7,X5,X6)))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__le)). 1.08/1.43 fof(fact_linorder__antisym__conv1, axiom, ![X6, X5, X7]:(class_Orderings_Olinorder(X7)=>((X6=X5<=>c_Orderings_Oord__class_Oless__eq(X7,X5,X6))<=~(c_Orderings_Oord__class_Oless(X7,X5,X6)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__antisym__conv1)). 1.08/1.43 fof(fact_order__le__imp__less__or__eq, axiom, ![X21, X14, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X14,X21)=>(X21=X14|c_Orderings_Oord__class_Oless(X7,X14,X21)))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__le__imp__less__or__eq)). 1.08/1.43 fof(fact_order__le__less, axiom, ![X6, X5, X7]:(((c_Orderings_Oord__class_Oless(X7,X5,X6)|X6=X5)<=>c_Orderings_Oord__class_Oless__eq(X7,X5,X6))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__le__less)). 1.08/1.43 fof(fact_xt1_I11_J, axiom, ![X13, X12, X7]:(class_Orderings_Oorder(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X12,X13)=>(X12!=X13=>c_Orderings_Oord__class_Oless(X7,X12,X13)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_xt1_I11_J)). 1.08/1.43 fof(fact_order__le__neq__trans, axiom, ![X12, X13, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X13,X12)=>(c_Orderings_Oord__class_Oless(X7,X13,X12)<=X13!=X12))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__le__neq__trans)). 1.08/1.43 fof(fact_xt1_I12_J, axiom, ![X12, X13, X7]:(((c_Orderings_Oord__class_Oless(X7,X12,X13)<=c_Orderings_Oord__class_Oless__eq(X7,X12,X13))<=X13!=X12)<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_xt1_I12_J)). 1.08/1.43 fof(fact_order__neq__le__trans, axiom, ![X12, X13, X7]:((X12!=X13=>(c_Orderings_Oord__class_Oless(X7,X13,X12)<=c_Orderings_Oord__class_Oless__eq(X7,X13,X12)))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__neq__le__trans)). 1.08/1.43 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, axiom, ![X14, X7]:(class_Rings_Ocomm__ring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7))),X14)=c_Groups_Ouminus__class_Ouminus(X7,X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J)). 1.08/1.43 fof(fact_natfloor__mono, axiom, ![X21, X14]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X14),c_RComplete_Onatfloor(X21))<=c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__mono)). 1.08/1.43 fof(fact_natceiling__mono, axiom, ![X21, X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X21)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X14),c_RComplete_Onatceiling(X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__mono)). 1.08/1.43 fof(fact_abs__le__zero__iff, axiom, ![X8, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X8),c_Groups_Ozero__class_Ozero(X7))<=>X8=c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__le__zero__iff)). 1.08/1.43 fof(fact_order__less__imp__le, axiom, ![X21, X14, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X14,X21)<=c_Orderings_Oord__class_Oless(X7,X14,X21))<=class_Orderings_Opreorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__imp__le)). 1.08/1.43 fof(fact_ln__less__self, axiom, ![X14]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X14),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__less__self)). 1.08/1.43 fof(fact_abs__minus__le__zero, axiom, ![X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oabs__class_Oabs(X7,X13)),c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__minus__le__zero)). 1.08/1.43 fof(fact_int__one__le__iff__zero__less, axiom, ![X48]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X48)<=>c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_int__one__le__iff__zero__less)). 1.08/1.43 fof(fact_zero__less__norm__iff, axiom, ![X5, X7]:((c_Groups_Ozero__class_Ozero(X7)!=X5<=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X5)))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__norm__iff)). 1.08/1.43 fof(fact_complex__mod__minus__le__complex__mod, axiom, ![X14]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_complex__mod__minus__le__complex__mod)). 1.08/1.43 fof(fact_abs__not__less__zero, axiom, ![X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>~(c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,X13),c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__not__less__zero)). 1.08/1.43 fof(fact_le__square, axiom, ![X3]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__square)). 1.08/1.43 fof(fact_ab__diff__minus, axiom, ![X12, X13, X7]:(c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Ouminus__class_Ouminus(X7,X12))=c_Groups_Ominus__class_Ominus(X7,X13,X12)<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ab__diff__minus)). 1.08/1.43 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, axiom, ![X21, X14, X7]:(c_Groups_Oplus__class_Oplus(X7,X14,c_Groups_Ouminus__class_Ouminus(X7,X21))=c_Groups_Ominus__class_Ominus(X7,X14,X21)<=class_Rings_Ocomm__ring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J)). 1.08/1.43 fof(fact_diff__def, axiom, ![X12, X13, X7]:(class_Groups_Ogroup__add(X7)=>c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Ouminus__class_Ouminus(X7,X12))=c_Groups_Ominus__class_Ominus(X7,X13,X12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__def)). 1.08/1.43 fof(fact_diff__minus__eq__add, axiom, ![X12, X13, X7]:(class_Groups_Ogroup__add(X7)=>c_Groups_Oplus__class_Oplus(X7,X13,X12)=c_Groups_Ominus__class_Ominus(X7,X13,c_Groups_Ouminus__class_Ouminus(X7,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__minus__eq__add)). 1.08/1.43 fof(fact_norm__le__zero__iff, axiom, ![X5, X7]:(class_RealVector_Oreal__normed__vector(X7)=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X5),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<=>c_Groups_Ozero__class_Ozero(X7)=X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__le__zero__iff)). 1.08/1.43 fof(fact_diff__is__0__eq, axiom, ![X19, X29]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X19)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__is__0__eq)). 1.08/1.43 fof(fact_zless__le, axiom, ![X49, X48]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X49)<=>(X48!=X49&c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X49))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zless__le)). 1.08/1.43 fof(fact_le__eq__less__or__eq, axiom, ![X19, X29]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)|X29=X19)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__eq__less__or__eq)). 1.08/1.43 fof(fact_nat__less__le, axiom, ![X19, X29]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X19)&X29!=X19)<=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__less__le)). 1.08/1.43 fof(fact_le__neq__implies__less, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)=>(X2!=X3=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__neq__implies__less)). 1.08/1.43 fof(fact_less__eq__real__def, axiom, ![X6, X5]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X6)<=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,X6)|X6=X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__eq__real__def)). 1.08/1.43 fof(fact_real__less__def, axiom, ![X6, X5]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X6)&X5!=X6)<=>c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,X6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__less__def)). 1.08/1.43 fof(fact_div__less, axiom, ![X2, X3]:(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__less)). 1.08/1.43 fof(fact_diff__is__0__eq_H, axiom, ![X2, X3]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)<=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__is__0__eq_H)). 1.08/1.43 fof(fact_uminus__apply, axiom, ![X5, X92, X72, X7]:(c_Groups_Ouminus__class_Ouminus(X7,hAPP(X92,X5))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X72,X7),X92),X5)<=class_Groups_Ouminus(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_uminus__apply)). 1.08/1.43 fof(fact_mult__sgn__abs, axiom, ![X14, X7]:(class_Rings_Olinordered__idom(X7)=>X14=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Osgn__class_Osgn(X7,X14)),c_Groups_Oabs__class_Oabs(X7,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__sgn__abs)). 1.08/1.43 fof(fact_sgn__1__neg, axiom, ![X8, X7]:((c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Ozero__class_Ozero(X7))<=>c_Groups_Osgn__class_Osgn(X7,X8)=c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7)))<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__1__neg)). 1.08/1.43 fof(fact_sgn__neg, axiom, ![X13, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Groups_Osgn__class_Osgn(X7,X13)=c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7))<=c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__neg)). 1.08/1.43 fof(fact_termination__basic__simps_I5_J, axiom, ![X21, X14]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X21)<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_termination__basic__simps_I5_J)). 1.08/1.43 fof(fact_less__imp__le__nat, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__imp__le__nat)). 1.08/1.43 fof(fact_less__or__eq__imp__le, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)<=(X2=X3|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__or__eq__imp__le)). 1.08/1.43 fof(fact_norm__not__less__zero, axiom, ![X14, X7]:(~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__not__less__zero)). 1.08/1.43 fof(fact_abs__if, axiom, ![X13, X7]:(((c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Ozero__class_Ozero(X7))=>c_Groups_Oabs__class_Oabs(X7,X13)=c_Groups_Ouminus__class_Ouminus(X7,X13))&(~(c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Ozero__class_Ozero(X7)))=>X13=c_Groups_Oabs__class_Oabs(X7,X13)))<=class_Groups_Oabs__if(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__if)). 1.08/1.43 fof(fact_abs__of__neg, axiom, ![X13, X7]:((c_Orderings_Oord__class_Oless(X7,X13,c_Groups_Ozero__class_Ozero(X7))=>c_Groups_Ouminus__class_Ouminus(X7,X13)=c_Groups_Oabs__class_Oabs(X7,X13))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__of__neg)). 1.08/1.43 fof(fact_abs__of__nonpos, axiom, ![X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Ozero__class_Ozero(X7))=>c_Groups_Ouminus__class_Ouminus(X7,X13)=c_Groups_Oabs__class_Oabs(X7,X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__of__nonpos)). 1.08/1.43 fof(fact_real__of__nat__one, axiom, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__one)). 1.08/1.43 fof(fact_mult__poly__0__left, axiom, ![X15, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))),X15)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))<=class_Rings_Ocomm__semiring__0(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__poly__0__left)). 1.08/1.43 fof(fact_diff__int__def__symmetric, axiom, ![X43, X10]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X43))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X10,X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__int__def__symmetric)). 1.08/1.43 fof(fact_diff__int__def, axiom, ![X43, X10]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X43))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X10,X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__int__def)). 1.08/1.43 fof(fact_real__diff__def, axiom, ![X46, X47]:c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X47,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X46))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X47,X46), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__diff__def)). 1.08/1.43 fof(fact_minus__real__def, axiom, ![X21, X14]:c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X21)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__real__def)). 1.08/1.43 fof(fact_complex__diff__def, axiom, ![X21, X14]:c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,X21)=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X14,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_complex__diff__def)). 1.08/1.43 fof(fact_zabs__less__one__iff, axiom, ![X48]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X48),c_Groups_Oone__class_Oone(tc_Int_Oint))<=>c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X48), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zabs__less__one__iff)). 1.08/1.43 fof(fact_real__of__nat__le__zero__cancel__iff, axiom, ![X19]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X19), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__le__zero__cancel__iff)). 1.08/1.43 fof(fact_ext, axiom, ![X71, X27]:(X71=X27<=![X25]:hAPP(X71,X25)=hAPP(X27,X25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ext)). 1.08/1.43 fof(fact_sgn__if, axiom, ![X14, X7]:(class_Groups_Osgn__if(X7)=>((X14!=c_Groups_Ozero__class_Ozero(X7)=>((~(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X14))=>c_Groups_Osgn__class_Osgn(X7,X14)=c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7)))&(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X14)=>c_Groups_Oone__class_Oone(X7)=c_Groups_Osgn__class_Osgn(X7,X14))))&(X14=c_Groups_Ozero__class_Ozero(X7)=>c_Groups_Osgn__class_Osgn(X7,X14)=c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__if)). 1.08/1.43 fof(fact_real__add__minus__iff, axiom, ![X8, X5]:(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X8))<=>X5=X8), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__add__minus__iff)). 1.08/1.43 fof(fact_not__real__of__nat__less__zero, axiom, ![X2]:~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__real__of__nat__less__zero)). 1.08/1.43 fof(fact_power__eq__0__iff, axiom, ![X19, X8, X7]:(((c_Groups_Ozero__class_Ozero(X7)=X8&X19!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X8),X19)=c_Groups_Ozero__class_Ozero(X7))<=(((class_Rings_Omult__zero(X7)&class_Rings_Ozero__neq__one(X7))&class_Rings_Ono__zero__divisors(X7))&class_Power_Opower(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__eq__0__iff)). 1.08/1.43 fof(fact_square__eq__1__iff, axiom, ![X5, X7]:(((X5=c_Groups_Oone__class_Oone(X7)|c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7))=X5)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X5),X5)=c_Groups_Oone__class_Oone(X7))<=class_Rings_Oring__1__no__zero__divisors(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_square__eq__1__iff)). 1.08/1.43 fof(fact_sgn__1__pos, axiom, ![X8, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Groups_Osgn__class_Osgn(X7,X8)=c_Groups_Oone__class_Oone(X7)<=>c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X8))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__1__pos)). 1.08/1.43 fof(fact_sgn__pos, axiom, ![X13, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)=>c_Groups_Osgn__class_Osgn(X7,X13)=c_Groups_Oone__class_Oone(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__pos)). 1.08/1.43 fof(fact_linorder__neq__iff, axiom, ![X6, X5, X7]:(((c_Orderings_Oord__class_Oless(X7,X6,X5)|c_Orderings_Oord__class_Oless(X7,X5,X6))<=>X5!=X6)<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__neq__iff)). 1.08/1.43 fof(fact_linorder__neqE__linordered__idom, axiom, ![X21, X14, X7]:(((~(c_Orderings_Oord__class_Oless(X7,X14,X21))=>c_Orderings_Oord__class_Oless(X7,X21,X14))<=X14!=X21)<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__neqE__linordered__idom)). 1.08/1.43 fof(fact_linorder__neqE, axiom, ![X21, X14, X7]:(class_Orderings_Olinorder(X7)=>((c_Orderings_Oord__class_Oless(X7,X21,X14)<=~(c_Orderings_Oord__class_Oless(X7,X14,X21)))<=X21!=X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__neqE)). 1.08/1.43 fof(fact_linorder__cases, axiom, ![X21, X14, X7]:(((X21!=X14=>c_Orderings_Oord__class_Oless(X7,X21,X14))<=~(c_Orderings_Oord__class_Oless(X7,X14,X21)))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__cases)). 1.08/1.43 fof(fact_linorder__less__linear, axiom, ![X21, X14, X7]:(class_Orderings_Olinorder(X7)=>(c_Orderings_Oord__class_Oless(X7,X21,X14)|X21=X14|c_Orderings_Oord__class_Oless(X7,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__less__linear)). 1.08/1.43 fof(fact_linorder__antisym__conv3, axiom, ![X5, X6, X7]:(class_Orderings_Olinorder(X7)=>(~(c_Orderings_Oord__class_Oless(X7,X6,X5))=>(~(c_Orderings_Oord__class_Oless(X7,X5,X6))<=>X5=X6))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__antisym__conv3)). 1.08/1.43 fof(fact_abs__of__pos, axiom, ![X13, X7]:((X13=c_Groups_Oabs__class_Oabs(X7,X13)<=c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__of__pos)). 1.08/1.43 fof(fact_abs__of__nonneg, axiom, ![X13, X7]:((X13=c_Groups_Oabs__class_Oabs(X7,X13)<=c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X13))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__of__nonneg)). 1.08/1.43 fof(fact_linorder__le__less__linear, axiom, ![X21, X14, X7]:(class_Orderings_Olinorder(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X14,X21)|c_Orderings_Oord__class_Oless(X7,X21,X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__le__less__linear)). 1.08/1.43 fof(fact_not__leE, axiom, ![X14, X21, X7]:(class_Orderings_Olinorder(X7)=>(c_Orderings_Oord__class_Oless(X7,X14,X21)<=~(c_Orderings_Oord__class_Oless__eq(X7,X21,X14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__leE)). 1.08/1.43 fof(fact_leI, axiom, ![X21, X14, X7]:(class_Orderings_Olinorder(X7)=>(c_Orderings_Oord__class_Oless__eq(X7,X21,X14)<=~(c_Orderings_Oord__class_Oless(X7,X14,X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_leI)). 1.08/1.43 fof(fact_linorder__le__cases, axiom, ![X21, X14, X7]:((~(c_Orderings_Oord__class_Oless__eq(X7,X14,X21))=>c_Orderings_Oord__class_Oless__eq(X7,X21,X14))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__le__cases)). 1.08/1.43 fof(fact_linorder__linear, axiom, ![X21, X14, X7]:((c_Orderings_Oord__class_Oless__eq(X7,X21,X14)|c_Orderings_Oord__class_Oless__eq(X7,X14,X21))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__linear)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, axiom, ![X20, X13, X7]:(c_Groups_Oplus__class_Oplus(X7,X13,X20)=c_Groups_Oplus__class_Oplus(X7,X20,X13)<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 1.08/1.43 fof(fact_minus__unique, axiom, ![X12, X13, X7]:(class_Groups_Ogroup__add(X7)=>(c_Groups_Ouminus__class_Ouminus(X7,X13)=X12<=c_Groups_Ozero__class_Ozero(X7)=c_Groups_Oplus__class_Oplus(X7,X13,X12))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__unique)). 1.08/1.43 fof(fact_eq__neg__iff__add__eq__0, axiom, ![X11, X8, X7]:(class_Groups_Ogroup__add(X7)=>(X8=c_Groups_Ouminus__class_Ouminus(X7,X11)<=>c_Groups_Oplus__class_Oplus(X7,X8,X11)=c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_eq__neg__iff__add__eq__0)). 1.08/1.43 fof(fact_add__eq__0__iff, axiom, ![X6, X5, X7]:((c_Groups_Ozero__class_Ozero(X7)=c_Groups_Oplus__class_Oplus(X7,X5,X6)<=>X6=c_Groups_Ouminus__class_Ouminus(X7,X5))<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__eq__0__iff)). 1.08/1.43 fof(fact_abs__ge__minus__self, axiom, ![X13, X7]:(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X13),c_Groups_Oabs__class_Oabs(X7,X13))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__ge__minus__self)). 1.08/1.43 fof(fact_zabs__def, axiom, ![X18]:((c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=>c_Groups_Oabs__class_Oabs(tc_Int_Oint,X18)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X18))&(~(c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>c_Groups_Oabs__class_Oabs(tc_Int_Oint,X18)=X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zabs__def)). 1.08/1.43 fof(fact_real__abs__def, axiom, ![X47]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X47,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X47)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X47))&(X47=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X47)<=~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X47,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__abs__def)). 1.08/1.43 fof(fact_abs__real__def, axiom, ![X13]:((c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13)=X13<=~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))&(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13)<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__real__def)). 1.08/1.43 fof(fact_not__one__less__zero, axiom, ![X7]:(class_Rings_Olinordered__semidom(X7)=>~(c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__one__less__zero)). 1.08/1.43 fof(fact_not__one__le__zero, axiom, ![X7]:(~(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Ozero__class_Ozero(X7)))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__one__le__zero)). 1.08/1.43 fof(fact_mult__poly__0__right, axiom, ![X16, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X16),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))<=class_Rings_Ocomm__semiring__0(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__poly__0__right)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, axiom, ![X12, X13, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),X13)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 1.08/1.43 fof(fact_zless__linear, axiom, ![X21, X14]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X14,X21)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X14)|X14=X21), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zless__linear)). 1.08/1.43 fof(fact_linorder__neqE__nat, axiom, ![X21, X14]:((~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X21))=>c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X14))<=X21!=X14), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_linorder__neqE__nat)). 1.08/1.43 fof(fact_nat__neq__iff, axiom, ![X19, X29]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X19)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X29))<=>X29!=X19), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__neq__iff)). 1.08/1.43 fof(fact_real__sgn__def, axiom, ![X14]:((X14=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=>c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X14)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))&(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X14=>((c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X14)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14))&(~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14))=>c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X14)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__sgn__def)). 1.08/1.43 fof(fact_sgn__real__def, axiom, ![X13]:((c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X13)<=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X13)&(((c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X13)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13))&(~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13))=>c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X13)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))<=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__real__def)). 1.08/1.43 fof(fact_zsgn__def, axiom, ![X18]:((X18!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>((c_Groups_Osgn__class_Osgn(tc_Int_Oint,X18)=c_Groups_Oone__class_Oone(tc_Int_Oint)<=c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18))&(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X18)<=~(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)))))&(X18=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>c_Groups_Osgn__class_Osgn(tc_Int_Oint,X18)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zsgn__def)). 1.08/1.43 fof(fact_zle__linear, axiom, ![X43, X10]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X43)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X43,X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zle__linear)). 1.08/1.43 fof(fact_nat__le__linear, axiom, ![X2, X3]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__le__linear)). 1.08/1.43 fof(fact_real__le__linear, axiom, ![X43, X10]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X43,X10)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__le__linear)). 1.08/1.43 fof(fact_mult__eq__0__iff, axiom, ![X11, X8, X7]:(class_Rings_Oring__no__zero__divisors(X7)=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X11)=c_Groups_Ozero__class_Ozero(X7)<=>(c_Groups_Ozero__class_Ozero(X7)=X8|c_Groups_Ozero__class_Ozero(X7)=X11))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__eq__0__iff)). 1.08/1.43 fof(fact_no__zero__divisors, axiom, ![X12, X13, X7]:(((c_Groups_Ozero__class_Ozero(X7)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12)<=c_Groups_Ozero__class_Ozero(X7)!=X12)<=c_Groups_Ozero__class_Ozero(X7)!=X13)<=class_Rings_Ono__zero__divisors(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_no__zero__divisors)). 1.08/1.43 fof(fact_divisors__zero, axiom, ![X12, X13, X7]:(((c_Groups_Ozero__class_Ozero(X7)=X12|X13=c_Groups_Ozero__class_Ozero(X7))<=c_Groups_Ozero__class_Ozero(X7)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X12))<=class_Rings_Ono__zero__divisors(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_divisors__zero)). 1.08/1.43 fof(fact_diff__poly__code_I1_J, axiom, ![X15, X7]:(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X15)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X15)<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__poly__code_I1_J)). 1.08/1.43 fof(fact_zadd__commute, axiom, ![X43, X10]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,X43,X10)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__commute)). 1.08/1.43 fof(fact_nat__add__commute, axiom, ![X2, X3]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__add__commute)). 1.08/1.43 fof(fact_double__eq__0__iff, axiom, ![X8, X7]:(class_Groups_Olinordered__ab__group__add(X7)=>(c_Groups_Ozero__class_Ozero(X7)=X8<=>c_Groups_Oplus__class_Oplus(X7,X8,X8)=c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_double__eq__0__iff)). 1.08/1.43 fof(fact_double__zero__sym, axiom, ![X8, X7]:(class_Groups_Olinordered__ab__group__add(X7)=>(c_Groups_Ozero__class_Ozero(X7)=c_Groups_Oplus__class_Oplus(X7,X8,X8)<=>X8=c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_double__zero__sym)). 1.08/1.43 fof(fact_real__sgn__pos, axiom, ![X14]:(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X14)<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__sgn__pos)). 1.08/1.43 fof(fact_ln__eq__zero__iff, axiom, ![X5]:((c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=X5<=>c_Transcendental_Oln(X5)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<=c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__eq__zero__iff)). 1.08/1.43 fof(fact_eq__iff__diff__eq__0, axiom, ![X11, X8, X7]:((X8=X11<=>c_Groups_Ozero__class_Ozero(X7)=c_Groups_Ominus__class_Ominus(X7,X8,X11))<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_eq__iff__diff__eq__0)). 1.08/1.43 fof(fact_right__minus__eq, axiom, ![X11, X8, X7]:((X11=X8<=>c_Groups_Ozero__class_Ozero(X7)=c_Groups_Ominus__class_Ominus(X7,X8,X11))<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_right__minus__eq)). 1.08/1.43 fof(fact_field__power__not__zero, axiom, ![X2, X13, X7]:(class_Rings_Oring__1__no__zero__divisors(X7)=>(hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),X2)!=c_Groups_Ozero__class_Ozero(X7)<=c_Groups_Ozero__class_Ozero(X7)!=X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_field__power__not__zero)). 1.08/1.43 fof(fact_real__add__eq__0__iff, axiom, ![X6, X5]:(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5)=X6<=>c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__add__eq__0__iff)). 1.08/1.43 fof(fact_add__0__iff, axiom, ![X8, X11, X7]:((X11=c_Groups_Oplus__class_Oplus(X7,X11,X8)<=>c_Groups_Ozero__class_Ozero(X7)=X8)<=class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__0__iff)). 1.08/1.43 fof(fact_abs__sgn, axiom, ![X4, X7]:(class_Rings_Olinordered__idom(X7)=>c_Groups_Oabs__class_Oabs(X7,X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X4),c_Groups_Osgn__class_Osgn(X7,X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__sgn)). 1.08/1.43 fof(fact_poly__zero, axiom, ![X9, X7]:((class_Int_Oring__char__0(X7)&class_Rings_Oidom(X7))=>(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))=X9<=>c_Polynomial_Opoly(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))=c_Polynomial_Opoly(X7,X9))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__zero)). 1.08/1.43 fof(fact_order__less__imp__not__eq2, axiom, ![X21, X14, X7]:(class_Orderings_Oorder(X7)=>(X21!=X14<=c_Orderings_Oord__class_Oless(X7,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__imp__not__eq2)). 1.08/1.43 fof(fact_less__imp__neq, axiom, ![X21, X14, X7]:((X14!=X21<=c_Orderings_Oord__class_Oless(X7,X14,X21))<=class_Orderings_Oorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__imp__neq)). 1.08/1.43 fof(fact_order__less__imp__not__eq, axiom, ![X21, X14, X7]:(class_Orderings_Oorder(X7)=>(X14!=X21<=c_Orderings_Oord__class_Oless(X7,X14,X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__imp__not__eq)). 1.08/1.43 fof(fact_natfloor__neg, axiom, ![X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_RComplete_Onatfloor(X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__neg)). 1.08/1.43 fof(fact_natceiling__neg, axiom, ![X14]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_RComplete_Onatceiling(X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__neg)). 1.08/1.43 fof(fact_neq0__conv, axiom, ![X19]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X19), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neq0__conv)). 1.08/1.43 fof(fact_abs__ge__zero, axiom, ![X13, X7]:(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oabs__class_Oabs(X7,X13))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__ge__zero)). 1.08/1.43 fof(fact_coeff__1, axiom, ![X2, X7]:(class_Rings_Ocomm__semiring__1(X7)=>((X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>c_Groups_Ozero__class_Ozero(X7)=hAPP(c_Polynomial_Ocoeff(X7,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7))),X2))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2=>hAPP(c_Polynomial_Ocoeff(X7,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7))),X2)=c_Groups_Oone__class_Oone(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_coeff__1)). 1.08/1.43 fof(fact_order__less__irrefl, axiom, ![X14, X7]:(~(c_Orderings_Oord__class_Oless(X7,X14,X14))<=class_Orderings_Opreorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__less__irrefl)). 1.08/1.43 fof(fact_le__0__eq, axiom, ![X19]:(X19=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__0__eq)). 1.08/1.43 fof(fact_zmult__commute, axiom, ![X43, X10]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10),X43)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),X10), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zmult__commute)). 1.08/1.43 fof(fact_nat__mult__commute, axiom, ![X2, X3]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__commute)). 1.08/1.43 fof(fact_real__mult__commute, axiom, ![X43, X10]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X43),X10)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__commute)). 1.08/1.43 fof(fact_ab__left__minus, axiom, ![X13, X7]:(class_Groups_Oab__group__add(X7)=>c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X13),X13)=c_Groups_Ozero__class_Ozero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ab__left__minus)). 1.08/1.43 fof(fact_left__minus, axiom, ![X13, X7]:(c_Groups_Ozero__class_Ozero(X7)=c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X13),X13)<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_left__minus)). 1.08/1.43 fof(fact_right__minus, axiom, ![X13, X7]:(c_Groups_Ozero__class_Ozero(X7)=c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Ouminus__class_Ouminus(X7,X13))<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_right__minus)). 1.08/1.43 fof(fact_add__is__0, axiom, ![X19, X29]:(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X19)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=>(X19=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__is__0)). 1.08/1.43 fof(fact_gr__implies__not0, axiom, ![X2, X3]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_gr__implies__not0)). 1.08/1.43 fof(fact_norm__ge__zero, axiom, ![X14, X7]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X14))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__ge__zero)). 1.08/1.43 fof(fact_power__0__left, axiom, ![X2, X7]:((class_Rings_Osemiring__0(X7)&class_Power_Opower(X7))=>((hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Ozero__class_Ozero(X7)),X2)=c_Groups_Oone__class_Oone(X7)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Ozero__class_Ozero(X7)),X2)=c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__0__left)). 1.08/1.43 fof(fact_add__eq__self__zero, axiom, ![X2, X3]:(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)=X3=>X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__eq__self__zero)). 1.08/1.43 fof(fact_less__nat__zero__code, axiom, ![X2]:~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__nat__zero__code)). 1.08/1.43 fof(fact_not__less0, axiom, ![X2]:~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__less0)). 1.08/1.43 fof(fact_less__zeroE, axiom, ![X2]:~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__zeroE)). 1.08/1.43 fof(fact_real__natceiling__ge, axiom, ![X14]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__natceiling__ge)). 1.08/1.43 fof(fact_coeff__0, axiom, ![X2, X7]:(class_Groups_Ozero(X7)=>hAPP(c_Polynomial_Ocoeff(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))),X2)=c_Groups_Ozero__class_Ozero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_coeff__0)). 1.08/1.43 fof(fact_poly__0, axiom, ![X14, X7]:(class_Rings_Ocomm__semiring__0(X7)=>hAPP(c_Polynomial_Opoly(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))),X14)=c_Groups_Ozero__class_Ozero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__0)). 1.08/1.43 fof(fact_poly__1, axiom, ![X14, X7]:(class_Rings_Ocomm__semiring__1(X7)=>c_Groups_Oone__class_Oone(X7)=hAPP(c_Polynomial_Opoly(X7,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7))),X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__1)). 1.08/1.43 fof(fact_abs__ge__self, axiom, ![X13, X7]:(c_Orderings_Oord__class_Oless__eq(X7,X13,c_Groups_Oabs__class_Oabs(X7,X13))<=class_Groups_Oordered__ab__group__add__abs(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__ge__self)). 1.08/1.43 fof(fact_less__not__refl2, axiom, ![X3, X2]:(X3!=X2<=c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__not__refl2)). 1.08/1.43 fof(fact_less__not__refl3, axiom, ![X56, X46]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X46,X56)=>X46!=X56), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__not__refl3)). 1.08/1.43 fof(fact_sgn__minus, axiom, ![X14, X7]:(c_Groups_Osgn__class_Osgn(X7,c_Groups_Ouminus__class_Ouminus(X7,X14))=c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Osgn__class_Osgn(X7,X14))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__minus)). 1.08/1.43 fof(fact_add__poly__code_I1_J, axiom, ![X15, X7]:(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X15)=X15<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__poly__code_I1_J)). 1.08/1.43 fof(fact_diff__poly__code_I2_J, axiom, ![X16, X7]:(X16=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X7),X16,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__poly__code_I2_J)). 1.08/1.43 fof(fact_add__poly__code_I2_J, axiom, ![X16, X7]:(X16=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),X16,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__poly__code_I2_J)). 1.08/1.43 fof(fact_pos__poly__total, axiom, ![X16, X7]:((c_Polynomial_Opos__poly(X7,X16)|c_Polynomial_Opos__poly(X7,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X16))|X16=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_pos__poly__total)). 1.08/1.43 fof(fact_mult__is__0, axiom, ![X19, X29]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X29|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X19)<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__is__0)). 1.08/1.43 fof(fact_less__not__refl, axiom, ![X2]:~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__not__refl)). 1.08/1.43 fof(fact_less__irrefl__nat, axiom, ![X2]:~(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__irrefl__nat)). 1.08/1.43 fof(fact_mult__eq__self__implies__10, axiom, ![X2, X3]:(X3=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3|c_Groups_Oone__class_Oone(tc_Nat_Onat)=X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__eq__self__implies__10)). 1.08/1.43 fof(fact_diff__0, axiom, ![X13, X7]:(c_Groups_Ominus__class_Ominus(X7,c_Groups_Ozero__class_Ozero(X7),X13)=c_Groups_Ouminus__class_Ouminus(X7,X13)<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__0)). 1.08/1.43 fof(fact_nat__1__eq__mult__iff, axiom, ![X19, X29]:((X19=c_Groups_Oone__class_Oone(tc_Nat_Onat)&c_Groups_Oone__class_Oone(tc_Nat_Onat)=X29)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X19)=c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__1__eq__mult__iff)). 1.08/1.43 fof(fact_nat__mult__eq__1__iff, axiom, ![X19, X29]:(c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X19)<=>(X19=c_Groups_Oone__class_Oone(tc_Nat_Onat)&X29=c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__eq__1__iff)). 1.08/1.43 fof(fact_real__of__nat__ge__zero, axiom, ![X2]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__ge__zero)). 1.08/1.43 fof(fact_zadd__zminus__inverse2, axiom, ![X10]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X10),X10), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__zminus__inverse2)). 1.08/1.43 fof(fact_power__power__power, axiom, ![X7]:(class_Power_Opower(X7)=>c_Power_Opower_Opower(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Otimes__class_Otimes(X7))=c_Power_Opower__class_Opower(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__power__power)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, axiom, ![X13, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X13)=c_Groups_Ozero__class_Ozero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 1.08/1.43 fof(fact_mult_Ozero__left, axiom, ![X12, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X12)=c_Groups_Ozero__class_Ozero(X7)<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Ozero__left)). 1.08/1.43 fof(fact_mult__zero__left, axiom, ![X13, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X13)=c_Groups_Ozero__class_Ozero(X7)<=class_Rings_Omult__zero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__zero__left)). 1.08/1.43 fof(fact_power__one, axiom, ![X2, X7]:(c_Groups_Oone__class_Oone(X7)=hAPP(hAPP(c_Power_Opower__class_Opower(X7),c_Groups_Oone__class_Oone(X7)),X2)<=class_Groups_Omonoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__one)). 1.08/1.43 fof(fact_mult__left_Ozero, axiom, ![X21, X7]:(c_Groups_Ozero__class_Ozero(X7)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X21)<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__left_Ozero)). 1.08/1.43 fof(fact_zero__less__one, axiom, ![X7]:(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oone__class_Oone(X7))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__less__one)). 1.08/1.43 fof(fact_zero__le__one, axiom, ![X7]:(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oone__class_Oone(X7))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__le__one)). 1.08/1.43 fof(fact_mult__1, axiom, ![X13, X7]:(X13=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oone__class_Oone(X7)),X13)<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__1)). 1.08/1.43 fof(fact_mult__1__left, axiom, ![X13, X7]:(X13=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oone__class_Oone(X7)),X13)<=class_Groups_Omonoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__1__left)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, axiom, ![X13, X7]:(X13=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oone__class_Oone(X7)),X13)<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 1.08/1.43 fof(fact_div__0, axiom, ![X13, X7]:(c_Divides_Odiv__class_Odiv(X7,c_Groups_Ozero__class_Ozero(X7),X13)=c_Groups_Ozero__class_Ozero(X7)<=class_Divides_Osemiring__div(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__0)). 1.08/1.43 fof(fact_div__by__0, axiom, ![X13, X7]:(class_Divides_Osemiring__div(X7)=>c_Divides_Odiv__class_Odiv(X7,X13,c_Groups_Ozero__class_Ozero(X7))=c_Groups_Ozero__class_Ozero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__by__0)). 1.08/1.43 fof(fact_div__self, axiom, ![X13, X7]:(class_Divides_Osemiring__div(X7)=>(c_Divides_Odiv__class_Odiv(X7,X13,X13)=c_Groups_Oone__class_Oone(X7)<=c_Groups_Ozero__class_Ozero(X7)!=X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__self)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, axiom, ![X13, X7]:(class_Rings_Ocomm__semiring__1(X7)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Ozero__class_Ozero(X7))=c_Groups_Ozero__class_Ozero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 1.08/1.43 fof(fact_mult__right_Ozero, axiom, ![X14, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),c_Groups_Ozero__class_Ozero(X7))=c_Groups_Ozero__class_Ozero(X7)<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__right_Ozero)). 1.08/1.43 fof(fact_mult_Ozero__right, axiom, ![X13, X7]:(c_Groups_Ozero__class_Ozero(X7)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Ozero__class_Ozero(X7))<=class_RealVector_Oreal__normed__algebra(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Ozero__right)). 1.08/1.43 fof(fact_mult__zero__right, axiom, ![X13, X7]:(c_Groups_Ozero__class_Ozero(X7)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Ozero__class_Ozero(X7))<=class_Rings_Omult__zero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__zero__right)). 1.08/1.43 fof(fact_add__0, axiom, ![X13, X7]:(class_Groups_Ocomm__monoid__add(X7)=>c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X13)=X13), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__0)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, axiom, ![X13, X7]:(c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X13)=X13<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 1.08/1.43 fof(fact_add_Ocomm__neutral, axiom, ![X13, X7]:(c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Ozero__class_Ozero(X7))=X13<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add_Ocomm__neutral)). 1.08/1.43 fof(fact_add__0__left, axiom, ![X13, X7]:(X13=c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X13)<=class_Groups_Omonoid__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__0__left)). 1.08/1.43 fof(fact_div__by__1, axiom, ![X13, X7]:(class_Divides_Osemiring__div(X7)=>X13=c_Divides_Odiv__class_Odiv(X7,X13,c_Groups_Oone__class_Oone(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_div__by__1)). 1.08/1.43 fof(fact_diff__0__right, axiom, ![X13, X7]:(X13=c_Groups_Ominus__class_Ominus(X7,X13,c_Groups_Ozero__class_Ozero(X7))<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__0__right)). 1.08/1.43 fof(fact_add__0__right, axiom, ![X13, X7]:(class_Groups_Omonoid__add(X7)=>X13=c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_add__0__right)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, axiom, ![X13, X7]:(X13=c_Groups_Oplus__class_Oplus(X7,X13,c_Groups_Ozero__class_Ozero(X7))<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 1.08/1.43 fof(fact_power__0, axiom, ![X13, X7]:(class_Power_Opower(X7)=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__0)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, axiom, ![X14, X7]:(class_Rings_Ocomm__semiring__1(X7)=>c_Groups_Oone__class_Oone(X7)=hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 1.08/1.43 fof(fact_mult__1__right, axiom, ![X13, X7]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Oone__class_Oone(X7))=X13<=class_Groups_Omonoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__1__right)). 1.08/1.43 fof(fact_mult_Ocomm__neutral, axiom, ![X13, X7]:(X13=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Oone__class_Oone(X7))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult_Ocomm__neutral)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, axiom, ![X13, X7]:(X13=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),c_Groups_Oone__class_Oone(X7))<=class_Rings_Ocomm__semiring__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 1.08/1.43 fof(fact_diff__self, axiom, ![X13, X7]:(c_Groups_Ominus__class_Ominus(X7,X13,X13)=c_Groups_Ozero__class_Ozero(X7)<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__self)). 1.08/1.43 fof(fact_order__eq__refl, axiom, ![X21, X14, X7]:((X21=X14=>c_Orderings_Oord__class_Oless__eq(X7,X14,X21))<=class_Orderings_Opreorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__eq__refl)). 1.08/1.43 fof(fact_power__one__right, axiom, ![X13, X7]:(hAPP(hAPP(c_Power_Opower__class_Opower(X7),X13),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X13<=class_Groups_Omonoid__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_power__one__right)). 1.08/1.43 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, axiom, ![X14, X7]:(class_Rings_Ocomm__semiring__1(X7)=>X14=hAPP(hAPP(c_Power_Opower__class_Opower(X7),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 1.08/1.43 fof(fact_zero__le__natfloor, axiom, ![X14]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__le__natfloor)). 1.08/1.43 fof(fact_zero__le__natceiling, axiom, ![X14]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__le__natceiling)). 1.08/1.43 fof(fact_order__refl, axiom, ![X14, X7]:(c_Orderings_Oord__class_Oless__eq(X7,X14,X14)<=class_Orderings_Opreorder(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_order__refl)). 1.08/1.43 fof(fact_One__nat__def, axiom, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_One__nat__def)). 1.08/1.43 fof(fact_abs__minus__cancel, axiom, ![X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Groups_Oabs__class_Oabs(X7,c_Groups_Ouminus__class_Ouminus(X7,X13))=c_Groups_Oabs__class_Oabs(X7,X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__minus__cancel)). 1.08/1.43 fof(fact_sgn__sgn, axiom, ![X13, X7]:(class_Rings_Olinordered__idom(X7)=>c_Groups_Osgn__class_Osgn(X7,c_Groups_Osgn__class_Osgn(X7,X13))=c_Groups_Osgn__class_Osgn(X7,X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__sgn)). 1.08/1.43 fof(fact_abs__idempotent, axiom, ![X13, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Groups_Oabs__class_Oabs(X7,X13)=c_Groups_Oabs__class_Oabs(X7,c_Groups_Oabs__class_Oabs(X7,X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__idempotent)). 1.08/1.43 fof(fact_norm__minus__cancel, axiom, ![X14, X7]:(c_RealVector_Onorm__class_Onorm(X7,X14)=c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ouminus__class_Ouminus(X7,X14))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__minus__cancel)). 1.08/1.43 fof(fact_poly__eq__iff, axiom, ![X87, X9, X7]:((c_Polynomial_Opoly(X7,X87)=c_Polynomial_Opoly(X7,X9)<=>X87=X9)<=(class_Int_Oring__char__0(X7)&class_Rings_Oidom(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_poly__eq__iff)). 1.08/1.43 fof(fact_times_Oidem, axiom, ![X13, X7]:(X13=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X13),X13)<=class_Lattices_Oab__semigroup__idem__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_times_Oidem)). 1.08/1.43 fof(fact_mult__idem, axiom, ![X14, X7]:(X14=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X14),X14)<=class_Lattices_Oab__semigroup__idem__mult(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__idem)). 1.08/1.43 fof(fact_gr0I, axiom, ![X2]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_gr0I)). 1.08/1.43 fof(fact_abs__norm__cancel, axiom, ![X13, X7]:(c_RealVector_Onorm__class_Onorm(X7,X13)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X13))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__norm__cancel)). 1.08/1.43 fof(fact_zdiv__self, axiom, ![X13]:(c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X13)=c_Groups_Oone__class_Oone(tc_Int_Oint)<=X13!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__self)). 1.08/1.43 fof(fact_not__pos__poly__0, axiom, ![X7]:(~(c_Polynomial_Opos__poly(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))))<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_not__pos__poly__0)). 1.08/1.43 fof(fact_zdiv__zero, axiom, ![X12]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zdiv__zero)). 1.08/1.43 fof(fact_diff__0__eq__0, axiom, ![X2]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__0__eq__0)). 1.08/1.43 fof(fact_norm__sgn, axiom, ![X14, X7]:(class_RealVector_Oreal__normed__vector(X7)=>((c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(X7,c_Groups_Osgn__class_Osgn(X7,X14))<=X14!=c_Groups_Ozero__class_Ozero(X7))&(c_RealVector_Onorm__class_Onorm(X7,c_Groups_Osgn__class_Osgn(X7,X14))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<=X14=c_Groups_Ozero__class_Ozero(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__sgn)). 1.08/1.43 fof(fact_zadd__0, axiom, ![X10]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)=X10, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__0)). 1.08/1.43 fof(fact_plus__nat_Oadd__0, axiom, ![X2]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=X2, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_plus__nat_Oadd__0)). 1.08/1.43 fof(fact_minus__nat_Odiff__0, axiom, ![X3]:X3=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__nat_Odiff__0)). 1.08/1.43 fof(fact_zadd__0__right, axiom, ![X10]:X10=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zadd__0__right)). 1.08/1.43 fof(fact_Nat_Oadd__0__right, axiom, ![X3]:X3=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat_Oadd__0__right)). 1.08/1.43 fof(fact_eq__imp__le, axiom, ![X2, X3]:(X2=X3=>c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_eq__imp__le)). 1.08/1.43 fof(fact_le0, axiom, ![X2]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le0)). 1.08/1.43 fof(fact_less__eq__nat_Osimps_I1_J, axiom, ![X2]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_less__eq__nat_Osimps_I1_J)). 1.08/1.43 fof(fact_minus__poly__code_I1_J, axiom, ![X7]:(class_Groups_Oab__group__add(X7)=>c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__poly__code_I1_J)). 1.08/1.43 fof(fact_diff__self__eq__0, axiom, ![X3]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_diff__self__eq__0)). 1.08/1.43 fof(fact_mult__0, axiom, ![X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__0)). 1.08/1.43 fof(fact_coeff__inject, axiom, ![X6, X5, X7]:((c_Polynomial_Ocoeff(X7,X6)=c_Polynomial_Ocoeff(X7,X5)<=>X5=X6)<=class_Groups_Ozero(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_coeff__inject)). 1.08/1.43 fof(fact_compl__eq__compl__iff, axiom, ![X6, X5, X7]:(class_Lattices_Oboolean__algebra(X7)=>(X6=X5<=>c_Groups_Ouminus__class_Ouminus(X7,X6)=c_Groups_Ouminus__class_Ouminus(X7,X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_compl__eq__compl__iff)). 1.08/1.43 fof(fact_neg__equal__iff__equal, axiom, ![X11, X8, X7]:((c_Groups_Ouminus__class_Ouminus(X7,X11)=c_Groups_Ouminus__class_Ouminus(X7,X8)<=>X11=X8)<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__equal__iff__equal)). 1.08/1.43 fof(fact_real__mult__1, axiom, ![X10]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10)=X10, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__mult__1)). 1.08/1.43 fof(fact_zmult__1, axiom, ![X10]:X10=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X10), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zmult__1)). 1.08/1.43 fof(fact_nat__mult__1, axiom, ![X2]:X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__1)). 1.08/1.43 fof(fact_zle__refl, axiom, ![X43]:c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X43,X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zle__refl)). 1.08/1.43 fof(fact_le__refl, axiom, ![X2]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_le__refl)). 1.08/1.43 fof(fact_real__le__refl, axiom, ![X43]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X43,X43), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__le__refl)). 1.08/1.43 fof(fact_mult__0__right, axiom, ![X3]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mult__0__right)). 1.08/1.43 fof(fact_nat__mult__1__right, axiom, ![X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_nat__mult__1__right)). 1.08/1.43 fof(fact_zmult__1__right, axiom, ![X10]:X10=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10),c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zmult__1__right)). 1.08/1.43 fof(fact_double__compl, axiom, ![X14, X7]:(class_Lattices_Oboolean__algebra(X7)=>c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ouminus__class_Ouminus(X7,X14))=X14), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_double__compl)). 1.08/1.43 fof(fact_minus__minus, axiom, ![X13, X7]:(class_Groups_Ogroup__add(X7)=>X13=c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ouminus__class_Ouminus(X7,X13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__minus)). 1.08/1.43 fof(fact_abs__real__of__nat__cancel, axiom, ![X14]:c_RealDef_Oreal(tc_Nat_Onat,X14)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__real__of__nat__cancel)). 1.08/1.43 fof(fact_equation__minus__iff, axiom, ![X11, X8, X7]:((X8=c_Groups_Ouminus__class_Ouminus(X7,X11)<=>c_Groups_Ouminus__class_Ouminus(X7,X8)=X11)<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_equation__minus__iff)). 1.08/1.43 fof(fact_minus__equation__iff, axiom, ![X11, X8, X7]:(class_Groups_Ogroup__add(X7)=>(X11=c_Groups_Ouminus__class_Ouminus(X7,X8)<=>X8=c_Groups_Ouminus__class_Ouminus(X7,X11))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__equation__iff)). 1.08/1.43 fof(fact_real__of__nat__inject, axiom, ![X29, X19]:(X29=X19<=>c_RealDef_Oreal(tc_Nat_Onat,X29)=c_RealDef_Oreal(tc_Nat_Onat,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__inject)). 1.08/1.43 fof(fact_sgn__0__0, axiom, ![X8, X7]:(class_Rings_Olinordered__idom(X7)=>(c_Groups_Ozero__class_Ozero(X7)=X8<=>c_Groups_Ozero__class_Ozero(X7)=c_Groups_Osgn__class_Osgn(X7,X8))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__0__0)). 1.08/1.43 fof(fact_sgn__zero__iff, axiom, ![X5, X7]:((c_Groups_Ozero__class_Ozero(X7)=X5<=>c_Groups_Ozero__class_Ozero(X7)=c_Groups_Osgn__class_Osgn(X7,X5))<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__zero__iff)). 1.08/1.43 fof(fact_neg__equal__0__iff__equal, axiom, ![X8, X7]:(class_Groups_Ogroup__add(X7)=>(c_Groups_Ouminus__class_Ouminus(X7,X8)=c_Groups_Ozero__class_Ozero(X7)<=>X8=c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__equal__0__iff__equal)). 1.08/1.43 fof(fact_neg__0__equal__iff__equal, axiom, ![X8, X7]:((X8=c_Groups_Ozero__class_Ozero(X7)<=>c_Groups_Ouminus__class_Ouminus(X7,X8)=c_Groups_Ozero__class_Ozero(X7))<=class_Groups_Ogroup__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__0__equal__iff__equal)). 1.08/1.43 fof(fact_abs__eq__0, axiom, ![X8, X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>(X8=c_Groups_Ozero__class_Ozero(X7)<=>c_Groups_Ozero__class_Ozero(X7)=c_Groups_Oabs__class_Oabs(X7,X8))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__eq__0)). 1.08/1.43 fof(fact_norm__eq__zero, axiom, ![X5, X7]:(class_RealVector_Oreal__normed__vector(X7)=>(c_RealVector_Onorm__class_Onorm(X7,X5)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<=>c_Groups_Ozero__class_Ozero(X7)=X5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__eq__zero)). 1.08/1.43 fof(arity_fun__Lattices_Oboolean__algebra, axiom, ![X58, X1]:(class_Lattices_Oboolean__algebra(X1)=>class_Lattices_Oboolean__algebra(tc_fun(X58,X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_fun__Lattices_Oboolean__algebra)). 1.08/1.43 fof(arity_fun__Orderings_Oord, axiom, ![X58, X1]:(class_Orderings_Oord(X1)=>class_Orderings_Oord(tc_fun(X58,X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_fun__Orderings_Oord)). 1.08/1.43 fof(arity_fun__Groups_Ominus, axiom, ![X58, X1]:(class_Groups_Ominus(X1)=>class_Groups_Ominus(tc_fun(X58,X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_fun__Groups_Ominus)). 1.08/1.43 fof(arity_fun__Groups_Ouminus, axiom, ![X58, X1]:(class_Groups_Ouminus(tc_fun(X58,X1))<=class_Groups_Ouminus(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_fun__Groups_Ouminus)). 1.08/1.43 fof(arity_fun__Orderings_Opreorder, axiom, ![X58, X1]:(class_Orderings_Opreorder(X1)=>class_Orderings_Opreorder(tc_fun(X58,X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_fun__Orderings_Opreorder)). 1.08/1.43 fof(arity_fun__Orderings_Oorder, axiom, ![X58, X1]:(class_Orderings_Oorder(tc_fun(X58,X1))<=class_Orderings_Oorder(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_fun__Orderings_Oorder)). 1.08/1.43 fof(fact_zminus__zminus, axiom, ![X10]:c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X10))=X10, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zminus__zminus)). 1.08/1.43 fof(fact_equal__neg__zero, axiom, ![X8, X7]:((X8=c_Groups_Ouminus__class_Ouminus(X7,X8)<=>X8=c_Groups_Ozero__class_Ozero(X7))<=class_Groups_Olinordered__ab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_equal__neg__zero)). 1.08/1.43 fof(fact_neg__equal__zero, axiom, ![X8, X7]:((X8=c_Groups_Ouminus__class_Ouminus(X7,X8)<=>X8=c_Groups_Ozero__class_Ozero(X7))<=class_Groups_Olinordered__ab__group__add(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_neg__equal__zero)). 1.08/1.43 fof(fact_abs__one, axiom, ![X7]:(c_Groups_Oabs__class_Oabs(X7,c_Groups_Oone__class_Oone(X7))=c_Groups_Oone__class_Oone(X7)<=class_Rings_Olinordered__idom(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__one)). 1.08/1.43 fof(fact_sgn__one, axiom, ![X7]:(c_Groups_Osgn__class_Osgn(X7,c_Groups_Oone__class_Oone(X7))=c_Groups_Oone__class_Oone(X7)<=class_RealVector_Oreal__normed__algebra__1(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__one)). 1.08/1.43 fof(fact_sgn__zero, axiom, ![X7]:(c_Groups_Osgn__class_Osgn(X7,c_Groups_Ozero__class_Ozero(X7))=c_Groups_Ozero__class_Ozero(X7)<=class_RealVector_Oreal__normed__vector(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn__zero)). 1.08/1.43 fof(fact_abs__zero, axiom, ![X7]:(class_Groups_Oordered__ab__group__add__abs(X7)=>c_Groups_Ozero__class_Ozero(X7)=c_Groups_Oabs__class_Oabs(X7,c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_abs__zero)). 1.08/1.43 fof(fact_sgn0, axiom, ![X7]:(class_Groups_Osgn__if(X7)=>c_Groups_Ozero__class_Ozero(X7)=c_Groups_Osgn__class_Osgn(X7,c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_sgn0)). 1.08/1.43 fof(fact_minus__zero, axiom, ![X7]:(class_Groups_Ogroup__add(X7)=>c_Groups_Ozero__class_Ozero(X7)=c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ozero__class_Ozero(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_minus__zero)). 1.08/1.43 fof(fact_norm__zero, axiom, ![X7]:(class_RealVector_Oreal__normed__vector(X7)=>c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ozero__class_Ozero(X7))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__zero)). 1.08/1.43 fof(fact_norm__one, axiom, ![X7]:(class_RealVector_Oreal__normed__algebra__1(X7)=>c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oone__class_Oone(X7))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_norm__one)). 1.08/1.43 fof(fact_natfloor__real__of__nat, axiom, ![X2]:c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X2))=X2, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__real__of__nat)). 1.08/1.43 fof(fact_natceiling__real__of__nat, axiom, ![X2]:c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X2))=X2, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__real__of__nat)). 1.08/1.43 fof(fact_real__of__nat__zero__iff, axiom, ![X19]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X19<=>c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_RealDef_Oreal(tc_Nat_Onat,X19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__zero__iff)). 1.08/1.43 fof(fact_real__norm__def, axiom, ![X47]:c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X47)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X47), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__norm__def)). 1.08/1.43 fof(fact_one__neq__zero, axiom, ![X7]:(c_Groups_Ozero__class_Ozero(X7)!=c_Groups_Oone__class_Oone(X7)<=class_Rings_Ozero__neq__one(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_one__neq__zero)). 1.08/1.43 fof(fact_zero__neq__one, axiom, ![X7]:(class_Rings_Ozero__neq__one(X7)=>c_Groups_Ozero__class_Ozero(X7)!=c_Groups_Oone__class_Oone(X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zero__neq__one)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Osgn__if, axiom, ![X1]:(class_Groups_Osgn__if(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Osgn__if)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oone, axiom, ![X1]:(class_Rings_Ocomm__semiring__1(X1)=>class_Groups_Oone(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oone)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring, axiom, ![X1]:(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oordered__comm__semiring)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring, axiom, ![X1]:(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))<=class_Rings_Ocomm__semiring__0(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Ocomm__semiring)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one, axiom, ![X1]:(class_Rings_Ocomm__semiring__1(X1)=>class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Ozero__neq__one)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Ozero, axiom, ![X1]:(class_Groups_Ozero(X1)=>class_Groups_Ozero(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Ozero)). 1.08/1.43 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, ![X1]:(class_Rings_Oidom(X1)=>class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oabs__if, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Groups_Oabs__if(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oabs__if)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, axiom, ![X1]:(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))<=class_Rings_Ocomm__semiring__1(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oring__1, axiom, ![X1]:(class_Rings_Oring__1(tc_Polynomial_Opoly(X1))<=class_Rings_Ocomm__ring__1(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oring__1)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring, axiom, ![X1]:(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Olinordered__semiring)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add, axiom, ![X1]:(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le)). 1.08/1.43 fof(arity_Polynomial__Opoly__Int_Oring__char__0, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Int_Oring__char__0)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Osemiring, axiom, ![X1]:(class_Rings_Osemiring(tc_Polynomial_Opoly(X1))<=class_Rings_Ocomm__semiring__0(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Osemiring)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Olinordered__semiring__1)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, axiom, ![X1]:(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))<=class_Groups_Ocancel__comm__monoid__add(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, axiom, ![X1]:(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Olinordered__ring__strict)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oordered__ring, axiom, ![X1]:(class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oordered__ring)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, axiom, ![X1]:(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring, axiom, ![X1]:(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oordered__semiring)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Omonoid__add, axiom, ![X1]:(class_Groups_Ocomm__monoid__add(X1)=>class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Omonoid__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, axiom, ![X1]:(class_Rings_Oidom(X1)=>class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, axiom, ![X1]:(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))<=class_Groups_Ocancel__comm__monoid__add(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oordered__ring__abs)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors, axiom, ![X1]:(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))<=class_Rings_Oidom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Ono__zero__divisors)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult, axiom, ![X1]:(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))<=class_Rings_Ocomm__semiring__1(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Omonoid__mult)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, axiom, ![X1]:(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring, axiom, ![X1]:(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Olinordered__ring)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oab__group__add, axiom, ![X1]:(class_Groups_Oab__group__add(X1)=>class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oab__group__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Orderings_Oord, axiom, ![X1]:(class_Orderings_Oord(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Orderings_Oord)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Ominus, axiom, ![X1]:(class_Groups_Oab__group__add(X1)=>class_Groups_Ominus(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Ominus)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, axiom, ![X1]:(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))<=class_Groups_Ocomm__monoid__add(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Ocomm__monoid__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Divides_Osemiring__div, axiom, ![X1]:(class_Fields_Ofield(X1)=>class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Divides_Osemiring__div)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, axiom, ![X1]:(class_Groups_Ocancel__comm__monoid__add(X1)=>class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oring, axiom, ![X1]:(class_Rings_Oring(tc_Polynomial_Opoly(X1))<=class_Rings_Ocomm__ring(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oring)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, axiom, ![X1]:(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Ouminus, axiom, ![X1]:(class_Groups_Oab__group__add(X1)=>class_Groups_Ouminus(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Ouminus)). 1.08/1.43 fof(arity_Polynomial__Opoly__Power_Opower, axiom, ![X1]:(class_Rings_Ocomm__semiring__1(X1)=>class_Power_Opower(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Power_Opower)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Olinordered__idom)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Osemiring__0, axiom, ![X1]:(class_Rings_Ocomm__semiring__0(X1)=>class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Osemiring__0)). 1.08/1.43 fof(arity_Polynomial__Opoly__Orderings_Olinorder, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Orderings_Olinorder)). 1.08/1.43 fof(arity_Polynomial__Opoly__Orderings_Opreorder, axiom, ![X1]:(class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Orderings_Opreorder)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1, axiom, ![X1]:(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))<=class_Rings_Ocomm__ring__1(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Ocomm__ring__1)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, axiom, ![X1]:(class_Rings_Oidom(X1)=>class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, axiom, ![X1]:(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add, axiom, ![X1]:(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))<=class_Groups_Ocomm__monoid__add(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oab__semigroup__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, axiom, ![X1]:(class_Rings_Ocomm__semiring__1(X1)=>class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Ocomm__semiring__1)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Ogroup__add, axiom, ![X1]:(class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))<=class_Groups_Oab__group__add(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Ogroup__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, axiom, ![X1]:(class_Rings_Ocomm__semiring__0(X1)=>class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Ocomm__semiring__0)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add, axiom, ![X1]:(class_Rings_Olinordered__idom(X1)=>class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oordered__ab__group__add)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom, axiom, ![X1]:(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Olinordered__semidom)). 1.08/1.43 fof(arity_Polynomial__Opoly__Orderings_Oorder, axiom, ![X1]:(class_Orderings_Oorder(tc_Polynomial_Opoly(X1))<=class_Rings_Olinordered__idom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Orderings_Oorder)). 1.08/1.43 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, axiom, ![X1]:(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))<=class_Rings_Ocomm__semiring__0(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Groups_Oab__semigroup__mult)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Oidom, axiom, ![X1]:(class_Rings_Oidom(tc_Polynomial_Opoly(X1))<=class_Rings_Oidom(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Oidom)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Omult__zero, axiom, ![X1]:(class_Rings_Ocomm__semiring__0(X1)=>class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Omult__zero)). 1.08/1.43 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring, axiom, ![X1]:(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))<=class_Rings_Ocomm__ring(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Polynomial__Opoly__Rings_Ocomm__ring)). 1.08/1.43 fof(fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096, axiom, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096)). 1.08/1.43 fof(fact__0960_A_060_061_Acmod_Ac_096, axiom, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact__0960_A_060_061_Acmod_Ac_096)). 1.08/1.43 fof(fact_int__0__less__1, axiom, c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_int__0__less__1)). 1.08/1.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, axiom, c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)). 1.08/1.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, axiom, c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J)). 1.08/1.43 fof(fact_real__of__nat__1, axiom, c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__1)). 1.08/1.43 fof(fact_zminus__0, axiom, c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_zminus__0)). 1.08/1.43 fof(fact_real__of__nat__zero, axiom, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__of__nat__zero)). 1.08/1.43 fof(fact_natfloor__zero, axiom, c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__zero)). 1.08/1.43 fof(fact_natceiling__one, axiom, c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__one)). 1.08/1.43 fof(fact_natfloor__one, axiom, c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natfloor__one)). 1.08/1.43 fof(fact_natceiling__zero, axiom, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_natceiling__zero)). 1.08/1.43 fof(fact_ln__one, axiom, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ln__one)). 1.08/1.43 fof(fact_int__0__neq__1, axiom, c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_int__0__neq__1)). 1.08/1.43 fof(fact_real__zero__not__eq__one, axiom, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_real__zero__not__eq__one)). 1.08/1.43 fof(arity_RealDef__Oreal__Fields_Ofield, axiom, class_Fields_Ofield(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Fields_Ofield)). 1.08/1.43 fof(arity_Complex__Ocomplex__Fields_Ofield, axiom, class_Fields_Ofield(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Fields_Ofield)). 1.08/1.43 fof(arity_Int__Oint__Groups_Osgn__if, axiom, class_Groups_Osgn__if(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Osgn__if)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Osgn__if, axiom, class_Groups_Osgn__if(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Osgn__if)). 1.08/1.43 fof(arity_HOL__Obool__Lattices_Oboolean__algebra, axiom, class_Lattices_Oboolean__algebra(tc_HOL_Obool), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Oboolean__algebra)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oone, axiom, class_Groups_Oone(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oone)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Oone, axiom, class_Groups_Oone(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oone)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oone, axiom, class_Groups_Oone(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oone)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Oone, axiom, class_Groups_Oone(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Oone)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oordered__comm__semiring, axiom, class_Rings_Oordered__comm__semiring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__comm__semiring)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring, axiom, class_Rings_Oordered__comm__semiring(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Oordered__comm__semiring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring, axiom, class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oordered__comm__semiring)). 1.08/1.43 fof(arity_Int__Oint__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__semiring)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ocomm__semiring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Ocomm__semiring)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Ocomm__semiring)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__cancel__semiring)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Oordered__cancel__semiring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oordered__cancel__semiring)). 1.08/1.43 fof(arity_Int__Oint__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ozero__neq__one)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ozero__neq__one)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Ozero__neq__one)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Ozero__neq__one)). 1.08/1.43 fof(arity_Int__Oint__Groups_Ozero, axiom, class_Groups_Ozero(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ozero)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Ozero, axiom, class_Groups_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ozero)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Ozero, axiom, class_Groups_Ozero(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Ozero)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Ozero, axiom, class_Groups_Ozero(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Ozero)). 1.08/1.43 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 1.08/1.43 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 1.08/1.43 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 1.08/1.43 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oabs__if, axiom, class_Groups_Oabs__if(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oabs__if)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oabs__if, axiom, class_Groups_Oabs__if(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oabs__if)). 1.08/1.43 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocomm__monoid__mult)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocomm__monoid__mult)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Ocomm__monoid__mult)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oring__1, axiom, class_Rings_Oring__1(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring__1)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oring__1, axiom, class_Rings_Oring__1(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oring__1)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Oring__1, axiom, class_Rings_Oring__1(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Oring__1)). 1.08/1.43 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, axiom, class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero)). 1.08/1.43 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, axiom, class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra)). 1.08/1.43 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, axiom, class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra)). 1.08/1.43 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, axiom, class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1)). 1.08/1.43 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, axiom, class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1)). 1.08/1.43 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict, axiom, class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring__1__strict)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, axiom, class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict)). 1.08/1.43 fof(arity_Int__Oint__Rings_Olinordered__semiring, axiom, class_Rings_Olinordered__semiring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Olinordered__semiring, axiom, class_Rings_Olinordered__semiring(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__semiring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring, axiom, class_Rings_Olinordered__semiring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__semiring)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, axiom, class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, axiom, class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add, axiom, class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, axiom, class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, axiom, class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, axiom, class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le)). 1.08/1.43 fof(arity_Int__Oint__Int_Oring__char__0, axiom, class_Int_Oring__char__0(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Int_Oring__char__0)). 1.08/1.43 fof(arity_RealDef__Oreal__Int_Oring__char__0, axiom, class_Int_Oring__char__0(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Int_Oring__char__0)). 1.08/1.43 fof(arity_Complex__Ocomplex__Int_Oring__char__0, axiom, class_Int_Oring__char__0(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Int_Oring__char__0)). 1.08/1.43 fof(arity_Int__Oint__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Osemiring)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Osemiring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Osemiring)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Osemiring)). 1.08/1.43 fof(arity_Int__Oint__Rings_Olinordered__semiring__1, axiom, class_Rings_Olinordered__semiring__1(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring__1)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1, axiom, class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__semiring__1)). 1.08/1.43 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocancel__semigroup__add)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocancel__semigroup__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Ocancel__semigroup__add)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add)). 1.08/1.43 fof(arity_Int__Oint__Rings_Olinordered__ring__strict, axiom, class_Rings_Olinordered__ring__strict(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__ring__strict)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict, axiom, class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__ring__strict)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oordered__ring, axiom, class_Rings_Oordered__ring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__ring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oordered__ring, axiom, class_Rings_Oordered__ring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oordered__ring)). 1.08/1.43 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__comm__semiring__strict)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict)). 1.08/1.43 fof(arity_RealDef__Oreal__Fields_Olinordered__field, axiom, class_Fields_Olinordered__field(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Fields_Olinordered__field)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__semiring)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Oordered__semiring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oordered__semiring)). 1.08/1.43 fof(arity_Int__Oint__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Omonoid__add)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Omonoid__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Omonoid__add)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Omonoid__add)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors, axiom, class_Rings_Oring__no__zero__divisors(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring__no__zero__divisors)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors, axiom, class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oring__no__zero__divisors)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, axiom, class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors)). 1.08/1.43 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocancel__ab__semigroup__add)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oordered__ring__abs, axiom, class_Rings_Oordered__ring__abs(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__ring__abs)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs, axiom, class_Rings_Oordered__ring__abs(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oordered__ring__abs)). 1.08/1.43 fof(arity_Int__Oint__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ono__zero__divisors)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ono__zero__divisors)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Ono__zero__divisors)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Ono__zero__divisors)). 1.08/1.43 fof(arity_Int__Oint__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Omonoid__mult)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Omonoid__mult)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Omonoid__mult)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Omonoid__mult)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add, axiom, class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__semigroup__add)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, axiom, class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__ab__semigroup__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, axiom, class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add)). 1.08/1.43 fof(arity_Int__Oint__Rings_Olinordered__ring, axiom, class_Rings_Olinordered__ring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__ring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Olinordered__ring, axiom, class_Rings_Olinordered__ring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__ring)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oab__group__add, axiom, class_Groups_Oab__group__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oab__group__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oab__group__add, axiom, class_Groups_Oab__group__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oab__group__add)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Oab__group__add, axiom, class_Groups_Oab__group__add(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Oab__group__add)). 1.08/1.43 fof(arity_HOL__Obool__Orderings_Oord, axiom, class_Orderings_Oord(tc_HOL_Obool), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Oord)). 1.08/1.43 fof(arity_Int__Oint__Orderings_Oord, axiom, class_Orderings_Oord(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Oord)). 1.08/1.43 fof(arity_Nat__Onat__Orderings_Oord, axiom, class_Orderings_Oord(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Oord)). 1.08/1.43 fof(arity_RealDef__Oreal__Orderings_Oord, axiom, class_Orderings_Oord(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Orderings_Oord)). 1.08/1.43 fof(arity_HOL__Obool__Groups_Ominus, axiom, class_Groups_Ominus(tc_HOL_Obool), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_HOL__Obool__Groups_Ominus)). 1.08/1.43 fof(arity_Int__Oint__Groups_Ominus, axiom, class_Groups_Ominus(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ominus)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Ominus, axiom, class_Groups_Ominus(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ominus)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Ominus, axiom, class_Groups_Ominus(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Ominus)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Ominus, axiom, class_Groups_Ominus(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Ominus)). 1.08/1.43 fof(arity_Int__Oint__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocomm__monoid__add)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocomm__monoid__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Ocomm__monoid__add)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Ocomm__monoid__add)). 1.08/1.43 fof(arity_Int__Oint__Divides_Osemiring__div, axiom, class_Divides_Osemiring__div(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Divides_Osemiring__div)). 1.08/1.43 fof(arity_Nat__Onat__Divides_Osemiring__div, axiom, class_Divides_Osemiring__div(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Divides_Osemiring__div)). 1.08/1.43 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add, axiom, class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocancel__comm__monoid__add)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add, axiom, class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocancel__comm__monoid__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, axiom, class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, axiom, class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oring, axiom, class_Rings_Oring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oring, axiom, class_Rings_Oring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oring)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Oring, axiom, class_Rings_Oring(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Oring)). 1.08/1.43 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add, axiom, class_Groups_Olinordered__ab__group__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Olinordered__ab__group__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, axiom, class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Olinordered__ab__group__add)). 1.08/1.43 fof(arity_HOL__Obool__Groups_Ouminus, axiom, class_Groups_Ouminus(tc_HOL_Obool), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_HOL__Obool__Groups_Ouminus)). 1.08/1.43 fof(arity_Int__Oint__Groups_Ouminus, axiom, class_Groups_Ouminus(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ouminus)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Ouminus, axiom, class_Groups_Ouminus(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Ouminus)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Ouminus, axiom, class_Groups_Ouminus(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Ouminus)). 1.08/1.43 fof(arity_Int__Oint__Power_Opower, axiom, class_Power_Opower(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Power_Opower)). 1.08/1.43 fof(arity_Nat__Onat__Power_Opower, axiom, class_Power_Opower(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Power_Opower)). 1.08/1.43 fof(arity_RealDef__Oreal__Power_Opower, axiom, class_Power_Opower(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Power_Opower)). 1.08/1.43 fof(arity_Complex__Ocomplex__Power_Opower, axiom, class_Power_Opower(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Power_Opower)). 1.08/1.43 fof(arity_Int__Oint__Rings_Olinordered__idom, axiom, class_Rings_Olinordered__idom(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__idom)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Olinordered__idom, axiom, class_Rings_Olinordered__idom(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__idom)). 1.08/1.43 fof(arity_Int__Oint__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Osemiring__0)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Osemiring__0)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Osemiring__0)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Osemiring__0)). 1.08/1.43 fof(arity_Int__Oint__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Olinorder)). 1.08/1.43 fof(arity_Nat__Onat__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Olinorder)). 1.08/1.43 fof(arity_RealDef__Oreal__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Orderings_Olinorder)). 1.08/1.43 fof(arity_HOL__Obool__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_HOL_Obool), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Opreorder)). 1.08/1.43 fof(arity_Int__Oint__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Opreorder)). 1.08/1.43 fof(arity_Nat__Onat__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Opreorder)). 1.08/1.43 fof(arity_RealDef__Oreal__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Orderings_Opreorder)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs, axiom, class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__group__add__abs)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs, axiom, class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs)). 1.08/1.43 fof(arity_Int__Oint__Rings_Ocomm__ring__1, axiom, class_Rings_Ocomm__ring__1(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__ring__1)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1, axiom, class_Rings_Ocomm__ring__1(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Ocomm__ring__1)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1, axiom, class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Ocomm__ring__1)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors, axiom, class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring__1__no__zero__divisors)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, axiom, class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors, axiom, class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add, axiom, class_Groups_Oordered__comm__monoid__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__comm__monoid__add)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add, axiom, class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__comm__monoid__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, axiom, class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add)). 1.08/1.43 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict, axiom, class_Rings_Olinordered__semiring__strict(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring__strict)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict, axiom, class_Rings_Olinordered__semiring__strict(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__semiring__strict)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict, axiom, class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__semiring__strict)). 1.08/1.43 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__RealVector_Oreal__normed__vector)). 1.08/1.43 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__RealVector_Oreal__normed__vector)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oab__semigroup__add)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oab__semigroup__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oab__semigroup__add)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Oab__semigroup__add)). 1.08/1.43 fof(arity_Int__Oint__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__semiring__1)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ocomm__semiring__1)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Ocomm__semiring__1)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Ocomm__semiring__1)). 1.08/1.43 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra, axiom, class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__RealVector_Oreal__normed__algebra)). 1.08/1.43 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, axiom, class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra)). 1.08/1.43 fof(arity_Int__Oint__Groups_Ogroup__add, axiom, class_Groups_Ogroup__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ogroup__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Ogroup__add, axiom, class_Groups_Ogroup__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Ogroup__add)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Ogroup__add, axiom, class_Groups_Ogroup__add(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Ogroup__add)). 1.08/1.43 fof(arity_Int__Oint__Rings_Ocomm__semiring__0, axiom, class_Rings_Ocomm__semiring__0(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__semiring__0)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0, axiom, class_Rings_Ocomm__semiring__0(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ocomm__semiring__0)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0, axiom, class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Ocomm__semiring__0)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, axiom, class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Ocomm__semiring__0)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oordered__ab__group__add, axiom, class_Groups_Oordered__ab__group__add(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__group__add)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add, axiom, class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oordered__ab__group__add)). 1.08/1.43 fof(arity_Int__Oint__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semidom)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__semidom)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__semidom)). 1.08/1.43 fof(arity_HOL__Obool__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_HOL_Obool), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Oorder)). 1.08/1.43 fof(arity_Int__Oint__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Oorder)). 1.08/1.43 fof(arity_Nat__Onat__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Oorder)). 1.08/1.43 fof(arity_RealDef__Oreal__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Orderings_Oorder)). 1.08/1.43 fof(arity_Int__Oint__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oab__semigroup__mult)). 1.08/1.43 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oab__semigroup__mult)). 1.08/1.43 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Groups_Oab__semigroup__mult)). 1.08/1.43 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Groups_Oab__semigroup__mult)). 1.08/1.43 fof(arity_Int__Oint__Rings_Oidom, axiom, class_Rings_Oidom(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oidom)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Oidom, axiom, class_Rings_Oidom(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oidom)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Oidom, axiom, class_Rings_Oidom(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Oidom)). 1.08/1.43 fof(arity_Int__Oint__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Omult__zero)). 1.08/1.43 fof(arity_Nat__Onat__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_Nat_Onat), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Omult__zero)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Omult__zero)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Omult__zero)). 1.08/1.43 fof(arity_Int__Oint__Rings_Ocomm__ring, axiom, class_Rings_Ocomm__ring(tc_Int_Oint), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__ring)). 1.08/1.43 fof(arity_RealDef__Oreal__Rings_Ocomm__ring, axiom, class_Rings_Ocomm__ring(tc_RealDef_Oreal), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Ocomm__ring)). 1.08/1.43 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring, axiom, class_Rings_Ocomm__ring(tc_Complex_Ocomplex), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_Complex__Ocomplex__Rings_Ocomm__ring)). 1.08/1.43 fof(c_0_1265, plain, ![X2077, X2078, X2079]:(~class_Rings_Ocomm__ring__1(X2079)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2079),c_Groups_Ominus__class_Ominus(X2079,X2078,X2077)),c_Groups_Oplus__class_Oplus(X2079,X2078,X2077))=c_Groups_Ominus__class_Ominus(X2079,hAPP(hAPP(c_Power_Opower__class_Opower(X2079),X2078),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2079),X2077),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_realpow__two__diff])])])). 1.08/1.43 fof(c_0_1266, plain, ![X2810]:c_Nat_OSuc(X2810)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2810,c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1])). 1.08/1.43 fof(c_0_1267, plain, ![X2693, X2694, X2695]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2695)),X2694),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2695)),X2693))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2694,X2693))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2694,X2693)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2695)),X2694),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2695)),X2693)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])])). 1.08/1.43 fof(c_0_1268, plain, ![X297, X298, X299]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X299)),X298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X299)),X297))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X298,X297))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X298,X297)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X299)),X298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X299)),X297)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])])). 1.08/1.43 fof(c_0_1269, plain, ![X150, X151]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X150,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk1_2(X150,X151)))),X151))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X150)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X151))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk1_2(X150,X151))),X151),X150)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X150)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X151))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reals__Archimedean4])])])])])). 1.08/1.43 fof(c_0_1270, plain, ![X1999, X2000, X2001, X2004, X2005, X2008]:(((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2000,hAPP(X1999,X2004)),esk58_2(X1999,X2000))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2000,hAPP(X1999,esk57_3(X1999,X2000,X2001))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X2001)))|~class_RealVector_Oreal__normed__vector(X2000))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk58_2(X1999,X2000))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2000,hAPP(X1999,esk57_3(X1999,X2000,X2001))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X2001)))|~class_RealVector_Oreal__normed__vector(X2000)))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2000,hAPP(X1999,esk59_3(X1999,X2000,X2005))),X2005)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2005)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2000,hAPP(X1999,X2008)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk60_2(X1999,X2000))))|~class_RealVector_Oreal__normed__vector(X2000))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def2])])])])])). 1.08/1.43 fof(c_0_1271, plain, ![X957, X958, X959, X962, X963, X966]:(((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X958,hAPP(X957,X962)),esk28_2(X957,X958))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X958,hAPP(X957,esk27_3(X957,X958,X959))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X959)))|~class_RealVector_Oreal__normed__vector(X958))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk28_2(X957,X958))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X958,hAPP(X957,esk27_3(X957,X958,X959))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X959)))|~class_RealVector_Oreal__normed__vector(X958)))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X958,hAPP(X957,esk29_3(X957,X958,X963))),X963)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X963)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X958,hAPP(X957,X966)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk30_2(X957,X958))))|~class_RealVector_Oreal__normed__vector(X958))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lemma__NBseq__def])])])])])])). 1.08/1.43 fof(c_0_1272, negated_conjecture, ~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))), inference(assume_negation,[status(cth)],[conj_0])). 1.08/1.43 fof(c_0_1273, plain, ![X2672, X2673, X2674, X2677]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2673,hAPP(X2672,esk71_3(X2672,X2673,X2674))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X2674)))|c_SEQ_OBseq(X2673,X2672)|~class_RealVector_Oreal__normed__vector(X2673))&(~c_SEQ_OBseq(X2673,X2672)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2673,hAPP(X2672,X2677)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk72_2(X2672,X2673))))|~class_RealVector_Oreal__normed__vector(X2673))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Bseq__iff1a])])])])])])). 1.08/1.43 fof(c_0_1274, plain, ![X1146, X1147, X1149, X1150]:((~c_SEQ_OBseq(X1147,X1146)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1147,hAPP(X1146,X1149)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk34_2(X1146,X1147))))|~class_RealVector_Oreal__normed__vector(X1147))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1147,hAPP(X1146,esk35_3(X1146,X1147,X1150))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1150)))|c_SEQ_OBseq(X1147,X1146)|~class_RealVector_Oreal__normed__vector(X1147))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Bseq__iff])])])])])])). 1.08/1.43 fof(c_0_1275, plain, ![X2449, X2450, X2451]:(((X2450!=X2449|hAPP(hAPP(c_Power_Opower__class_Opower(X2451),X2450),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X2451),X2449),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~class_Rings_Oidom(X2451))&(c_Groups_Ouminus__class_Ouminus(X2451,X2449)!=X2450|hAPP(hAPP(c_Power_Opower__class_Opower(X2451),X2450),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X2451),X2449),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~class_Rings_Oidom(X2451)))&(hAPP(hAPP(c_Power_Opower__class_Opower(X2451),X2450),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(X2451),X2449),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|(X2450=X2449|c_Groups_Ouminus__class_Ouminus(X2451,X2449)=X2450)|~class_Rings_Oidom(X2451))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__two__disj])])])). 1.08/1.43 fof(c_0_1276, plain, ![X552, X553, X554, X555]:(~class_Rings_Olinordered__semidom(X555)|(~c_Orderings_Oord__class_Oless__eq(X555,hAPP(hAPP(c_Power_Opower__class_Opower(X555),X554),c_Nat_OSuc(X553)),hAPP(hAPP(c_Power_Opower__class_Opower(X555),X552),c_Nat_OSuc(X553)))|(~c_Orderings_Oord__class_Oless__eq(X555,c_Groups_Ozero__class_Ozero(X555),X552)|c_Orderings_Oord__class_Oless__eq(X555,X554,X552)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__le__imp__le__base])])])). 1.08/1.43 fof(c_0_1277, plain, ![X718, X719, X720, X721]:(~class_Groups_Omonoid__mult(X721)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X720,X719)|hAPP(hAPP(c_Power_Opower__class_Opower(X721),X718),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X719),X720))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X721),hAPP(hAPP(c_Power_Opower__class_Opower(X721),X718),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X719,X720))),X718))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lemma__realpow__diff])])])). 1.08/1.43 fof(c_0_1278, plain, ![X1624, X1625, X1626, X1627, X1628]:hAPP(hAPP(c_Power_Opower_Opower(X1628,X1627,X1626),X1625),c_Nat_OSuc(X1624))=hAPP(hAPP(X1626,X1625),hAPP(hAPP(c_Power_Opower_Opower(X1628,X1627,X1626),X1625),X1624)), inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc])). 1.08/1.43 fof(c_0_1279, plain, ![X2492, X2493, X2494]:((X2492!=X2493|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2494)),X2492)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2494)),X2493))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2494)),X2492)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2494)),X2493)|X2492=X2493)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])])). 1.08/1.43 fof(c_0_1280, plain, ![X664, X665]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X665)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X664)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X664),X665)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__less__mult])])])). 1.08/1.43 fof(c_0_1281, plain, ![X2857, X2858]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2857)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2858)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2858),X2857)))&((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2857)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2858),X2857)))&(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2858)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2858),X2857))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])])). 1.08/1.43 fof(c_0_1282, plain, ![X1005, X1006, X1007]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1007,X1006)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1006,X1007)),X1005)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1006),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1007,X1005))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__Suc__diff__eq2])])])). 1.08/1.43 fof(c_0_1283, plain, ![X812, X813, X814]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X814,X813)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X812,X814),c_Nat_OSuc(X813))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X812,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X813,X814)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__Suc__diff__eq1])])])). 1.08/1.43 fof(c_0_1284, plain, ![X1379, X1380, X1381, X1382]:(~class_Rings_Olinordered__semidom(X1382)|(hAPP(hAPP(c_Power_Opower__class_Opower(X1382),X1379),c_Nat_OSuc(X1380))!=hAPP(hAPP(c_Power_Opower__class_Opower(X1382),X1381),c_Nat_OSuc(X1380))|(~c_Orderings_Oord__class_Oless__eq(X1382,c_Groups_Ozero__class_Ozero(X1382),X1381)|(~c_Orderings_Oord__class_Oless__eq(X1382,c_Groups_Ozero__class_Ozero(X1382),X1379)|X1379=X1381)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__inject__base])])])). 1.08/1.43 fof(c_0_1285, plain, ![X1760, X1761]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1761)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1760)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1760),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1761,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1760),X1761),X1760))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__power__div__base])])])). 1.08/1.43 fof(c_0_1286, plain, ![X2190]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2190,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2190|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2190)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__lt__two__imp__zero__or__one])])). 1.08/1.43 fof(c_0_1287, plain, ![X1123, X1124]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1124)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1123)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1124,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1124),X1123)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])])). 1.08/1.43 fof(c_0_1288, plain, ![X975, X976]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X976)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X975)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X976,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X975),X976)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_n__less__m__mult__n])])])). 1.08/1.43 fof(c_0_1289, plain, ![X1012, X1013, X1014]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1014,X1013),X1012)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1014),X1013),c_Nat_OSuc(X1012)), inference(variable_rename,[status(thm)],[fact_Suc__diff__diff])). 1.08/1.43 fof(c_0_1290, plain, ![X574, X575, X576]:(~class_Rings_Olinordered__semidom(X576)|(~c_Orderings_Oord__class_Oless(X576,c_Groups_Ozero__class_Ozero(X576),X575)|(~c_Orderings_Oord__class_Oless(X576,X575,c_Groups_Oone__class_Oone(X576))|c_Orderings_Oord__class_Oless(X576,hAPP(hAPP(c_Power_Opower__class_Opower(X576),X575),c_Nat_OSuc(X574)),c_Groups_Oone__class_Oone(X576))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc__less__one])])])). 1.08/1.43 fof(c_0_1291, plain, ![X1064, X1065, X1066]:(~class_Rings_Olinordered__semidom(X1066)|(~c_Orderings_Oord__class_Oless__eq(X1066,c_Groups_Ozero__class_Ozero(X1066),X1065)|(~c_Orderings_Oord__class_Oless__eq(X1066,X1065,c_Groups_Oone__class_Oone(X1066))|c_Orderings_Oord__class_Oless__eq(X1066,hAPP(hAPP(c_Power_Opower__class_Opower(X1066),X1065),c_Nat_OSuc(X1064)),X1065)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self])])). 1.08/1.43 fof(c_0_1292, plain, ![X1348, X1349]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1349)|(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1348,X1349)|c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1348,X1349),X1349))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1348,X1349))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__geq])])])). 1.08/1.43 fof(c_0_1293, plain, ![X1305, X1306]:((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1305,X1306)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1305,X1306)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1305,X1306),X1306))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1306))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1305,X1306)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1305,X1306)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1306))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__if])])])])). 1.08/1.43 fof(c_0_1294, plain, ![X2488, X2489]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2489)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2489),X2488))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])])). 1.08/1.43 fof(c_0_1295, plain, ![X294, X295, X296]:(~class_Rings_Olinordered__semidom(X296)|(~c_Orderings_Oord__class_Oless(X296,c_Groups_Oone__class_Oone(X296),X295)|c_Orderings_Oord__class_Oless(X296,c_Groups_Oone__class_Oone(X296),hAPP(hAPP(c_Power_Opower__class_Opower(X296),X295),c_Nat_OSuc(X294))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__gt1])])])). 1.08/1.43 fof(c_0_1296, plain, ![X2772, X2773]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2773),c_Nat_OSuc(X2772))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2773,X2772)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__less__SucD])])])). 1.08/1.43 fof(c_0_1297, plain, ![X227, X228]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X228),c_Nat_OSuc(X227))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X228,X227))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X228,X227)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X228),c_Nat_OSuc(X227)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])])). 1.08/1.43 fof(c_0_1298, plain, ![X993, X994]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X994,X993)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X994),c_Nat_OSuc(X993)))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X994),c_Nat_OSuc(X993))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X994,X993))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])])). 1.08/1.43 fof(c_0_1299, plain, ![X2467]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2467)|X2467=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2467,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__pred])])])). 1.08/1.43 fof(c_0_1300, plain, ![X129, X130]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X130)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X130,c_Nat_OSuc(X129)),X130)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])])). 1.08/1.43 fof(c_0_1301, plain, ![X448, X449]:((X449=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X449,X448)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X449,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X448)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X449|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X449,X448)=X448)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__eq__if])])])). 1.08/1.43 fof(c_0_1302, plain, ![X1524, X1525, X1526]:(~class_Groups_Omonoid__mult(X1526)|hAPP(hAPP(c_Power_Opower__class_Opower(X1526),X1525),c_Nat_OSuc(X1524))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1526),hAPP(hAPP(c_Power_Opower__class_Opower(X1526),X1525),X1524)),X1525)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc2])])])). 1.08/1.43 fof(c_0_1303, plain, ![X2231, X2232, X2233]:(~class_Rings_Ocomm__semiring__1(X2233)|hAPP(hAPP(c_Power_Opower__class_Opower(X2233),X2232),c_Nat_OSuc(X2231))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2233),hAPP(hAPP(c_Power_Opower__class_Opower(X2233),X2232),X2231)),X2232)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])])). 1.08/1.43 fof(c_0_1304, plain, ![X1287]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1287,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk36_1(X1287))))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1287))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,esk36_1(X1287)),X1287)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1287))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reals__Archimedean6a])])])])])). 1.08/1.43 fof(c_0_1305, plain, ![X2565, X2566]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2566)),X2565)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2565,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2566),X2565)), inference(variable_rename,[status(thm)],[fact_mult__Suc])). 1.08/1.43 fof(c_0_1306, plain, ![X2396, X2397]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2397,X2396)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2396),X2397)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2396,X2397))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])])). 1.08/1.43 fof(c_0_1307, plain, ![X2368, X2369]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2369,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2369,X2368))), inference(variable_rename,[status(thm)],[fact_less__add__Suc1])). 1.08/1.43 fof(c_0_1308, plain, ![X2767, X2768]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2768,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2767,X2768))), inference(variable_rename,[status(thm)],[fact_less__add__Suc2])). 1.08/1.43 fof(c_0_1309, plain, ![X2749, X2750]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2750,c_Nat_OSuc(X2749))|(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2750,X2749)|c_Nat_OSuc(X2749)=X2750))&((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2750,X2749)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2750,c_Nat_OSuc(X2749)))&(c_Nat_OSuc(X2749)!=X2750|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2750,c_Nat_OSuc(X2749))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])])). 1.08/1.43 fof(c_0_1310, plain, ![X1894, X1895]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1895,c_Nat_OSuc(X1894))|(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1895,X1894)|X1895=c_Nat_OSuc(X1894))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__SucE])])])). 1.08/1.43 fof(c_0_1311, plain, ![X479, X480]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X480,X479)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X480),c_Nat_OSuc(X479))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])])). 1.08/1.43 fof(c_0_1312, plain, ![X832, X833, X835, X836, X837]:(((c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk25_2(X832,X833),X832)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X833|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X833,c_Nat_OSuc(X832)))&(X833=c_Nat_OSuc(esk25_2(X832,X833))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X833|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X833,c_Nat_OSuc(X832))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X836|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X836,c_Nat_OSuc(X835)))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X837,X835)|X836!=c_Nat_OSuc(X837)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X836,c_Nat_OSuc(X835))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj])])])])])])). 1.08/1.43 fof(c_0_1313, plain, ![X1546, X1547]:((X1546!=X1547|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1546,c_Nat_OSuc(X1547))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1547,X1546))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1546,c_Nat_OSuc(X1547))|X1546=X1547|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1547,X1546))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__less__Suc__eq])])])])). 1.08/1.43 fof(c_0_1314, plain, ![X536, X537]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X537,X536)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X536),X537))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X536),X537)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X537,X536))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq])])])). 1.08/1.43 fof(c_0_1315, plain, ![X347, X348]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X347,c_Nat_OSuc(X348))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X348,X347))&(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X348,X347)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X347,c_Nat_OSuc(X348)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__eq])])])). 1.08/1.43 fof(c_0_1316, plain, ![X102]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X102)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_power__Suc__0])). 1.08/1.43 fof(c_0_1317, plain, ![X704, X705, X706]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X706,X705)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X705,X704)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X706),X704))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__trans__Suc])])])). 1.08/1.43 fof(c_0_1318, plain, ![X209, X210]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X210,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X209)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X210,c_Nat_OSuc(X209)), inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred])). 1.08/1.43 fof(c_0_1319, plain, ![X256, X257]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X257,c_Nat_OSuc(X256))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X257),X256), inference(variable_rename,[status(thm)],[fact_add__Suc__shift])). 1.08/1.43 fof(c_0_1320, plain, ![X2879, X2880]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2880,X2879)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2880),c_Nat_OSuc(X2879)), inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc])). 1.08/1.43 fof(c_0_1321, plain, ![X2764, X2765, X2766]:(~class_Rings_Ocomm__semiring__1(X2766)|hAPP(hAPP(c_Power_Opower__class_Opower(X2766),X2765),c_Nat_OSuc(X2764))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2766),X2765),hAPP(hAPP(c_Power_Opower__class_Opower(X2766),X2765),X2764))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])])])). 1.08/1.43 fof(c_0_1322, plain, ![X2346, X2347, X2348]:(~class_Rings_Ocomm__semiring__1(X2348)|hAPP(hAPP(c_Power_Opower__class_Opower(X2348),X2347),c_Nat_OSuc(X2346))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2348),X2347),hAPP(hAPP(c_Power_Opower__class_Opower(X2348),X2347),X2346))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])])). 1.08/1.43 fof(c_0_1323, plain, ![X280, X281, X282]:(~class_Power_Opower(X282)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X282),X281),hAPP(hAPP(c_Power_Opower__class_Opower(X282),X281),X280))=hAPP(hAPP(c_Power_Opower__class_Opower(X282),X281),c_Nat_OSuc(X280))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])])). 1.08/1.43 fof(c_0_1324, plain, ![X338, X339]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X339),X338)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X339,X338)), inference(variable_rename,[status(thm)],[fact_add__Suc])). 1.08/1.43 fof(c_0_1325, plain, ![X998, X999]:c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X999,X998))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X999,c_Nat_OSuc(X998)), inference(variable_rename,[status(thm)],[fact_add__Suc__right])). 1.08/1.43 fof(c_0_1326, plain, ![X2715, X2716]:(((X2715!=X2716|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2716,c_Nat_OSuc(X2715)))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2716,X2715)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2716,c_Nat_OSuc(X2715))))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2716,c_Nat_OSuc(X2715))|(X2715=X2716|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2716,X2715)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])])). 1.08/1.43 fof(c_0_1327, plain, ![X2087, X2088]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2088,c_Nat_OSuc(X2087))|(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2088,X2087)|X2087=X2088)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__SucE])])])). 1.08/1.43 fof(c_0_1328, plain, ![X1929, X1930]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1930,c_Nat_OSuc(X1929))|X1929=X1930|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1930,X1929))&(X1929!=X1930|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1930,c_Nat_OSuc(X1929))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1930,X1929))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq])])])])). 1.08/1.43 fof(c_0_1329, plain, ![X1812, X1813]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1813,X1812)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1813,c_Nat_OSuc(X1812))|X1812=X1813)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__antisym])])])). 1.08/1.43 fof(c_0_1330, plain, ![X1898, X1899]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1899),X1898)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1899,X1898)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])])). 1.08/1.43 fof(c_0_1331, plain, ![X2898, X2899]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2899),X2898)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2899,X2898)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__le__lessD])])])). 1.08/1.43 fof(c_0_1332, plain, ![X1215, X1216]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1216,X1215)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1216),X1215))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1216),X1215)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1216,X1215))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])])). 1.08/1.43 fof(c_0_1333, plain, ![X1042, X1043]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1043,X1042)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1043),X1042))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1043),X1042)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1043,X1042))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])])). 1.08/1.43 fof(c_0_1334, plain, ![X2434, X2435]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2435),X2434)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2435,X2434)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])])). 1.08/1.43 fof(c_0_1335, plain, ![X2169, X2170]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2170,c_Nat_OSuc(X2169))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2170,X2169))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2170,X2169)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2170,c_Nat_OSuc(X2169)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])])). 1.08/1.43 fof(c_0_1336, plain, ![X495, X496, X497, X498, X499]:((c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X496,X497))!=X495|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X496,X495))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X499,X498)|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X499,esk16_2(X498,X499)))=X498)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add])])])])])). 1.08/1.43 fof(c_0_1337, plain, ![X917, X918]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X918,X917)|(c_Nat_OSuc(X918)=X917|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X918),X917))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])])). 1.08/1.43 fof(c_0_1338, plain, ![X1437, X1438]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1438,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1438),X1437))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1438),c_Nat_OSuc(X1437)), inference(variable_rename,[status(thm)],[fact_mult__Suc__right])). 1.08/1.43 fof(c_0_1339, plain, ![X680]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X680))), inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc__gt__zero])). 1.08/1.43 fof(c_0_1340, plain, ![X2068, X2069]:((((X2069=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2068=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2069,X2068))&(X2068=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X2068=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2069,X2068)))&((X2069=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2069|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2069,X2068))&(X2068=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2069|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2069,X2068))))&((X2068!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X2069|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2069,X2068))&(X2069!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2068!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2069,X2068)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])])). 1.08/1.43 fof(c_0_1341, plain, ![X1405, X1406]:((((X1406=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1406|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1406,X1405)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X1405=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1406|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1406,X1405)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&((X1406=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1405|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1406,X1405)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X1405=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1405|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1406,X1405)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1406|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X1405|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1406,X1405)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X1406!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1405!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1406,X1405)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])])). 1.08/1.43 fof(c_0_1342, plain, ![X194, X195]:((c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X194|X195!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X195),X194)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&((c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X194|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X195),X194)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X195=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X195),X194)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff])])])). 1.08/1.43 fof(c_0_1343, plain, ![X132]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X132|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X132,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X132,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X132)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])])). 1.08/1.43 fof(c_0_1344, plain, ![X970, X971]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X971,X970),c_Nat_OSuc(X971)), inference(variable_rename,[status(thm)],[fact_diff__less__Suc])). 1.08/1.43 fof(c_0_1345, plain, ![X1787]:~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1787),X1787), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n])])). 1.08/1.43 fof(c_0_1346, plain, ![X2387]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2387)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2387,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X2387), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__pred_H])])])). 1.08/1.43 fof(c_0_1347, plain, ![X1645]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1645)|X1645=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1645,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__diff__1])])])). 1.08/1.43 fof(c_0_1348, plain, ![X1430, X1431]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1431,X1430)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1431),X1430)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])])). 1.08/1.43 fof(c_0_1349, plain, ![X1417, X1418]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1418,X1417)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1418,c_Nat_OSuc(X1417))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__SucI])])])). 1.08/1.43 fof(c_0_1350, plain, ![X578, X579]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X579,X578)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X579,c_Nat_OSuc(X578))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__imp__less__Suc])])])). 1.08/1.43 fof(c_0_1351, plain, ![X1037, X1038]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1038,X1037)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1038,c_Nat_OSuc(X1037))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])])). 1.08/1.43 fof(c_0_1352, plain, ![X2224, X2225]:((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2225),X2224)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2224|X2225=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2224|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2225),X2224)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X2225!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2225),X2224)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff])])])). 1.08/1.43 fof(c_0_1353, plain, ![X845]:c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X845))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X845),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc])). 1.08/1.43 fof(c_0_1354, plain, ![X2825, X2826]:(~class_Rings_Osemiring__0(X2826)|~class_Power_Opower(X2826)|hAPP(hAPP(c_Power_Opower__class_Opower(X2826),c_Groups_Ozero__class_Ozero(X2826)),c_Nat_OSuc(X2825))=c_Groups_Ozero__class_Ozero(X2826)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])])). 1.08/1.43 fof(c_0_1355, plain, ![X1633, X1634]:(c_Nat_OSuc(X1634)!=c_Nat_OSuc(X1633)|X1633=X1634), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])])). 1.08/1.43 fof(c_0_1356, plain, ![X1067, X1068]:((c_Nat_OSuc(X1067)!=c_Nat_OSuc(X1068)|X1068=X1067)&(X1068!=X1067|c_Nat_OSuc(X1067)=c_Nat_OSuc(X1068))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])])). 1.08/1.43 fof(c_0_1357, plain, ![X2861]:X2861=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2861,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_div__1])). 1.08/1.43 fof(c_0_1358, plain, ![X1756]:X1756=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1756),c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_diff__Suc__1])). 1.08/1.43 fof(c_0_1359, plain, ![X208]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X208)), inference(variable_rename,[status(thm)],[fact_zero__less__Suc])). 1.08/1.43 fof(c_0_1360, plain, ![X125]:c_Orderings_Oord__class_Oless(tc_Nat_Onat,X125,c_Nat_OSuc(X125)), inference(variable_rename,[status(thm)],[fact_lessI])). 1.08/1.43 fof(c_0_1361, plain, ![X898, X899, X900]:((c_Nat_OSuc(X899)!=X898|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X898))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X900)|c_Nat_OSuc(esk26_1(X900))=X900)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])])). 1.08/1.43 fof(c_0_1362, plain, ![X2189]:c_Nat_OSuc(X2189)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2189), inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left])). 1.08/1.43 fof(c_0_1363, plain, ![X1698]:c_Nat_OSuc(X1698)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J])). 1.08/1.43 fof(c_0_1364, plain, ![X2533]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X2533), inference(variable_rename,[status(thm)],[fact_Suc__not__Zero])). 1.08/1.43 fof(c_0_1365, plain, ![X2294]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X2294), inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero])). 1.08/1.43 fof(c_0_1366, plain, ![X1363]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X1363), inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J])). 1.08/1.43 fof(c_0_1367, plain, ![X1234]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X1234), inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc])). 1.08/1.43 fof(c_0_1368, plain, ![X263]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X263), inference(variable_rename,[status(thm)],[fact_Zero__not__Suc])). 1.08/1.43 fof(c_0_1369, plain, ![X2253]:X2253!=c_Nat_OSuc(X2253), inference(variable_rename,[status(thm)],[fact_n__not__Suc__n])). 1.08/1.43 fof(c_0_1370, plain, ![X2179]:X2179!=c_Nat_OSuc(X2179), inference(variable_rename,[status(thm)],[fact_Suc__n__not__n])). 1.08/1.43 fof(c_0_1371, plain, ![X2525, X2526, X2527, X2528, X2530]:((c_Orderings_Oord__class_Oless__eq(X2527,X2526,esk70_4(X2525,X2526,X2527,X2528))|(~c_Orderings_Oord__class_Oless__eq(X2527,X2526,X2530)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2528,hAPP(X2525,X2530)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2528,hAPP(X2525,X2526)))))|(~class_Orderings_Oord(X2527)|~class_RealVector_Oreal__normed__vector(X2528)))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2528,c_Groups_Ominus__class_Ominus(X2528,hAPP(X2525,X2526),hAPP(X2525,esk70_4(X2525,X2526,X2527,X2528)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|(~c_Orderings_Oord__class_Oless__eq(X2527,X2526,X2530)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2528,hAPP(X2525,X2530)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2528,hAPP(X2525,X2526)))))|(~class_Orderings_Oord(X2527)|~class_RealVector_Oreal__normed__vector(X2528)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lemmaCauchy])])])])])])). 1.08/1.43 fof(c_0_1372, plain, ![X402, X403, X406, X407, X408]:(((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X403,c_Groups_Oplus__class_Oplus(X403,hAPP(X402,X406),c_Groups_Ouminus__class_Ouminus(X403,hAPP(X402,esk11_2(X402,X403))))),esk10_2(X402,X403))|~c_SEQ_OBseq(X403,X402)|~class_RealVector_Oreal__normed__vector(X403))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk10_2(X402,X403))|~c_SEQ_OBseq(X403,X402)|~class_RealVector_Oreal__normed__vector(X403)))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X403,c_Groups_Oplus__class_Oplus(X403,hAPP(X402,esk12_4(X402,X403,X407,X408)),c_Groups_Ouminus__class_Ouminus(X403,hAPP(X402,X408)))),X407)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X407)|c_SEQ_OBseq(X403,X402)|~class_RealVector_Oreal__normed__vector(X403))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Bseq__iff3])])])])])])). 1.08/1.43 fof(c_0_1373, plain, ![X157, X158, X159, X160, X164]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X158,c_Groups_Oplus__class_Oplus(X158,hAPP(X157,esk2_4(X157,X158,X159,X160)),c_Groups_Ouminus__class_Ouminus(X158,X160))),X159)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X159)|c_SEQ_OBseq(X158,X157)|~class_RealVector_Oreal__normed__vector(X158))&((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X158,c_Groups_Oplus__class_Oplus(X158,hAPP(X157,X164),c_Groups_Ouminus__class_Ouminus(X158,esk4_2(X157,X158)))),esk3_2(X157,X158))|~c_SEQ_OBseq(X158,X157)|~class_RealVector_Oreal__normed__vector(X158))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_2(X157,X158))|~c_SEQ_OBseq(X158,X157)|~class_RealVector_Oreal__normed__vector(X158)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Bseq__iff2])])])])])])). 1.08/1.43 fof(c_0_1374, plain, ![X1338, X1339, X1340]:(((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk39_3(X1338,X1339,X1340),X1340)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1338,hAPP(X1339,X1340))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X1339,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1338)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk38_3(X1338,X1339,X1340),X1340))&(X1338=hAPP(X1339,esk39_3(X1338,X1339,X1340))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1338,hAPP(X1339,X1340))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X1339,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1338)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk38_3(X1338,X1339,X1340),X1340)))&((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk39_3(X1338,X1339,X1340),X1340)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1338,hAPP(X1339,X1340))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X1339,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1338)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X1339,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk38_3(X1338,X1339,X1340),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X1339,esk38_3(X1338,X1339,X1340)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))&(X1338=hAPP(X1339,esk39_3(X1338,X1339,X1340))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1338,hAPP(X1339,X1340))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X1339,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1338)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X1339,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk38_3(X1338,X1339,X1340),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X1339,esk38_3(X1338,X1339,X1340)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__val__lemma])])])])])). 1.08/1.43 fof(c_0_1375, plain, ![X186, X187, X188]:(((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk6_3(X186,X187,X188),X188)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X186,hAPP(X187,X188))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X187,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X186)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk5_3(X186,X187,X188),X188))&(X186=hAPP(X187,esk6_3(X186,X187,X188))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X186,hAPP(X187,X188))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X187,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X186)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk5_3(X186,X187,X188),X188)))&((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk6_3(X186,X187,X188),X188)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X186,hAPP(X187,X188))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X187,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X186)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X187,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_3(X186,X187,X188),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X187,esk5_3(X186,X187,X188)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))&(X186=hAPP(X187,esk6_3(X186,X187,X188))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X186,hAPP(X187,X188))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X187,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X186)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X187,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_3(X186,X187,X188),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X187,esk5_3(X186,X187,X188)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat0__intermed__int__val])])])])])). 1.08/1.43 fof(c_0_1376, plain, ![X967, X968, X969]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X969)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X968,X967)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X969)),X967)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_decr__lemma])])])). 1.08/1.43 fof(c_0_1377, plain, ![X2084, X2085, X2086]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2086)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2085,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2084,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2084,X2085)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2086)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_incr__lemma])])])). 1.08/1.43 fof(c_0_1378, plain, ![X1983, X1984, X1985, X1986, X1987]:((~c_Orderings_Oord__class_Oless__eq(tc_fun(X1985,X1986),X1984,X1983)|c_Orderings_Oord__class_Oless__eq(X1986,hAPP(X1984,X1987),hAPP(X1983,X1987))|~class_Orderings_Oord(X1986))&(~c_Orderings_Oord__class_Oless__eq(X1986,hAPP(X1984,esk56_4(X1983,X1984,X1985,X1986)),hAPP(X1983,esk56_4(X1983,X1984,X1985,X1986)))|c_Orderings_Oord__class_Oless__eq(tc_fun(X1985,X1986),X1984,X1983)|~class_Orderings_Oord(X1986))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__fun__def])])])])])). 1.08/1.43 fof(c_0_1379, plain, ![X1820, X1821, X1822, X1823]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1822,esk54_4(X1820,X1821,X1822,X1823))|c_SEQ_OBseq(X1823,X1821)|~class_RealVector_Oreal__normed__vector(X1823))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1823,hAPP(X1821,esk54_4(X1820,X1821,X1822,X1823))),X1820)|c_SEQ_OBseq(X1823,X1821)|~class_RealVector_Oreal__normed__vector(X1823))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_BseqI2_H])])])])])). 1.08/1.43 fof(c_0_1380, plain, ![X840, X841, X842, X843, X844]:(~class_RealVector_Oreal__normed__algebra(X844)|c_Groups_Ominus__class_Ominus(X844,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X844),X843),X842),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X844),X841),X840))=c_Groups_Oplus__class_Oplus(X844,c_Groups_Oplus__class_Oplus(X844,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X844),c_Groups_Ominus__class_Ominus(X844,X843,X841)),c_Groups_Ominus__class_Ominus(X844,X842,X840)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X844),c_Groups_Ominus__class_Ominus(X844,X843,X841)),X840)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X844),X841),c_Groups_Ominus__class_Ominus(X844,X842,X840)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])])). 1.08/1.43 fof(c_0_1381, plain, ![X1995, X1996, X1997, X1998]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1998,X1997),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1996),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1995)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1998,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1996))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1997,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1995))))), inference(variable_rename,[status(thm)],[fact_abs__sum__triangle__ineq])). 1.08/1.43 fof(c_0_1382, plain, ![X868, X869, X870, X871, X872, X873]:((~c_Orderings_Oord__class_Oless(X873,c_Groups_Oplus__class_Oplus(X873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X873),c_Groups_Ominus__class_Ominus(X873,X872,X869)),X871),X870),X868)|c_Orderings_Oord__class_Oless(X873,c_Groups_Oplus__class_Oplus(X873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X873),X872),X871),X870),c_Groups_Oplus__class_Oplus(X873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X873),X869),X871),X868))|~class_Rings_Oordered__ring(X873))&(~c_Orderings_Oord__class_Oless(X873,c_Groups_Oplus__class_Oplus(X873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X873),X872),X871),X870),c_Groups_Oplus__class_Oplus(X873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X873),X869),X871),X868))|c_Orderings_Oord__class_Oless(X873,c_Groups_Oplus__class_Oplus(X873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X873),c_Groups_Ominus__class_Ominus(X873,X872,X869)),X871),X870),X868)|~class_Rings_Oordered__ring(X873))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])])). 1.08/1.43 fof(c_0_1383, plain, ![X525, X526, X527, X528, X529, X530]:((~c_Orderings_Oord__class_Oless__eq(X530,c_Groups_Oplus__class_Oplus(X530,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X530),X529),X528),X527),c_Groups_Oplus__class_Oplus(X530,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X530),X526),X528),X525))|c_Orderings_Oord__class_Oless__eq(X530,c_Groups_Oplus__class_Oplus(X530,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X530),c_Groups_Ominus__class_Ominus(X530,X529,X526)),X528),X527),X525)|~class_Rings_Oordered__ring(X530))&(~c_Orderings_Oord__class_Oless__eq(X530,c_Groups_Oplus__class_Oplus(X530,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X530),c_Groups_Ominus__class_Ominus(X530,X529,X526)),X528),X527),X525)|c_Orderings_Oord__class_Oless__eq(X530,c_Groups_Oplus__class_Oplus(X530,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X530),X529),X528),X527),c_Groups_Oplus__class_Oplus(X530,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X530),X526),X528),X525))|~class_Rings_Oordered__ring(X530))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])])). 1.08/1.43 fof(c_0_1384, plain, ![X1164, X1165, X1166, X1167, X1168, X1169]:((~c_Orderings_Oord__class_Oless(X1169,c_Groups_Oplus__class_Oplus(X1169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1169),X1168),X1167),X1166),c_Groups_Oplus__class_Oplus(X1169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1169),X1165),X1167),X1164))|c_Orderings_Oord__class_Oless(X1169,X1166,c_Groups_Oplus__class_Oplus(X1169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1169),c_Groups_Ominus__class_Ominus(X1169,X1165,X1168)),X1167),X1164))|~class_Rings_Oordered__ring(X1169))&(~c_Orderings_Oord__class_Oless(X1169,X1166,c_Groups_Oplus__class_Oplus(X1169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1169),c_Groups_Ominus__class_Ominus(X1169,X1165,X1168)),X1167),X1164))|c_Orderings_Oord__class_Oless(X1169,c_Groups_Oplus__class_Oplus(X1169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1169),X1168),X1167),X1166),c_Groups_Oplus__class_Oplus(X1169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1169),X1165),X1167),X1164))|~class_Rings_Oordered__ring(X1169))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])])). 1.08/1.43 fof(c_0_1385, plain, ![X1854, X1855, X1856, X1857, X1858, X1859]:((~c_Orderings_Oord__class_Oless__eq(X1859,c_Groups_Oplus__class_Oplus(X1859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1859),X1858),X1857),X1856),c_Groups_Oplus__class_Oplus(X1859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1859),X1855),X1857),X1854))|c_Orderings_Oord__class_Oless__eq(X1859,X1856,c_Groups_Oplus__class_Oplus(X1859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1859),c_Groups_Ominus__class_Ominus(X1859,X1855,X1858)),X1857),X1854))|~class_Rings_Oordered__ring(X1859))&(~c_Orderings_Oord__class_Oless__eq(X1859,X1856,c_Groups_Oplus__class_Oplus(X1859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1859),c_Groups_Ominus__class_Ominus(X1859,X1855,X1858)),X1857),X1854))|c_Orderings_Oord__class_Oless__eq(X1859,c_Groups_Oplus__class_Oplus(X1859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1859),X1858),X1857),X1856),c_Groups_Oplus__class_Oplus(X1859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1859),X1855),X1857),X1854))|~class_Rings_Oordered__ring(X1859))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])])). 1.08/1.43 fof(c_0_1386, plain, ![X2570, X2571, X2572, X2573, X2574]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2573,X2574)),X2572),X2571),X2570)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2573),X2572),X2571),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2574),X2572),X2570))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2574,X2573))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2573),X2572),X2571),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2574),X2572),X2570))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2573,X2574)),X2572),X2571),X2570)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2574,X2573))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__less__add__iff1])])])])). 1.08/1.43 fof(c_0_1387, plain, ![X2207, X2208, X2209, X2210, X2211]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2210,X2211)),X2209),X2208),X2207)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2210),X2209),X2208),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2211),X2209),X2207))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2211,X2210))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2210),X2209),X2208),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2211),X2209),X2207))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2210,X2211)),X2209),X2208),X2207)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2211,X2210))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])])). 1.08/1.43 fof(c_0_1388, plain, ![X1032, X1033, X1034, X1035, X1036]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1036),X1034),X1033),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1035),X1034),X1032))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1033,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1035,X1036)),X1034),X1032))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1036,X1035))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1033,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1035,X1036)),X1034),X1032))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1036),X1034),X1033),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1035),X1034),X1032))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1036,X1035))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])])). 1.08/1.43 fof(c_0_1389, plain, ![X2657, X2658, X2659, X2660, X2661]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2658,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2660,X2661)),X2659),X2657))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2661),X2659),X2658),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2660),X2659),X2657))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2661,X2660))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2661),X2659),X2658),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2660),X2659),X2657))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2658,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2660,X2661)),X2659),X2657))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2661,X2660))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__le__add__iff2])])])])). 1.08/1.43 fof(c_0_1390, plain, ![X2891, X2892, X2893, X2894, X2895]:(~class_Groups_Oordered__ab__group__add__abs(X2895)|c_Orderings_Oord__class_Oless__eq(X2895,c_Groups_Oabs__class_Oabs(X2895,c_Groups_Ominus__class_Ominus(X2895,c_Groups_Oplus__class_Oplus(X2895,X2894,X2893),c_Groups_Oplus__class_Oplus(X2895,X2892,X2891))),c_Groups_Oplus__class_Oplus(X2895,c_Groups_Oabs__class_Oabs(X2895,c_Groups_Ominus__class_Ominus(X2895,X2894,X2892)),c_Groups_Oabs__class_Oabs(X2895,c_Groups_Ominus__class_Ominus(X2895,X2893,X2891))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])])). 1.08/1.43 fof(c_0_1391, plain, ![X1814, X1815, X1816, X1817, X1818]:(~class_RealVector_Oreal__normed__vector(X1818)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1818,c_Groups_Ominus__class_Ominus(X1818,c_Groups_Oplus__class_Oplus(X1818,X1817,X1816),c_Groups_Oplus__class_Oplus(X1818,X1815,X1814))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1818,c_Groups_Ominus__class_Ominus(X1818,X1817,X1815)),c_RealVector_Onorm__class_Onorm(X1818,c_Groups_Ominus__class_Ominus(X1818,X1816,X1814))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__diff__triangle__ineq])])])). 1.08/1.43 cnf(c_0_1392, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,X2,X3))=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))|~class_Rings_Ocomm__ring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1265])). 1.08/1.43 cnf(c_0_1393, plain, (c_Nat_OSuc(X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1266])). 1.08/1.43 fof(c_0_1394, plain, ![X2281, X2282, X2283, X2284, X2285]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2285,X2284)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2284),X2283),X2282),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2285),X2283),X2281))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2284,X2285)),X2283),X2282),X2281)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])])). 1.08/1.44 fof(c_0_1395, plain, ![X1571, X1572, X1573, X1574, X1575]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1575,X1574)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1572,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1574,X1575)),X1573),X1571))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1575),X1573),X1572),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1574),X1573),X1571))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])])). 1.08/1.44 fof(c_0_1396, plain, ![X543, X544, X545, X547]:((hBOOL(hAPP(X544,esk20_3(X543,X544,X545)))|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X543)|(~hBOOL(hAPP(X544,X547))|hBOOL(hAPP(X544,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X543),X545))))))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X545))&(~hBOOL(hAPP(X544,c_Groups_Ominus__class_Ominus(tc_Int_Oint,esk20_3(X543,X544,X545),X545)))|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X543)|(~hBOOL(hAPP(X544,X547))|hBOOL(hAPP(X544,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X543),X545))))))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X545))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_decr__mult__lemma])])])])])])). 1.08/1.44 fof(c_0_1397, plain, ![X2328, X2329, X2330, X2332]:((hBOOL(hAPP(X2329,esk65_3(X2328,X2329,X2330)))|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2328)|(~hBOOL(hAPP(X2329,X2332))|hBOOL(hAPP(X2329,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2332,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2328),X2330))))))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2330))&(~hBOOL(hAPP(X2329,c_Groups_Oplus__class_Oplus(tc_Int_Oint,esk65_3(X2328,X2329,X2330),X2330)))|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2328)|(~hBOOL(hAPP(X2329,X2332))|hBOOL(hAPP(X2329,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2332,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2328),X2330))))))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2330))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_incr__mult__lemma])])])])])])). 1.08/1.44 cnf(c_0_1398, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_1267])). 1.08/1.44 cnf(c_0_1399, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_1268])). 1.08/1.44 cnf(c_0_1400, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk1_2(X1,X2)))),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(split_conjunct,[status(thm)],[c_0_1269])). 1.08/1.44 fof(c_0_1401, plain, ![X948, X949, X950, X951]:(~class_Groups_Ozero(X951)|(X949!=hAPP(hAPP(hAPP(X950,c_Groups_Ozero__class_Ozero(X951)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X951))),X949)|c_Polynomial_Opoly__rec(X948,X951,X949,X950,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X951)))=X949)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_poly__rec__0])])])). 1.08/1.44 cnf(c_0_1402, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk60_2(X2,X1))))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk59_3(X2,X1,X3))),X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1270])). 1.08/1.44 cnf(c_0_1403, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk30_2(X2,X1))))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk29_3(X2,X1,X3))),X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1271])). 1.08/1.44 cnf(c_0_1404, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk58_2(X2,X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk57_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4)))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1270])). 1.08/1.44 cnf(c_0_1405, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk28_2(X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk27_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4)))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1271])). 1.08/1.44 fof(c_0_1406, plain, ![X2664, X2665, X2666, X2667, X2668, X2669]:(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2666),X2665),X2664)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2669),X2668),X2667)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2666),X2665),X2664),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2667,X2669)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2664)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2666)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2666,X2669)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2665,X2668))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__neg__lemma])])])). 1.08/1.44 fof(c_0_1407, plain, ![X2191, X2192, X2193, X2194, X2195, X2196]:(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2196),X2195),X2194)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2193),X2192),X2191)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2193),X2192),X2191))|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2191,X2193)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2194)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2193)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2193,X2196)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2195,X2192))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__lemma])])])). 1.08/1.44 fof(c_0_1408, plain, ![X1666, X1668, X1669]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1666,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1666),X1668),X1669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1666,X1668)),c_RealVector_Onorm__class_Onorm(X1666,X1669))),esk47_1(X1666)))|~class_RealVector_Oreal__normed__algebra(X1666))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk47_1(X1666))|~class_RealVector_Oreal__normed__algebra(X1666))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult_Opos__bounded])])])])])])). 1.08/1.44 fof(c_0_1409, plain, ![X1095, X1097, X1098]:(~class_RealVector_Oreal__normed__algebra(X1095)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1095,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1095),X1097),X1098)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1095,X1097)),c_RealVector_Onorm__class_Onorm(X1095,X1098))),esk32_1(X1095)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult_Obounded])])])])])). 1.08/1.44 fof(c_0_1410, plain, ![X252, X254, X255]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X252),X254),X255)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X252,X254)),c_RealVector_Onorm__class_Onorm(X252,X255))),esk7_1(X252)))|~class_RealVector_Oreal__normed__algebra(X252))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_1(X252))|~class_RealVector_Oreal__normed__algebra(X252))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ononneg__bounded])])])])])). 1.08/1.44 cnf(c_0_1411, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk58_2(X1,X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk57_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))|~class_RealVector_Oreal__normed__vector(X2)), inference(split_conjunct,[status(thm)],[c_0_1270])). 1.08/1.44 cnf(c_0_1412, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk28_2(X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk27_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))|~class_RealVector_Oreal__normed__vector(X2)), inference(split_conjunct,[status(thm)],[c_0_1271])). 1.08/1.44 fof(c_0_1413, negated_conjecture, ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))), inference(fof_simplification,[status(thm)],[c_0_1272])). 1.08/1.44 fof(c_0_1414, plain, ![X2129, X2130, X2131, X2132, X2133]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2133),X2132),X2131),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2133),X2130),X2129))|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2131)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2131,X2133)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2129,X2133)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2132,X2130))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient__lemma])])])). 1.08/1.44 fof(c_0_1415, plain, ![X2865, X2866, X2867, X2868, X2869]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2869),X2868),X2867),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2869),X2866),X2865))|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2865,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2869,X2865)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2869,X2867)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2866,X2868))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient__lemma__neg])])])). 1.08/1.44 cnf(c_0_1416, plain, (c_SEQ_OBseq(X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk71_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1273])). 1.08/1.44 cnf(c_0_1417, plain, (c_SEQ_OBseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk35_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1274])). 1.08/1.44 cnf(c_0_1418, plain, (X2=X3|c_Groups_Ouminus__class_Ouminus(X1,X3)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_1275])). 1.08/1.44 cnf(c_0_1419, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Nat_OSuc(X3)))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1276])). 1.08/1.44 fof(c_0_1420, plain, ![X1913, X1914, X1915, X1916, X1917]:((c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1916,X1917)),X1915),X1914)!=X1913|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1916),X1915),X1914)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1917),X1915),X1913)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1917,X1916))&(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1916),X1915),X1914)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1917),X1915),X1913)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1916,X1917)),X1915),X1914)=X1913|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1917,X1916))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])])). 1.08/1.44 fof(c_0_1421, plain, ![X2536, X2537, X2538, X2539, X2540]:((c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2540),X2538),X2537)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2539),X2538),X2536)|X2537=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2539,X2540)),X2538),X2536)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2540,X2539))&(X2537!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2539,X2540)),X2538),X2536)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2540),X2538),X2537)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2539),X2538),X2536)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2540,X2539))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__eq__add__iff2])])])])). 1.08/1.44 fof(c_0_1422, plain, ![X419, X420, X421, X422, X423, X424]:((c_Groups_Oplus__class_Oplus(X424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X424),X420),X422),X419)!=c_Groups_Oplus__class_Oplus(X424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X424),X423),X422),X421)|c_Groups_Oplus__class_Oplus(X424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X424),c_Groups_Ominus__class_Ominus(X424,X420,X423)),X422),X419)=X421|~class_Rings_Oring(X424))&(c_Groups_Oplus__class_Oplus(X424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X424),c_Groups_Ominus__class_Ominus(X424,X420,X423)),X422),X419)!=X421|c_Groups_Oplus__class_Oplus(X424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X424),X420),X422),X419)=c_Groups_Oplus__class_Oplus(X424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X424),X423),X422),X421)|~class_Rings_Oring(X424))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__add__iff2])])])])). 1.08/1.44 fof(c_0_1423, plain, ![X1055, X1056, X1057, X1058, X1059, X1060]:((c_Groups_Oplus__class_Oplus(X1060,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1060),X1056),X1058),X1055)!=c_Groups_Oplus__class_Oplus(X1060,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1060),X1059),X1058),X1057)|X1055=c_Groups_Oplus__class_Oplus(X1060,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1060),c_Groups_Ominus__class_Ominus(X1060,X1059,X1056)),X1058),X1057)|~class_Rings_Oring(X1060))&(X1055!=c_Groups_Oplus__class_Oplus(X1060,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1060),c_Groups_Ominus__class_Ominus(X1060,X1059,X1056)),X1058),X1057)|c_Groups_Oplus__class_Oplus(X1060,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1060),X1056),X1058),X1055)=c_Groups_Oplus__class_Oplus(X1060,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1060),X1059),X1058),X1057)|~class_Rings_Oring(X1060))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])])). 1.08/1.44 fof(c_0_1424, plain, ![X1483, X1484, X1485, X1486, X1487, X1488, X1489, X1490, X1491, X1492]:((((~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1483,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1483),X1486),X1487)!=X1484|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1487,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1483,X1487)|hBOOL(hAPP(X1485,X1486)))|~hBOOL(hAPP(X1485,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1484,X1483))))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1483)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1489)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1489,X1483)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1483),X1488),X1489)!=X1484|hBOOL(hAPP(X1485,X1488)))|~hBOOL(hAPP(X1485,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1484,X1483)))))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1483|hBOOL(hAPP(X1485,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1485,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1484,X1483)))))&((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&(((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))))&((((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&(((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk42_3(X1490,X1491,X1492)),esk43_3(X1490,X1491,X1492))=X1491)|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))))&(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&(((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1490,X1491,X1492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))))&(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&(((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1490,esk43_3(X1490,X1491,X1492)))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))))&(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1490)|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&(((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1490,X1491,X1492))|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1490,X1491,X1492),X1490)|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1490),esk44_3(X1490,X1491,X1492)),esk45_3(X1490,X1491,X1492))=X1491|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1490|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490))))&(~hBOOL(hAPP(X1492,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X1492,esk44_3(X1490,X1491,X1492)))|~hBOOL(hAPP(X1492,esk42_3(X1490,X1491,X1492))))|hBOOL(hAPP(X1492,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1491,X1490)))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__zdiv])])])])])])])). 1.08/1.44 cnf(c_0_1425, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1267])). 1.08/1.44 cnf(c_0_1426, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1268])). 1.08/1.44 fof(c_0_1427, plain, ![X380, X381, X382, X383, X384]:(~class_Rings_Oring(X384)|c_Groups_Oplus__class_Oplus(X384,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X384),X383),c_Groups_Ominus__class_Ominus(X384,X382,X380)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X384),c_Groups_Ominus__class_Ominus(X384,X383,X381)),X380))=c_Groups_Ominus__class_Ominus(X384,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X384),X383),X382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X384),X381),X380))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])])). 1.08/1.44 fof(c_0_1428, plain, ![X1296, X1297]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1297)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1296)),X1297),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1297,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1296))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LIMSEQ__inverse__realpow__zero__lemma])])). 1.08/1.44 cnf(c_0_1429, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))),X4)|~class_Groups_Omonoid__mult(X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1277])). 1.08/1.44 fof(c_0_1430, plain, ![X2436, X2437, X2438, X2439, X2440]:(~class_Rings_Osemiring(X2440)|c_Groups_Oplus__class_Oplus(X2440,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2440),X2439),X2438),c_Groups_Oplus__class_Oplus(X2440,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2440),X2437),X2438),X2436))=c_Groups_Oplus__class_Oplus(X2440,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2440),c_Groups_Oplus__class_Oplus(X2440,X2439,X2437)),X2438),X2436)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_combine__common__factor])])])). 1.08/1.44 fof(c_0_1431, plain, ![X2414, X2415, X2416, X2417, X2418, X2419]:(~class_Rings_Olinordered__semiring__1__strict(X2419)|(~c_Orderings_Oord__class_Oless(X2419,X2418,X2417)|(~c_Orderings_Oord__class_Oless(X2419,X2416,X2417)|(~c_Orderings_Oord__class_Oless__eq(X2419,c_Groups_Ozero__class_Ozero(X2419),X2415)|(~c_Orderings_Oord__class_Oless__eq(X2419,c_Groups_Ozero__class_Ozero(X2419),X2414)|(c_Groups_Oone__class_Oone(X2419)!=c_Groups_Oplus__class_Oplus(X2419,X2415,X2414)|c_Orderings_Oord__class_Oless(X2419,c_Groups_Oplus__class_Oplus(X2419,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2419),X2415),X2418),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2419),X2414),X2416)),X2417))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])])). 1.08/1.44 fof(c_0_1432, plain, ![X1072, X1073, X1074, X1075, X1076, X1077]:(~class_Rings_Olinordered__semiring__1(X1077)|(~c_Orderings_Oord__class_Oless__eq(X1077,X1076,X1075)|(~c_Orderings_Oord__class_Oless__eq(X1077,X1074,X1075)|(~c_Orderings_Oord__class_Oless__eq(X1077,c_Groups_Ozero__class_Ozero(X1077),X1073)|(~c_Orderings_Oord__class_Oless__eq(X1077,c_Groups_Ozero__class_Ozero(X1077),X1072)|(c_Groups_Oone__class_Oone(X1077)!=c_Groups_Oplus__class_Oplus(X1077,X1073,X1072)|c_Orderings_Oord__class_Oless__eq(X1077,c_Groups_Oplus__class_Oplus(X1077,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1077),X1073),X1076),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1077),X1072),X1074)),X1075))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_convex__bound__le])])])). 1.08/1.44 fof(c_0_1433, plain, ![X2155, X2156, X2157]:(~class_RealVector_Oreal__normed__vector(X2157)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2156)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2157,hAPP(X2155,esk63_3(X2155,X2156,X2157))),X2156)|c_SEQ_OBseq(X2157,X2155)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_BseqI])])])])). 1.08/1.44 fof(c_0_1434, plain, ![X1730, X1731, X1733, X1734]:(((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk50_2(X1730,X1731))|~c_SEQ_OBseq(X1731,X1730)|~class_RealVector_Oreal__normed__vector(X1731))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1731,hAPP(X1730,X1733)),esk50_2(X1730,X1731))|~c_SEQ_OBseq(X1731,X1730)|~class_RealVector_Oreal__normed__vector(X1731)))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1734)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1731,hAPP(X1730,esk51_3(X1730,X1731,X1734))),X1734)|c_SEQ_OBseq(X1731,X1730)|~class_RealVector_Oreal__normed__vector(X1731))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Bseq__def])])])])])])). 1.08/1.44 fof(c_0_1435, plain, ![X1082, X1083, X1084, X1085]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1085),X1084),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1083),X1084),X1082))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1085,X1083)),X1084),X1082), inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib])). 1.08/1.44 fof(c_0_1436, plain, ![X1142, X1143, X1144]:((c_Orderings_Oord__class_Oless(X1144,c_Groups_Ozero__class_Ozero(X1144),esk33_3(X1142,X1143,X1144))|c_Orderings_Oord__class_Oless__eq(X1144,X1143,X1142)|~class_Fields_Olinordered__field__inverse__zero(X1144))&((c_Orderings_Oord__class_Oless(X1144,esk33_3(X1142,X1143,X1144),c_Groups_Oone__class_Oone(X1144))|c_Orderings_Oord__class_Oless__eq(X1144,X1143,X1142)|~class_Fields_Olinordered__field__inverse__zero(X1144))&(~c_Orderings_Oord__class_Oless__eq(X1144,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1144),esk33_3(X1142,X1143,X1144)),X1143),X1142)|c_Orderings_Oord__class_Oless__eq(X1144,X1143,X1142)|~class_Fields_Olinordered__field__inverse__zero(X1144)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_field__le__mult__one__interval])])])])])). 1.08/1.44 fof(c_0_1437, plain, ![X852, X853, X854]:(((X852=c_Groups_Ozero__class_Ozero(X854)|c_Orderings_Oord__class_Oless(X854,c_Groups_Ozero__class_Ozero(X854),c_Groups_Oplus__class_Oplus(X854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X854),X853),X853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X854),X852),X852)))|~class_Rings_Olinordered__ring__strict(X854))&(X853=c_Groups_Ozero__class_Ozero(X854)|c_Orderings_Oord__class_Oless(X854,c_Groups_Ozero__class_Ozero(X854),c_Groups_Oplus__class_Oplus(X854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X854),X853),X853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X854),X852),X852)))|~class_Rings_Olinordered__ring__strict(X854)))&(~c_Orderings_Oord__class_Oless(X854,c_Groups_Ozero__class_Ozero(X854),c_Groups_Oplus__class_Oplus(X854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X854),X853),X853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X854),X852),X852)))|(X852!=c_Groups_Ozero__class_Ozero(X854)|X853!=c_Groups_Ozero__class_Ozero(X854))|~class_Rings_Olinordered__ring__strict(X854))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__squares__gt__zero__iff])])])])). 1.08/1.44 fof(c_0_1438, plain, ![X1655, X1656, X1657, X1658, X1659]:(~class_Rings_Ocomm__semiring__1(X1659)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1659),X1656),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1659),X1658),X1657)),X1655))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1659),X1658),X1657)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1659),X1656),X1655))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])])). 1.08/1.44 fof(c_0_1439, plain, ![X1870, X1871, X1872]:((X1870!=c_Groups_Ozero__class_Ozero(X1872)|X1871!=c_Groups_Ozero__class_Ozero(X1872)|c_Orderings_Oord__class_Oless__eq(X1872,c_Groups_Oplus__class_Oplus(X1872,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1872),X1871),X1871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1872),X1870),X1870)),c_Groups_Ozero__class_Ozero(X1872))|~class_Rings_Olinordered__ring__strict(X1872))&((X1870=c_Groups_Ozero__class_Ozero(X1872)|~c_Orderings_Oord__class_Oless__eq(X1872,c_Groups_Oplus__class_Oplus(X1872,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1872),X1871),X1871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1872),X1870),X1870)),c_Groups_Ozero__class_Ozero(X1872))|~class_Rings_Olinordered__ring__strict(X1872))&(X1871=c_Groups_Ozero__class_Ozero(X1872)|~c_Orderings_Oord__class_Oless__eq(X1872,c_Groups_Oplus__class_Oplus(X1872,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1872),X1871),X1871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1872),X1870),X1870)),c_Groups_Ozero__class_Ozero(X1872))|~class_Rings_Olinordered__ring__strict(X1872)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__squares__le__zero__iff])])])])). 1.08/1.44 fof(c_0_1440, plain, ![X1412, X1413, X1414]:(~class_Rings_Olinordered__ring(X1414)|~c_Orderings_Oord__class_Oless(X1414,c_Groups_Oplus__class_Oplus(X1414,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1414),X1413),X1413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1414),X1412),X1412)),c_Groups_Ozero__class_Ozero(X1414))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero])])])). 1.08/1.44 cnf(c_0_1441, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Nat_OSuc(X5))=hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_1278])). 1.08/1.44 fof(c_0_1442, plain, ![X2146, X2147, X2148]:(~class_Groups_Omonoid__mult(X2148)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2147)|hAPP(hAPP(c_Power_Opower__class_Opower(X2148),X2146),X2147)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2148),hAPP(hAPP(c_Power_Opower__class_Opower(X2148),X2146),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2147,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2146))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_realpow__minus__mult])])])). 1.08/1.44 cnf(c_0_1443, plain, (X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_1279])). 1.08/1.44 fof(c_0_1444, plain, ![X329, X330, X331, X333]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_3(X329,X330,X331))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X330,X329)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X331,X330))&((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X333,X329)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X330,X333)),esk8_3(X329,X330,X331))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X330,X329)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X331,X330))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X331,X333)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X330,X333)),esk8_3(X329,X330,X331))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X330,X329)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X331,X330)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__interval__lt])])])])])). 1.08/1.44 fof(c_0_1445, plain, ![X483, X484, X485, X487]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk15_3(X483,X484,X485))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X484,X483)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X485,X484))&((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X487,X483)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X484,X487)),esk15_3(X483,X484,X485))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X484,X483)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X485,X484))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X485,X487)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X484,X487)),esk15_3(X483,X484,X485))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X484,X483)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X485,X484)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lemma__interval])])])])])])). 1.08/1.44 fof(c_0_1446, plain, ![X1279, X1280, X1281, X1282, X1283]:(((X1281!=X1282|c_Groups_Oplus__class_Oplus(X1283,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1282),X1280),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1281),X1279))=c_Groups_Oplus__class_Oplus(X1283,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1282),X1279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1281),X1280))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1283))&(X1279!=X1280|c_Groups_Oplus__class_Oplus(X1283,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1282),X1280),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1281),X1279))=c_Groups_Oplus__class_Oplus(X1283,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1282),X1279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1281),X1280))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1283)))&(X1281=X1282|X1279=X1280|c_Groups_Oplus__class_Oplus(X1283,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1282),X1280),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1281),X1279))!=c_Groups_Oplus__class_Oplus(X1283,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1282),X1279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1283),X1281),X1280))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1283))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_crossproduct__noteq])])])])). 1.08/1.44 fof(c_0_1447, plain, ![X2619, X2620, X2621, X2622, X2623]:(((X2621!=X2619|c_Groups_Oplus__class_Oplus(X2623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2622),X2619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2620),X2621))=c_Groups_Oplus__class_Oplus(X2623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2622),X2621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2620),X2619))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2623))&(X2620!=X2622|c_Groups_Oplus__class_Oplus(X2623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2622),X2619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2620),X2621))=c_Groups_Oplus__class_Oplus(X2623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2622),X2621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2620),X2619))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2623)))&(c_Groups_Oplus__class_Oplus(X2623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2622),X2619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2620),X2621))!=c_Groups_Oplus__class_Oplus(X2623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2622),X2621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2623),X2620),X2619))|(X2621=X2619|X2620=X2622)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2623))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])])). 1.08/1.44 cnf(c_0_1448, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|c_Groups_Ouminus__class_Ouminus(X1,X2)!=X3|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_1275])). 1.08/1.44 fof(c_0_1449, plain, ![X1585, X1586, X1587, X1588]:((~c_Orderings_Oord__class_Oless(X1588,c_Groups_Ominus__class_Ominus(X1588,X1586,X1585),X1587)|~c_Orderings_Oord__class_Oless(X1588,X1587,c_Groups_Oplus__class_Oplus(X1588,X1586,X1585))|c_Orderings_Oord__class_Oless(X1588,c_Groups_Oabs__class_Oabs(X1588,c_Groups_Ominus__class_Ominus(X1588,X1587,X1586)),X1585)|~class_Rings_Olinordered__idom(X1588))&((c_Orderings_Oord__class_Oless(X1588,c_Groups_Ominus__class_Ominus(X1588,X1586,X1585),X1587)|~c_Orderings_Oord__class_Oless(X1588,c_Groups_Oabs__class_Oabs(X1588,c_Groups_Ominus__class_Ominus(X1588,X1587,X1586)),X1585)|~class_Rings_Olinordered__idom(X1588))&(c_Orderings_Oord__class_Oless(X1588,X1587,c_Groups_Oplus__class_Oplus(X1588,X1586,X1585))|~c_Orderings_Oord__class_Oless(X1588,c_Groups_Oabs__class_Oabs(X1588,c_Groups_Ominus__class_Ominus(X1588,X1587,X1586)),X1585)|~class_Rings_Olinordered__idom(X1588)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff])])])). 1.08/1.44 cnf(c_0_1450, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), inference(split_conjunct,[status(thm)],[c_0_1280])). 1.08/1.44 cnf(c_0_1451, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), inference(split_conjunct,[status(thm)],[c_0_1281])). 1.08/1.44 fof(c_0_1452, plain, ![X743, X744, X745]:(~class_Rings_Oring__1(X745)|hAPP(hAPP(c_Power_Opower__class_Opower(X745),c_Groups_Ouminus__class_Ouminus(X745,X744)),X743)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X745),hAPP(hAPP(c_Power_Opower__class_Opower(X745),c_Groups_Ouminus__class_Ouminus(X745,c_Groups_Oone__class_Oone(X745))),X743)),hAPP(hAPP(c_Power_Opower__class_Opower(X745),X744),X743))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])])). 1.08/1.44 fof(c_0_1453, plain, ![X2289, X2290, X2291]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2291),X2290),X2289),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2289)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2291)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2290,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__neg__lemma])])). 1.08/1.44 fof(c_0_1454, plain, ![X1308, X1309, X1310]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1310),X1309),X1308))|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1308,X1310)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1310)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1309)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_q__pos__lemma])])])). 1.08/1.44 fof(c_0_1455, plain, ![X2404, X2405, X2406, X2407, X2408, X2409, X2410, X2411]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2404|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2408,X2404)|(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2404),X2407),X2408)!=X2405|hBOOL(hAPP(X2406,X2407))))|~hBOOL(hAPP(X2406,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2405,X2404))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2404|hBOOL(hAPP(X2406,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2406,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2405,X2404)))))&(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2409|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2409|hBOOL(hAPP(X2411,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2410,X2409))))&(~hBOOL(hAPP(X2411,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2409|hBOOL(hAPP(X2411,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2410,X2409)))))&(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2409|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk67_3(X2409,X2410,X2411),X2409)|hBOOL(hAPP(X2411,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2410,X2409))))&(~hBOOL(hAPP(X2411,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk67_3(X2409,X2410,X2411),X2409)|hBOOL(hAPP(X2411,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2410,X2409)))))&(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2409|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2409),esk66_3(X2409,X2410,X2411)),esk67_3(X2409,X2410,X2411))=X2410|hBOOL(hAPP(X2411,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2410,X2409))))&(~hBOOL(hAPP(X2411,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2409),esk66_3(X2409,X2410,X2411)),esk67_3(X2409,X2410,X2411))=X2410|hBOOL(hAPP(X2411,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2410,X2409)))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2409|~hBOOL(hAPP(X2411,esk66_3(X2409,X2410,X2411)))|hBOOL(hAPP(X2411,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2410,X2409))))&(~hBOOL(hAPP(X2411,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2411,esk66_3(X2409,X2410,X2411)))|hBOOL(hAPP(X2411,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2410,X2409))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__div])])])])])])])). 1.08/1.44 fof(c_0_1456, plain, ![X1715, X1716, X1717]:(~class_Groups_Oordered__ab__group__add__abs(X1717)|c_Orderings_Oord__class_Oless__eq(X1717,c_Groups_Oabs__class_Oabs(X1717,c_Groups_Ominus__class_Ominus(X1717,c_Groups_Oabs__class_Oabs(X1717,X1716),c_Groups_Oabs__class_Oabs(X1717,X1715))),c_Groups_Oabs__class_Oabs(X1717,c_Groups_Ominus__class_Ominus(X1717,X1716,X1715)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])])). 1.08/1.44 fof(c_0_1457, plain, ![X1022, X1023, X1024]:(~class_RealVector_Oreal__normed__vector(X1024)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1024,X1023),c_RealVector_Onorm__class_Onorm(X1024,X1022))),c_RealVector_Onorm__class_Onorm(X1024,c_Groups_Ominus__class_Ominus(X1024,X1023,X1022)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__triangle__ineq3])])])). 1.08/1.44 fof(c_0_1458, plain, ![X2635, X2636, X2637, X2638, X2639]:(~class_Rings_Ocomm__semiring__1(X2639)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2639),X2638),X2637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2639),X2636),X2635))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2639),X2638),X2636)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2639),X2637),X2635))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])])])). 1.08/1.44 fof(c_0_1459, plain, ![X1769, X1770, X1771, X1772, X1773]:(~class_Rings_Ocomm__semiring__1(X1773)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1773),X1772),X1771)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1773),X1770),X1769))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1773),X1772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1773),X1771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1773),X1770),X1769)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])])). 1.08/1.44 cnf(c_0_1460, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1282])). 1.08/1.44 cnf(c_0_1461, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Nat_OSuc(X2))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1283])). 1.08/1.44 cnf(c_0_1462, plain, (X2=X4|~class_Rings_Olinordered__semidom(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Nat_OSuc(X3))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1284])). 1.08/1.44 cnf(c_0_1463, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1285])). 1.08/1.44 fof(c_0_1464, plain, ![X605, X606]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X606,X605)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X606)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X605)), inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__ineq2])). 1.08/1.44 fof(c_0_1465, plain, ![X481, X482]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X482),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X482,X481)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X481))), inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub])). 1.08/1.44 cnf(c_0_1466, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(split_conjunct,[status(thm)],[c_0_1286])). 1.08/1.44 fof(c_0_1467, plain, ![X1842, X1843, X1844, X1845]:(~class_Rings_Ocomm__semiring__0(X1845)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1845),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1845)),X1844),X1842),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1845)),X1843),X1842))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1845)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1845),X1844,X1843)),X1842)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__poly__add__left])])])). 1.08/1.44 fof(c_0_1468, plain, ![X2477, X2478, X2479, X2481, X2482, X2483, X2484]:((((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2478,X2477)|X2478=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2477,esk68_3(X2477,X2478,X2479))|hBOOL(hAPP(X2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2478,X2477))))&(~hBOOL(hAPP(X2479,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X2478=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2477,esk68_3(X2477,X2478,X2479))|hBOOL(hAPP(X2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2478,X2477)))))&((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2478,X2477)|~hBOOL(hAPP(X2479,esk68_3(X2477,X2478,X2479)))|hBOOL(hAPP(X2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2478,X2477))))&(~hBOOL(hAPP(X2479,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2479,esk68_3(X2477,X2478,X2479)))|hBOOL(hAPP(X2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2478,X2477))))))&((X2482!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2481,X2484)|hBOOL(hAPP(X2483,X2484))|~hBOOL(hAPP(X2483,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2482,X2481))))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2482,X2481)|hBOOL(hAPP(X2483,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2483,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2482,X2481)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__split])])])])])])])). 1.08/1.44 fof(c_0_1469, plain, ![X622, X623, X624, X626, X627, X628, X629]:((((~hBOOL(hAPP(X624,esk23_3(X622,X623,X624)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X623,X622)|hBOOL(hAPP(X624,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X623,X622))))&(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X622,esk23_3(X622,X623,X624))=X623|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X623,X622)|hBOOL(hAPP(X624,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X623,X622)))))&((~hBOOL(hAPP(X624,esk23_3(X622,X623,X624)))|~hBOOL(hAPP(X624,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X624,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X623,X622))))&(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X622,esk23_3(X622,X623,X624))=X623|~hBOOL(hAPP(X624,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X624,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X623,X622))))))&((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X627,X626)|hBOOL(hAPP(X628,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X628,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X627,X626))))&(hBOOL(hAPP(X628,X629))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X626,X629)!=X627|~hBOOL(hAPP(X628,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X627,X626)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm])])])])])])])). 1.08/1.44 fof(c_0_1470, plain, ![X2358, X2359, X2360, X2361, X2362]:(~class_Rings_Olinordered__idom(X2362)|(~c_Orderings_Oord__class_Oless(X2362,c_Groups_Oabs__class_Oabs(X2362,X2361),X2360)|(~c_Orderings_Oord__class_Oless(X2362,c_Groups_Oabs__class_Oabs(X2362,X2359),X2358)|c_Orderings_Oord__class_Oless(X2362,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2362),c_Groups_Oabs__class_Oabs(X2362,X2361)),c_Groups_Oabs__class_Oabs(X2362,X2359)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2362),X2360),X2358))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__less])])])). 1.08/1.44 cnf(c_0_1471, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), inference(split_conjunct,[status(thm)],[c_0_1287])). 1.08/1.44 cnf(c_0_1472, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), inference(split_conjunct,[status(thm)],[c_0_1288])). 1.08/1.44 fof(c_0_1473, plain, ![X2712, X2713, X2714]:(~class_Rings_Olinordered__semidom(X2714)|(~c_Orderings_Oord__class_Oless(X2714,c_Groups_Ozero__class_Ozero(X2714),X2713)|(~c_Orderings_Oord__class_Oless(X2714,X2713,c_Groups_Oone__class_Oone(X2714))|c_Orderings_Oord__class_Oless(X2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2714),X2713),hAPP(hAPP(c_Power_Opower__class_Opower(X2714),X2713),X2712)),hAPP(hAPP(c_Power_Opower__class_Opower(X2714),X2713),X2712))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc__less])])])). 1.08/1.44 fof(c_0_1474, plain, ![X1694]:((~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1694),X1694),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1694,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1694,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1694),X1694),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__less__0])])). 1.08/1.44 fof(c_0_1475, plain, ![X608, X609, X610, X611, X612]:(~class_RealVector_Oreal__normed__vector(X612)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X612,X611),X610)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X612,X609),X608)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X612,c_Groups_Oplus__class_Oplus(X612,X611,X609)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X610,X608))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__add__less])])])). 1.08/1.44 fof(c_0_1476, plain, ![X425, X426, X427]:((c_Orderings_Oord__class_Oless(X427,c_Groups_Ozero__class_Ozero(X427),esk14_3(X425,X426,X427))|c_Orderings_Oord__class_Oless__eq(X427,X426,X425)|~class_Fields_Olinordered__field(X427))&(~c_Orderings_Oord__class_Oless__eq(X427,X426,c_Groups_Oplus__class_Oplus(X427,X425,esk14_3(X425,X426,X427)))|c_Orderings_Oord__class_Oless__eq(X427,X426,X425)|~class_Fields_Olinordered__field(X427))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_field__le__epsilon])])])])])). 1.08/1.44 cnf(c_0_1477, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3))), inference(split_conjunct,[status(thm)],[c_0_1289])). 1.08/1.44 fof(c_0_1478, plain, ![X804, X805, X806, X807]:(~class_Rings_Ocomm__semiring__0(X807)|hAPP(c_Polynomial_Opoly(X807,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X807)),X806),X805)),X804)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X807),hAPP(c_Polynomial_Opoly(X807,X806),X804)),hAPP(c_Polynomial_Opoly(X807,X805),X804))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])])). 1.08/1.44 fof(c_0_1479, plain, ![X2662, X2663]:((X2663=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2662,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2663,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2662))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2663),X2662))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2663|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2663),X2662)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__eq__if])])])). 1.08/1.44 fof(c_0_1480, plain, ![X1475, X1476, X1477]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1476,X1475)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1476,X1477),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1475,X1477))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1477,X1475)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1477,X1476))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1476,X1477),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1475,X1477))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1476,X1475)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1477,X1475)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1477,X1476))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__diff__iff])])])])). 1.08/1.44 fof(c_0_1481, plain, ![X463, X464, X465]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X464,X465),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X463,X465))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X464,X463)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X465,X463)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X465,X464))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X464,X463)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X464,X465),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X463,X465))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X465,X463)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X465,X464))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__diff__iff])])])])). 1.08/1.44 fof(c_0_1482, plain, ![X531, X532, X533, X534, X535]:(~class_Rings_Olinordered__semiring__strict(X535)|(~c_Orderings_Oord__class_Oless(X535,X534,X533)|(~c_Orderings_Oord__class_Oless(X535,X532,X531)|(~c_Orderings_Oord__class_Oless(X535,c_Groups_Ozero__class_Ozero(X535),X533)|(~c_Orderings_Oord__class_Oless__eq(X535,c_Groups_Ozero__class_Ozero(X535),X532)|c_Orderings_Oord__class_Oless(X535,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X535),X534),X532),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X535),X533),X531))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__mono])])])). 1.08/1.44 fof(c_0_1483, plain, ![X1159, X1160, X1161, X1162, X1163]:(~class_Rings_Olinordered__semiring__strict(X1163)|(~c_Orderings_Oord__class_Oless(X1163,X1162,X1161)|(~c_Orderings_Oord__class_Oless(X1163,X1160,X1159)|(~c_Orderings_Oord__class_Oless__eq(X1163,c_Groups_Ozero__class_Ozero(X1163),X1162)|(~c_Orderings_Oord__class_Oless__eq(X1163,c_Groups_Ozero__class_Ozero(X1163),X1160)|c_Orderings_Oord__class_Oless(X1163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1163),X1162),X1160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1163),X1161),X1159))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])])). 1.08/1.44 fof(c_0_1484, plain, ![X2735, X2736, X2737, X2738, X2739]:(~class_Rings_Olinordered__semiring__strict(X2739)|(~c_Orderings_Oord__class_Oless__eq(X2739,X2738,X2737)|(~c_Orderings_Oord__class_Oless(X2739,X2736,X2735)|(~c_Orderings_Oord__class_Oless(X2739,c_Groups_Ozero__class_Ozero(X2739),X2738)|(~c_Orderings_Oord__class_Oless__eq(X2739,c_Groups_Ozero__class_Ozero(X2739),X2736)|c_Orderings_Oord__class_Oless(X2739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2739),X2738),X2736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2739),X2737),X2735))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__less__imp__less])])])). 1.08/1.44 fof(c_0_1485, plain, ![X1154, X1155, X1156, X1157, X1158]:(~class_Rings_Olinordered__semiring__strict(X1158)|(~c_Orderings_Oord__class_Oless(X1158,X1157,X1156)|(~c_Orderings_Oord__class_Oless__eq(X1158,X1155,X1154)|(~c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1157)|(~c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)|c_Orderings_Oord__class_Oless(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1157),X1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1156),X1154))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__le__imp__less])])])). 1.08/1.44 fof(c_0_1486, plain, ![X2756, X2757, X2758, X2759, X2760]:(~class_Rings_Oordered__semiring(X2760)|(~c_Orderings_Oord__class_Oless__eq(X2760,X2759,X2758)|(~c_Orderings_Oord__class_Oless__eq(X2760,X2757,X2756)|(~c_Orderings_Oord__class_Oless__eq(X2760,c_Groups_Ozero__class_Ozero(X2760),X2759)|(~c_Orderings_Oord__class_Oless__eq(X2760,c_Groups_Ozero__class_Ozero(X2760),X2757)|c_Orderings_Oord__class_Oless__eq(X2760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2760),X2759),X2757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2760),X2758),X2756))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__mono_H])])])). 1.08/1.44 fof(c_0_1487, plain, ![X2870, X2871, X2872, X2873, X2874]:(~class_Rings_Oordered__semiring(X2874)|(~c_Orderings_Oord__class_Oless__eq(X2874,X2873,X2872)|(~c_Orderings_Oord__class_Oless__eq(X2874,X2871,X2870)|(~c_Orderings_Oord__class_Oless__eq(X2874,c_Groups_Ozero__class_Ozero(X2874),X2872)|(~c_Orderings_Oord__class_Oless__eq(X2874,c_Groups_Ozero__class_Ozero(X2874),X2871)|c_Orderings_Oord__class_Oless__eq(X2874,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2874),X2873),X2871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2874),X2872),X2870))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__mono])])])). 1.08/1.44 fof(c_0_1488, plain, ![X1513, X1514, X1515, X1516, X1517]:(~class_RealVector_Oreal__normed__algebra(X1517)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1517,X1516),X1515)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1517,X1514),X1513)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1517,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1517),X1516),X1514)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1515),X1513))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__mult__less])])])). 1.08/1.44 fof(c_0_1489, plain, ![X1548, X1549, X1550, X1551]:(((~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1550)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1550)|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1550|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1551,X1550)=X1549)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1550),X1549),X1548)!=X1551)&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1550,X1548)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1548,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1550)|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1550|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1551,X1550)=X1549)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1550),X1549),X1548)!=X1551))&((~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1550)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1548,X1550)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1548))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1550|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1551,X1550)=X1549)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1550),X1549),X1548)!=X1551)&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1550,X1548)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1548,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1548,X1550)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1548))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1550|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1551,X1550)=X1549)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1550),X1549),X1548)!=X1551))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq])])])])). 1.08/1.44 fof(c_0_1490, plain, ![X2324, X2325, X2326, X2327]:(~class_Rings_Ocomm__semiring__1(X2327)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2327),hAPP(hAPP(c_Power_Opower__class_Opower(X2327),X2326),X2324)),hAPP(hAPP(c_Power_Opower__class_Opower(X2327),X2325),X2324))=hAPP(hAPP(c_Power_Opower__class_Opower(X2327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2327),X2326),X2325)),X2324)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])])). 1.08/1.44 fof(c_0_1491, plain, ![X2777, X2778, X2779, X2780]:(~class_Groups_Ocomm__monoid__mult(X2780)|hAPP(hAPP(c_Power_Opower__class_Opower(X2780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2780),X2779),X2778)),X2777)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2780),hAPP(hAPP(c_Power_Opower__class_Opower(X2780),X2779),X2777)),hAPP(hAPP(c_Power_Opower__class_Opower(X2780),X2778),X2777))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__mult__distrib])])])). 1.08/1.44 fof(c_0_1492, plain, ![X2250, X2251, X2252]:(~class_Rings_Olinordered__ring(X2252)|c_Orderings_Oord__class_Oless__eq(X2252,c_Groups_Ozero__class_Ozero(X2252),c_Groups_Oplus__class_Oplus(X2252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2252),X2251),X2251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2252),X2250),X2250)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__squares__ge__zero])])])). 1.08/1.44 cnf(c_0_1493, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_1290])). 1.08/1.44 fof(c_0_1494, plain, ![X689, X690]:(~class_Rings_Oring__1(X690)|c_Groups_Ominus__class_Ominus(X690,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X690),X689),X689),c_Groups_Oone__class_Oone(X690))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X690),c_Groups_Oplus__class_Oplus(X690,X689,c_Groups_Oone__class_Oone(X690))),c_Groups_Ominus__class_Ominus(X690,X689,c_Groups_Oone__class_Oone(X690)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored])])). 1.08/1.44 cnf(c_0_1495, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_1281])). 1.08/1.44 cnf(c_0_1496, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_1281])). 1.08/1.44 cnf(c_0_1497, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),X2)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_1291])). 1.08/1.44 fof(c_0_1498, plain, ![X1503, X1504, X1505]:(~class_Rings_Olinordered__semidom(X1505)|(~c_Orderings_Oord__class_Oless(X1505,c_Groups_Oone__class_Oone(X1505),X1504)|c_Orderings_Oord__class_Oless(X1505,hAPP(hAPP(c_Power_Opower__class_Opower(X1505),X1504),X1503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1505),X1504),hAPP(hAPP(c_Power_Opower__class_Opower(X1505),X1504),X1503))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__power__Suc])])])). 1.08/1.44 fof(c_0_1499, plain, ![X1963, X1964, X1965, X1966]:(~class_Rings_Olinordered__semiring(X1966)|(~c_Orderings_Oord__class_Oless(X1966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1966),X1965),X1964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1966),X1963),X1964))|(~c_Orderings_Oord__class_Oless__eq(X1966,c_Groups_Ozero__class_Ozero(X1966),X1964)|c_Orderings_Oord__class_Oless(X1966,X1965,X1963)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])])). 1.08/1.44 fof(c_0_1500, plain, ![X913, X914, X915, X916]:(~class_Rings_Olinordered__semiring__strict(X916)|(~c_Orderings_Oord__class_Oless(X916,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X916),X915),X914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X916),X913),X914))|(~c_Orderings_Oord__class_Oless__eq(X916,c_Groups_Ozero__class_Ozero(X916),X914)|c_Orderings_Oord__class_Oless(X916,X915,X913)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__imp__less__right])])])). 1.08/1.44 fof(c_0_1501, plain, ![X1629, X1630, X1631, X1632]:(~class_Rings_Olinordered__semidom(X1632)|(~c_Orderings_Oord__class_Oless(X1632,hAPP(hAPP(c_Power_Opower__class_Opower(X1632),X1631),X1630),hAPP(hAPP(c_Power_Opower__class_Opower(X1632),X1629),X1630))|(~c_Orderings_Oord__class_Oless__eq(X1632,c_Groups_Ozero__class_Ozero(X1632),X1629)|c_Orderings_Oord__class_Oless(X1632,X1631,X1629)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__imp__less__base])])])). 1.08/1.44 fof(c_0_1502, plain, ![X2100, X2101, X2102, X2103]:(~class_Rings_Olinordered__semiring(X2103)|(~c_Orderings_Oord__class_Oless(X2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2103),X2102),X2101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2103),X2102),X2100))|(~c_Orderings_Oord__class_Oless__eq(X2103,c_Groups_Ozero__class_Ozero(X2103),X2102)|c_Orderings_Oord__class_Oless(X2103,X2101,X2100)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__less__imp__less])])])). 1.08/1.44 fof(c_0_1503, plain, ![X1048, X1049, X1050, X1051]:((~c_Orderings_Oord__class_Oless(X1051,X1049,X1048)|c_Orderings_Oord__class_Oless(X1051,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1051),X1050),X1049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1051),X1050),X1048))|~c_Orderings_Oord__class_Oless(X1051,c_Groups_Ozero__class_Ozero(X1051),X1050)|~class_Rings_Olinordered__ring__strict(X1051))&(~c_Orderings_Oord__class_Oless(X1051,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1051),X1050),X1049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1051),X1050),X1048))|c_Orderings_Oord__class_Oless(X1051,X1049,X1048)|~c_Orderings_Oord__class_Oless(X1051,c_Groups_Ozero__class_Ozero(X1051),X1050)|~class_Rings_Olinordered__ring__strict(X1051))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__left__pos])])])])). 1.08/1.44 fof(c_0_1504, plain, ![X1116, X1117, X1118, X1119]:(~class_Rings_Olinordered__semiring__strict(X1119)|(~c_Orderings_Oord__class_Oless(X1119,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1119),X1118),X1117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1119),X1118),X1116))|(~c_Orderings_Oord__class_Oless__eq(X1119,c_Groups_Ozero__class_Ozero(X1119),X1118)|c_Orderings_Oord__class_Oless(X1119,X1117,X1116)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__imp__less__left])])])). 1.08/1.44 fof(c_0_1505, plain, ![X685, X686, X687, X688]:(~class_Rings_Olinordered__semiring__strict(X688)|(~c_Orderings_Oord__class_Oless__eq(X688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X688),X687),X686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X688),X685),X686))|(~c_Orderings_Oord__class_Oless(X688,c_Groups_Ozero__class_Ozero(X688),X686)|c_Orderings_Oord__class_Oless__eq(X688,X687,X685)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__le__imp__le])])])). 1.08/1.44 fof(c_0_1506, plain, ![X2214, X2215, X2216, X2217]:((~c_Orderings_Oord__class_Oless__eq(X2217,X2215,X2214)|c_Orderings_Oord__class_Oless__eq(X2217,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2217),X2216),X2215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2217),X2216),X2214))|~c_Orderings_Oord__class_Oless(X2217,c_Groups_Ozero__class_Ozero(X2217),X2216)|~class_Rings_Olinordered__ring__strict(X2217))&(~c_Orderings_Oord__class_Oless__eq(X2217,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2217),X2216),X2215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2217),X2216),X2214))|c_Orderings_Oord__class_Oless__eq(X2217,X2215,X2214)|~c_Orderings_Oord__class_Oless(X2217,c_Groups_Ozero__class_Ozero(X2217),X2216)|~class_Rings_Olinordered__ring__strict(X2217))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__cancel__left__pos])])])])). 1.08/1.44 fof(c_0_1507, plain, ![X2354, X2355, X2356, X2357]:(~class_Rings_Olinordered__semiring__strict(X2357)|(~c_Orderings_Oord__class_Oless__eq(X2357,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2357),X2356),X2355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2357),X2356),X2354))|(~c_Orderings_Oord__class_Oless(X2357,c_Groups_Ozero__class_Ozero(X2357),X2356)|c_Orderings_Oord__class_Oless__eq(X2357,X2355,X2354)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])])). 1.08/1.44 fof(c_0_1508, plain, ![X2646, X2647, X2648, X2649]:((~c_Orderings_Oord__class_Oless(X2649,X2646,X2647)|c_Orderings_Oord__class_Oless(X2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2649),X2648),X2647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2649),X2648),X2646))|~c_Orderings_Oord__class_Oless(X2649,X2648,c_Groups_Ozero__class_Ozero(X2649))|~class_Rings_Olinordered__ring__strict(X2649))&(~c_Orderings_Oord__class_Oless(X2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2649),X2648),X2647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2649),X2648),X2646))|c_Orderings_Oord__class_Oless(X2649,X2646,X2647)|~c_Orderings_Oord__class_Oless(X2649,X2648,c_Groups_Ozero__class_Ozero(X2649))|~class_Rings_Olinordered__ring__strict(X2649))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])])). 1.08/1.44 fof(c_0_1509, plain, ![X2462, X2463, X2464, X2465]:((~c_Orderings_Oord__class_Oless__eq(X2465,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2465),X2464),X2463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2465),X2464),X2462))|c_Orderings_Oord__class_Oless__eq(X2465,X2462,X2463)|~c_Orderings_Oord__class_Oless(X2465,X2464,c_Groups_Ozero__class_Ozero(X2465))|~class_Rings_Olinordered__ring__strict(X2465))&(~c_Orderings_Oord__class_Oless__eq(X2465,X2462,X2463)|c_Orderings_Oord__class_Oless__eq(X2465,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2465),X2464),X2463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2465),X2464),X2462))|~c_Orderings_Oord__class_Oless(X2465,X2464,c_Groups_Ozero__class_Ozero(X2465))|~class_Rings_Olinordered__ring__strict(X2465))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])])). 1.08/1.44 fof(c_0_1510, plain, ![X1125, X1126, X1127, X1128]:(~class_Rings_Olinordered__semidom(X1128)|(~c_Orderings_Oord__class_Oless(X1128,c_Groups_Oone__class_Oone(X1128),X1127)|(~c_Orderings_Oord__class_Oless(X1128,hAPP(hAPP(c_Power_Opower__class_Opower(X1128),X1127),X1126),hAPP(hAPP(c_Power_Opower__class_Opower(X1128),X1127),X1125))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1126,X1125)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__imp__less__exp])])])). 1.08/1.44 fof(c_0_1511, plain, ![X109, X110, X111, X112]:((~c_Orderings_Oord__class_Oless(X112,hAPP(hAPP(c_Power_Opower__class_Opower(X112),X111),X110),hAPP(hAPP(c_Power_Opower__class_Opower(X112),X111),X109))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X110,X109)|~c_Orderings_Oord__class_Oless(X112,c_Groups_Oone__class_Oone(X112),X111)|~class_Rings_Olinordered__semidom(X112))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X110,X109)|c_Orderings_Oord__class_Oless(X112,hAPP(hAPP(c_Power_Opower__class_Opower(X112),X111),X110),hAPP(hAPP(c_Power_Opower__class_Opower(X112),X111),X109))|~c_Orderings_Oord__class_Oless(X112,c_Groups_Oone__class_Oone(X112),X111)|~class_Rings_Olinordered__semidom(X112))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__increasing__iff])])])])). 1.08/1.44 fof(c_0_1512, plain, ![X1802, X1803, X1804, X1805]:(~class_Rings_Olinordered__semidom(X1805)|(~c_Orderings_Oord__class_Oless(X1805,c_Groups_Oone__class_Oone(X1805),X1804)|(~c_Orderings_Oord__class_Oless__eq(X1805,hAPP(hAPP(c_Power_Opower__class_Opower(X1805),X1804),X1803),hAPP(hAPP(c_Power_Opower__class_Opower(X1805),X1804),X1802))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1803,X1802)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])])). 1.08/1.44 fof(c_0_1513, plain, ![X726, X727, X728, X729]:((~c_Orderings_Oord__class_Oless__eq(X729,hAPP(hAPP(c_Power_Opower__class_Opower(X729),X728),X727),hAPP(hAPP(c_Power_Opower__class_Opower(X729),X728),X726))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X727,X726)|~c_Orderings_Oord__class_Oless(X729,c_Groups_Oone__class_Oone(X729),X728)|~class_Rings_Olinordered__semidom(X729))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X727,X726)|c_Orderings_Oord__class_Oless__eq(X729,hAPP(hAPP(c_Power_Opower__class_Opower(X729),X728),X727),hAPP(hAPP(c_Power_Opower__class_Opower(X729),X728),X726))|~c_Orderings_Oord__class_Oless(X729,c_Groups_Oone__class_Oone(X729),X728)|~class_Rings_Olinordered__semidom(X729))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__increasing__iff])])])])). 1.08/1.44 cnf(c_0_1514, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1292])). 1.08/1.44 cnf(c_0_1515, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1293])). 1.08/1.44 fof(c_0_1516, plain, ![X984, X985, X986, X987]:(~class_Rings_Ocomm__semiring__1(X987)|hAPP(c_Polynomial_Opoly(X987,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X987)),X986),X985)),X984)=hAPP(hAPP(c_Power_Opower__class_Opower(X987),hAPP(c_Polynomial_Opoly(X987,X986),X984)),X985)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__power])])). 1.08/1.44 fof(c_0_1517, plain, ![X2258, X2259]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2259)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2258)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X2259)),c_RComplete_Onatfloor(X2258)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2259),X2258))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__mult__natfloor])])])). 1.08/1.44 fof(c_0_1518, plain, ![X1192, X1193, X1194, X1195, X1196]:(~class_Groups_Oab__group__add(X1196)|c_Groups_Oplus__class_Oplus(X1196,c_Groups_Ominus__class_Ominus(X1196,X1195,X1193),c_Groups_Ominus__class_Ominus(X1196,X1194,X1192))=c_Groups_Ominus__class_Ominus(X1196,c_Groups_Oplus__class_Oplus(X1196,X1195,X1194),c_Groups_Oplus__class_Oplus(X1196,X1193,X1192))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add])])). 1.08/1.44 fof(c_0_1519, plain, ![X1562, X1563, X1564, X1565, X1566]:(~class_Rings_Ocomm__semiring__1(X1566)|c_Groups_Oplus__class_Oplus(X1566,c_Groups_Oplus__class_Oplus(X1566,X1565,X1564),c_Groups_Oplus__class_Oplus(X1566,X1563,X1562))=c_Groups_Oplus__class_Oplus(X1566,c_Groups_Oplus__class_Oplus(X1566,X1565,X1563),c_Groups_Oplus__class_Oplus(X1566,X1564,X1562))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])])])). 1.08/1.44 fof(c_0_1520, plain, ![X2171, X2172, X2173, X2174]:(~class_Rings_Olinordered__semidom(X2174)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2173,X2172)|(~c_Orderings_Oord__class_Oless(X2174,c_Groups_Ozero__class_Ozero(X2174),X2171)|(~c_Orderings_Oord__class_Oless(X2174,X2171,c_Groups_Oone__class_Oone(X2174))|c_Orderings_Oord__class_Oless(X2174,hAPP(hAPP(c_Power_Opower__class_Opower(X2174),X2171),X2172),hAPP(hAPP(c_Power_Opower__class_Opower(X2174),X2171),X2173)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__decreasing])])])). 1.08/1.44 fof(c_0_1521, plain, ![X1383, X1384, X1385, X1386]:(~class_Rings_Olinordered__semidom(X1386)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1385,X1384)|(~c_Orderings_Oord__class_Oless__eq(X1386,c_Groups_Ozero__class_Ozero(X1386),X1383)|(~c_Orderings_Oord__class_Oless__eq(X1386,X1383,c_Groups_Oone__class_Oone(X1386))|c_Orderings_Oord__class_Oless__eq(X1386,hAPP(hAPP(c_Power_Opower__class_Opower(X1386),X1383),X1384),hAPP(hAPP(c_Power_Opower__class_Opower(X1386),X1383),X1385)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__decreasing])])])). 1.08/1.44 fof(c_0_1522, plain, ![X1344, X1345, X1346, X1347]:(~class_Divides_Osemiring__div(X1347)|(c_Groups_Ozero__class_Ozero(X1347)=X1346|c_Groups_Oplus__class_Oplus(X1347,X1344,c_Divides_Odiv__class_Odiv(X1347,X1345,X1346))=c_Divides_Odiv__class_Odiv(X1347,c_Groups_Oplus__class_Oplus(X1347,X1345,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1347),X1346),X1344)),X1346))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])])). 1.08/1.44 fof(c_0_1523, plain, ![X1301, X1302, X1303, X1304]:(~class_Divides_Osemiring__div(X1304)|(c_Groups_Ozero__class_Ozero(X1304)=X1303|c_Groups_Oplus__class_Oplus(X1304,X1301,c_Divides_Odiv__class_Odiv(X1304,X1302,X1303))=c_Divides_Odiv__class_Odiv(X1304,c_Groups_Oplus__class_Oplus(X1304,X1302,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1304),X1301),X1303)),X1303))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self1])])])). 1.08/1.44 fof(c_0_1524, plain, ![X2338, X2339, X2340, X2341]:(~class_Rings_Olinordered__semidom(X2341)|(~c_Orderings_Oord__class_Oless(X2341,X2340,X2339)|(~c_Orderings_Oord__class_Oless__eq(X2341,c_Groups_Ozero__class_Ozero(X2341),X2340)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2338)|c_Orderings_Oord__class_Oless(X2341,hAPP(hAPP(c_Power_Opower__class_Opower(X2341),X2340),X2338),hAPP(hAPP(c_Power_Opower__class_Opower(X2341),X2339),X2338)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])])). 1.08/1.44 fof(c_0_1525, plain, ![X1736, X1737, X1738, X1739]:((((c_Orderings_Oord__class_Oless(X1739,X1738,c_Groups_Ozero__class_Ozero(X1739))|c_Orderings_Oord__class_Oless(X1739,c_Groups_Ozero__class_Ozero(X1739),X1738)|~c_Orderings_Oord__class_Oless(X1739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1736))|~class_Rings_Olinordered__ring__strict(X1739))&(c_Orderings_Oord__class_Oless(X1739,X1736,X1737)|c_Orderings_Oord__class_Oless(X1739,c_Groups_Ozero__class_Ozero(X1739),X1738)|~c_Orderings_Oord__class_Oless(X1739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1736))|~class_Rings_Olinordered__ring__strict(X1739)))&((c_Orderings_Oord__class_Oless(X1739,X1738,c_Groups_Ozero__class_Ozero(X1739))|c_Orderings_Oord__class_Oless(X1739,X1737,X1736)|~c_Orderings_Oord__class_Oless(X1739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1736))|~class_Rings_Olinordered__ring__strict(X1739))&(c_Orderings_Oord__class_Oless(X1739,X1736,X1737)|c_Orderings_Oord__class_Oless(X1739,X1737,X1736)|~c_Orderings_Oord__class_Oless(X1739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1736))|~class_Rings_Olinordered__ring__strict(X1739))))&((~c_Orderings_Oord__class_Oless(X1739,c_Groups_Ozero__class_Ozero(X1739),X1738)|~c_Orderings_Oord__class_Oless(X1739,X1737,X1736)|c_Orderings_Oord__class_Oless(X1739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1736))|~class_Rings_Olinordered__ring__strict(X1739))&(~c_Orderings_Oord__class_Oless(X1739,X1738,c_Groups_Ozero__class_Ozero(X1739))|~c_Orderings_Oord__class_Oless(X1739,X1736,X1737)|c_Orderings_Oord__class_Oless(X1739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1739),X1738),X1736))|~class_Rings_Olinordered__ring__strict(X1739)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__left__disj])])])])). 1.08/1.44 fof(c_0_1526, plain, ![X1078, X1079, X1080, X1081]:((((c_Orderings_Oord__class_Oless(X1081,X1079,c_Groups_Ozero__class_Ozero(X1081))|c_Orderings_Oord__class_Oless(X1081,X1080,X1078)|~c_Orderings_Oord__class_Oless(X1081,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1080),X1079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1078),X1079))|~class_Rings_Olinordered__ring__strict(X1081))&(c_Orderings_Oord__class_Oless(X1081,X1078,X1080)|c_Orderings_Oord__class_Oless(X1081,X1080,X1078)|~c_Orderings_Oord__class_Oless(X1081,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1080),X1079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1078),X1079))|~class_Rings_Olinordered__ring__strict(X1081)))&((c_Orderings_Oord__class_Oless(X1081,X1079,c_Groups_Ozero__class_Ozero(X1081))|c_Orderings_Oord__class_Oless(X1081,c_Groups_Ozero__class_Ozero(X1081),X1079)|~c_Orderings_Oord__class_Oless(X1081,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1080),X1079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1078),X1079))|~class_Rings_Olinordered__ring__strict(X1081))&(c_Orderings_Oord__class_Oless(X1081,X1078,X1080)|c_Orderings_Oord__class_Oless(X1081,c_Groups_Ozero__class_Ozero(X1081),X1079)|~c_Orderings_Oord__class_Oless(X1081,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1080),X1079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1078),X1079))|~class_Rings_Olinordered__ring__strict(X1081))))&((~c_Orderings_Oord__class_Oless(X1081,X1080,X1078)|~c_Orderings_Oord__class_Oless(X1081,c_Groups_Ozero__class_Ozero(X1081),X1079)|c_Orderings_Oord__class_Oless(X1081,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1080),X1079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1078),X1079))|~class_Rings_Olinordered__ring__strict(X1081))&(~c_Orderings_Oord__class_Oless(X1081,X1079,c_Groups_Ozero__class_Ozero(X1081))|~c_Orderings_Oord__class_Oless(X1081,X1078,X1080)|c_Orderings_Oord__class_Oless(X1081,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1080),X1079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1081),X1078),X1079))|~class_Rings_Olinordered__ring__strict(X1081)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__right__disj])])])])). 1.08/1.44 fof(c_0_1527, plain, ![X2055, X2056, X2058]:(~class_RealVector_Oreal__normed__algebra(X2056)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2056,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2056),X2058),X2055)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2056,X2058)),esk61_2(X2055,X2056)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Obounded])])])])). 1.08/1.44 fof(c_0_1528, plain, ![X1509, X1510, X1512]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk46_2(X1509,X1510))|~class_RealVector_Oreal__normed__algebra(X1510))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1510,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1510),X1512),X1509)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1510,X1512)),esk46_2(X1509,X1510)))|~class_RealVector_Oreal__normed__algebra(X1510))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ononneg__bounded])])])])])). 1.08/1.44 fof(c_0_1529, plain, ![X515, X516, X518]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk17_2(X515,X516))|~class_RealVector_Oreal__normed__algebra(X516))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X516,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X516),X518),X515)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X516,X518)),esk17_2(X515,X516)))|~class_RealVector_Oreal__normed__algebra(X516))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Opos__bounded])])])])])). 1.08/1.44 fof(c_0_1530, plain, ![X2541, X2542, X2543]:(~class_RealVector_Oreal__normed__algebra(X2543)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2543,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2543),X2542),X2541)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2543,X2542)),c_RealVector_Onorm__class_Onorm(X2543,X2541)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])])). 1.08/1.44 fof(c_0_1531, plain, ![X1971, X1972, X1974]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk55_2(X1971,X1972))|~class_RealVector_Oreal__normed__algebra(X1972))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1972,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1972),X1971),X1974)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1972,X1974)),esk55_2(X1971,X1972)))|~class_RealVector_Oreal__normed__algebra(X1972))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right_Ononneg__bounded])])])])])])). 1.08/1.44 fof(c_0_1532, plain, ![X1774, X1775, X1777]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1775,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1775),X1774),X1777)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1775,X1777)),esk52_2(X1774,X1775)))|~class_RealVector_Oreal__normed__algebra(X1775))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk52_2(X1774,X1775))|~class_RealVector_Oreal__normed__algebra(X1775))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right_Opos__bounded])])])])])])). 1.08/1.44 fof(c_0_1533, plain, ![X639, X640, X642]:(~class_RealVector_Oreal__normed__algebra(X640)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X640),X639),X642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X640,X642)),esk24_2(X639,X640)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Obounded])])])])). 1.08/1.44 fof(c_0_1534, plain, ![X2507, X2508, X2509, X2510]:(~class_Rings_Ocomm__semiring__1(X2510)|c_Groups_Oplus__class_Oplus(X2510,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2510),X2509),X2507),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2510),X2508),X2507))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2510),c_Groups_Oplus__class_Oplus(X2510,X2509,X2508)),X2507)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])])])). 1.08/1.44 fof(c_0_1535, plain, ![X1610, X1611, X1612, X1613]:(~class_RealVector_Oreal__normed__algebra(X1613)|c_Groups_Oplus__class_Oplus(X1613,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1613),X1612),X1610),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1613),X1611),X1610))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1613),c_Groups_Oplus__class_Oplus(X1613,X1612,X1611)),X1610)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])])). 1.08/1.44 fof(c_0_1536, plain, ![X2624, X2625, X2626, X2627]:(~class_RealVector_Oreal__normed__algebra(X2627)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2627),c_Groups_Ominus__class_Ominus(X2627,X2626,X2625)),X2624)=c_Groups_Ominus__class_Ominus(X2627,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2627),X2626),X2624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2627),X2625),X2624))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left])])). 1.08/1.44 fof(c_0_1537, plain, ![X1315, X1316, X1317, X1318]:(~class_RealVector_Oreal__normed__algebra(X1318)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1318),c_Groups_Ominus__class_Ominus(X1318,X1317,X1316)),X1315)=c_Groups_Ominus__class_Ominus(X1318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1318),X1317),X1315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1318),X1316),X1315))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff])])). 1.08/1.44 fof(c_0_1538, plain, ![X2703, X2704, X2705, X2706]:(~class_Rings_Ocomm__semiring(X2706)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2706),c_Groups_Oplus__class_Oplus(X2706,X2705,X2704)),X2703)=c_Groups_Oplus__class_Oplus(X2706,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2706),X2705),X2703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2706),X2704),X2703))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])])). 1.08/1.44 fof(c_0_1539, plain, ![X1393, X1394, X1395, X1396]:(~class_Rings_Ocomm__semiring__1(X1396)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1396),c_Groups_Oplus__class_Oplus(X1396,X1395,X1393)),X1394)=c_Groups_Oplus__class_Oplus(X1396,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1396),X1395),X1394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1396),X1393),X1394))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])])])). 1.08/1.44 fof(c_0_1540, plain, ![X1662, X1663, X1664, X1665]:(~class_RealVector_Oreal__normed__algebra(X1665)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1665),c_Groups_Oplus__class_Oplus(X1665,X1664,X1663)),X1662)=c_Groups_Oplus__class_Oplus(X1665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1665),X1664),X1662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1665),X1663),X1662))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left_Oadd])])])). 1.08/1.44 fof(c_0_1541, plain, ![X582, X583]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X582)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X583,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk21_2(X582,X583))),X582))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean3])])])])). 1.08/1.44 cnf(c_0_1542, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_1294])). 1.08/1.44 fof(c_0_1543, plain, ![X2039, X2040, X2041]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2041)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2040)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2040,X2039)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2041,X2039),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2041,X2040))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2])])])). 1.08/1.44 fof(c_0_1544, plain, ![X932, X933, X934]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X934,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X933)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X933,X932)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X934,X933),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X934,X932))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__neg])])])). 1.08/1.44 fof(c_0_1545, plain, ![X2080, X2081, X2082, X2083]:(~class_Rings_Ocomm__semiring__1(X2083)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2083),hAPP(hAPP(c_Power_Opower__class_Opower(X2083),X2082),X2081)),hAPP(hAPP(c_Power_Opower__class_Opower(X2083),X2082),X2080))=hAPP(hAPP(c_Power_Opower__class_Opower(X2083),X2082),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2081,X2080))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])])])). 1.08/1.44 fof(c_0_1546, plain, ![X1197, X1198, X1199, X1200]:(~class_Groups_Omonoid__mult(X1200)|hAPP(hAPP(c_Power_Opower__class_Opower(X1200),X1199),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1198,X1197))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1200),hAPP(hAPP(c_Power_Opower__class_Opower(X1200),X1199),X1198)),hAPP(hAPP(c_Power_Opower__class_Opower(X1200),X1199),X1197))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])])). 1.08/1.44 fof(c_0_1547, plain, ![X216, X217, X218, X219]:(~class_Rings_Ocomm__semiring__1(X219)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X219),X218),X216)),X217)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X219),X218),X217)),X216)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])])])). 1.08/1.44 fof(c_0_1548, plain, ![X879, X880, X881]:(~class_Groups_Oordered__ab__group__add__abs(X881)|c_Orderings_Oord__class_Oless__eq(X881,c_Groups_Ominus__class_Ominus(X881,c_Groups_Oabs__class_Oabs(X881,X880),c_Groups_Oabs__class_Oabs(X881,X879)),c_Groups_Oabs__class_Oabs(X881,c_Groups_Ominus__class_Ominus(X881,X880,X879)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__triangle__ineq2])])])). 1.08/1.44 fof(c_0_1549, plain, ![X2032, X2033, X2034]:(~class_Groups_Oordered__ab__group__add__abs(X2034)|c_Orderings_Oord__class_Oless__eq(X2034,c_Groups_Ominus__class_Ominus(X2034,c_Groups_Oabs__class_Oabs(X2034,X2033),c_Groups_Oabs__class_Oabs(X2034,X2032)),c_Groups_Oabs__class_Oabs(X2034,c_Groups_Ominus__class_Ominus(X2034,X2032,X2033)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])])). 1.08/1.44 fof(c_0_1550, plain, ![X1990, X1991, X1992]:(~class_Groups_Oordered__ab__group__add__abs(X1992)|c_Orderings_Oord__class_Oless__eq(X1992,c_Groups_Oabs__class_Oabs(X1992,c_Groups_Ominus__class_Ominus(X1992,X1991,X1990)),c_Groups_Oplus__class_Oplus(X1992,c_Groups_Oabs__class_Oabs(X1992,X1991),c_Groups_Oabs__class_Oabs(X1992,X1990)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])])). 1.08/1.44 fof(c_0_1551, plain, ![X274, X275, X276]:(~class_Groups_Oordered__ab__group__add__abs(X276)|c_Orderings_Oord__class_Oless__eq(X276,c_Groups_Oabs__class_Oabs(X276,c_Groups_Oplus__class_Oplus(X276,X275,X274)),c_Groups_Oplus__class_Oplus(X276,c_Groups_Oabs__class_Oabs(X276,X275),c_Groups_Oabs__class_Oabs(X276,X274)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])])). 1.08/1.44 fof(c_0_1552, plain, ![X907, X908, X909, X910, X911, X912]:(~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X912)|(c_Groups_Ozero__class_Ozero(X912)=X911|(X910!=X909|X908=X907|c_Groups_Oplus__class_Oplus(X912,X909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X912),X911),X907))!=c_Groups_Oplus__class_Oplus(X912,X910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X912),X911),X908))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__scale__eq__noteq])])])). 1.08/1.44 fof(c_0_1553, plain, ![X2686, X2687, X2688]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2688)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2688),X2687),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2688),X2686))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2687,X2686))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__power__less__imp__less])])])). 1.08/1.44 fof(c_0_1554, plain, ![X790, X791, X792]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X792),X791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X792),X790))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X791,X790)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X792))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X791,X790)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X792),X791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X792),X790))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X792))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__less__cancel1])])])])). 1.08/1.44 fof(c_0_1555, plain, ![X459, X460, X461]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X460),X461),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X459),X461))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X460,X459)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X461))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X460,X459)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X460),X461),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X459),X461))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X461))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__mult__less__iff1])])])])). 1.08/1.44 fof(c_0_1556, plain, ![X2519, X2520, X2521]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2521),X2520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2519),X2520))|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2520)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2521,X2519)))&((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2520)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2521),X2520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2519),X2520)))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2521,X2519)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2521),X2520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2519),X2520))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])])). 1.08/1.44 fof(c_0_1557, plain, ![X2380, X2381, X2382]:(((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2382)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2382),X2381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2382),X2380)))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2381,X2380)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2382),X2381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2382),X2380))))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2382),X2381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2382),X2380))|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2382)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2381,X2380)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])])). 1.08/1.44 fof(c_0_1558, plain, ![X1595, X1596, X1597]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1596,X1595)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1597),X1596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1597),X1595))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1597))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1597),X1596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1597),X1595))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1596,X1595)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1597))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__le__cancel1])])])])). 1.08/1.44 fof(c_0_1559, plain, ![X512, X513, X514]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X513),X514),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X512),X514))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X513,X512)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X514))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X513,X512)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X513),X514),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X512),X514))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X514))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__mult__le__cancel__iff1])])])])). 1.08/1.44 fof(c_0_1560, plain, ![X981, X982, X983]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X983),X982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X983),X981))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X982,X981)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X983))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X982,X981)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X983),X982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X983),X981))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X983))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__mult__le__cancel__iff2])])])])). 1.08/1.44 fof(c_0_1561, plain, ![X142, X143]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X143),X142)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X142,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X143),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(X142)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X143,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_natceiling__eq])])])). 1.08/1.44 fof(c_0_1562, plain, ![X1498, X1499, X1500]:(~class_RealVector_Oreal__normed__vector(X1500)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1500,X1499),c_RealVector_Onorm__class_Onorm(X1500,X1498)),c_RealVector_Onorm__class_Onorm(X1500,c_Groups_Ominus__class_Ominus(X1500,X1499,X1498)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2])])). 1.08/1.44 fof(c_0_1563, plain, ![X846, X847, X848]:(~class_RealVector_Oreal__normed__vector(X848)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X848,X847),c_RealVector_Onorm__class_Onorm(X848,X846)),c_RealVector_Onorm__class_Onorm(X848,c_Groups_Oplus__class_Oplus(X848,X847,X846)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq])])). 1.08/1.44 fof(c_0_1564, plain, ![X2513, X2514, X2515]:(~class_RealVector_Oreal__normed__vector(X2515)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2515,c_Groups_Ominus__class_Ominus(X2515,X2514,X2513)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2515,X2514),c_RealVector_Onorm__class_Onorm(X2515,X2513)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4])])). 1.08/1.44 fof(c_0_1565, plain, ![X471, X472, X473]:(~class_RealVector_Oreal__normed__vector(X473)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X473,c_Groups_Oplus__class_Oplus(X473,X472,X471)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X473,X472),c_RealVector_Onorm__class_Onorm(X473,X471)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq])])). 1.08/1.44 cnf(c_0_1566, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk72_2(X2,X1))))|~c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1273])). 1.08/1.44 cnf(c_0_1567, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk34_2(X2,X1))))|~c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1274])). 1.08/1.44 fof(c_0_1568, plain, ![X119, X120, X121, X122]:(~class_Rings_Ocomm__semiring__0(X122)|c_Groups_Oplus__class_Oplus(X122,hAPP(c_Polynomial_Opoly(X122,X121),X119),hAPP(c_Polynomial_Opoly(X122,X120),X119))=hAPP(c_Polynomial_Opoly(X122,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X122),X121,X120)),X119)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__add])])). 1.08/1.44 fof(c_0_1569, plain, ![X1230, X1231, X1232, X1233]:(~class_Groups_Oab__group__add(X1233)|hAPP(c_Polynomial_Ocoeff(X1233,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1233),X1232,X1231)),X1230)=c_Groups_Ominus__class_Ominus(X1233,hAPP(c_Polynomial_Ocoeff(X1233,X1232),X1230),hAPP(c_Polynomial_Ocoeff(X1233,X1231),X1230))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_coeff__diff])])])). 1.08/1.44 fof(c_0_1570, plain, ![X1479, X1480, X1481, X1482]:(~class_Groups_Ocomm__monoid__add(X1482)|hAPP(c_Polynomial_Ocoeff(X1482,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1482),X1481,X1480)),X1479)=c_Groups_Oplus__class_Oplus(X1482,hAPP(c_Polynomial_Ocoeff(X1482,X1481),X1479),hAPP(c_Polynomial_Ocoeff(X1482,X1480),X1479))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__add])])). 1.08/1.44 fof(c_0_1571, plain, ![X1711, X1712, X1713, X1714]:(~class_Rings_Ocomm__ring(X1714)|hAPP(c_Polynomial_Opoly(X1714,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1714),X1713,X1712)),X1711)=c_Groups_Ominus__class_Ominus(X1714,hAPP(c_Polynomial_Opoly(X1714,X1713),X1711),hAPP(c_Polynomial_Opoly(X1714,X1712),X1711))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__diff])])). 1.08/1.44 fof(c_0_1572, plain, ![X2769, X2770, X2771]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2769,X2771),X2770)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2769,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2770,X2771))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2771,X2770))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2769,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2770,X2771))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2769,X2771),X2770)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2771,X2770))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])])). 1.08/1.44 fof(c_0_1573, plain, ![X2567, X2568, X2569]:c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2569),X2567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2568),X2567))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2569,X2568)),X2567), inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib])). 1.08/1.44 fof(c_0_1574, plain, ![X488, X489, X490]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X490),X488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X489),X488))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X490,X489)),X488), inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib])). 1.08/1.44 fof(c_0_1575, plain, ![X1462, X1463, X1464]:c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1464),X1462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1463),X1462))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1464,X1463)),X1462), inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib])). 1.08/1.44 fof(c_0_1576, plain, ![X1170, X1171, X1172]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1172,X1171)),X1170)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1172),X1170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1171),X1170)), inference(variable_rename,[status(thm)],[fact_diff__mult__distrib])). 1.08/1.44 fof(c_0_1577, plain, ![X2052, X2053, X2054]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2054,X2053)),X2052)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2054),X2052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2053),X2052)), inference(variable_rename,[status(thm)],[fact_add__mult__distrib])). 1.08/1.44 cnf(c_0_1578, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1295])). 1.08/1.44 fof(c_0_1579, plain, ![X2301, X2302, X2303]:(~class_RealVector_Oreal__normed__algebra__1(X2303)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2303,hAPP(hAPP(c_Power_Opower__class_Opower(X2303),X2302),X2301)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2303,X2302)),X2301))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power__ineq])])). 1.08/1.44 fof(c_0_1580, plain, ![X1465, X1466, X1467, X1468]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X1468)|(~c_Orderings_Oord__class_Oless(X1468,c_Groups_Oplus__class_Oplus(X1468,X1467,X1466),c_Groups_Oplus__class_Oplus(X1468,X1465,X1466))|c_Orderings_Oord__class_Oless(X1468,X1467,X1465))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__imp__less__right])])])). 1.08/1.44 fof(c_0_1581, plain, ![X920, X921, X922, X923]:((~c_Orderings_Oord__class_Oless(X923,X922,X920)|c_Orderings_Oord__class_Oless(X923,c_Groups_Oplus__class_Oplus(X923,X922,X921),c_Groups_Oplus__class_Oplus(X923,X920,X921))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X923))&(~c_Orderings_Oord__class_Oless(X923,c_Groups_Oplus__class_Oplus(X923,X922,X921),c_Groups_Oplus__class_Oplus(X923,X920,X921))|c_Orderings_Oord__class_Oless(X923,X922,X920)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X923))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])])). 1.08/1.44 fof(c_0_1582, plain, ![X1838, X1839, X1840, X1841]:((~c_Orderings_Oord__class_Oless(X1841,X1839,X1838)|c_Orderings_Oord__class_Oless(X1841,c_Groups_Oplus__class_Oplus(X1841,X1840,X1839),c_Groups_Oplus__class_Oplus(X1841,X1840,X1838))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1841))&(~c_Orderings_Oord__class_Oless(X1841,c_Groups_Oplus__class_Oplus(X1841,X1840,X1839),c_Groups_Oplus__class_Oplus(X1841,X1840,X1838))|c_Orderings_Oord__class_Oless(X1841,X1839,X1838)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1841))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])])). 1.08/1.44 fof(c_0_1583, plain, ![X652, X653, X654, X655]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X655)|(~c_Orderings_Oord__class_Oless(X655,c_Groups_Oplus__class_Oplus(X655,X654,X653),c_Groups_Oplus__class_Oplus(X655,X654,X652))|c_Orderings_Oord__class_Oless(X655,X653,X652))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__imp__less__left])])])). 1.08/1.44 fof(c_0_1584, plain, ![X1778, X1779, X1780, X1781]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X1781)|(~c_Orderings_Oord__class_Oless__eq(X1781,c_Groups_Oplus__class_Oplus(X1781,X1780,X1779),c_Groups_Oplus__class_Oplus(X1781,X1778,X1779))|c_Orderings_Oord__class_Oless__eq(X1781,X1780,X1778))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__imp__le__right])])])). 1.08/1.44 fof(c_0_1585, plain, ![X1271, X1272, X1273, X1274]:((~c_Orderings_Oord__class_Oless__eq(X1274,X1273,X1271)|c_Orderings_Oord__class_Oless__eq(X1274,c_Groups_Oplus__class_Oplus(X1274,X1273,X1272),c_Groups_Oplus__class_Oplus(X1274,X1271,X1272))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1274))&(~c_Orderings_Oord__class_Oless__eq(X1274,c_Groups_Oplus__class_Oplus(X1274,X1273,X1272),c_Groups_Oplus__class_Oplus(X1274,X1271,X1272))|c_Orderings_Oord__class_Oless__eq(X1274,X1273,X1271)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1274))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__cancel__right])])])])). 1.08/1.44 fof(c_0_1586, plain, ![X2875, X2876, X2877, X2878]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X2878)|(~c_Orderings_Oord__class_Oless__eq(X2878,c_Groups_Oplus__class_Oplus(X2878,X2877,X2876),c_Groups_Oplus__class_Oplus(X2878,X2877,X2875))|c_Orderings_Oord__class_Oless__eq(X2878,X2876,X2875))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__imp__le__left])])])). 1.08/1.44 fof(c_0_1587, plain, ![X1888, X1889, X1890, X1891]:((~c_Orderings_Oord__class_Oless__eq(X1891,c_Groups_Oplus__class_Oplus(X1891,X1890,X1889),c_Groups_Oplus__class_Oplus(X1891,X1890,X1888))|c_Orderings_Oord__class_Oless__eq(X1891,X1889,X1888)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1891))&(~c_Orderings_Oord__class_Oless__eq(X1891,X1889,X1888)|c_Orderings_Oord__class_Oless__eq(X1891,c_Groups_Oplus__class_Oplus(X1891,X1890,X1889),c_Groups_Oplus__class_Oplus(X1891,X1890,X1888))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1891))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__cancel__left])])])])). 1.08/1.44 cnf(c_0_1588, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1296])). 1.08/1.44 cnf(c_0_1589, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1297])). 1.08/1.44 cnf(c_0_1590, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1298])). 1.08/1.44 cnf(c_0_1591, plain, (X1=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1299])). 1.08/1.44 fof(c_0_1592, plain, ![X1536, X1537, X1538]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1538,X1537)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1538,X1536)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1537,X1538),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1536,X1538))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1537,X1536))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat_Odiff__diff__eq])])])). 1.08/1.44 fof(c_0_1593, plain, ![X1678, X1679, X1680, X1681]:((X1678!=X1679|hAPP(c_Polynomial_Ocoeff(X1680,X1678),X1681)=hAPP(c_Polynomial_Ocoeff(X1680,X1679),X1681)|~class_Groups_Ozero(X1680))&(hAPP(c_Polynomial_Ocoeff(X1680,X1678),esk48_3(X1678,X1679,X1680))!=hAPP(c_Polynomial_Ocoeff(X1680,X1679),esk48_3(X1678,X1679,X1680))|X1678=X1679|~class_Groups_Ozero(X1680))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_expand__poly__eq])])])])])])). 1.08/1.44 fof(c_0_1594, plain, ![X1921, X1922, X1923]:(~class_Rings_Olinordered__semidom(X1923)|(~c_Orderings_Oord__class_Oless(X1923,c_Groups_Oone__class_Oone(X1923),X1922)|c_Orderings_Oord__class_Oless(X1923,c_Groups_Oone__class_Oone(X1923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1923),X1922),hAPP(hAPP(c_Power_Opower__class_Opower(X1923),X1922),X1921))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__gt1__lemma])])])). 1.08/1.44 fof(c_0_1595, plain, ![X1432, X1433, X1434]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1434),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1433,X1432))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1434),X1433)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1434),X1432)), inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib])). 1.08/1.44 cnf(c_0_1596, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1300])). 1.08/1.44 fof(c_0_1597, plain, ![X2120, X2121, X2122]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2121,X2120)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2122,X2121),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2122,X2120)))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2122,X2121),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2122,X2120))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2121,X2120))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])])). 1.08/1.44 fof(c_0_1598, plain, ![X756, X757, X758]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X757,X756)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X758,X757),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X758,X756)))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X758,X757),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X758,X756))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X757,X756))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])])). 1.08/1.44 fof(c_0_1599, plain, ![X1978, X1979, X1980]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1980)|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1980),X1978))!=X1980|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1979)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1978,c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_self__quotient__aux2])])])). 1.08/1.44 fof(c_0_1600, plain, ![X823, X824, X825]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X825)|(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X824,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X825),X823))!=X825|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X824,X825)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X823)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])])). 1.08/1.44 fof(c_0_1601, plain, ![X2104, X2105, X2106, X2107]:(~class_Rings_Olinordered__semidom(X2107)|(hAPP(hAPP(c_Power_Opower__class_Opower(X2107),X2106),X2105)!=hAPP(hAPP(c_Power_Opower__class_Opower(X2107),X2104),X2105)|(~c_Orderings_Oord__class_Oless__eq(X2107,c_Groups_Ozero__class_Ozero(X2107),X2106)|(~c_Orderings_Oord__class_Oless__eq(X2107,c_Groups_Ozero__class_Ozero(X2107),X2104)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2105)|X2106=X2104))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__eq__imp__eq__base])])])). 1.08/1.44 fof(c_0_1602, plain, ![X1860, X1861, X1862]:(~class_Rings_Ocomm__semiring__1(X1862)|c_Groups_Oplus__class_Oplus(X1862,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1862),X1861),X1860),X1860)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1862),c_Groups_Oplus__class_Oplus(X1862,X1861,c_Groups_Oone__class_Oone(X1862))),X1860)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])])). 1.08/1.44 fof(c_0_1603, plain, ![X941, X942, X943]:(~class_Rings_Ocomm__semiring__1(X943)|c_Groups_Oplus__class_Oplus(X943,X942,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X943),X941),X942))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X943),c_Groups_Oplus__class_Oplus(X943,X941,c_Groups_Oone__class_Oone(X943))),X942)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])])])). 1.08/1.44 fof(c_0_1604, plain, ![X1353, X1354]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1354),X1353)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1353,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1354),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(X1353)=X1354)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__eq])])). 1.08/1.44 fof(c_0_1605, plain, ![X1445, X1446, X1447]:(~class_Rings_Olinordered__idom(X1447)|(~c_Orderings_Oord__class_Oless__eq(X1447,c_Groups_Ozero__class_Ozero(X1447),X1446)|(~c_Orderings_Oord__class_Oless__eq(X1447,c_Groups_Ozero__class_Ozero(X1447),X1445)|(~c_Orderings_Oord__class_Oless__eq(X1447,X1445,c_Groups_Oone__class_Oone(X1447))|c_Orderings_Oord__class_Oless__eq(X1447,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1447),X1446),X1445),X1446))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__le__one__le])])])). 1.08/1.44 fof(c_0_1606, plain, ![X972, X973, X974]:(~class_Rings_Olinordered__idom(X974)|(~c_Orderings_Oord__class_Oless__eq(X974,c_Groups_Ozero__class_Ozero(X974),X973)|(~c_Orderings_Oord__class_Oless__eq(X974,c_Groups_Ozero__class_Ozero(X974),X972)|(~c_Orderings_Oord__class_Oless__eq(X974,X972,c_Groups_Oone__class_Oone(X974))|c_Orderings_Oord__class_Oless__eq(X974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X974),X972),X973),X973))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__le__one__le])])])). 1.08/1.44 fof(c_0_1607, plain, ![X144, X145, X146, X147]:(~class_RealVector_Oreal__normed__vector(X147)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X146,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X147,X145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X146),c_RealVector_Onorm__class_Onorm(X147,X144)))|c_Groups_Ozero__class_Ozero(X147)=X145))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__ratiotest__lemma])])])). 1.08/1.44 fof(c_0_1608, plain, ![X1791, X1792, X1793, X1794]:(~class_Rings_Olinordered__semiring__strict(X1794)|(~c_Orderings_Oord__class_Oless(X1794,X1793,X1792)|(~c_Orderings_Oord__class_Oless(X1794,c_Groups_Ozero__class_Ozero(X1794),X1791)|c_Orderings_Oord__class_Oless(X1794,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1794),X1793),X1791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1794),X1792),X1791))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__right__mono])])])). 1.08/1.44 fof(c_0_1609, plain, ![X1752, X1753, X1754, X1755]:(~class_Rings_Olinordered__comm__semiring__strict(X1755)|(~c_Orderings_Oord__class_Oless(X1755,X1754,X1753)|(~c_Orderings_Oord__class_Oless(X1755,c_Groups_Ozero__class_Ozero(X1755),X1752)|c_Orderings_Oord__class_Oless(X1755,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1755),X1752),X1754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1755),X1752),X1753))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__mult__strict__left__mono])])])). 1.08/1.44 fof(c_0_1610, plain, ![X698, X699, X700, X701]:(~class_Rings_Olinordered__semiring__strict(X701)|(~c_Orderings_Oord__class_Oless(X701,X700,X699)|(~c_Orderings_Oord__class_Oless(X701,c_Groups_Ozero__class_Ozero(X701),X698)|c_Orderings_Oord__class_Oless(X701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X701),X698),X700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X701),X698),X699))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__left__mono])])])). 1.08/1.44 fof(c_0_1611, plain, ![X548, X549, X550, X551]:(~class_Rings_Olinordered__semidom(X551)|(~c_Orderings_Oord__class_Oless__eq(X551,X550,X549)|(~c_Orderings_Oord__class_Oless__eq(X551,c_Groups_Ozero__class_Ozero(X551),X550)|c_Orderings_Oord__class_Oless__eq(X551,hAPP(hAPP(c_Power_Opower__class_Opower(X551),X550),X548),hAPP(hAPP(c_Power_Opower__class_Opower(X551),X549),X548))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__mono])])])). 1.08/1.44 fof(c_0_1612, plain, ![X2042, X2043, X2044, X2045]:(~class_Rings_Oordered__semiring(X2045)|(~c_Orderings_Oord__class_Oless__eq(X2045,X2044,X2043)|(~c_Orderings_Oord__class_Oless__eq(X2045,c_Groups_Ozero__class_Ozero(X2045),X2042)|c_Orderings_Oord__class_Oless__eq(X2045,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2045),X2044),X2042),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2045),X2043),X2042))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__mono])])])). 1.08/1.44 fof(c_0_1613, plain, ![X2096, X2097, X2098, X2099]:(~class_Rings_Oordered__comm__semiring(X2099)|(~c_Orderings_Oord__class_Oless__eq(X2099,X2098,X2097)|(~c_Orderings_Oord__class_Oless__eq(X2099,c_Groups_Ozero__class_Ozero(X2099),X2096)|c_Orderings_Oord__class_Oless__eq(X2099,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2099),X2096),X2098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2099),X2096),X2097))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__mult__left__mono])])])). 1.08/1.44 fof(c_0_1614, plain, ![X1471, X1472, X1473, X1474]:(~class_Rings_Oordered__semiring(X1474)|(~c_Orderings_Oord__class_Oless__eq(X1474,X1473,X1472)|(~c_Orderings_Oord__class_Oless__eq(X1474,c_Groups_Ozero__class_Ozero(X1474),X1471)|c_Orderings_Oord__class_Oless__eq(X1474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1474),X1471),X1473),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1474),X1471),X1472))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__mono])])])). 1.08/1.44 fof(c_0_1615, plain, ![X1136, X1137, X1138, X1139]:(~class_Rings_Olinordered__ring__strict(X1139)|(~c_Orderings_Oord__class_Oless(X1139,X1138,X1137)|(~c_Orderings_Oord__class_Oless(X1139,X1136,c_Groups_Ozero__class_Ozero(X1139))|c_Orderings_Oord__class_Oless(X1139,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1139),X1137),X1136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1139),X1138),X1136))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__right__mono__neg])])])). 1.08/1.44 fof(c_0_1616, plain, ![X1455, X1456, X1457, X1458]:(~class_Rings_Olinordered__ring__strict(X1458)|(~c_Orderings_Oord__class_Oless(X1458,X1457,X1456)|(~c_Orderings_Oord__class_Oless(X1458,X1455,c_Groups_Ozero__class_Ozero(X1458))|c_Orderings_Oord__class_Oless(X1458,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1458),X1455),X1456),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1458),X1455),X1457))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__left__mono__neg])])])). 1.08/1.44 fof(c_0_1617, plain, ![X2070, X2071, X2072, X2073]:(~class_Rings_Oordered__ring(X2073)|(~c_Orderings_Oord__class_Oless__eq(X2073,X2072,X2071)|(~c_Orderings_Oord__class_Oless__eq(X2073,X2070,c_Groups_Ozero__class_Ozero(X2073))|c_Orderings_Oord__class_Oless__eq(X2073,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2073),X2071),X2070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2073),X2072),X2070))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])])). 1.08/1.44 fof(c_0_1618, plain, ![X432, X433, X434, X435]:(~class_Rings_Oordered__ring(X435)|(~c_Orderings_Oord__class_Oless__eq(X435,X434,X433)|(~c_Orderings_Oord__class_Oless__eq(X435,X432,c_Groups_Ozero__class_Ozero(X435))|c_Orderings_Oord__class_Oless__eq(X435,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X435),X432),X433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X435),X432),X434))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])])). 1.08/1.44 fof(c_0_1619, plain, ![X677, X678, X679]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X679,X678)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X677,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X678,X677),X679))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__diff])])])). 1.08/1.44 fof(c_0_1620, plain, ![X596, X597, X598, X599, X600]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X600)|(~c_Orderings_Oord__class_Oless(X600,X599,X598)|(~c_Orderings_Oord__class_Oless(X600,X597,X596)|c_Orderings_Oord__class_Oless(X600,c_Groups_Oplus__class_Oplus(X600,X599,X597),c_Groups_Oplus__class_Oplus(X600,X598,X596))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__mono])])])). 1.08/1.44 fof(c_0_1621, plain, ![X2797, X2798, X2799, X2800, X2801]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X2801)|(~c_Orderings_Oord__class_Oless__eq(X2801,X2800,X2799)|(~c_Orderings_Oord__class_Oless(X2801,X2798,X2797)|c_Orderings_Oord__class_Oless(X2801,c_Groups_Oplus__class_Oplus(X2801,X2800,X2798),c_Groups_Oplus__class_Oplus(X2801,X2799,X2797))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])])). 1.08/1.44 fof(c_0_1622, plain, ![X874, X875, X876, X877, X878]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X878)|(~c_Orderings_Oord__class_Oless(X878,X877,X876)|(~c_Orderings_Oord__class_Oless__eq(X878,X875,X874)|c_Orderings_Oord__class_Oless(X878,c_Groups_Oplus__class_Oplus(X878,X877,X875),c_Groups_Oplus__class_Oplus(X878,X876,X874))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__le__mono])])])). 1.08/1.44 fof(c_0_1623, plain, ![X324, X325, X326, X327, X328]:(~class_Groups_Oordered__ab__semigroup__add(X328)|(~c_Orderings_Oord__class_Oless__eq(X328,X327,X326)|(~c_Orderings_Oord__class_Oless__eq(X328,X325,X324)|c_Orderings_Oord__class_Oless__eq(X328,c_Groups_Oplus__class_Oplus(X328,X327,X325),c_Groups_Oplus__class_Oplus(X328,X326,X324))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__mono])])])). 1.08/1.44 fof(c_0_1624, plain, ![X370, X371, X372, X373]:(~class_Rings_Olinordered__semidom(X373)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X372,X371)|(~c_Orderings_Oord__class_Oless(X373,c_Groups_Oone__class_Oone(X373),X370)|c_Orderings_Oord__class_Oless(X373,hAPP(hAPP(c_Power_Opower__class_Opower(X373),X370),X372),hAPP(hAPP(c_Power_Opower__class_Opower(X373),X370),X371))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__increasing])])])). 1.08/1.44 fof(c_0_1625, plain, ![X2832, X2833, X2834, X2835]:(~class_Rings_Olinordered__semidom(X2835)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2834,X2833)|(~c_Orderings_Oord__class_Oless__eq(X2835,c_Groups_Oone__class_Oone(X2835),X2832)|c_Orderings_Oord__class_Oless__eq(X2835,hAPP(hAPP(c_Power_Opower__class_Opower(X2835),X2832),X2834),hAPP(hAPP(c_Power_Opower__class_Opower(X2835),X2832),X2833))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__increasing])])])). 1.08/1.44 fof(c_0_1626, plain, ![X374, X375, X376]:(((~c_Orderings_Oord__class_Oless__eq(X376,X374,c_Groups_Ozero__class_Ozero(X376))|~c_Orderings_Oord__class_Oless__eq(X376,c_Groups_Ozero__class_Ozero(X376),X375)|c_Groups_Oabs__class_Oabs(X376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X376),X375),X374))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X376),c_Groups_Oabs__class_Oabs(X376,X375)),c_Groups_Oabs__class_Oabs(X376,X374))|~class_Rings_Oordered__ring__abs(X376))&(~c_Orderings_Oord__class_Oless__eq(X376,c_Groups_Ozero__class_Ozero(X376),X374)|~c_Orderings_Oord__class_Oless__eq(X376,c_Groups_Ozero__class_Ozero(X376),X375)|c_Groups_Oabs__class_Oabs(X376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X376),X375),X374))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X376),c_Groups_Oabs__class_Oabs(X376,X375)),c_Groups_Oabs__class_Oabs(X376,X374))|~class_Rings_Oordered__ring__abs(X376)))&((~c_Orderings_Oord__class_Oless__eq(X376,X374,c_Groups_Ozero__class_Ozero(X376))|~c_Orderings_Oord__class_Oless__eq(X376,X375,c_Groups_Ozero__class_Ozero(X376))|c_Groups_Oabs__class_Oabs(X376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X376),X375),X374))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X376),c_Groups_Oabs__class_Oabs(X376,X375)),c_Groups_Oabs__class_Oabs(X376,X374))|~class_Rings_Oordered__ring__abs(X376))&(~c_Orderings_Oord__class_Oless__eq(X376,c_Groups_Ozero__class_Ozero(X376),X374)|~c_Orderings_Oord__class_Oless__eq(X376,X375,c_Groups_Ozero__class_Ozero(X376))|c_Groups_Oabs__class_Oabs(X376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X376),X375),X374))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X376),c_Groups_Oabs__class_Oabs(X376,X375)),c_Groups_Oabs__class_Oabs(X376,X374))|~class_Rings_Oordered__ring__abs(X376)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__eq__mult])])])])). 1.08/1.44 fof(c_0_1627, plain, ![X1720, X1721, X1723]:(((c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk49_2(X1720,X1721),X1720)|~hBOOL(hAPP(X1721,X1720))|hBOOL(hAPP(X1721,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(hBOOL(hAPP(X1721,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk49_2(X1720,X1721),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~hBOOL(hAPP(X1721,X1720))|hBOOL(hAPP(X1721,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1723,esk49_2(X1720,X1721))|~hBOOL(hAPP(X1721,X1723))|~hBOOL(hAPP(X1721,X1720))|hBOOL(hAPP(X1721,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less])])])])])])). 1.08/1.44 fof(c_0_1628, plain, ![X2093, X2094, X2095]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2094|hAPP(hAPP(c_Power_Opower__class_Opower(X2095),X2093),X2094)=c_Groups_Oone__class_Oone(X2095)|~class_Power_Opower(X2095))&(X2094=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X2095),X2093),X2094)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2095),X2093),hAPP(hAPP(c_Power_Opower__class_Opower(X2095),X2093),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2094,c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Power_Opower(X2095))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_realpow__num__eq__if])])])])). 1.08/1.44 cnf(c_0_1629, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_1301])). 1.08/1.44 fof(c_0_1630, plain, ![X730, X731, X732]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X732,X731)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X730)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X732,X730),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X731,X730)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono1])])])). 1.08/1.44 fof(c_0_1631, plain, ![X1061, X1062, X1063]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1063)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1063,X1062)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1061,X1062),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1061,X1063)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])])). 1.08/1.44 fof(c_0_1632, plain, ![X2600, X2601, X2602]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2602,X2601)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2600,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2601,X2600),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2602,X2600)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono1__neg])])])). 1.08/1.44 fof(c_0_1633, plain, ![X342, X343, X344, X345]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X345,X344)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X343,X342)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X345,X343),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X344,X342)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zadd__zless__mono])])])). 1.08/1.44 fof(c_0_1634, plain, ![X1830, X1831, X1832]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1832,X1831)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1830,X1832)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1832,X1830),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1831,X1830)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__less__mono])])])). 1.08/1.44 fof(c_0_1635, plain, ![X2743, X2744, X2745]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2745,X2744)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2745,X2743)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2743,X2744),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2743,X2745)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__less__mono2])])])). 1.08/1.44 fof(c_0_1636, plain, ![X1311, X1312, X1313, X1314]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1314,X1313)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1312,X1311)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1314,X1312),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1313,X1311)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__mono])])])). 1.08/1.44 fof(c_0_1637, plain, ![X797, X798, X799, X800]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X800,X799)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X798,X797)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X800,X798),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X799,X797)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__mono])])])). 1.08/1.44 fof(c_0_1638, plain, ![X630, X631, X632]:(((c_Groups_Ozero__class_Ozero(X632)=X631|c_Groups_Oplus__class_Oplus(X632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X632),X631),X631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X632),X630),X630))!=c_Groups_Ozero__class_Ozero(X632)|~class_Rings_Olinordered__ring__strict(X632))&(c_Groups_Ozero__class_Ozero(X632)=X630|c_Groups_Oplus__class_Oplus(X632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X632),X631),X631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X632),X630),X630))!=c_Groups_Ozero__class_Ozero(X632)|~class_Rings_Olinordered__ring__strict(X632)))&(c_Groups_Ozero__class_Ozero(X632)!=X631|c_Groups_Ozero__class_Ozero(X632)!=X630|c_Groups_Oplus__class_Oplus(X632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X632),X631),X631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X632),X630),X630))=c_Groups_Ozero__class_Ozero(X632)|~class_Rings_Olinordered__ring__strict(X632))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__squares__eq__zero__iff])])])])). 1.08/1.44 cnf(c_0_1639, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_1302])). 1.08/1.44 cnf(c_0_1640, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1303])). 1.08/1.44 fof(c_0_1641, plain, ![X320, X321, X322]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X322,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X322),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X320)))|X321=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rabs__ratiotest__lemma])])). 1.08/1.44 fof(c_0_1642, plain, ![X1873, X1874, X1875, X1876]:(~class_RealVector_Oreal__normed__algebra(X1876)|c_Groups_Ominus__class_Ominus(X1876,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1876),X1875),X1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1876),X1875),X1873))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1876),X1875),c_Groups_Ominus__class_Ominus(X1876,X1874,X1873))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff])])). 1.08/1.44 fof(c_0_1643, plain, ![X953, X954, X955, X956]:(~class_Rings_Ocomm__semiring__1(X956)|c_Groups_Oplus__class_Oplus(X956,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X956),X955),X954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X956),X955),X953))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X956),X955),c_Groups_Oplus__class_Oplus(X956,X954,X953))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])])). 1.08/1.44 fof(c_0_1644, plain, ![X2175, X2176, X2177, X2178]:(~class_RealVector_Oreal__normed__algebra(X2178)|c_Groups_Oplus__class_Oplus(X2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2178),X2177),X2176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2178),X2177),X2175))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2178),X2177),c_Groups_Oplus__class_Oplus(X2178,X2176,X2175))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])])). 1.08/1.44 fof(c_0_1645, plain, ![X558, X559, X560, X561]:(~class_RealVector_Oreal__normed__algebra(X561)|c_Groups_Oplus__class_Oplus(X561,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X561),X560),X559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X561),X560),X558))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X561),X560),c_Groups_Oplus__class_Oplus(X561,X559,X558))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])])). 1.08/1.44 fof(c_0_1646, plain, ![X232, X233, X234, X235]:(~class_RealVector_Oreal__normed__algebra(X235)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X235),X234),c_Groups_Ominus__class_Ominus(X235,X233,X232))=c_Groups_Ominus__class_Ominus(X235,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X235),X234),X233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X235),X234),X232))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult_Odiff__right])])])). 1.08/1.44 fof(c_0_1647, plain, ![X1521, X1522, X1523]:(((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1523)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1523),X1522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1523),X1521)))&(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1522,X1521)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1523),X1522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1523),X1521))))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1523)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1522,X1521)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1523),X1522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1523),X1521)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])])). 1.08/1.44 fof(c_0_1648, plain, ![X1703, X1704, X1705]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1704)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1705,X1703)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1705),X1704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1703),X1704)))&((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1704)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1705),X1704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1703),X1704)))&(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1705,X1703)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1705),X1704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1703),X1704))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])])). 1.08/1.44 fof(c_0_1649, plain, ![X1120, X1121]:((~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1120,X1121)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1120)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1121,X1120))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1121))&((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1120,X1121)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1121,X1120))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1121))&(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1120)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1121,X1120))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1121)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])])])). 1.08/1.44 fof(c_0_1650, plain, ![X738, X739, X740]:(~class_Rings_Olinordered__semiring__strict(X740)|(~c_Orderings_Oord__class_Oless(X740,c_Groups_Ozero__class_Ozero(X740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X740),X739),X738))|(~c_Orderings_Oord__class_Oless(X740,c_Groups_Ozero__class_Ozero(X740),X738)|c_Orderings_Oord__class_Oless(X740,c_Groups_Ozero__class_Ozero(X740),X739)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__mult__pos2])])])). 1.08/1.44 fof(c_0_1651, plain, ![X302, X303, X304]:(~class_Rings_Olinordered__semiring__strict(X304)|(~c_Orderings_Oord__class_Oless(X304,c_Groups_Ozero__class_Ozero(X304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X304),X303),X302))|(~c_Orderings_Oord__class_Oless(X304,c_Groups_Ozero__class_Ozero(X304),X303)|c_Orderings_Oord__class_Oless(X304,c_Groups_Ozero__class_Ozero(X304),X302)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])])). 1.08/1.44 fof(c_0_1652, plain, ![X656, X657, X658]:(~class_Groups_Omonoid__mult(X658)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X658),hAPP(hAPP(c_Power_Opower__class_Opower(X658),X657),X656)),X657)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X658),X657),hAPP(hAPP(c_Power_Opower__class_Opower(X658),X657),X656))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__commutes])])])). 1.08/1.44 fof(c_0_1653, plain, ![X1742, X1743, X1744, X1745]:(~class_Rings_Ocomm__semiring__1(X1745)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1745),X1744),X1743)),X1742)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1745),X1744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1745),X1743),X1742))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])])). 1.08/1.44 fof(c_0_1654, plain, ![X722, X723, X724, X725]:(~class_Rings_Ocomm__semiring__1(X725)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X725),X724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X725),X723),X722))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X725),X724),X723)),X722)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])])). 1.08/1.44 fof(c_0_1655, plain, ![X935, X936, X937, X938]:(~class_Groups_Oab__semigroup__mult(X938)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X938),X937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X938),X936),X935))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X938),X937),X936)),X935)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])])). 1.08/1.44 fof(c_0_1656, plain, ![X580, X581]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X581,X580)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X581),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X580)))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X581),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X580))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X581,X580))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__real__le])])). 1.08/1.44 fof(c_0_1657, plain, ![X410, X411]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X411,X410)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X411),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X410),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X411),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X410),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X411,X410))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__real__less])])). 1.08/1.44 fof(c_0_1658, plain, ![X2218]:((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk64_1(X2218),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2218)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2218))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2218,c_RealDef_Oreal(tc_Nat_Onat,esk64_1(X2218)))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2218))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6])])])])). 1.08/1.44 cnf(c_0_1659, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk36_1(X1))))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1304])). 1.08/1.44 cnf(c_0_1660, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_1305])). 1.08/1.44 cnf(c_0_1661, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),X1)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1306])). 1.08/1.44 fof(c_0_1662, plain, ![X2561, X2562, X2563, X2564]:(~class_Groups_Omonoid__mult(X2564)|hAPP(hAPP(c_Power_Opower__class_Opower(X2564),X2563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2562),X2561))=hAPP(hAPP(c_Power_Opower__class_Opower(X2564),hAPP(hAPP(c_Power_Opower__class_Opower(X2564),X2563),X2562)),X2561)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])])). 1.08/1.44 fof(c_0_1663, plain, ![X361, X362, X363, X364]:(~class_Rings_Ocomm__semiring__1(X364)|hAPP(hAPP(c_Power_Opower__class_Opower(X364),X363),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X362),X361))=hAPP(hAPP(c_Power_Opower__class_Opower(X364),hAPP(hAPP(c_Power_Opower__class_Opower(X364),X363),X362)),X361)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])])])). 1.08/1.44 fof(c_0_1664, plain, ![X2558, X2559, X2560]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2560,X2559)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2558)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2558),X2560),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2558),X2559)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult__zless__mono2])])])). 1.08/1.44 fof(c_0_1665, plain, ![X849, X850, X851]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X851,X850)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X849)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X851),X849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X850),X849)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__mono1])])])). 1.08/1.44 fof(c_0_1666, plain, ![X2707, X2708, X2709]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2709,X2708)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2707)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2707),X2709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2707),X2708)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__mono2])])])). 1.08/1.44 fof(c_0_1667, plain, ![X1069, X1070, X1071]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1071)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1070,X1069)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1071),X1070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1071),X1069)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__mult__less__mono2])])])). 1.08/1.44 fof(c_0_1668, plain, ![X2670, X2671]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2671|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2670),X2671))&(X2671=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2670),X2671)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2670),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2670),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2671,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__if])])). 1.08/1.44 fof(c_0_1669, plain, ![X1245, X1246, X1247]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1247,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1246,X1245))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1247,X1245),X1246))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1247,X1245),X1246)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1247,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1246,X1245)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])])). 1.08/1.44 fof(c_0_1670, plain, ![X1398, X1399, X1400]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1400,X1399),X1398)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1400,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1398,X1399)))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1400,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1398,X1399))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1400,X1399),X1398))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])])). 1.08/1.44 fof(c_0_1671, plain, ![X2552, X2553, X2554, X2555]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2555,X2554)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2553,X2552)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2555),X2553),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2554),X2552)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])])). 1.08/1.44 fof(c_0_1672, plain, ![X2246, X2247, X2248, X2249]:(~class_Fields_Ofield(X2249)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X2249),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X2249),X2248,X2247),X2246)=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X2249),X2248,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2249)),X2247),X2246))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_poly__div__mult__right])])])). 1.08/1.44 fof(c_0_1673, plain, ![X1092, X1093, X1094]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1094,X1093)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1093,X1094),X1092)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1093,X1092),X1094)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__diff__assoc2])])])). 1.08/1.44 fof(c_0_1674, plain, ![X884, X885, X886]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X886,X885)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X885,X884),X886)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X885,X886),X884)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__add__assoc2])])])). 1.08/1.44 fof(c_0_1675, plain, ![X1019, X1020, X1021]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1021,X1020)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1019,X1021),X1020)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1019,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1020,X1021))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])])). 1.08/1.44 fof(c_0_1676, plain, ![X2268, X2269, X2270]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2270,X2269)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2268,X2269),X2270)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2268,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2269,X2270))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__diff__assoc])])])). 1.08/1.44 fof(c_0_1677, plain, ![X643, X644, X645]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X645,X644)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X643,X644),X645)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X643,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X644,X645))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__add__assoc])])])). 1.08/1.44 fof(c_0_1678, plain, ![X317, X318]:((~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X317)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X317,X318))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X318))&(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X317,X318))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X317)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X318))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])])])). 1.08/1.44 fof(c_0_1679, plain, ![X395, X396]:((~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X395)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X395,X396),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X396,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X395,X396),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X395)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X396,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__imp__zdiv__neg__iff])])])])). 1.08/1.44 fof(c_0_1680, plain, ![X2241, X2242]:((~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2241,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2241,X2242),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2242))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2241,X2242),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2241,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2242))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])])). 1.16/1.44 fof(c_0_1681, plain, ![X2142, X2143]:((~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2142,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2142,X2143))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2143,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2142,X2143))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2142,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2143,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff])])])])). 1.16/1.44 fof(c_0_1682, plain, ![X761, X762]:((~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X761,X762))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X762,X761)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X762))&(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X762,X761)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X761,X762))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X762))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])])])). 1.16/1.44 fof(c_0_1683, plain, ![X1178, X1179, X1180]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1180)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1179,X1178),X1180)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1179,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1178),X1180))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__zmult2__eq])])])). 1.16/1.44 fof(c_0_1684, plain, ![X1252, X1253, X1254]:(((~c_Orderings_Oord__class_Oless__eq(X1254,X1252,c_Groups_Ozero__class_Ozero(X1254))|~c_Orderings_Oord__class_Oless__eq(X1254,c_Groups_Ozero__class_Ozero(X1254),X1253)|c_Orderings_Oord__class_Oless__eq(X1254,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1254),X1253),X1252),c_Groups_Ozero__class_Ozero(X1254))|~class_Rings_Olinordered__ring__strict(X1254))&(~c_Orderings_Oord__class_Oless__eq(X1254,X1253,c_Groups_Ozero__class_Ozero(X1254))|~c_Orderings_Oord__class_Oless__eq(X1254,c_Groups_Ozero__class_Ozero(X1254),X1252)|c_Orderings_Oord__class_Oless__eq(X1254,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1254),X1253),X1252),c_Groups_Ozero__class_Ozero(X1254))|~class_Rings_Olinordered__ring__strict(X1254)))&(((c_Orderings_Oord__class_Oless__eq(X1254,X1253,c_Groups_Ozero__class_Ozero(X1254))|c_Orderings_Oord__class_Oless__eq(X1254,X1252,c_Groups_Ozero__class_Ozero(X1254))|~c_Orderings_Oord__class_Oless__eq(X1254,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1254),X1253),X1252),c_Groups_Ozero__class_Ozero(X1254))|~class_Rings_Olinordered__ring__strict(X1254))&(c_Orderings_Oord__class_Oless__eq(X1254,c_Groups_Ozero__class_Ozero(X1254),X1252)|c_Orderings_Oord__class_Oless__eq(X1254,X1252,c_Groups_Ozero__class_Ozero(X1254))|~c_Orderings_Oord__class_Oless__eq(X1254,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1254),X1253),X1252),c_Groups_Ozero__class_Ozero(X1254))|~class_Rings_Olinordered__ring__strict(X1254)))&((c_Orderings_Oord__class_Oless__eq(X1254,X1253,c_Groups_Ozero__class_Ozero(X1254))|c_Orderings_Oord__class_Oless__eq(X1254,c_Groups_Ozero__class_Ozero(X1254),X1253)|~c_Orderings_Oord__class_Oless__eq(X1254,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1254),X1253),X1252),c_Groups_Ozero__class_Ozero(X1254))|~class_Rings_Olinordered__ring__strict(X1254))&(c_Orderings_Oord__class_Oless__eq(X1254,c_Groups_Ozero__class_Ozero(X1254),X1252)|c_Orderings_Oord__class_Oless__eq(X1254,c_Groups_Ozero__class_Ozero(X1254),X1253)|~c_Orderings_Oord__class_Oless__eq(X1254,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1254),X1253),X1252),c_Groups_Ozero__class_Ozero(X1254))|~class_Rings_Olinordered__ring__strict(X1254))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__0__iff])])])])). 1.16/1.44 fof(c_0_1685, plain, ![X2522, X2523, X2524]:((((c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),X2522)|c_Orderings_Oord__class_Oless__eq(X2524,X2522,c_Groups_Ozero__class_Ozero(X2524))|~c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2524),X2523),X2522))|~class_Rings_Olinordered__ring__strict(X2524))&(c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),X2523)|c_Orderings_Oord__class_Oless__eq(X2524,X2522,c_Groups_Ozero__class_Ozero(X2524))|~c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2524),X2523),X2522))|~class_Rings_Olinordered__ring__strict(X2524)))&((c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),X2522)|c_Orderings_Oord__class_Oless__eq(X2524,X2523,c_Groups_Ozero__class_Ozero(X2524))|~c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2524),X2523),X2522))|~class_Rings_Olinordered__ring__strict(X2524))&(c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),X2523)|c_Orderings_Oord__class_Oless__eq(X2524,X2523,c_Groups_Ozero__class_Ozero(X2524))|~c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2524),X2523),X2522))|~class_Rings_Olinordered__ring__strict(X2524))))&((~c_Orderings_Oord__class_Oless__eq(X2524,X2522,c_Groups_Ozero__class_Ozero(X2524))|~c_Orderings_Oord__class_Oless__eq(X2524,X2523,c_Groups_Ozero__class_Ozero(X2524))|c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2524),X2523),X2522))|~class_Rings_Olinordered__ring__strict(X2524))&(~c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),X2522)|~c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),X2523)|c_Orderings_Oord__class_Oless__eq(X2524,c_Groups_Ozero__class_Ozero(X2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2524),X2523),X2522))|~class_Rings_Olinordered__ring__strict(X2524)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__mult__iff])])])])). 1.16/1.44 fof(c_0_1686, plain, ![X802, X803]:(((X802!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X803)),X802)))&(X803=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X803)),X802))))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X803)),X802))|(X802=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X803!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])])). 1.16/1.44 fof(c_0_1687, plain, ![X2883, X2884, X2885]:c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2885),X2884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2885),X2883))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2885),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2884,X2883)), inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2])). 1.16/1.44 fof(c_0_1688, plain, ![X96, X97, X98]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X96))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X97,X96)), inference(variable_rename,[status(thm)],[fact_add__mult__distrib2])). 1.16/1.44 fof(c_0_1689, plain, ![X1543, X1544, X1545]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1545),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1544,X1543))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1545),X1544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1545),X1543)), inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2])). 1.16/1.44 fof(c_0_1690, plain, ![X1638, X1639, X1640]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1640),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1639,X1638))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1640),X1639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1640),X1638)), inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2])). 1.16/1.44 fof(c_0_1691, plain, ![X1423, X1424]:(~class_Rings_Ocomm__semiring__1(X1424)|c_Groups_Oplus__class_Oplus(X1424,X1423,X1423)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1424),c_Groups_Oplus__class_Oplus(X1424,c_Groups_Oone__class_Oone(X1424),c_Groups_Oone__class_Oone(X1424))),X1423)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])])])). 1.16/1.44 fof(c_0_1692, plain, ![X1635, X1636, X1637]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1637)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1637),X1636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1637),X1635))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1636,X1635)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])])). 1.16/1.44 fof(c_0_1693, plain, ![X1695, X1696]:(((X1695=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1696),X1696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1695),X1695))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))&(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1696|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1696),X1696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1695),X1695))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))&(X1695!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X1696|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1696),X1696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1695),X1695))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff])])])). 1.16/1.44 cnf(c_0_1694, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_1307])). 1.16/1.44 cnf(c_0_1695, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1308])). 1.16/1.44 fof(c_0_1696, plain, ![X2363]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2363)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2363)),X2363)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ln__add__one__self__le__self])])])). 1.16/1.44 cnf(c_0_1697, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|c_Nat_OSuc(X2)=X1|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1309])). 1.16/1.44 cnf(c_0_1698, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|X1=c_Nat_OSuc(X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1310])). 1.16/1.44 fof(c_0_1699, plain, ![X2114, X2115, X2116]:(~class_Groups_Oordered__comm__monoid__add(X2116)|(~c_Orderings_Oord__class_Oless(X2116,X2115,c_Groups_Ozero__class_Ozero(X2116))|(~c_Orderings_Oord__class_Oless(X2116,X2114,c_Groups_Ozero__class_Ozero(X2116))|c_Orderings_Oord__class_Oless(X2116,c_Groups_Oplus__class_Oplus(X2116,X2115,X2114),c_Groups_Ozero__class_Ozero(X2116))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__neg__neg])])])). 1.16/1.44 fof(c_0_1700, plain, ![X2013, X2014, X2015]:(~class_Groups_Oordered__comm__monoid__add(X2015)|(~c_Orderings_Oord__class_Oless__eq(X2015,X2014,c_Groups_Ozero__class_Ozero(X2015))|(~c_Orderings_Oord__class_Oless(X2015,X2013,c_Groups_Ozero__class_Ozero(X2015))|c_Orderings_Oord__class_Oless(X2015,c_Groups_Oplus__class_Oplus(X2015,X2014,X2013),c_Groups_Ozero__class_Ozero(X2015))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonpos__neg])])])). 1.16/1.44 fof(c_0_1701, plain, ![X1607, X1608, X1609]:(~class_Groups_Oordered__comm__monoid__add(X1609)|(~c_Orderings_Oord__class_Oless(X1609,X1608,c_Groups_Ozero__class_Ozero(X1609))|(~c_Orderings_Oord__class_Oless__eq(X1609,X1607,c_Groups_Ozero__class_Ozero(X1609))|c_Orderings_Oord__class_Oless(X1609,c_Groups_Oplus__class_Oplus(X1609,X1608,X1607),c_Groups_Ozero__class_Ozero(X1609))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__neg__nonpos])])])). 1.16/1.44 fof(c_0_1702, plain, ![X746, X747, X748]:(~class_Groups_Oordered__comm__monoid__add(X748)|(~c_Orderings_Oord__class_Oless__eq(X748,X747,c_Groups_Ozero__class_Ozero(X748))|(~c_Orderings_Oord__class_Oless__eq(X748,X746,c_Groups_Ozero__class_Ozero(X748))|c_Orderings_Oord__class_Oless__eq(X748,c_Groups_Oplus__class_Oplus(X748,X747,X746),c_Groups_Ozero__class_Ozero(X748))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonpos__nonpos])])])). 1.16/1.44 fof(c_0_1703, plain, ![X567, X568, X569]:(~class_Groups_Oordered__comm__monoid__add(X569)|(~c_Orderings_Oord__class_Oless(X569,c_Groups_Ozero__class_Ozero(X569),X568)|(~c_Orderings_Oord__class_Oless(X569,c_Groups_Ozero__class_Ozero(X569),X567)|c_Orderings_Oord__class_Oless(X569,c_Groups_Ozero__class_Ozero(X569),c_Groups_Oplus__class_Oplus(X569,X568,X567))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__pos__pos])])])). 1.16/1.44 fof(c_0_1704, plain, ![X1298, X1299, X1300]:(~class_Groups_Oordered__comm__monoid__add(X1300)|(~c_Orderings_Oord__class_Oless__eq(X1300,c_Groups_Ozero__class_Ozero(X1300),X1299)|(~c_Orderings_Oord__class_Oless(X1300,c_Groups_Ozero__class_Ozero(X1300),X1298)|c_Orderings_Oord__class_Oless(X1300,c_Groups_Ozero__class_Ozero(X1300),c_Groups_Oplus__class_Oplus(X1300,X1299,X1298))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonneg__pos])])])). 1.16/1.44 fof(c_0_1705, plain, ![X2632, X2633, X2634]:(~class_Groups_Oordered__comm__monoid__add(X2634)|(~c_Orderings_Oord__class_Oless(X2634,c_Groups_Ozero__class_Ozero(X2634),X2633)|(~c_Orderings_Oord__class_Oless__eq(X2634,c_Groups_Ozero__class_Ozero(X2634),X2632)|c_Orderings_Oord__class_Oless(X2634,c_Groups_Ozero__class_Ozero(X2634),c_Groups_Oplus__class_Oplus(X2634,X2633,X2632))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])])). 1.16/1.44 fof(c_0_1706, plain, ![X674, X675, X676]:(~class_Groups_Oordered__comm__monoid__add(X676)|(~c_Orderings_Oord__class_Oless__eq(X676,c_Groups_Ozero__class_Ozero(X676),X675)|(~c_Orderings_Oord__class_Oless__eq(X676,c_Groups_Ozero__class_Ozero(X676),X674)|c_Orderings_Oord__class_Oless__eq(X676,c_Groups_Ozero__class_Ozero(X676),c_Groups_Oplus__class_Oplus(X676,X675,X674))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonneg__nonneg])])])). 1.16/1.44 fof(c_0_1707, plain, ![X1718, X1719]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1719,X1718))|(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1719)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1718)))&((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1719)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1719,X1718)))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1718)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1719,X1718))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])])). 1.16/1.44 fof(c_0_1708, plain, ![X691, X692, X693]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X693),X692)),X691)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X692),X691)), inference(variable_rename,[status(thm)],[fact_zpower__zpower])). 1.16/1.44 fof(c_0_1709, plain, ![X2829, X2830, X2831]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2831),X2830)),X2829)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2830),X2829)), inference(variable_rename,[status(thm)],[fact_real__mult__assoc])). 1.16/1.44 fof(c_0_1710, plain, ![X782, X783, X784]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X783),X782))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X784),X783)),X782), inference(variable_rename,[status(thm)],[fact_zmult__assoc])). 1.16/1.44 fof(c_0_1711, plain, ![X570, X571, X572]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X571),X570))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X572),X571)),X570), inference(variable_rename,[status(thm)],[fact_nat__mult__assoc])). 1.16/1.44 fof(c_0_1712, plain, ![X2862, X2863, X2864]:(~class_Rings_Olinordered__semiring__strict(X2864)|(~c_Orderings_Oord__class_Oless(X2864,X2863,c_Groups_Ozero__class_Ozero(X2864))|(~c_Orderings_Oord__class_Oless(X2864,c_Groups_Ozero__class_Ozero(X2864),X2862)|c_Orderings_Oord__class_Oless(X2864,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2864),X2863),X2862),c_Groups_Ozero__class_Ozero(X2864))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__neg__pos])])])). 1.16/1.44 fof(c_0_1713, plain, ![X785, X786, X787]:(~class_Rings_Olinordered__semiring__strict(X787)|(~c_Orderings_Oord__class_Oless(X787,c_Groups_Ozero__class_Ozero(X787),X786)|(~c_Orderings_Oord__class_Oless(X787,X785,c_Groups_Ozero__class_Ozero(X787))|c_Orderings_Oord__class_Oless(X787,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X787),X786),X785),c_Groups_Ozero__class_Ozero(X787))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__neg])])])). 1.16/1.44 fof(c_0_1714, plain, ![X165, X166, X167]:(~class_Rings_Olinordered__semiring__strict(X167)|(~c_Orderings_Oord__class_Oless(X167,c_Groups_Ozero__class_Ozero(X167),X166)|(~c_Orderings_Oord__class_Oless(X167,X165,c_Groups_Ozero__class_Ozero(X167))|c_Orderings_Oord__class_Oless(X167,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X167),X165),X166),c_Groups_Ozero__class_Ozero(X167))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__neg2])])])). 1.16/1.44 fof(c_0_1715, plain, ![X2317, X2318, X2319]:((~c_Orderings_Oord__class_Oless__eq(X2319,X2318,c_Groups_Ozero__class_Ozero(X2319))|~c_Orderings_Oord__class_Oless__eq(X2319,c_Groups_Ozero__class_Ozero(X2319),X2317)|c_Orderings_Oord__class_Oless__eq(X2319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2319),X2318),X2317),c_Groups_Ozero__class_Ozero(X2319))|~class_Rings_Oordered__cancel__semiring(X2319))&(~c_Orderings_Oord__class_Oless__eq(X2319,c_Groups_Ozero__class_Ozero(X2319),X2318)|~c_Orderings_Oord__class_Oless__eq(X2319,X2317,c_Groups_Ozero__class_Ozero(X2319))|c_Orderings_Oord__class_Oless__eq(X2319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2319),X2318),X2317),c_Groups_Ozero__class_Ozero(X2319))|~class_Rings_Oordered__cancel__semiring(X2319))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])])). 1.16/1.44 fof(c_0_1716, plain, ![X2049, X2050, X2051]:(~class_Rings_Oordered__cancel__semiring(X2051)|(~c_Orderings_Oord__class_Oless__eq(X2051,X2050,c_Groups_Ozero__class_Ozero(X2051))|(~c_Orderings_Oord__class_Oless__eq(X2051,c_Groups_Ozero__class_Ozero(X2051),X2049)|c_Orderings_Oord__class_Oless__eq(X2051,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2051),X2050),X2049),c_Groups_Ozero__class_Ozero(X2051))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__nonpos__nonneg])])])). 1.16/1.44 fof(c_0_1717, plain, ![X1008, X1009, X1010]:(~class_Rings_Oordered__cancel__semiring(X1010)|(~c_Orderings_Oord__class_Oless__eq(X1010,c_Groups_Ozero__class_Ozero(X1010),X1009)|(~c_Orderings_Oord__class_Oless__eq(X1010,X1008,c_Groups_Ozero__class_Ozero(X1010))|c_Orderings_Oord__class_Oless__eq(X1010,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1010),X1009),X1008),c_Groups_Ozero__class_Ozero(X1010))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])])). 1.16/1.44 fof(c_0_1718, plain, ![X2585, X2586, X2587]:(~class_Rings_Oordered__cancel__semiring(X2587)|(~c_Orderings_Oord__class_Oless__eq(X2587,c_Groups_Ozero__class_Ozero(X2587),X2586)|(~c_Orderings_Oord__class_Oless__eq(X2587,X2585,c_Groups_Ozero__class_Ozero(X2587))|c_Orderings_Oord__class_Oless__eq(X2587,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2587),X2585),X2586),c_Groups_Ozero__class_Ozero(X2587))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__nonneg__nonpos2])])])). 1.16/1.44 fof(c_0_1719, plain, ![X1540, X1541, X1542]:(~class_Rings_Olinordered__semidom(X1542)|(~c_Orderings_Oord__class_Oless(X1542,c_Groups_Oone__class_Oone(X1542),X1541)|(~c_Orderings_Oord__class_Oless(X1542,c_Groups_Oone__class_Oone(X1542),X1540)|c_Orderings_Oord__class_Oless(X1542,c_Groups_Oone__class_Oone(X1542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1542),X1541),X1540))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__1__mult])])])). 1.16/1.44 fof(c_0_1720, plain, ![X1108, X1109, X1110]:(~class_Rings_Olinordered__semiring__strict(X1110)|(~c_Orderings_Oord__class_Oless(X1110,c_Groups_Ozero__class_Ozero(X1110),X1109)|(~c_Orderings_Oord__class_Oless(X1110,c_Groups_Ozero__class_Ozero(X1110),X1108)|c_Orderings_Oord__class_Oless(X1110,c_Groups_Ozero__class_Ozero(X1110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1110),X1109),X1108))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__pos])])])). 1.16/1.44 fof(c_0_1721, plain, ![X1673, X1674, X1675]:(~class_Rings_Oordered__cancel__semiring(X1675)|(~c_Orderings_Oord__class_Oless__eq(X1675,c_Groups_Ozero__class_Ozero(X1675),X1674)|(~c_Orderings_Oord__class_Oless__eq(X1675,c_Groups_Ozero__class_Ozero(X1675),X1673)|c_Orderings_Oord__class_Oless__eq(X1675,c_Groups_Ozero__class_Ozero(X1675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1675),X1674),X1673))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__nonneg__nonneg])])])). 1.16/1.44 fof(c_0_1722, plain, ![X2853, X2854, X2855]:((~c_Orderings_Oord__class_Oless__eq(X2855,X2854,c_Groups_Ozero__class_Ozero(X2855))|~c_Orderings_Oord__class_Oless__eq(X2855,X2853,c_Groups_Ozero__class_Ozero(X2855))|c_Orderings_Oord__class_Oless__eq(X2855,c_Groups_Ozero__class_Ozero(X2855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2855),X2854),X2853))|~class_Rings_Oordered__ring(X2855))&(~c_Orderings_Oord__class_Oless__eq(X2855,c_Groups_Ozero__class_Ozero(X2855),X2854)|~c_Orderings_Oord__class_Oless__eq(X2855,c_Groups_Ozero__class_Ozero(X2855),X2853)|c_Orderings_Oord__class_Oless__eq(X2855,c_Groups_Ozero__class_Ozero(X2855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2855),X2854),X2853))|~class_Rings_Oordered__ring(X2855))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__mult__pos__le])])])])). 1.16/1.44 fof(c_0_1723, plain, ![X1000, X1001, X1002]:(~class_Rings_Olinordered__ring__strict(X1002)|(~c_Orderings_Oord__class_Oless(X1002,X1001,c_Groups_Ozero__class_Ozero(X1002))|(~c_Orderings_Oord__class_Oless(X1002,X1000,c_Groups_Ozero__class_Ozero(X1002))|c_Orderings_Oord__class_Oless(X1002,c_Groups_Ozero__class_Ozero(X1002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1002),X1001),X1000))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__neg__neg])])])). 1.16/1.44 fof(c_0_1724, plain, ![X1407, X1408, X1409]:(~class_Rings_Oordered__ring(X1409)|(~c_Orderings_Oord__class_Oless__eq(X1409,X1408,c_Groups_Ozero__class_Ozero(X1409))|(~c_Orderings_Oord__class_Oless__eq(X1409,X1407,c_Groups_Ozero__class_Ozero(X1409))|c_Orderings_Oord__class_Oless__eq(X1409,c_Groups_Ozero__class_Ozero(X1409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1409),X1408),X1407))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])])). 1.16/1.44 fof(c_0_1725, plain, ![X1686, X1687, X1688, X1689]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X1689)|(~c_Orderings_Oord__class_Oless(X1689,X1688,X1687)|c_Orderings_Oord__class_Oless(X1689,c_Groups_Oplus__class_Oplus(X1689,X1688,X1686),c_Groups_Oplus__class_Oplus(X1689,X1687,X1686)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])])). 1.16/1.44 fof(c_0_1726, plain, ![X2320, X2321, X2322, X2323]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X2323)|(~c_Orderings_Oord__class_Oless(X2323,X2322,X2321)|c_Orderings_Oord__class_Oless(X2323,c_Groups_Oplus__class_Oplus(X2323,X2320,X2322),c_Groups_Oplus__class_Oplus(X2323,X2320,X2321)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__left__mono])])])). 1.16/1.44 fof(c_0_1727, plain, ![X1292, X1293, X1294, X1295]:(~class_Groups_Oordered__ab__semigroup__add(X1295)|(~c_Orderings_Oord__class_Oless__eq(X1295,X1294,X1293)|c_Orderings_Oord__class_Oless__eq(X1295,c_Groups_Oplus__class_Oplus(X1295,X1294,X1292),c_Groups_Oplus__class_Oplus(X1295,X1293,X1292)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__right__mono])])])). 1.16/1.44 fof(c_0_1728, plain, ![X455, X456, X457, X458]:(~class_Groups_Oordered__ab__semigroup__add(X458)|(~c_Orderings_Oord__class_Oless__eq(X458,X457,X456)|c_Orderings_Oord__class_Oless__eq(X458,c_Groups_Oplus__class_Oplus(X458,X455,X457),c_Groups_Oplus__class_Oplus(X458,X455,X456)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__left__mono])])])). 1.16/1.44 cnf(c_0_1729, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1311])). 1.16/1.44 cnf(c_0_1730, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1297])). 1.16/1.44 cnf(c_0_1731, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1298])). 1.16/1.44 fof(c_0_1732, plain, ![X334, X335, X337]:(((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk9_2(X334,X335))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X334)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X335))&(X334=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk9_2(X334,X335)),X335)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X334)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X335)))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X337)|X334!=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X337),X335)|X337=esk9_2(X334,X335)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X334)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X335))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_realpow__pos__nth__unique])])])])])])). 1.16/1.44 fof(c_0_1733, plain, ![X770, X771, X772]:(~class_Rings_Olinordered__semidom(X772)|(~c_Orderings_Oord__class_Oless(X772,c_Groups_Oone__class_Oone(X772),X771)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X770)|c_Orderings_Oord__class_Oless(X772,c_Groups_Oone__class_Oone(X772),hAPP(hAPP(c_Power_Opower__class_Opower(X772),X771),X770))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__less__power])])])). 1.16/1.44 fof(c_0_1734, plain, ![X1355, X1356, X1357, X1358]:((~c_SEQ_Oincseq(X1356,X1355)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1357,X1358)|c_Orderings_Oord__class_Oless__eq(X1356,hAPP(X1355,X1357),hAPP(X1355,X1358)))|~class_Orderings_Oorder(X1356))&((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk40_2(X1355,X1356),esk41_2(X1355,X1356))|c_SEQ_Oincseq(X1356,X1355)|~class_Orderings_Oorder(X1356))&(~c_Orderings_Oord__class_Oless__eq(X1356,hAPP(X1355,esk40_2(X1355,X1356)),hAPP(X1355,esk41_2(X1355,X1356)))|c_SEQ_Oincseq(X1356,X1355)|~class_Orderings_Oorder(X1356)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_incseq__def])])])])])])). 1.16/1.44 fof(c_0_1735, plain, ![X519, X520, X523, X524]:(((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk18_2(X519,X520),esk19_2(X519,X520))|c_SEQ_Odecseq(X520,X519)|~class_Orderings_Oorder(X520))&(~c_Orderings_Oord__class_Oless__eq(X520,hAPP(X519,esk19_2(X519,X520)),hAPP(X519,esk18_2(X519,X520)))|c_SEQ_Odecseq(X520,X519)|~class_Orderings_Oorder(X520)))&(~c_SEQ_Odecseq(X520,X519)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X523,X524)|c_Orderings_Oord__class_Oless__eq(X520,hAPP(X519,X524),hAPP(X519,X523)))|~class_Orderings_Oorder(X520))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decseq__def])])])])])). 1.16/1.44 fof(c_0_1736, plain, ![X2544, X2545]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X2545),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2544)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2545,c_RealDef_Oreal(tc_Nat_Onat,X2544))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt])])])). 1.16/1.44 fof(c_0_1737, plain, ![X944, X945, X946, X947]:(~class_Groups_Oordered__comm__monoid__add(X947)|(~c_Orderings_Oord__class_Oless__eq(X947,c_Groups_Ozero__class_Ozero(X947),X946)|(~c_Orderings_Oord__class_Oless(X947,X945,X944)|c_Orderings_Oord__class_Oless(X947,X945,c_Groups_Oplus__class_Oplus(X947,X946,X944))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__increasing2])])])). 1.16/1.44 fof(c_0_1738, plain, ![X2297, X2298, X2299, X2300]:(~class_Groups_Oordered__comm__monoid__add(X2300)|(~c_Orderings_Oord__class_Oless(X2300,c_Groups_Ozero__class_Ozero(X2300),X2299)|(~c_Orderings_Oord__class_Oless__eq(X2300,X2298,X2297)|c_Orderings_Oord__class_Oless(X2300,X2298,c_Groups_Oplus__class_Oplus(X2300,X2299,X2297))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__increasing])])])). 1.16/1.44 fof(c_0_1739, plain, ![X887, X888, X889, X890]:(~class_Rings_Olinordered__semidom(X890)|(~c_Orderings_Oord__class_Oless(X890,c_Groups_Ozero__class_Ozero(X890),X889)|(~c_Orderings_Oord__class_Oless(X890,X888,X887)|c_Orderings_Oord__class_Oless(X890,X888,c_Groups_Oplus__class_Oplus(X890,X889,X887))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__add__strict])])])). 1.16/1.44 fof(c_0_1740, plain, ![X1783, X1784, X1785, X1786]:(~class_Groups_Oordered__comm__monoid__add(X1786)|(~c_Orderings_Oord__class_Oless__eq(X1786,c_Groups_Ozero__class_Ozero(X1786),X1785)|(~c_Orderings_Oord__class_Oless__eq(X1786,X1784,X1783)|c_Orderings_Oord__class_Oless__eq(X1786,X1784,c_Groups_Oplus__class_Oplus(X1786,X1785,X1783))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__increasing])])])). 1.16/1.44 fof(c_0_1741, plain, ![X1174, X1175, X1176, X1177]:(~class_Groups_Oordered__comm__monoid__add(X1177)|(~c_Orderings_Oord__class_Oless__eq(X1177,c_Groups_Ozero__class_Ozero(X1177),X1176)|(~c_Orderings_Oord__class_Oless__eq(X1177,X1175,X1174)|c_Orderings_Oord__class_Oless__eq(X1177,X1175,c_Groups_Oplus__class_Oplus(X1177,X1174,X1176))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__increasing2])])])). 1.16/1.44 fof(c_0_1742, plain, ![X1389, X1390]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1390),X1390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1389),X1389)), inference(variable_rename,[status(thm)],[fact_real__minus__mult__self__le])). 1.16/1.44 fof(c_0_1743, plain, ![X196, X197, X198]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X198,X197)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X198,X196),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X197,X196))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])])). 1.16/1.44 fof(c_0_1744, plain, ![X2388, X2389, X2390]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2390,X2389)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2390,X2388),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2389,X2388))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])])). 1.16/1.44 fof(c_0_1745, plain, ![X2610, X2611, X2612]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2612,X2611)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2610,X2612),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2610,X2611))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])])). 1.16/1.44 fof(c_0_1746, plain, ![X2375, X2376, X2377]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2377,X2376)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2377,X2375),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2376,X2375))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])])). 1.16/1.44 fof(c_0_1747, plain, ![X224, X225, X226]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X226,X225)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X226,X224),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X225,X224))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])])). 1.16/1.44 fof(c_0_1748, plain, ![X735, X736, X737]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X737,X736)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X735,X736),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X735,X737))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__le__mono2])])])). 1.16/1.44 fof(c_0_1749, plain, ![X2124, X2125, X2126]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2126,X2125)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2126,X2124),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2125,X2124))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__mono1])])])). 1.16/1.44 fof(c_0_1750, plain, ![X1936, X1937, X1938]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1938,X1937)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1936,X1938),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1936,X1937))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__add__left__mono])])])). 1.16/1.44 fof(c_0_1751, plain, ![X1375, X1376, X1377]:(~class_Rings_Olinordered__idom(X1377)|c_Groups_Oabs__class_Oabs(X1377,hAPP(hAPP(c_Power_Opower__class_Opower(X1377),c_Groups_Ouminus__class_Ouminus(X1377,X1376)),X1375))=c_Groups_Oabs__class_Oabs(X1377,hAPP(hAPP(c_Power_Opower__class_Opower(X1377),X1376),X1375))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])])). 1.16/1.44 cnf(c_0_1752, plain, (X1=c_Nat_OSuc(esk25_2(X2,X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1312])). 1.16/1.44 cnf(c_0_1753, plain, (X1=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1313])). 1.16/1.44 fof(c_0_1754, plain, ![X2228, X2229, X2230]:(~class_Divides_Osemiring__div(X2230)|(X2229=c_Groups_Ozero__class_Ozero(X2230)|c_Groups_Oplus__class_Oplus(X2230,c_Divides_Odiv__class_Odiv(X2230,X2228,X2229),c_Groups_Oone__class_Oone(X2230))=c_Divides_Odiv__class_Odiv(X2230,c_Groups_Oplus__class_Oplus(X2230,X2229,X2228),X2229))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__add__self1])])])). 1.16/1.44 fof(c_0_1755, plain, ![X1401, X1402, X1403]:(~class_Divides_Osemiring__div(X1403)|(X1402=c_Groups_Ozero__class_Ozero(X1403)|c_Groups_Oplus__class_Oplus(X1403,c_Divides_Odiv__class_Odiv(X1403,X1401,X1402),c_Groups_Oone__class_Oone(X1403))=c_Divides_Odiv__class_Odiv(X1403,c_Groups_Oplus__class_Oplus(X1403,X1401,X1402),X1402))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__add__self2])])])). 1.16/1.44 cnf(c_0_1756, plain, (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1314])). 1.16/1.44 cnf(c_0_1757, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1315])). 1.16/1.44 cnf(c_0_1758, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk25_2(X1,X2),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))), inference(split_conjunct,[status(thm)],[c_0_1312])). 1.16/1.44 fof(c_0_1759, plain, ![X1907, X1908, X1909]:(~class_Groups_Oordered__ab__group__add__abs(X1909)|c_Groups_Oabs__class_Oabs(X1909,c_Groups_Oplus__class_Oplus(X1909,c_Groups_Oabs__class_Oabs(X1909,X1908),c_Groups_Oabs__class_Oabs(X1909,X1907)))=c_Groups_Oplus__class_Oplus(X1909,c_Groups_Oabs__class_Oabs(X1909,X1908),c_Groups_Oabs__class_Oabs(X1909,X1907))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])])). 1.16/1.44 fof(c_0_1760, plain, ![X1226, X1227]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1227,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1226)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1227,X1226),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0])])). 1.16/1.44 fof(c_0_1761, plain, ![X290, X291]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X291)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X290,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X291,X290),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__nonneg__neg__le0])])])). 1.16/1.44 fof(c_0_1762, plain, ![X2603, X2604]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2604,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2603)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2604,X2603),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__nonpos__pos__le0])])])). 1.16/1.44 fof(c_0_1763, plain, ![X2420, X2421]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2421)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2420)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2421,X2420)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])])])). 1.16/1.44 fof(c_0_1764, plain, ![X2613, X2614]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2614)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2613)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2614,X2613)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])])). 1.16/1.44 cnf(c_0_1765, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1316])). 1.16/1.44 cnf(c_0_1766, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X3!=c_Nat_OSuc(X1)), inference(split_conjunct,[status(thm)],[c_0_1312])). 1.16/1.44 fof(c_0_1767, plain, ![X1501, X1502]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1502)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1501)|c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1502),X1501))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(X1502),c_Transcendental_Oln(X1501)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ln__mult])])])). 1.16/1.44 fof(c_0_1768, plain, ![X199, X200, X201]:((X199!=X200|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X199,X201)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X200,X201)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X201,X199)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X201,X200))&(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X199,X201)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X200,X201)|X199=X200|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X201,X199)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X201,X200))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__diff__iff])])])])). 1.16/1.44 fof(c_0_1769, plain, ![X2710, X2711]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2711)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2710)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2711,X2710),X2711))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__div__less__self])])])). 1.16/1.44 fof(c_0_1770, plain, ![X1258, X1259]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1259)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1258)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1258,X1259),X1258))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])])). 1.16/1.44 fof(c_0_1771, plain, ![X2889, X2890]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2890)|(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2889)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2889,X2890),X2889))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__less])])])). 1.16/1.44 fof(c_0_1772, plain, ![X2062, X2063]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2063,X2062)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X2063),c_Transcendental_Oln(X2062))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2062)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2063))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X2063),c_Transcendental_Oln(X2062))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2063,X2062)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2062)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2063))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__less__cancel__iff])])])). 1.16/1.44 fof(c_0_1773, plain, ![X2181, X2182]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2182,X2181)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X2182),c_Transcendental_Oln(X2181))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2181)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2182))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X2182),c_Transcendental_Oln(X2181))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2182,X2181)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2181)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2182))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ln__le__cancel__iff])])])])). 1.16/1.44 fof(c_0_1774, plain, ![X1740, X1741]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1741),X1740)|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1740,c_RealDef_Oreal(tc_Nat_Onat,X1741)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X1740),X1741)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__subtract])])). 1.16/1.44 fof(c_0_1775, plain, ![X1961, X1962]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1962),X1961)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X1961),X1962)=c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1961,c_RealDef_Oreal(tc_Nat_Onat,X1962)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__subtract])])). 1.16/1.44 fof(c_0_1776, plain, ![X390, X391]:((~c_Orderings_Oord__class_Oless(X391,c_Groups_Ozero__class_Ozero(X391),c_Groups_Oplus__class_Oplus(X391,X390,X390))|c_Orderings_Oord__class_Oless(X391,c_Groups_Ozero__class_Ozero(X391),X390)|~class_Groups_Olinordered__ab__group__add(X391))&(~c_Orderings_Oord__class_Oless(X391,c_Groups_Ozero__class_Ozero(X391),X390)|c_Orderings_Oord__class_Oless(X391,c_Groups_Ozero__class_Ozero(X391),c_Groups_Oplus__class_Oplus(X391,X390,X390))|~class_Groups_Olinordered__ab__group__add(X391))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add])])])). 1.16/1.44 fof(c_0_1777, plain, ![X1599, X1600]:((~c_Orderings_Oord__class_Oless__eq(X1600,c_Groups_Ozero__class_Ozero(X1600),X1599)|c_Orderings_Oord__class_Oless__eq(X1600,c_Groups_Ozero__class_Ozero(X1600),c_Groups_Oplus__class_Oplus(X1600,X1599,X1599))|~class_Groups_Olinordered__ab__group__add(X1600))&(~c_Orderings_Oord__class_Oless__eq(X1600,c_Groups_Ozero__class_Ozero(X1600),c_Groups_Oplus__class_Oplus(X1600,X1599,X1599))|c_Orderings_Oord__class_Oless__eq(X1600,c_Groups_Ozero__class_Ozero(X1600),X1599)|~class_Groups_Olinordered__ab__group__add(X1600))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add])])])). 1.16/1.44 fof(c_0_1778, plain, ![X220, X221]:((~c_Orderings_Oord__class_Oless(X221,c_Groups_Oplus__class_Oplus(X221,X220,X220),c_Groups_Ozero__class_Ozero(X221))|c_Orderings_Oord__class_Oless(X221,X220,c_Groups_Ozero__class_Ozero(X221))|~class_Groups_Olinordered__ab__group__add(X221))&(~c_Orderings_Oord__class_Oless(X221,X220,c_Groups_Ozero__class_Ozero(X221))|c_Orderings_Oord__class_Oless(X221,c_Groups_Oplus__class_Oplus(X221,X220,X220),c_Groups_Ozero__class_Ozero(X221))|~class_Groups_Olinordered__ab__group__add(X221))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero])])])). 1.16/1.44 fof(c_0_1779, plain, ![X206, X207]:((~c_Orderings_Oord__class_Oless(X207,c_Groups_Oplus__class_Oplus(X207,X206,X206),c_Groups_Ozero__class_Ozero(X207))|c_Orderings_Oord__class_Oless(X207,X206,c_Groups_Ozero__class_Ozero(X207))|~class_Rings_Olinordered__idom(X207))&(~c_Orderings_Oord__class_Oless(X207,X206,c_Groups_Ozero__class_Ozero(X207))|c_Orderings_Oord__class_Oless(X207,c_Groups_Oplus__class_Oplus(X207,X206,X206),c_Groups_Ozero__class_Ozero(X207))|~class_Rings_Olinordered__idom(X207))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])])). 1.16/1.44 fof(c_0_1780, plain, ![X683, X684]:((~c_Orderings_Oord__class_Oless__eq(X684,c_Groups_Oplus__class_Oplus(X684,X683,X683),c_Groups_Ozero__class_Ozero(X684))|c_Orderings_Oord__class_Oless__eq(X684,X683,c_Groups_Ozero__class_Ozero(X684))|~class_Groups_Olinordered__ab__group__add(X684))&(~c_Orderings_Oord__class_Oless__eq(X684,X683,c_Groups_Ozero__class_Ozero(X684))|c_Orderings_Oord__class_Oless__eq(X684,c_Groups_Oplus__class_Oplus(X684,X683,X683),c_Groups_Ozero__class_Ozero(X684))|~class_Groups_Olinordered__ab__group__add(X684))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])])])). 1.16/1.44 cnf(c_0_1781, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1317])). 1.16/1.44 fof(c_0_1782, plain, ![X2035, X2036, X2037, X2038]:(~class_Rings_Ocomm__semiring__1(X2038)|c_Groups_Oplus__class_Oplus(X2038,c_Groups_Oplus__class_Oplus(X2038,X2037,X2036),X2035)=c_Groups_Oplus__class_Oplus(X2038,c_Groups_Oplus__class_Oplus(X2038,X2037,X2035),X2036)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])])])). 1.16/1.44 fof(c_0_1783, plain, ![X491, X492, X493, X494]:(~class_Groups_Oab__semigroup__add(X494)|c_Groups_Oplus__class_Oplus(X494,X493,c_Groups_Oplus__class_Oplus(X494,X492,X491))=c_Groups_Oplus__class_Oplus(X494,c_Groups_Oplus__class_Oplus(X494,X493,X492),X491)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])])])). 1.16/1.44 fof(c_0_1784, plain, ![X2548, X2549, X2550, X2551]:(~class_Rings_Ocomm__semiring__1(X2551)|c_Groups_Oplus__class_Oplus(X2551,X2550,c_Groups_Oplus__class_Oplus(X2551,X2549,X2548))=c_Groups_Oplus__class_Oplus(X2551,c_Groups_Oplus__class_Oplus(X2551,X2550,X2549),X2548)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])])])). 1.16/1.44 fof(c_0_1785, plain, ![X601, X602, X603, X604]:(~class_Rings_Ocomm__semiring__1(X604)|c_Groups_Oplus__class_Oplus(X604,X603,c_Groups_Oplus__class_Oplus(X604,X602,X601))=c_Groups_Oplus__class_Oplus(X604,c_Groups_Oplus__class_Oplus(X604,X603,X602),X601)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])])). 1.16/1.44 fof(c_0_1786, plain, ![X2262, X2263, X2264, X2265]:(~class_Rings_Ocomm__semiring__1(X2265)|c_Groups_Oplus__class_Oplus(X2265,X2264,c_Groups_Oplus__class_Oplus(X2265,X2263,X2262))=c_Groups_Oplus__class_Oplus(X2265,X2263,c_Groups_Oplus__class_Oplus(X2265,X2264,X2262))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])])])). 1.16/1.44 fof(c_0_1787, plain, ![X277]:~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X277),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X277), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__add__one__not__less__self])])). 1.16/1.44 fof(c_0_1788, plain, ![X2455, X2456]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2456,X2455))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2456),X2455))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2456),X2455)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2456,X2455)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])])). 1.16/1.44 fof(c_0_1789, plain, ![X2741, X2742]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2742,X2741))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2742),X2741))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2742),X2741)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2742,X2741)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff])])). 1.16/1.44 fof(c_0_1790, plain, ![X1834, X1835]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1835,X1834),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1834,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1835)))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1834,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1835))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1835,X1834),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff])])). 1.16/1.44 fof(c_0_1791, plain, ![X979, X980]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X979,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X980))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X980,X979),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X980,X979),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X979,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X980)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff])])). 1.16/1.44 fof(c_0_1792, plain, ![X270, X271, X272, X273]:(~class_Divides_Osemiring__div(X273)|(c_Groups_Ozero__class_Ozero(X273)=X272|c_Divides_Odiv__class_Odiv(X273,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X273),X271),X272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X273),X270),X272))=c_Divides_Odiv__class_Odiv(X273,X271,X270))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult2])])])). 1.16/1.44 fof(c_0_1793, plain, ![X1181, X1182, X1183, X1184]:(~class_Divides_Osemiring__div(X1184)|(X1183=c_Groups_Ozero__class_Ozero(X1184)|c_Divides_Odiv__class_Odiv(X1184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1184),X1183),X1182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1184),X1183),X1181))=c_Divides_Odiv__class_Odiv(X1184,X1182,X1181))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])])). 1.16/1.44 fof(c_0_1794, plain, ![X2422, X2423, X2424, X2425]:((X2424!=c_Groups_Ozero__class_Ozero(X2425)|c_Divides_Odiv__class_Odiv(X2425,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2425),X2424),X2423),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2425),X2424),X2422))=c_Groups_Ozero__class_Ozero(X2425)|~class_Divides_Osemiring__div(X2425))&(X2424=c_Groups_Ozero__class_Ozero(X2425)|c_Divides_Odiv__class_Odiv(X2425,X2423,X2422)=c_Divides_Odiv__class_Odiv(X2425,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2425),X2424),X2423),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2425),X2424),X2422))|~class_Divides_Osemiring__div(X2425))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult1__if])])])])). 1.16/1.44 fof(c_0_1795, plain, ![X1955, X1956, X1957]:((~c_Orderings_Oord__class_Oless(X1957,c_Groups_Ominus__class_Ominus(X1957,X1956,X1955),c_Groups_Ozero__class_Ozero(X1957))|c_Orderings_Oord__class_Oless(X1957,X1956,X1955)|~class_Groups_Oordered__ab__group__add(X1957))&(~c_Orderings_Oord__class_Oless(X1957,X1956,X1955)|c_Orderings_Oord__class_Oless(X1957,c_Groups_Ominus__class_Ominus(X1957,X1956,X1955),c_Groups_Ozero__class_Ozero(X1957))|~class_Groups_Oordered__ab__group__add(X1957))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])])). 1.16/1.44 fof(c_0_1796, plain, ![X113, X114, X115]:((~c_Orderings_Oord__class_Oless__eq(X115,X114,X113)|c_Orderings_Oord__class_Oless__eq(X115,c_Groups_Ominus__class_Ominus(X115,X114,X113),c_Groups_Ozero__class_Ozero(X115))|~class_Groups_Oordered__ab__group__add(X115))&(~c_Orderings_Oord__class_Oless__eq(X115,c_Groups_Ominus__class_Ominus(X115,X114,X113),c_Groups_Ozero__class_Ozero(X115))|c_Orderings_Oord__class_Oless__eq(X115,X114,X113)|~class_Groups_Oordered__ab__group__add(X115))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__iff__diff__le__0])])])])). 1.16/1.44 cnf(c_0_1797, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1318])). 1.16/1.44 cnf(c_0_1798, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1319])). 1.16/1.44 cnf(c_0_1799, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1320])). 1.16/1.44 fof(c_0_1800, plain, ![X1319, X1320]:c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1320,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1319)))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1319,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1320))), inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel])). 1.16/1.44 fof(c_0_1801, plain, ![X1676, X1677]:(((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1677)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1677),X1676)))&(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1676)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1677),X1676))))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1677)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1676)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1677),X1676)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])])). 1.16/1.44 fof(c_0_1802, plain, ![X780, X781]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X781)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X780)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X781),X780)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__mult__order])])])). 1.16/1.44 fof(c_0_1803, plain, ![X1746, X1747]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1747)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1746)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1747),X1746)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])])])). 1.16/1.44 cnf(c_0_1804, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1321])). 1.16/1.44 cnf(c_0_1805, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1322])). 1.16/1.44 cnf(c_0_1806, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_1323])). 1.16/1.44 fof(c_0_1807, plain, ![X314, X315, X316]:(~class_Rings_Olinordered__idom(X316)|(~c_Orderings_Oord__class_Oless__eq(X316,c_Groups_Ozero__class_Ozero(X316),X315)|c_Groups_Oabs__class_Oabs(X316,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X316),X314),X315))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X316),c_Groups_Oabs__class_Oabs(X316,X314)),X315))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__pos])])])). 1.16/1.44 fof(c_0_1808, plain, ![X1796]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1796),v_r)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1796)),esk53_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])])])). 1.16/1.44 fof(c_0_1809, plain, ![X1004]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1004),v_r)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1004)),esk31_0))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk31_0)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons])])])])). 1.16/1.44 fof(c_0_1810, plain, ![X779]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X779),v_r)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X779)),v_m____)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_m])])])). 1.16/1.44 fof(c_0_1811, plain, ![X400]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X400,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X400),X400))), inference(variable_rename,[status(thm)],[fact_le__cube])). 1.16/1.44 cnf(c_0_1812, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_1324])). 1.16/1.44 cnf(c_0_1813, plain, (c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1325])). 1.16/1.44 fof(c_0_1814, plain, ![X1102, X1103, X1104, X1105, X1106]:((~c_Orderings_Oord__class_Oless(X1106,X1105,X1104)|c_Orderings_Oord__class_Oless(X1106,X1103,X1102)|c_Groups_Ominus__class_Ominus(X1106,X1103,X1102)!=c_Groups_Ominus__class_Ominus(X1106,X1105,X1104)|~class_Groups_Oordered__ab__group__add(X1106))&(~c_Orderings_Oord__class_Oless(X1106,X1103,X1102)|c_Orderings_Oord__class_Oless(X1106,X1105,X1104)|c_Groups_Ominus__class_Ominus(X1106,X1103,X1102)!=c_Groups_Ominus__class_Ominus(X1106,X1105,X1104)|~class_Groups_Oordered__ab__group__add(X1106))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])])). 1.16/1.44 fof(c_0_1815, plain, ![X1931, X1932, X1933, X1934, X1935]:((~c_Orderings_Oord__class_Oless__eq(X1935,X1932,X1931)|c_Orderings_Oord__class_Oless__eq(X1935,X1934,X1933)|c_Groups_Ominus__class_Ominus(X1935,X1934,X1933)!=c_Groups_Ominus__class_Ominus(X1935,X1932,X1931)|~class_Groups_Oordered__ab__group__add(X1935))&(~c_Orderings_Oord__class_Oless__eq(X1935,X1934,X1933)|c_Orderings_Oord__class_Oless__eq(X1935,X1932,X1931)|c_Groups_Ominus__class_Ominus(X1935,X1934,X1933)!=c_Groups_Ominus__class_Ominus(X1935,X1932,X1931)|~class_Groups_Oordered__ab__group__add(X1935))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__eq__diff__less__eq])])])])). 1.16/1.44 fof(c_0_1816, plain, ![X2594, X2595, X2596]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2596,X2595)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2596),X2594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2595),X2594))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__mono1])])])). 1.16/1.44 fof(c_0_1817, plain, ![X1262, X1263, X1264]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1264,X1263)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1262),X1264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1262),X1263))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])])). 1.16/1.44 fof(c_0_1818, plain, ![X2697, X2698, X2699, X2700]:(~class_Rings_Ocomm__semiring__1(X2700)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2700),X2698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2700),X2699),X2697))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2700),X2699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2700),X2698),X2697))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])])). 1.16/1.44 fof(c_0_1819, plain, ![X501, X502, X503]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X503,X502),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X503,X501))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X502,X501), inference(variable_rename,[status(thm)],[fact_diff__cancel])). 1.16/1.44 fof(c_0_1820, plain, ![X2370, X2371, X2372]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2372,X2371),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2370,X2371))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2372,X2370), inference(variable_rename,[status(thm)],[fact_diff__cancel2])). 1.16/1.44 fof(c_0_1821, plain, ![X891, X892, X893]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X893,X892),X891)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X893,X891),X892), inference(variable_rename,[status(thm)],[fact_diff__commute])). 1.16/1.44 fof(c_0_1822, plain, ![X633, X634, X635]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X635,X634),X633)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X635,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X634,X633)), inference(variable_rename,[status(thm)],[fact_zadd__assoc])). 1.16/1.44 fof(c_0_1823, plain, ![X2431, X2432, X2433]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2433,X2432),X2431)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2433,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2432,X2431)), inference(variable_rename,[status(thm)],[fact_nat__add__assoc])). 1.16/1.44 fof(c_0_1824, plain, ![X1617, X1618, X1619]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1619,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1618,X1617))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1619,X1618),X1617), inference(variable_rename,[status(thm)],[fact_diff__diff__left])). 1.16/1.44 fof(c_0_1825, plain, ![X1189, X1190, X1191]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1191,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1190,X1189))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1190,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1191,X1189)), inference(variable_rename,[status(thm)],[fact_zadd__left__commute])). 1.16/1.44 fof(c_0_1826, plain, ![X2516, X2517, X2518]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2518,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2517,X2516))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2517,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2518,X2516)), inference(variable_rename,[status(thm)],[fact_nat__add__left__commute])). 1.16/1.44 fof(c_0_1827, plain, ![X392, X393]:((~c_Orderings_Oord__class_Oless(tc_Int_Oint,X393,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X392,c_Groups_Oone__class_Oone(tc_Int_Oint)))|(c_Orderings_Oord__class_Oless(tc_Int_Oint,X393,X392)|X392=X393))&((~c_Orderings_Oord__class_Oless(tc_Int_Oint,X393,X392)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X393,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X392,c_Groups_Oone__class_Oone(tc_Int_Oint))))&(X392!=X393|c_Orderings_Oord__class_Oless(tc_Int_Oint,X393,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X392,c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])])). 1.16/1.44 cnf(c_0_1828, plain, (X2=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1326])). 1.16/1.44 cnf(c_0_1829, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X2=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1327])). 1.16/1.44 cnf(c_0_1830, plain, (X2=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1328])). 1.16/1.44 cnf(c_0_1831, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X2=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1329])). 1.16/1.44 fof(c_0_1832, plain, ![X1361, X1362]:((~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1362,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1361)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1362,X1361))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1362,X1361)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1362,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1361))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])])). 1.16/1.44 cnf(c_0_1833, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1330])). 1.16/1.44 cnf(c_0_1834, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1331])). 1.16/1.44 cnf(c_0_1835, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1332])). 1.16/1.44 cnf(c_0_1836, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1333])). 1.16/1.44 cnf(c_0_1837, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1334])). 1.16/1.44 fof(c_0_1838, plain, ![X1529, X1530]:((~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1530,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1529,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1530,X1529))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1530,X1529)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1530,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1529,c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])])). 1.16/1.44 fof(c_0_1839, plain, ![X1469, X1470]:((~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1470,X1469)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1470,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1469,c_Groups_Oone__class_Oone(tc_Int_Oint))))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1470,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1469,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1470,X1469))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])])). 1.16/1.44 cnf(c_0_1840, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1335])). 1.16/1.44 cnf(c_0_1841, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))!=X3), inference(split_conjunct,[status(thm)],[c_0_1336])). 1.16/1.44 fof(c_0_1842, plain, ![X2226, X2227]:((~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2227,X2226)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2227,X2226),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2227,X2226),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2227,X2226))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])])). 1.16/1.44 fof(c_0_1843, plain, ![X588, X589]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X589,X588)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X589,X588),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X589,X588),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X589,X588))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff])])). 1.16/1.44 fof(c_0_1844, plain, ![X1185, X1186]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1185,X1186)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1186,X1185)))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1186,X1185))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1185,X1186))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])])). 1.16/1.44 cnf(c_0_1845, plain, (c_Nat_OSuc(X1)=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1337])). 1.16/1.44 fof(c_0_1846, plain, ![X2306, X2307, X2308, X2309]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2309,X2308)|(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2307,X2308)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2309,X2306)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2307,X2306))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__add__eq__less])])])). 1.16/1.44 fof(c_0_1847, plain, ![X230, X231]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X231)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X231,c_RealDef_Oreal(tc_Nat_Onat,X230)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X231),X230)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add])])). 1.16/1.44 fof(c_0_1848, plain, ![X2608, X2609]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2609)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2609,c_RealDef_Oreal(tc_Nat_Onat,X2608)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X2609),X2608)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_natceiling__add])])])). 1.16/1.44 fof(c_0_1849, plain, ![X267, X268, X269]:(((c_Orderings_Oord__class_Oless(X269,X268,X267)|~c_Orderings_Oord__class_Oless(X269,c_Groups_Oabs__class_Oabs(X269,X268),X267)|~class_Rings_Olinordered__idom(X269))&(c_Orderings_Oord__class_Oless(X269,c_Groups_Ouminus__class_Ouminus(X269,X268),X267)|~c_Orderings_Oord__class_Oless(X269,c_Groups_Oabs__class_Oabs(X269,X268),X267)|~class_Rings_Olinordered__idom(X269)))&(~c_Orderings_Oord__class_Oless(X269,X268,X267)|~c_Orderings_Oord__class_Oless(X269,c_Groups_Ouminus__class_Ouminus(X269,X268),X267)|c_Orderings_Oord__class_Oless(X269,c_Groups_Oabs__class_Oabs(X269,X268),X267)|~class_Rings_Olinordered__idom(X269))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__less__iff])])])])). 1.16/1.44 fof(c_0_1850, plain, ![X2470, X2471, X2472]:((~c_Orderings_Oord__class_Oless__eq(X2472,X2471,X2470)|~c_Orderings_Oord__class_Oless__eq(X2472,c_Groups_Ouminus__class_Ouminus(X2472,X2471),X2470)|c_Orderings_Oord__class_Oless__eq(X2472,c_Groups_Oabs__class_Oabs(X2472,X2471),X2470)|~class_Groups_Oordered__ab__group__add__abs(X2472))&((c_Orderings_Oord__class_Oless__eq(X2472,X2471,X2470)|~c_Orderings_Oord__class_Oless__eq(X2472,c_Groups_Oabs__class_Oabs(X2472,X2471),X2470)|~class_Groups_Oordered__ab__group__add__abs(X2472))&(c_Orderings_Oord__class_Oless__eq(X2472,c_Groups_Ouminus__class_Ouminus(X2472,X2471),X2470)|~c_Orderings_Oord__class_Oless__eq(X2472,c_Groups_Oabs__class_Oabs(X2472,X2471),X2470)|~class_Groups_Oordered__ab__group__add__abs(X2472)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])])). 1.16/1.44 fof(c_0_1851, plain, ![X176, X177, X178]:(~class_Groups_Oordered__ab__group__add__abs(X178)|(~c_Orderings_Oord__class_Oless__eq(X178,X177,X176)|(~c_Orderings_Oord__class_Oless__eq(X178,c_Groups_Ouminus__class_Ouminus(X178,X177),X176)|c_Orderings_Oord__class_Oless__eq(X178,c_Groups_Oabs__class_Oabs(X178,X177),X176)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__leI])])])). 1.16/1.44 fof(c_0_1852, plain, ![X1764, X1765, X1766]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1766,X1765),X1764)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1766,X1764)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])])). 1.16/1.44 fof(c_0_1853, plain, ![X636, X637, X638]:((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X638,X636)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X638,X637),X636))&(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X637,X636)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X638,X637),X636))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__leE])])])])). 1.16/1.44 fof(c_0_1854, plain, ![X2774, X2775, X2776]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2776,X2775),X2774)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2776,X2774)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__leD1])])])). 1.16/1.44 fof(c_0_1855, plain, ![X585, X586, X587]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X587,X586),X585)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X586,X585)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__leD2])])])). 1.16/1.44 fof(c_0_1856, plain, ![X1555, X1556, X1557]:c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1557,X1556),X1555)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1557,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1556),X1555)), inference(variable_rename,[status(thm)],[fact_div__mult2__eq])). 1.16/1.44 fof(c_0_1857, plain, ![X1903, X1904]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1904,X1903)|c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1903,X1904))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1903),c_RealDef_Oreal(tc_Nat_Onat,X1904))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__of__nat__diff])])])). 1.16/1.44 cnf(c_0_1858, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))), inference(split_conjunct,[status(thm)],[c_0_1338])). 1.16/1.44 cnf(c_0_1859, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)))), inference(split_conjunct,[status(thm)],[c_0_1339])). 1.16/1.44 cnf(c_0_1860, plain, (X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1340])). 1.16/1.44 cnf(c_0_1861, plain, (X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1341])). 1.16/1.44 cnf(c_0_1862, plain, (c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk16_2(X2,X1)))=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1336])). 1.16/1.44 fof(c_0_1863, plain, ![X1506, X1507, X1508]:(((X1506=c_Groups_Ozero__class_Ozero(X1508)|c_Groups_Oplus__class_Oplus(X1508,X1507,X1506)!=c_Groups_Ozero__class_Ozero(X1508)|~c_Orderings_Oord__class_Oless__eq(X1508,c_Groups_Ozero__class_Ozero(X1508),X1506)|~c_Orderings_Oord__class_Oless__eq(X1508,c_Groups_Ozero__class_Ozero(X1508),X1507)|~class_Groups_Oordered__comm__monoid__add(X1508))&(c_Groups_Ozero__class_Ozero(X1508)=X1507|c_Groups_Oplus__class_Oplus(X1508,X1507,X1506)!=c_Groups_Ozero__class_Ozero(X1508)|~c_Orderings_Oord__class_Oless__eq(X1508,c_Groups_Ozero__class_Ozero(X1508),X1506)|~c_Orderings_Oord__class_Oless__eq(X1508,c_Groups_Ozero__class_Ozero(X1508),X1507)|~class_Groups_Oordered__comm__monoid__add(X1508)))&(X1506!=c_Groups_Ozero__class_Ozero(X1508)|c_Groups_Ozero__class_Ozero(X1508)!=X1507|c_Groups_Oplus__class_Oplus(X1508,X1507,X1506)=c_Groups_Ozero__class_Ozero(X1508)|~c_Orderings_Oord__class_Oless__eq(X1508,c_Groups_Ozero__class_Ozero(X1508),X1506)|~c_Orderings_Oord__class_Oless__eq(X1508,c_Groups_Ozero__class_Ozero(X1508),X1507)|~class_Groups_Oordered__comm__monoid__add(X1508))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonneg__eq__0__iff])])])])). 1.16/1.44 fof(c_0_1864, plain, ![X1826, X1827, X1828, X1829]:((~c_Orderings_Oord__class_Oless__eq(tc_fun(X1828,X1829),X1827,X1826)|c_Orderings_Oord__class_Oless__eq(tc_fun(X1828,X1829),X1826,X1827)|c_Orderings_Oord__class_Oless(tc_fun(X1828,X1829),X1827,X1826)|~class_Orderings_Oord(X1829))&((c_Orderings_Oord__class_Oless__eq(tc_fun(X1828,X1829),X1827,X1826)|~c_Orderings_Oord__class_Oless(tc_fun(X1828,X1829),X1827,X1826)|~class_Orderings_Oord(X1829))&(~c_Orderings_Oord__class_Oless__eq(tc_fun(X1828,X1829),X1826,X1827)|~c_Orderings_Oord__class_Oless(tc_fun(X1828,X1829),X1827,X1826)|~class_Orderings_Oord(X1829)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__fun__def])])])])). 1.16/1.44 cnf(c_0_1865, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X1|X2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1342])). 1.16/1.44 fof(c_0_1866, plain, ![X1428, X1429]:(((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1429)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1429),X1428)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1428|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1429),X1428))))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1429),X1428))|(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1429)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1428))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])])). 1.16/1.44 fof(c_0_1867, plain, ![X2199, X2200]:(((X2199!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2200),X2199)))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2200)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2200),X2199))))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2200),X2199))|(X2199=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2200)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])])). 1.16/1.44 fof(c_0_1868, plain, ![X1806, X1807, X1808]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1808|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1807,X1806)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1808),X1807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1808),X1806)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1808|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1808),X1807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1808),X1806)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__div__cancel__disj])])])). 1.16/1.44 fof(c_0_1869, plain, ![X2426, X2427, X2428, X2429, X2430]:(~class_Groups_Ominus(X2430)|c_Groups_Ominus__class_Ominus(X2430,hAPP(X2428,X2426),hAPP(X2427,X2426))=hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2429,X2430),X2428,X2427),X2426)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__apply])])])). 1.16/1.44 fof(c_0_1870, plain, ![X2490, X2491]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2491)|c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2491),X2490))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2490)),c_Transcendental_Oln(X2491))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ln__realpow])])])). 1.16/1.44 fof(c_0_1871, plain, ![X443, X444]:(((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X444,X443)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X444),X443))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X443),X444)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X444),X443)))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X444,X443)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X443),X444)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X444),X443))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__interval__iff])])])). 1.16/1.44 fof(c_0_1872, plain, ![X592, X593, X594]:((~c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X594),X593,X592)|c_Polynomial_Opos__poly(X594,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X594),X592,X593))|~class_Rings_Olinordered__idom(X594))&(~c_Polynomial_Opos__poly(X594,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X594),X592,X593))|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X594),X593,X592)|~class_Rings_Olinordered__idom(X594))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__poly__def])])])). 1.16/1.44 fof(c_0_1873, plain, ![X1113, X1114, X1115]:((~c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1115),X1114,X1113)|(c_Polynomial_Opos__poly(X1115,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1115),X1113,X1114))|X1113=X1114)|~class_Rings_Olinordered__idom(X1115))&((~c_Polynomial_Opos__poly(X1115,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1115),X1113,X1114))|c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1115),X1114,X1113)|~class_Rings_Olinordered__idom(X1115))&(X1113!=X1114|c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1115),X1114,X1113)|~class_Rings_Olinordered__idom(X1115)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__eq__poly__def])])])])). 1.16/1.44 fof(c_0_1874, plain, ![X617, X618]:((hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk22_2(X617,X618)),X618)=X617|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X617)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X618))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk22_2(X617,X618))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X617)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X618))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_realpow__pos__nth])])])])])). 1.16/1.44 fof(c_0_1875, plain, ![X1649, X1650, X1651]:(~class_Rings_Olinordered__idom(X1651)|c_Orderings_Oord__class_Oless__eq(X1651,c_Groups_Ozero__class_Ozero(X1651),hAPP(hAPP(c_Power_Opower__class_Opower(X1651),c_Groups_Oabs__class_Oabs(X1651,X1650)),X1649))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__power__abs])])])). 1.16/1.44 cnf(c_0_1876, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_1343])). 1.16/1.44 fof(c_0_1877, plain, ![X793, X794, X795, X796]:((X794!=X793|hAPP(hAPP(c_Power_Opower__class_Opower(X796),X795),X793)=hAPP(hAPP(c_Power_Opower__class_Opower(X796),X795),X794)|~c_Orderings_Oord__class_Oless(X796,c_Groups_Oone__class_Oone(X796),X795)|~class_Rings_Olinordered__semidom(X796))&(hAPP(hAPP(c_Power_Opower__class_Opower(X796),X795),X793)!=hAPP(hAPP(c_Power_Opower__class_Opower(X796),X795),X794)|X794=X793|~c_Orderings_Oord__class_Oless(X796,c_Groups_Oone__class_Oone(X796),X795)|~class_Rings_Olinordered__semidom(X796))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])])). 1.16/1.44 fof(c_0_1878, plain, ![X2373, X2374]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2374)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2374,c_RealDef_Oreal(tc_Nat_Onat,X2373))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X2374),X2373))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__natfloor])])). 1.16/1.44 fof(c_0_1879, plain, ![X716, X717]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X717),X716)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X717,c_RealDef_Oreal(tc_Nat_Onat,X716))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X717))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X717,c_RealDef_Oreal(tc_Nat_Onat,X716))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X717),X716)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X717))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq])])])). 1.16/1.44 fof(c_0_1880, plain, ![X2336, X2337]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2336,c_RComplete_Onatfloor(X2337))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2336),X2337)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2337))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2336),X2337)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2336,c_RComplete_Onatfloor(X2337))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2337))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__natfloor__eq])])])])). 1.16/1.44 cnf(c_0_1881, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1))), inference(split_conjunct,[status(thm)],[c_0_1344])). 1.16/1.44 fof(c_0_1882, plain, ![X776, X777, X778]:(~class_Rings_Olinordered__semidom(X778)|(~c_Orderings_Oord__class_Oless(X778,c_Groups_Ozero__class_Ozero(X778),X777)|c_Orderings_Oord__class_Oless(X778,c_Groups_Ozero__class_Ozero(X778),hAPP(hAPP(c_Power_Opower__class_Opower(X778),X777),X776)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])])). 1.16/1.44 fof(c_0_1883, plain, ![X2721, X2722, X2723]:(~class_Rings_Olinordered__semidom(X2723)|(~c_Orderings_Oord__class_Oless__eq(X2723,c_Groups_Oone__class_Oone(X2723),X2722)|c_Orderings_Oord__class_Oless__eq(X2723,c_Groups_Oone__class_Oone(X2723),hAPP(hAPP(c_Power_Opower__class_Opower(X2723),X2722),X2721)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])])). 1.16/1.44 fof(c_0_1884, plain, ![X2443, X2444, X2445]:(~class_Rings_Olinordered__semidom(X2445)|(~c_Orderings_Oord__class_Oless__eq(X2445,c_Groups_Ozero__class_Ozero(X2445),X2444)|c_Orderings_Oord__class_Oless__eq(X2445,c_Groups_Ozero__class_Ozero(X2445),hAPP(hAPP(c_Power_Opower__class_Opower(X2445),X2444),X2443)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])])). 1.16/1.44 fof(c_0_1885, plain, ![X2599]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2599)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2599,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X2599),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add__one])])). 1.16/1.44 fof(c_0_1886, plain, ![X2180]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2180)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2180,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X2180),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_natceiling__add__one])])])). 1.16/1.44 fof(c_0_1887, plain, ![X1724, X1725]:(~class_Rings_Olinordered__ring(X1725)|~c_Orderings_Oord__class_Oless(X1725,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1725),X1724),X1724),c_Groups_Ozero__class_Ozero(X1725))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__square__less__zero])])])). 1.16/1.44 fof(c_0_1888, plain, ![X1939]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1939),X1939), inference(variable_rename,[status(thm)],[fact_odd__nonzero])). 1.16/1.44 fof(c_0_1889, plain, ![X2260, X2261]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2261)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2260)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X2261,X2260)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])])). 1.16/1.44 fof(c_0_1890, plain, ![X815, X816, X817, X818]:hAPP(hAPP(c_Power_Opower_Opower(X818,X817,X816),X815),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X817, inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0])). 1.16/1.44 cnf(c_0_1891, plain, (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1)), inference(split_conjunct,[status(thm)],[c_0_1345])). 1.16/1.44 cnf(c_0_1892, plain, (c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1346])). 1.16/1.44 cnf(c_0_1893, plain, (X1=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1347])). 1.16/1.44 fof(c_0_1894, plain, ![X2631]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2631)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2631))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])])). 1.16/1.44 fof(c_0_1895, plain, ![X213, X214, X215]:(~class_Rings_Olinordered__idom(X215)|c_Groups_Oabs__class_Oabs(X215,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X215),X214),X213))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X215),c_Groups_Oabs__class_Oabs(X215,X214)),c_Groups_Oabs__class_Oabs(X215,X213))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])])). 1.16/1.44 fof(c_0_1896, plain, ![X2201, X2202, X2203]:(~class_RealVector_Oreal__normed__div__algebra(X2203)|c_Groups_Osgn__class_Osgn(X2203,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2203),X2202),X2201))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2203),c_Groups_Osgn__class_Osgn(X2203,X2202)),c_Groups_Osgn__class_Osgn(X2203,X2201))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__mult])])])). 1.16/1.44 fof(c_0_1897, plain, ![X1099, X1100, X1101]:(~class_Rings_Olinordered__idom(X1101)|c_Groups_Osgn__class_Osgn(X1101,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1101),X1100),X1099))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1101),c_Groups_Osgn__class_Osgn(X1101,X1100)),c_Groups_Osgn__class_Osgn(X1101,X1099))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])])). 1.16/1.44 cnf(c_0_1898, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Nat_OSuc(X1))|c_Nat_OSuc(X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_1309])). 1.16/1.44 cnf(c_0_1899, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|X1!=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1313])). 1.16/1.44 fof(c_0_1900, plain, ![X2578, X2579, X2580]:(~class_Groups_Oordered__ab__group__add__abs(X2580)|c_Groups_Oabs__class_Oabs(X2580,c_Groups_Ominus__class_Ominus(X2580,X2578,X2579))=c_Groups_Oabs__class_Oabs(X2580,c_Groups_Ominus__class_Ominus(X2580,X2579,X2578))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])])). 1.16/1.44 fof(c_0_1901, plain, ![X168, X169, X170]:(~class_RealVector_Oreal__normed__vector(X170)|c_RealVector_Onorm__class_Onorm(X170,c_Groups_Ominus__class_Ominus(X170,X169,X168))=c_RealVector_Onorm__class_Onorm(X170,c_Groups_Ominus__class_Ominus(X170,X168,X169))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])])). 1.16/1.44 fof(c_0_1902, plain, ![X2689, X2690, X2691]:(~class_RealVector_Oreal__normed__div__algebra(X2691)|c_RealVector_Onorm__class_Onorm(X2691,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2691),X2690),X2689))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2691,X2690)),c_RealVector_Onorm__class_Onorm(X2691,X2689))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])])). 1.16/1.44 fof(c_0_1903, plain, ![X2501, X2502]:(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2502,X2501)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2502,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2501)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])])). 1.16/1.44 cnf(c_0_1904, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1348])). 1.16/1.44 cnf(c_0_1905, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1332])). 1.16/1.44 cnf(c_0_1906, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1333])). 1.16/1.44 cnf(c_0_1907, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1326])). 1.16/1.44 cnf(c_0_1908, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1349])). 1.16/1.44 cnf(c_0_1909, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1335])). 1.16/1.44 cnf(c_0_1910, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1350])). 1.16/1.44 cnf(c_0_1911, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1309])). 1.16/1.44 cnf(c_0_1912, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1351])). 1.16/1.44 fof(c_0_1913, plain, ![X1391, X1392]:~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1392,X1391),X1392), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__add__less1])])). 1.16/1.44 fof(c_0_1914, plain, ![X896, X897]:~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X897,X896),X896), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__add__less2])])). 1.16/1.44 fof(c_0_1915, plain, ![X2843, X2844, X2845]:(~class_Fields_Ofield(X2845)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X2845),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2845),X2844),X2843)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2845),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X2845),X2844,X2843))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_poly__div__minus__left])])])). 1.16/1.44 fof(c_0_1916, plain, ![X1900, X1901, X1902]:(~class_Fields_Ofield(X1902)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1902),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1902),X1901,X1900))=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1902),X1901,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1902),X1900))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_poly__div__minus__right])])])). 1.16/1.44 fof(c_0_1917, plain, ![X1690]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1690))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1690)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1690))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1690)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1690))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1690))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ln__gt__zero__iff])])])])). 1.16/1.44 fof(c_0_1918, plain, ![X992]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X992))|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X992)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X992))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__gt__zero__imp__gt__one])])). 1.16/1.44 fof(c_0_1919, plain, ![X1212]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1212))|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1212)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1212))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ln__ge__zero__imp__ge__one])])])). 1.16/1.44 fof(c_0_1920, plain, ![X401]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X401)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X401))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X401))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X401))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X401)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X401))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__ge__zero__iff])])])). 1.16/1.44 fof(c_0_1921, plain, ![X173]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X173,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X173),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X173))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X173),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X173,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X173))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ln__less__zero__iff])])])])). 1.16/1.44 fof(c_0_1922, plain, ![X2021, X2022]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2022,X2021)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2021,X2022),X2022)=X2021), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__diff__inverse2])])])). 1.16/1.44 fof(c_0_1923, plain, ![X222, X223]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X223,X222)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X222,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X222,X223))=X223), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])])). 1.16/1.44 fof(c_0_1924, plain, ![X2237, X2238]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2238,X2237)|X2237=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2238,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2237,X2238))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])])). 1.16/1.44 fof(c_0_1925, plain, ![X2275, X2276, X2277, X2278, X2279]:(~class_Orderings_Oord(X2279)|(~c_Orderings_Oord__class_Oless__eq(tc_fun(X2278,X2279),X2277,X2276)|c_Orderings_Oord__class_Oless__eq(X2279,hAPP(X2277,X2275),hAPP(X2276,X2275)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__funD])])])). 1.16/1.44 fof(c_0_1926, plain, ![X858, X859, X860, X861, X862]:(~class_Orderings_Oord(X862)|(~c_Orderings_Oord__class_Oless__eq(tc_fun(X861,X862),X860,X859)|c_Orderings_Oord__class_Oless__eq(X862,hAPP(X860,X858),hAPP(X859,X858)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__funE])])])). 1.16/1.44 fof(c_0_1927, plain, ![X287, X288, X289]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X289,X288)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X289,X287),X288)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__imp__diff__less])])])). 1.16/1.44 fof(c_0_1928, plain, ![X1558, X1559, X1560]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1560,X1559)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1560,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1559,X1558))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])])). 1.16/1.44 fof(c_0_1929, plain, ![X249, X250, X251]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X251,X250)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X251,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X250,X249))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])])). 1.16/1.44 fof(c_0_1930, plain, ![X2575, X2576, X2577]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2577,X2576)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2577,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2575,X2576))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])])). 1.16/1.44 fof(c_0_1931, plain, ![X694, X695, X696]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X696,X695)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X696,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X694,X695))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])])). 1.16/1.44 fof(c_0_1932, plain, ![X1885, X1886, X1887]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1887,X1886)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1887,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1886,X1885))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trans__le__add1])])])). 1.16/1.44 fof(c_0_1933, plain, ![X1683, X1684, X1685]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1685,X1684)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1685,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1684,X1683))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])])). 1.16/1.44 fof(c_0_1934, plain, ![X1223, X1224, X1225]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1225,X1224)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1225,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1223,X1224))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_termination__basic__simps_I4_J])])])). 1.16/1.44 fof(c_0_1935, plain, ![X264, X265, X266]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X266,X265)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X266,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X264,X265))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trans__le__add2])])])). 1.16/1.44 cnf(c_0_1936, plain, (X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1341])). 1.16/1.44 cnf(c_0_1937, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1340])). 1.16/1.44 cnf(c_0_1938, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1341])). 1.16/1.44 cnf(c_0_1939, plain, (X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1340])). 1.16/1.44 fof(c_0_1940, plain, ![X2896]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2896)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2896,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X2896),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ln__less__zero])])])). 1.16/1.44 fof(c_0_1941, plain, ![X2717, X2718]:c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2718)),X2717)), inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs])). 1.16/1.44 fof(c_0_1942, plain, ![X1201]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1201),X1201))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1201)&(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X1201|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1201),X1201)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero])])])). 1.16/1.44 fof(c_0_1943, plain, ![X1267, X1268, X1269]:((X1267!=X1268|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1269),X1268)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1269),X1267)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1269))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1269),X1268)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1269),X1267)|X1267=X1268|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1269))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__eq__cancel1])])])])). 1.16/1.44 fof(c_0_1944, plain, ![X1967, X1968]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1968)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1968),X1967))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])])])). 1.16/1.44 fof(c_0_1945, plain, ![X182, X183, X184, X185]:(~class_Orderings_Opreorder(X185)|(~c_Orderings_Oord__class_Oless(X185,X184,X183)|(~c_Orderings_Oord__class_Oless(X185,X183,X182)|c_Orderings_Oord__class_Oless(X185,X184,X182)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__trans])])])). 1.16/1.44 fof(c_0_1946, plain, ![X244, X245, X246, X247]:(~class_Orderings_Opreorder(X247)|(~c_Orderings_Oord__class_Oless__eq(X247,X246,X245)|(~c_Orderings_Oord__class_Oless(X247,X245,X244)|c_Orderings_Oord__class_Oless(X247,X246,X244)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__le__less__trans])])])). 1.16/1.44 fof(c_0_1947, plain, ![X2781, X2782, X2783, X2784]:(~class_Orderings_Opreorder(X2784)|(~c_Orderings_Oord__class_Oless(X2784,X2783,X2782)|(~c_Orderings_Oord__class_Oless__eq(X2784,X2782,X2781)|c_Orderings_Oord__class_Oless(X2784,X2783,X2781)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__le__trans])])])). 1.16/1.44 fof(c_0_1948, plain, ![X259, X260, X261, X262]:(~class_Orderings_Oorder(X262)|(~c_Orderings_Oord__class_Oless(X262,X261,X260)|(~c_Orderings_Oord__class_Oless(X262,X259,X261)|c_Orderings_Oord__class_Oless(X262,X259,X260)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I10_J])])])). 1.16/1.44 fof(c_0_1949, plain, ![X2026, X2027, X2028, X2029]:(~class_Orderings_Oorder(X2029)|(~c_Orderings_Oord__class_Oless__eq(X2029,X2028,X2027)|(~c_Orderings_Oord__class_Oless(X2029,X2026,X2028)|c_Orderings_Oord__class_Oless(X2029,X2026,X2027)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I8_J])])])). 1.16/1.44 fof(c_0_1950, plain, ![X667, X668, X669, X670]:(~class_Orderings_Oorder(X670)|(~c_Orderings_Oord__class_Oless(X670,X669,X668)|(~c_Orderings_Oord__class_Oless__eq(X670,X667,X669)|c_Orderings_Oord__class_Oless(X670,X667,X668)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I7_J])])])). 1.16/1.44 fof(c_0_1951, plain, ![X2813, X2814, X2815, X2816]:(~class_Orderings_Opreorder(X2816)|(~c_Orderings_Oord__class_Oless__eq(X2816,X2815,X2814)|(~c_Orderings_Oord__class_Oless__eq(X2816,X2814,X2813)|c_Orderings_Oord__class_Oless__eq(X2816,X2815,X2813)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__trans])])])). 1.16/1.44 fof(c_0_1952, plain, ![X2364, X2365, X2366, X2367]:(~class_Orderings_Oorder(X2367)|(~c_Orderings_Oord__class_Oless__eq(X2367,X2366,X2365)|(~c_Orderings_Oord__class_Oless__eq(X2367,X2364,X2366)|c_Orderings_Oord__class_Oless__eq(X2367,X2364,X2365)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])])). 1.16/1.44 fof(c_0_1953, plain, ![X2732, X2733, X2734]:(~class_Groups_Oab__group__add(X2734)|c_Groups_Ominus__class_Ominus(X2734,c_Groups_Ouminus__class_Ouminus(X2734,X2733),c_Groups_Ouminus__class_Ouminus(X2734,X2732))=c_Groups_Ouminus__class_Ouminus(X2734,c_Groups_Ominus__class_Ominus(X2734,X2733,X2732))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus])])). 1.16/1.44 fof(c_0_1954, plain, ![X2391, X2392, X2393]:(~class_Groups_Ogroup__add(X2393)|c_Groups_Oplus__class_Oplus(X2393,c_Groups_Ouminus__class_Ouminus(X2393,X2391),c_Groups_Ouminus__class_Ouminus(X2393,X2392))=c_Groups_Ouminus__class_Ouminus(X2393,c_Groups_Oplus__class_Oplus(X2393,X2392,X2391))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])])). 1.16/1.44 fof(c_0_1955, plain, ![X353, X354, X355]:(~class_Groups_Oab__group__add(X355)|c_Groups_Ouminus__class_Ouminus(X355,c_Groups_Oplus__class_Oplus(X355,X354,X353))=c_Groups_Oplus__class_Oplus(X355,c_Groups_Ouminus__class_Ouminus(X355,X354),c_Groups_Ouminus__class_Ouminus(X355,X353))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])])). 1.16/1.44 fof(c_0_1956, plain, ![X1809]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1809,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1809)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), inference(variable_rename,[status(thm)],[fact_real__natfloor__add__one__gt])). 1.16/1.44 fof(c_0_1957, plain, ![X2531, X2532]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2532)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2532),X2531),X2532)=X2531), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])])). 1.16/1.44 fof(c_0_1958, plain, ![X367, X368]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X368)|X367=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X367),X368),X368)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self__is__m])])])). 1.16/1.44 fof(c_0_1959, plain, ![X863, X864]:((~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X864)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X863,X864)=c_SMT_Oz3div(X863,X864))&(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X864)|c_SMT_Oz3div(X863,X864)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X863,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X864))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_z3div__def])])])). 1.16/1.44 fof(c_0_1960, plain, ![X350, X351, X352]:((~c_Orderings_Oord__class_Oless(X352,X350,X351)|c_Orderings_Oord__class_Oless(X352,c_Groups_Ouminus__class_Ouminus(X352,X351),c_Groups_Ouminus__class_Ouminus(X352,X350))|~class_Groups_Oordered__ab__group__add(X352))&(~c_Orderings_Oord__class_Oless(X352,c_Groups_Ouminus__class_Ouminus(X352,X351),c_Groups_Ouminus__class_Ouminus(X352,X350))|c_Orderings_Oord__class_Oless(X352,X350,X351)|~class_Groups_Oordered__ab__group__add(X352))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])])). 1.16/1.44 fof(c_0_1961, plain, ![X2473, X2474, X2475]:((~c_Orderings_Oord__class_Oless__eq(X2475,c_Groups_Ouminus__class_Ouminus(X2475,X2474),c_Groups_Ouminus__class_Ouminus(X2475,X2473))|c_Orderings_Oord__class_Oless__eq(X2475,X2473,X2474)|~class_Lattices_Oboolean__algebra(X2475))&(~c_Orderings_Oord__class_Oless__eq(X2475,X2473,X2474)|c_Orderings_Oord__class_Oless__eq(X2475,c_Groups_Ouminus__class_Ouminus(X2475,X2474),c_Groups_Ouminus__class_Ouminus(X2475,X2473))|~class_Lattices_Oboolean__algebra(X2475))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__le__compl__iff])])])])). 1.16/1.44 fof(c_0_1962, plain, ![X1589, X1590, X1591]:((~c_Orderings_Oord__class_Oless__eq(X1591,X1589,X1590)|c_Orderings_Oord__class_Oless__eq(X1591,c_Groups_Ouminus__class_Ouminus(X1591,X1590),c_Groups_Ouminus__class_Ouminus(X1591,X1589))|~class_Groups_Oordered__ab__group__add(X1591))&(~c_Orderings_Oord__class_Oless__eq(X1591,c_Groups_Ouminus__class_Ouminus(X1591,X1590),c_Groups_Ouminus__class_Ouminus(X1591,X1589))|c_Orderings_Oord__class_Oless__eq(X1591,X1589,X1590)|~class_Groups_Oordered__ab__group__add(X1591))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])])). 1.16/1.44 cnf(c_0_1963, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1352])). 1.16/1.44 fof(c_0_1964, plain, ![X749, X750]:((((~c_Orderings_Oord__class_Oless(tc_Int_Oint,X749,X750)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X750,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X750,X749)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X750)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X750,X749)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X750,X749)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X749|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X750,X749)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X750)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X749,X750)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X749|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X750,X749)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Orderings_Oord__class_Oless(tc_Int_Oint,X750,X749)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X749,X750)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X749|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X750,X749)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X750)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X750,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X749|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X750,X749)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Orderings_Oord__class_Oless(tc_Int_Oint,X750,X749)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X750,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X749|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X750,X749)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff])])])). 1.16/1.44 fof(c_0_1965, plain, ![X1208, X1209]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1209,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1208,X1209)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1209,X1208)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__neg__neg__trivial])])])). 1.16/1.44 fof(c_0_1966, plain, ![X2859, X2860]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2860)|(~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2860,X2859)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2860,X2859))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__pos__pos__trivial])])])). 1.16/1.44 fof(c_0_1967, plain, ![X995, X996, X997]:(~class_RealVector_Oreal__normed__algebra(X997)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X997),c_Groups_Ouminus__class_Ouminus(X997,X996)),X995)=c_Groups_Ouminus__class_Ouminus(X997,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X997),X996),X995))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])])). 1.16/1.44 fof(c_0_1968, plain, ![X1016, X1017, X1018]:(~class_Rings_Olinordered__idom(X1018)|c_Groups_Oabs__class_Oabs(X1018,hAPP(hAPP(c_Power_Opower__class_Opower(X1018),X1017),X1016))=hAPP(hAPP(c_Power_Opower__class_Opower(X1018),c_Groups_Oabs__class_Oabs(X1018,X1017)),X1016)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])])). 1.16/1.44 fof(c_0_1969, plain, ![X1133, X1134, X1135]:(~class_Rings_Oring(X1135)|c_Groups_Ouminus__class_Ouminus(X1135,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1135),X1134),X1133))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1135),c_Groups_Ouminus__class_Ouminus(X1135,X1134)),X1133)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__mult__left])])])). 1.16/1.44 fof(c_0_1970, plain, ![X450, X451, X452]:(~class_RealVector_Oreal__normed__algebra(X452)|c_Groups_Ouminus__class_Ouminus(X452,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X452),X451),X450))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X452),c_Groups_Ouminus__class_Ouminus(X452,X451)),X450)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left])])). 1.16/1.44 cnf(c_0_1971, plain, (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1342])). 1.16/1.44 cnf(c_0_1972, plain, (X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1342])). 1.16/1.44 fof(c_0_1973, plain, ![X1670, X1671, X1672]:((X1671!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1670,X1672)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1671,X1672)=X1670|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1672,X1671))&(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1671,X1672)!=X1670|X1671=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1670,X1672)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1672,X1671))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])])). 1.16/1.44 fof(c_0_1974, plain, ![X671, X672, X673]:(~class_RealVector_Oreal__normed__div__algebra(X673)|c_RealVector_Onorm__class_Onorm(X673,hAPP(hAPP(c_Power_Opower__class_Opower(X673),X672),X671))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X673,X672)),X671)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power])])). 1.16/1.44 fof(c_0_1975, plain, ![X1518, X1519, X1520]:(~class_Groups_Ogroup__add(X1520)|X1518=c_Groups_Oplus__class_Oplus(X1520,X1519,c_Groups_Oplus__class_Oplus(X1520,c_Groups_Ouminus__class_Ouminus(X1520,X1519),X1518))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__minus__cancel])])])). 1.16/1.44 fof(c_0_1976, plain, ![X1086, X1087, X1088]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1088,X1087)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1087,X1086)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1088,X1086))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zle__trans])])])). 1.16/1.44 fof(c_0_1977, plain, ![X2886, X2887, X2888]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2888,X2887)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2887,X2886)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2888,X2886))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__trans])])])). 1.16/1.44 fof(c_0_1978, plain, ![X2628, X2629, X2630]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2630,X2629)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2629,X2628)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2630,X2628))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__le__trans])])])). 1.16/1.44 cnf(c_0_1979, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_1328])). 1.16/1.44 fof(c_0_1980, plain, ![X2802, X2803, X2804]:(~class_Rings_Olinordered__idom(X2804)|(~c_Polynomial_Opos__poly(X2804,X2803)|(~c_Polynomial_Opos__poly(X2804,X2802)|c_Polynomial_Opos__poly(X2804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2804)),X2803),X2802))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__poly__mult])])])). 1.16/1.44 fof(c_0_1981, plain, ![X556, X557]:c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X557),X556))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X557)),c_RealDef_Oreal(tc_Nat_Onat,X556)), inference(variable_rename,[status(thm)],[fact_real__of__nat__mult])). 1.16/1.44 cnf(c_0_1982, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_1314])). 1.16/1.44 cnf(c_0_1983, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))), inference(split_conjunct,[status(thm)],[c_0_1315])). 1.16/1.44 fof(c_0_1984, plain, ![X1089, X1090, X1091]:(~class_Groups_Oab__group__add(X1091)|hAPP(c_Polynomial_Ocoeff(X1091,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1091),X1090)),X1089)=c_Groups_Ouminus__class_Ouminus(X1091,hAPP(c_Polynomial_Ocoeff(X1091,X1090),X1089))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_coeff__minus])])])). 1.16/1.44 fof(c_0_1985, plain, ![X133, X134, X135]:(~class_Rings_Ocomm__ring(X135)|hAPP(c_Polynomial_Opoly(X135,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X135),X134)),X133)=c_Groups_Ouminus__class_Ouminus(X135,hAPP(c_Polynomial_Opoly(X135,X134),X133))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_poly__minus])])])). 1.16/1.44 fof(c_0_1986, plain, ![X2446, X2447, X2448]:((~c_Orderings_Oord__class_Oless(X2448,c_Groups_Ouminus__class_Ouminus(X2448,X2447),X2446)|c_Orderings_Oord__class_Oless(X2448,c_Groups_Ouminus__class_Ouminus(X2448,X2446),X2447)|~class_Groups_Oordered__ab__group__add(X2448))&(~c_Orderings_Oord__class_Oless(X2448,c_Groups_Ouminus__class_Ouminus(X2448,X2446),X2447)|c_Orderings_Oord__class_Oless(X2448,c_Groups_Ouminus__class_Ouminus(X2448,X2447),X2446)|~class_Groups_Oordered__ab__group__add(X2448))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])])). 1.16/1.44 fof(c_0_1987, plain, ![X2398, X2399, X2400]:(~class_Groups_Oordered__ab__group__add__abs(X2400)|(~c_Orderings_Oord__class_Oless__eq(X2400,c_Groups_Oabs__class_Oabs(X2400,X2399),X2398)|c_Orderings_Oord__class_Oless__eq(X2400,c_Groups_Ouminus__class_Ouminus(X2400,X2399),X2398))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__le__D2])])])). 1.16/1.44 fof(c_0_1988, plain, ![X648, X649, X650]:((~c_Orderings_Oord__class_Oless__eq(X650,c_Groups_Ouminus__class_Ouminus(X650,X648),X649)|c_Orderings_Oord__class_Oless__eq(X650,c_Groups_Ouminus__class_Ouminus(X650,X649),X648)|~class_Groups_Oordered__ab__group__add(X650))&(~c_Orderings_Oord__class_Oless__eq(X650,c_Groups_Ouminus__class_Ouminus(X650,X649),X648)|c_Orderings_Oord__class_Oless__eq(X650,c_Groups_Ouminus__class_Ouminus(X650,X648),X649)|~class_Groups_Oordered__ab__group__add(X650))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])])). 1.16/1.44 fof(c_0_1989, plain, ![X1237, X1238, X1239]:((~c_Orderings_Oord__class_Oless(X1239,X1238,c_Groups_Ouminus__class_Ouminus(X1239,X1237))|c_Orderings_Oord__class_Oless(X1239,X1237,c_Groups_Ouminus__class_Ouminus(X1239,X1238))|~class_Groups_Oordered__ab__group__add(X1239))&(~c_Orderings_Oord__class_Oless(X1239,X1237,c_Groups_Ouminus__class_Ouminus(X1239,X1238))|c_Orderings_Oord__class_Oless(X1239,X1238,c_Groups_Ouminus__class_Ouminus(X1239,X1237))|~class_Groups_Oordered__ab__group__add(X1239))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])])). 1.16/1.44 fof(c_0_1990, plain, ![X1366, X1367, X1368]:((~c_Orderings_Oord__class_Oless__eq(X1368,X1367,c_Groups_Ouminus__class_Ouminus(X1368,X1366))|c_Orderings_Oord__class_Oless__eq(X1368,X1366,c_Groups_Ouminus__class_Ouminus(X1368,X1367))|~class_Groups_Oordered__ab__group__add(X1368))&(~c_Orderings_Oord__class_Oless__eq(X1368,X1366,c_Groups_Ouminus__class_Ouminus(X1368,X1367))|c_Orderings_Oord__class_Oless__eq(X1368,X1367,c_Groups_Ouminus__class_Ouminus(X1368,X1366))|~class_Groups_Oordered__ab__group__add(X1368))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__minus__iff])])])])). 1.16/1.44 fof(c_0_1991, plain, ![X2841, X2842]:c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2842,X2841))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2842),c_RealDef_Oreal(tc_Nat_Onat,X2841)), inference(variable_rename,[status(thm)],[fact_real__of__nat__add])). 1.16/1.44 fof(c_0_1992, plain, ![X1152, X1153]:c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1153,X1152))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1153),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1152)), inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib])). 1.16/1.44 fof(c_0_1993, plain, ![X2149, X2150, X2151]:(~class_Lattices_Oab__semigroup__idem__mult(X2151)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2151),X2150),X2149)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2151),X2150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2151),X2150),X2149))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])])). 1.16/1.44 cnf(c_0_1994, plain, (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X2), inference(split_conjunct,[status(thm)],[c_0_1340])). 1.16/1.44 cnf(c_0_1995, plain, (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1340])). 1.16/1.44 cnf(c_0_1996, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X2), inference(split_conjunct,[status(thm)],[c_0_1341])). 1.16/1.44 cnf(c_0_1997, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_1341])). 1.16/1.44 fof(c_0_1998, plain, ![X919]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X919))), inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero])). 1.16/1.44 fof(c_0_1999, plain, ![X2315, X2316]:(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2316,X2315)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2315,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2316,X2315))=X2316), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__diff__inverse])])])). 1.16/1.44 fof(c_0_2000, plain, ![X2152, X2153]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2153),c_RealDef_Oreal(tc_Nat_Onat,X2152))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2153,X2152))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2153,X2152)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2153),c_RealDef_Oreal(tc_Nat_Onat,X2152)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff])])). 1.16/1.44 fof(c_0_2001, plain, ![X1576, X1577]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1577,X1576)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1577),c_RealDef_Oreal(tc_Nat_Onat,X1576)))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1577),c_RealDef_Oreal(tc_Nat_Onat,X1576))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1577,X1576))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff])])). 1.16/1.44 fof(c_0_2002, plain, ![X2617, X2618]:((~c_Orderings_Oord__class_Oless(X2618,c_Groups_Ozero__class_Ozero(X2618),X2617)|c_Orderings_Oord__class_Oless(X2618,c_Groups_Ouminus__class_Ouminus(X2618,X2617),c_Groups_Ozero__class_Ozero(X2618))|~class_Groups_Oordered__ab__group__add(X2618))&(~c_Orderings_Oord__class_Oless(X2618,c_Groups_Ouminus__class_Ouminus(X2618,X2617),c_Groups_Ozero__class_Ozero(X2618))|c_Orderings_Oord__class_Oless(X2618,c_Groups_Ozero__class_Ozero(X2618),X2617)|~class_Groups_Oordered__ab__group__add(X2618))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])])). 1.16/1.44 fof(c_0_2003, plain, ![X2785, X2786]:((~c_Orderings_Oord__class_Oless__eq(X2786,c_Groups_Ouminus__class_Ouminus(X2786,X2785),c_Groups_Ozero__class_Ozero(X2786))|c_Orderings_Oord__class_Oless__eq(X2786,c_Groups_Ozero__class_Ozero(X2786),X2785)|~class_Groups_Oordered__ab__group__add(X2786))&(~c_Orderings_Oord__class_Oless__eq(X2786,c_Groups_Ozero__class_Ozero(X2786),X2785)|c_Orderings_Oord__class_Oless__eq(X2786,c_Groups_Ouminus__class_Ouminus(X2786,X2785),c_Groups_Ozero__class_Ozero(X2786))|~class_Groups_Oordered__ab__group__add(X2786))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__le__0__iff__le])])])])). 1.16/1.44 fof(c_0_2004, plain, ![X1944, X1945]:((~c_Orderings_Oord__class_Oless(X1945,c_Groups_Ozero__class_Ozero(X1945),X1944)|c_Orderings_Oord__class_Oless(X1945,c_Groups_Ozero__class_Ozero(X1945),c_Groups_Osgn__class_Osgn(X1945,X1944))|~class_Rings_Olinordered__idom(X1945))&(~c_Orderings_Oord__class_Oless(X1945,c_Groups_Ozero__class_Ozero(X1945),c_Groups_Osgn__class_Osgn(X1945,X1944))|c_Orderings_Oord__class_Oless(X1945,c_Groups_Ozero__class_Ozero(X1945),X1944)|~class_Rings_Olinordered__idom(X1945))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])])). 1.16/1.44 fof(c_0_2005, plain, ![X2719, X2720]:((~c_Orderings_Oord__class_Oless(X2720,c_Groups_Osgn__class_Osgn(X2720,X2719),c_Groups_Ozero__class_Ozero(X2720))|c_Orderings_Oord__class_Oless(X2720,X2719,c_Groups_Ozero__class_Ozero(X2720))|~class_Rings_Olinordered__idom(X2720))&(~c_Orderings_Oord__class_Oless(X2720,X2719,c_Groups_Ozero__class_Ozero(X2720))|c_Orderings_Oord__class_Oless(X2720,c_Groups_Osgn__class_Osgn(X2720,X2719),c_Groups_Ozero__class_Ozero(X2720))|~class_Rings_Olinordered__idom(X2720))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__less])])])])). 1.16/1.44 fof(c_0_2006, plain, ![X1601, X1602]:((~c_Orderings_Oord__class_Oless(X1602,X1601,c_Groups_Ozero__class_Ozero(X1602))|c_Orderings_Oord__class_Oless(X1602,c_Groups_Ozero__class_Ozero(X1602),c_Groups_Ouminus__class_Ouminus(X1602,X1601))|~class_Groups_Oordered__ab__group__add(X1602))&(~c_Orderings_Oord__class_Oless(X1602,c_Groups_Ozero__class_Ozero(X1602),c_Groups_Ouminus__class_Ouminus(X1602,X1601))|c_Orderings_Oord__class_Oless(X1602,X1601,c_Groups_Ozero__class_Ozero(X1602))|~class_Groups_Oordered__ab__group__add(X1602))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])])). 1.16/1.44 fof(c_0_2007, plain, ![X2827, X2828]:((~c_Orderings_Oord__class_Oless__eq(X2828,X2827,c_Groups_Ozero__class_Ozero(X2828))|c_Orderings_Oord__class_Oless__eq(X2828,c_Groups_Ozero__class_Ozero(X2828),c_Groups_Ouminus__class_Ouminus(X2828,X2827))|~class_Groups_Oordered__ab__group__add(X2828))&(~c_Orderings_Oord__class_Oless__eq(X2828,c_Groups_Ozero__class_Ozero(X2828),c_Groups_Ouminus__class_Ouminus(X2828,X2827))|c_Orderings_Oord__class_Oless__eq(X2828,X2827,c_Groups_Ozero__class_Ozero(X2828))|~class_Groups_Oordered__ab__group__add(X2828))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])])). 1.16/1.44 fof(c_0_2008, plain, ![X1028, X1029, X1030]:((c_Orderings_Oord__class_Oless__eq(X1030,X1028,X1029)|~c_Orderings_Oord__class_Oless__eq(X1030,X1029,X1028)|c_Orderings_Oord__class_Oless(X1030,X1029,X1028)|~class_Orderings_Opreorder(X1030))&((~c_Orderings_Oord__class_Oless__eq(X1030,X1028,X1029)|~c_Orderings_Oord__class_Oless(X1030,X1029,X1028)|~class_Orderings_Opreorder(X1030))&(c_Orderings_Oord__class_Oless__eq(X1030,X1029,X1028)|~c_Orderings_Oord__class_Oless(X1030,X1029,X1028)|~class_Orderings_Opreorder(X1030)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__le__not__le])])])])). 1.16/1.44 fof(c_0_2009, plain, ![X2139, X2140, X2141]:(~class_Rings_Oring(X2141)|c_Groups_Ouminus__class_Ouminus(X2141,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2141),X2140),X2139))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2141),X2140),c_Groups_Ouminus__class_Ouminus(X2141,X2139))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])])). 1.16/1.44 fof(c_0_2010, plain, ![X1652, X1653, X1654]:(~class_RealVector_Oreal__normed__algebra(X1654)|c_Groups_Ouminus__class_Ouminus(X1654,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1654),X1653),X1652))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1654),X1653),c_Groups_Ouminus__class_Ouminus(X1654,X1652))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right])])). 1.16/1.44 fof(c_0_2011, plain, ![X126, X127, X128]:(~class_RealVector_Oreal__normed__algebra(X128)|c_Groups_Ouminus__class_Ouminus(X128,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X128),X127),X126))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X128),X127),c_Groups_Ouminus__class_Ouminus(X128,X126))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right_Ominus])])])). 1.16/1.44 cnf(c_0_2012, plain, (c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_1353])). 1.16/1.44 fof(c_0_2013, plain, ![X1129, X1130, X1131]:(~class_Lattices_Oboolean__algebra(X1131)|(~c_Orderings_Oord__class_Oless__eq(X1131,X1130,X1129)|c_Orderings_Oord__class_Oless__eq(X1131,c_Groups_Ouminus__class_Ouminus(X1131,X1129),c_Groups_Ouminus__class_Ouminus(X1131,X1130)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__mono])])])). 1.16/1.44 fof(c_0_2014, plain, ![X311, X312, X313]:(~class_Groups_Oordered__ab__group__add(X313)|(~c_Orderings_Oord__class_Oless__eq(X313,X312,X311)|c_Orderings_Oord__class_Oless__eq(X313,c_Groups_Ouminus__class_Ouminus(X313,X311),c_Groups_Ouminus__class_Ouminus(X313,X312)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__imp__neg__le])])])). 1.16/1.44 cnf(c_0_2015, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1352])). 1.16/1.44 fof(c_0_2016, plain, ![X1497]:(~class_Rings_Olinordered__semidom(X1497)|c_Orderings_Oord__class_Oless(X1497,c_Groups_Ozero__class_Ozero(X1497),c_Groups_Oplus__class_Oplus(X1497,c_Groups_Oone__class_Oone(X1497),c_Groups_Oone__class_Oone(X1497)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])])). 1.16/1.44 fof(c_0_2017, plain, ![X2012]:c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2012,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X2012))), inference(variable_rename,[status(thm)],[fact_real__natfloor__gt__diff__one])). 1.16/1.44 fof(c_0_2018, plain, ![X2652, X2653, X2654]:(~class_Groups_Ogroup__add(X2654)|X2652=c_Groups_Oplus__class_Oplus(X2654,c_Groups_Ouminus__class_Ouminus(X2654,X2653),c_Groups_Oplus__class_Oplus(X2654,X2653,X2652))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__add__cancel])])])). 1.16/1.44 fof(c_0_2019, plain, ![X1410, X1411]:((~c_Orderings_Oord__class_Oless(X1411,c_Groups_Ouminus__class_Ouminus(X1411,X1410),X1410)|c_Orderings_Oord__class_Oless(X1411,c_Groups_Ozero__class_Ozero(X1411),X1410)|~class_Groups_Olinordered__ab__group__add(X1411))&(~c_Orderings_Oord__class_Oless(X1411,c_Groups_Ozero__class_Ozero(X1411),X1410)|c_Orderings_Oord__class_Oless(X1411,c_Groups_Ouminus__class_Ouminus(X1411,X1410),X1410)|~class_Groups_Olinordered__ab__group__add(X1411))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])])). 1.16/1.44 fof(c_0_2020, plain, ![X2220, X2221]:((~c_Orderings_Oord__class_Oless__eq(X2221,c_Groups_Ouminus__class_Ouminus(X2221,X2220),X2220)|c_Orderings_Oord__class_Oless__eq(X2221,c_Groups_Ozero__class_Ozero(X2221),X2220)|~class_Groups_Olinordered__ab__group__add(X2221))&(~c_Orderings_Oord__class_Oless__eq(X2221,c_Groups_Ozero__class_Ozero(X2221),X2220)|c_Orderings_Oord__class_Oless__eq(X2221,c_Groups_Ouminus__class_Ouminus(X2221,X2220),X2220)|~class_Groups_Olinordered__ab__group__add(X2221))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])])). 1.16/1.44 fof(c_0_2021, plain, ![X2266, X2267]:((~c_Orderings_Oord__class_Oless(X2267,X2266,c_Groups_Ouminus__class_Ouminus(X2267,X2266))|c_Orderings_Oord__class_Oless(X2267,X2266,c_Groups_Ozero__class_Ozero(X2267))|~class_Rings_Olinordered__idom(X2267))&(~c_Orderings_Oord__class_Oless(X2267,X2266,c_Groups_Ozero__class_Ozero(X2267))|c_Orderings_Oord__class_Oless(X2267,X2266,c_Groups_Ouminus__class_Ouminus(X2267,X2266))|~class_Rings_Olinordered__idom(X2267))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__minus__self__iff])])])])). 1.16/1.44 fof(c_0_2022, plain, ![X2881, X2882]:((~c_Orderings_Oord__class_Oless__eq(X2882,X2881,c_Groups_Ozero__class_Ozero(X2882))|c_Orderings_Oord__class_Oless__eq(X2882,X2881,c_Groups_Ouminus__class_Ouminus(X2882,X2881))|~class_Groups_Olinordered__ab__group__add(X2882))&(~c_Orderings_Oord__class_Oless__eq(X2882,X2881,c_Groups_Ouminus__class_Ouminus(X2882,X2881))|c_Orderings_Oord__class_Oless__eq(X2882,X2881,c_Groups_Ozero__class_Ozero(X2882))|~class_Groups_Olinordered__ab__group__add(X2882))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__minus__self__iff])])])])). 1.16/1.44 fof(c_0_2023, plain, ![X1448, X1449]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1449)),X1448)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1449),X1448)), inference(variable_rename,[status(thm)],[fact_power__real__of__nat])). 1.16/1.44 fof(c_0_2024, plain, ![X1332, X1333]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1333)),X1332)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1333),X1332)), inference(variable_rename,[status(thm)],[fact_real__of__nat__power])). 1.16/1.44 fof(c_0_2025, plain, ![X504, X505]:c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X505),X504))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X505)),X504), inference(variable_rename,[status(thm)],[fact_zmult__zminus])). 1.16/1.44 fof(c_0_2026, plain, ![X1757, X1758]:((X1758!=X1757|c_Transcendental_Oln(X1758)=c_Transcendental_Oln(X1757)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1757)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1758))&(c_Transcendental_Oln(X1758)!=c_Transcendental_Oln(X1757)|X1758=X1757|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1757)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1758))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__inj__iff])])])). 1.16/1.44 cnf(c_0_2027, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__0(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_1354])). 1.16/1.44 fof(c_0_2028, plain, ![X1350, X1351, X1352]:((((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1351,X1352)|hBOOL(hAPP(hAPP(X1350,X1351),X1352))|X1352=X1351|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1352,X1351))&(~hBOOL(hAPP(hAPP(X1350,X1351),X1352))|hBOOL(hAPP(hAPP(X1350,X1351),X1352))|X1352=X1351|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1352,X1351)))&((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1351,X1352)|hBOOL(hAPP(hAPP(X1350,X1351),X1352))|~hBOOL(hAPP(hAPP(X1350,X1351),X1352))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1352,X1351))&(~hBOOL(hAPP(hAPP(X1350,X1351),X1352))|hBOOL(hAPP(hAPP(X1350,X1351),X1352))|~hBOOL(hAPP(hAPP(X1350,X1351),X1352))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1352,X1351))))&(((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1351,X1352)|hBOOL(hAPP(hAPP(X1350,X1351),X1352))|X1352=X1351|~hBOOL(hAPP(hAPP(X1350,X1351),X1352)))&(~hBOOL(hAPP(hAPP(X1350,X1351),X1352))|hBOOL(hAPP(hAPP(X1350,X1351),X1352))|X1352=X1351|~hBOOL(hAPP(hAPP(X1350,X1351),X1352))))&((c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1351,X1352)|hBOOL(hAPP(hAPP(X1350,X1351),X1352))|~hBOOL(hAPP(hAPP(X1350,X1351),X1352))|~hBOOL(hAPP(hAPP(X1350,X1351),X1352)))&(~hBOOL(hAPP(hAPP(X1350,X1351),X1352))|hBOOL(hAPP(hAPP(X1350,X1351),X1352))|~hBOOL(hAPP(hAPP(X1350,X1351),X1352))|~hBOOL(hAPP(hAPP(X1350,X1351),X1352)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__less__cases])])])])). 1.16/1.44 fof(c_0_2029, plain, ![X2159, X2160]:(~class_Rings_Olinordered__idom(X2160)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2160),c_Groups_Oabs__class_Oabs(X2160,X2159)),c_Groups_Oabs__class_Oabs(X2160,X2159))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2160),X2159),X2159)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])])). 1.16/1.44 fof(c_0_2030, plain, ![X562, X563, X564]:(~class_Rings_Oring(X564)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X564),X563),c_Groups_Ouminus__class_Ouminus(X564,X562))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X564),c_Groups_Ouminus__class_Ouminus(X564,X563)),X562)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__mult__commute])])])). 1.16/1.44 fof(c_0_2031, plain, ![X2643, X2644, X2645]:(~class_Rings_Oring(X2645)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2645),X2644),X2643)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2645),c_Groups_Ouminus__class_Ouminus(X2645,X2644)),c_Groups_Ouminus__class_Ouminus(X2645,X2643))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])])). 1.16/1.44 fof(c_0_2032, plain, ![X1706, X1707, X1708]:(~class_Groups_Oordered__ab__group__add__abs(X1708)|(~c_Orderings_Oord__class_Oless__eq(X1708,c_Groups_Oabs__class_Oabs(X1708,X1707),X1706)|c_Orderings_Oord__class_Oless__eq(X1708,X1707,X1706))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__le__D1])])])). 1.16/1.44 fof(c_0_2033, plain, ![X1217, X1218, X1219]:(((X1218!=c_Groups_Ouminus__class_Ouminus(X1219,X1217)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1219),X1218),X1218)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1219),X1217),X1217)|~class_Rings_Oidom(X1219))&(X1217!=X1218|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1219),X1218),X1218)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1219),X1217),X1217)|~class_Rings_Oidom(X1219)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1219),X1218),X1218)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1219),X1217),X1217)|(X1218=c_Groups_Ouminus__class_Ouminus(X1219,X1217)|X1217=X1218)|~class_Rings_Oidom(X1219))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])])). 1.16/1.44 fof(c_0_2034, plain, ![X1334, X1335, X1337]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk37_2(X1334,X1335))|~c_SEQ_OBseq(X1335,X1334)|~class_RealVector_Oreal__normed__vector(X1335))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1335,hAPP(X1334,X1337)),esk37_2(X1334,X1335))|~c_SEQ_OBseq(X1335,X1334)|~class_RealVector_Oreal__normed__vector(X1335))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_BseqD])])])])])])). 1.16/1.44 fof(c_0_2035, plain, ![X2018, X2019, X2020]:(~class_Rings_Olinordered__idom(X2020)|(~c_Polynomial_Opos__poly(X2020,X2019)|(~c_Polynomial_Opos__poly(X2020,X2018)|c_Polynomial_Opos__poly(X2020,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2020),X2019,X2018))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__add])])). 1.16/1.44 fof(c_0_2036, plain, ![X926, X927, X928, X929, X930]:((X926!=X927|X929=X928|c_Groups_Ominus__class_Ominus(X930,X927,X926)!=c_Groups_Ominus__class_Ominus(X930,X929,X928)|~class_Groups_Oab__group__add(X930))&(X929!=X928|X926=X927|c_Groups_Ominus__class_Ominus(X930,X927,X926)!=c_Groups_Ominus__class_Ominus(X930,X929,X928)|~class_Groups_Oab__group__add(X930))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__eq__diff__eq])])])])). 1.16/1.44 cnf(c_0_2037, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1341])). 1.16/1.44 cnf(c_0_2038, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1340])). 1.16/1.44 fof(c_0_2039, plain, ![X1789, X1790]:(X1790!=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1790))|c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1790),X1789))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1790)),X1789)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__power])])). 1.16/1.44 fof(c_0_2040, plain, ![X445, X446, X447]:((X445!=X446|~c_Orderings_Oord__class_Oless(X447,X446,X445)|~c_Orderings_Oord__class_Oless__eq(X447,X446,X445)|~class_Orderings_Olinorder(X447))&(c_Orderings_Oord__class_Oless(X447,X446,X445)|X445=X446|~c_Orderings_Oord__class_Oless__eq(X447,X446,X445)|~class_Orderings_Olinorder(X447))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2])])])])). 1.16/1.44 fof(c_0_2041, plain, ![X1578, X1579, X1580]:(~class_Groups_Oab__group__add(X1580)|c_Groups_Ouminus__class_Ouminus(X1580,c_Groups_Ominus__class_Ominus(X1580,X1579,X1578))=c_Groups_Ominus__class_Ominus(X1580,X1578,X1579)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__diff__eq])])])). 1.16/1.44 fof(c_0_2042, plain, ![X1958, X1959, X1960]:((~c_Orderings_Oord__class_Oless__eq(X1960,X1958,X1959)|~c_Orderings_Oord__class_Oless__eq(X1960,X1959,X1958)|X1958=X1959|~class_Orderings_Oorder(X1960))&((c_Orderings_Oord__class_Oless__eq(X1960,X1958,X1959)|X1958!=X1959|~class_Orderings_Oorder(X1960))&(c_Orderings_Oord__class_Oless__eq(X1960,X1959,X1958)|X1958!=X1959|~class_Orderings_Oorder(X1960)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])])). 1.16/1.44 fof(c_0_2043, plain, ![X1241, X1242, X1243]:(~class_Orderings_Oorder(X1243)|(~c_Orderings_Oord__class_Oless__eq(X1243,X1242,X1241)|(~c_Orderings_Oord__class_Oless__eq(X1243,X1241,X1242)|X1241=X1242))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__antisym])])])). 1.16/1.44 fof(c_0_2044, plain, ![X855, X856, X857]:(~class_Orderings_Oorder(X857)|(~c_Orderings_Oord__class_Oless__eq(X857,X856,X855)|(~c_Orderings_Oord__class_Oless__eq(X857,X855,X856)|X856=X855))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I5_J])])])). 1.16/1.44 fof(c_0_2045, plain, ![X99, X100, X101]:((~c_Orderings_Oord__class_Oless__eq(X101,X99,X100)|X99=X100|~c_Orderings_Oord__class_Oless__eq(X101,X100,X99)|~class_Orderings_Oorder(X101))&(X99!=X100|c_Orderings_Oord__class_Oless__eq(X101,X99,X100)|~c_Orderings_Oord__class_Oless__eq(X101,X100,X99)|~class_Orderings_Oorder(X101))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__antisym__conv])])])])). 1.16/1.44 fof(c_0_2046, plain, ![X229]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X229))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X229))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X229)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X229)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff])])). 1.16/1.44 fof(c_0_2047, plain, ![X378, X379]:(~class_Rings_Olinordered__semidom(X379)|c_Orderings_Oord__class_Oless(X379,X378,c_Groups_Oplus__class_Oplus(X379,X378,c_Groups_Oone__class_Oone(X379)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__add__one])])])). 1.16/1.44 fof(c_0_2048, plain, ![X1699, X1700, X1701, X1702]:((c_Groups_Oplus__class_Oplus(X1702,X1701,X1700)!=c_Groups_Oplus__class_Oplus(X1702,X1699,X1700)|X1699=X1701|~class_Groups_Ocancel__semigroup__add(X1702))&(X1699!=X1701|c_Groups_Oplus__class_Oplus(X1702,X1701,X1700)=c_Groups_Oplus__class_Oplus(X1702,X1699,X1700)|~class_Groups_Ocancel__semigroup__add(X1702))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__right__cancel])])])])). 1.16/1.44 fof(c_0_2049, plain, ![X438, X439, X440, X441]:(~class_Groups_Ocancel__semigroup__add(X441)|(c_Groups_Oplus__class_Oplus(X441,X438,X439)!=c_Groups_Oplus__class_Oplus(X441,X440,X439)|X440=X438)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__right__imp__eq])])])). 1.16/1.44 fof(c_0_2050, plain, ![X2752, X2753, X2754, X2755]:((c_Groups_Oplus__class_Oplus(X2755,X2754,X2753)!=c_Groups_Oplus__class_Oplus(X2755,X2754,X2752)|X2753=X2752|~class_Groups_Ocancel__semigroup__add(X2755))&(X2753!=X2752|c_Groups_Oplus__class_Oplus(X2755,X2754,X2753)=c_Groups_Oplus__class_Oplus(X2755,X2754,X2752)|~class_Groups_Ocancel__semigroup__add(X2755))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__left__cancel])])])])). 1.16/1.44 fof(c_0_2051, plain, ![X1419, X1420, X1421, X1422]:(~class_Groups_Ocancel__semigroup__add(X1422)|(c_Groups_Oplus__class_Oplus(X1422,X1421,X1419)!=c_Groups_Oplus__class_Oplus(X1422,X1421,X1420)|X1420=X1419)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__left__imp__eq])])])). 1.16/1.44 fof(c_0_2052, plain, ![X1581, X1582, X1583, X1584]:(~class_Groups_Ocancel__ab__semigroup__add(X1584)|(c_Groups_Oplus__class_Oplus(X1584,X1583,X1581)!=c_Groups_Oplus__class_Oplus(X1584,X1583,X1582)|X1582=X1581)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__imp__eq])])])). 1.16/1.44 fof(c_0_2053, plain, ![X1605, X1606]:(c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1606),X1605))!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1606)=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__zmult__eq__1])])])). 1.16/1.44 fof(c_0_2054, plain, ![X751, X752, X753]:((c_Orderings_Oord__class_Oless(X753,X752,X751)|(X752=X751|c_Orderings_Oord__class_Oless(X753,X751,X752))|~class_Orderings_Olinorder(X753))&((X752!=X751|~c_Orderings_Oord__class_Oless(X753,X752,X751)|~class_Orderings_Olinorder(X753))&(~c_Orderings_Oord__class_Oless(X753,X751,X752)|~c_Orderings_Oord__class_Oless(X753,X752,X751)|~class_Orderings_Olinorder(X753)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq])])])])). 1.16/1.44 fof(c_0_2055, plain, ![X2790, X2791, X2792]:((c_Orderings_Oord__class_Oless(X2792,X2791,X2790)|c_Orderings_Oord__class_Oless__eq(X2792,X2790,X2791)|~class_Orderings_Olinorder(X2792))&(~c_Orderings_Oord__class_Oless__eq(X2792,X2790,X2791)|~c_Orderings_Oord__class_Oless(X2792,X2791,X2790)|~class_Orderings_Olinorder(X2792))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__not__less])])])])). 1.16/1.44 fof(c_0_2056, plain, ![X2605, X2606, X2607]:(~class_Orderings_Olinorder(X2607)|(~c_Orderings_Oord__class_Oless__eq(X2607,X2606,X2605)|~c_Orderings_Oord__class_Oless(X2607,X2605,X2606))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_leD])])])). 1.16/1.44 fof(c_0_2057, plain, ![X429, X430, X431]:((~c_Orderings_Oord__class_Oless(X431,X429,X430)|~c_Orderings_Oord__class_Oless__eq(X431,X430,X429)|~class_Orderings_Olinorder(X431))&(c_Orderings_Oord__class_Oless__eq(X431,X430,X429)|c_Orderings_Oord__class_Oless(X431,X429,X430)|~class_Orderings_Olinorder(X431))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__not__le])])])])). 1.16/1.44 fof(c_0_2058, plain, ![X2254, X2255, X2256]:(~class_Orderings_Opreorder(X2256)|(~c_Orderings_Oord__class_Oless(X2256,X2255,X2254)|~c_Orderings_Oord__class_Oless(X2256,X2254,X2255))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__asym])])])). 1.16/1.44 fof(c_0_2059, plain, ![X1289, X1290, X1291]:(~class_Orderings_Opreorder(X1291)|(~c_Orderings_Oord__class_Oless(X1291,X1290,X1289)|~c_Orderings_Oord__class_Oless(X1291,X1289,X1290))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less])])])). 1.16/1.44 fof(c_0_2060, plain, ![X707, X708, X709]:(~class_Orderings_Opreorder(X709)|(~c_Orderings_Oord__class_Oless(X709,X708,X707)|~c_Orderings_Oord__class_Oless(X709,X707,X708))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__not__sym])])])). 1.16/1.44 fof(c_0_2061, plain, ![X540, X541, X542]:(~class_Orderings_Opreorder(X542)|(~c_Orderings_Oord__class_Oless(X542,X541,X540)|~c_Orderings_Oord__class_Oless(X542,X540,X541))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__asym_H])])])). 1.16/1.44 fof(c_0_2062, plain, ![X1552, X1553, X1554]:(~class_Orderings_Oorder(X1554)|(~c_Orderings_Oord__class_Oless(X1554,X1553,X1552)|~c_Orderings_Oord__class_Oless(X1554,X1552,X1553))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I9_J])])])). 1.16/1.44 fof(c_0_2063, plain, ![X1767, X1768]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1768,c_RealDef_Oreal(tc_Nat_Onat,X1767))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1768),X1767)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_natceiling__le])])])). 1.16/1.44 fof(c_0_2064, plain, ![X2534, X2535]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2535),X2534)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2535,c_RComplete_Onatfloor(X2534))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor])])). 1.16/1.44 cnf(c_0_2065, plain, (X2=X1|c_Nat_OSuc(X1)!=c_Nat_OSuc(X2)), inference(split_conjunct,[status(thm)],[c_0_1355])). 1.16/1.44 cnf(c_0_2066, plain, (X2=X1|c_Nat_OSuc(X1)!=c_Nat_OSuc(X2)), inference(split_conjunct,[status(thm)],[c_0_1356])). 1.16/1.44 fof(c_0_2067, plain, ![X103, X104, X105]:((c_Groups_Ozero__class_Ozero(X105)!=hAPP(c_Polynomial_Opoly(X105,X104),X103)|(c_Polynomial_Oorder(X105,X103,X104)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X105))=X104)|~class_Rings_Oidom(X105))&((c_Polynomial_Oorder(X105,X103,X104)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(X105)=hAPP(c_Polynomial_Opoly(X105,X104),X103)|~class_Rings_Oidom(X105))&(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X105))!=X104|c_Groups_Ozero__class_Ozero(X105)=hAPP(c_Polynomial_Opoly(X105,X104),X103)|~class_Rings_Oidom(X105)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__root])])])). 1.16/1.44 fof(c_0_2068, plain, ![X292, X293]:(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X293,X292)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X292,X293)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X293=X292)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diffs0__imp__equal])])])). 1.16/1.44 fof(c_0_2069, plain, ![X248]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X248)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X248)),X248)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__natfloor__le])])])). 1.16/1.44 cnf(c_0_2070, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_1343])). 1.16/1.44 fof(c_0_2071, plain, ![X2583, X2584]:((c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2584))!=X2583|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X2584),X2583)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2584))|~class_Rings_Olinordered__idom(X2584))&((~c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2584),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2584)),X2583)|c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2584))=c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X2584),X2583)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2584))=X2583|~class_Rings_Olinordered__idom(X2584))&(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2584),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2584)),X2583)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2584),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2584)))=c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X2584),X2583)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2584))=X2583|~class_Rings_Olinordered__idom(X2584)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__poly__def])])])])). 1.16/1.44 fof(c_0_2072, plain, ![X1250, X1251]:((c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1251),X1250,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1251)))|X1250=c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X1251),X1250)|~class_Rings_Olinordered__idom(X1251))&(~c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1251),X1250,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1251)))|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1251),X1250)=c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X1251),X1250)|~class_Rings_Olinordered__idom(X1251))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__poly__def])])])])). 1.16/1.44 fof(c_0_2073, plain, ![X2046, X2047, X2048]:(~class_Divides_Osemiring__div(X2048)|(c_Groups_Ozero__class_Ozero(X2048)=X2047|X2046=c_Divides_Odiv__class_Odiv(X2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2048),X2047),X2046),X2047))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self1__is__id])])])). 1.16/1.44 fof(c_0_2074, plain, ![X2724, X2725, X2726]:(~class_Divides_Osemiring__div(X2726)|(X2725=c_Groups_Ozero__class_Ozero(X2726)|X2724=c_Divides_Odiv__class_Odiv(X2726,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2726),X2724),X2725),X2725))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])])). 1.16/1.44 fof(c_0_2075, plain, ![X469, X470]:(~class_Rings_Olinordered__ring(X470)|c_Orderings_Oord__class_Oless__eq(X470,c_Groups_Ozero__class_Ozero(X470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X470),X469),X469))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__square])])])). 1.16/1.44 fof(c_0_2076, plain, ![X2295, X2296]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2296,X2295)|(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2295,X2296)|X2295=X2296)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])])). 1.16/1.44 fof(c_0_2077, plain, ![X1364, X1365]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1365,X1364)|(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1364,X1365)|X1365=X1364)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__antisym])])])). 1.16/1.44 fof(c_0_2078, plain, ![X1426, X1427]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1427,X1426)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1426,X1427)|X1427=X1426)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])])). 1.16/1.44 cnf(c_0_2079, plain, (X1=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_1357])). 1.16/1.44 fof(c_0_2080, plain, ![X1910, X1911, X1912]:(~class_Groups_Ogroup__add(X1912)|X1911=c_Groups_Ominus__class_Ominus(X1912,c_Groups_Oplus__class_Oplus(X1912,X1911,X1910),X1910)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])])). 1.16/1.44 fof(c_0_2081, plain, ![X2009, X2010, X2011]:(~class_Groups_Ogroup__add(X2011)|X2010=c_Groups_Oplus__class_Oplus(X2011,c_Groups_Ominus__class_Ominus(X2011,X2010,X2009),X2009)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__add__cancel])])])). 1.16/1.44 fof(c_0_2082, plain, ![X1567, X1568]:(((X1567=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1568),X1567)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1568))&(c_Groups_Oone__class_Oone(tc_Int_Oint)=X1568|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1568),X1567)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1568)))&(X1567!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=X1568|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1568),X1567)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1568))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__zmult__eq__1__iff])])])])). 1.16/1.44 cnf(c_0_2083, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_1312])). 1.16/1.44 fof(c_0_2084, plain, ![X2821, X2822, X2823]:((X2821!=X2823|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2821,X2822)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2823,X2822))&(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2821,X2822)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2823,X2822)|X2821=X2823)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])])). 1.16/1.44 fof(c_0_2085, plain, ![X1052, X1053, X1054]:((c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1054,X1052)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1054,X1053)|X1053=X1052)&(X1053!=X1052|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1054,X1052)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1054,X1053))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])])). 1.16/1.44 cnf(c_0_2086, plain, (X1=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_1358])). 1.16/1.44 cnf(c_0_2087, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_1326])). 1.16/1.44 cnf(c_0_2088, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1))), inference(split_conjunct,[status(thm)],[c_0_1359])). 1.16/1.44 fof(c_0_2089, plain, ![X2495, X2496, X2497, X2498, X2499]:((X2495!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2496,X2497)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2496,X2495))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2499,X2498)|X2498=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2499,esk69_2(X2498,X2499)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])])). 1.16/1.44 fof(c_0_2090, plain, ![X412, X413, X414, X415, X416]:((X412!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X413,X414)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X413,X412))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X416,X415)|X415=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X416,esk13_2(X415,X416)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__ex__iff])])])])])). 1.16/1.44 cnf(c_0_2091, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1))), inference(split_conjunct,[status(thm)],[c_0_1360])). 1.16/1.44 fof(c_0_2092, plain, ![X1810, X1811]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1811,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1811,X1810))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_diff__add__0])). 1.16/1.44 fof(c_0_2093, plain, ![X2144, X2145]:c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2145,X2144),X2145)=X2144, inference(variable_rename,[status(thm)],[fact_diff__add__inverse])). 1.16/1.44 fof(c_0_2094, plain, ![X2066, X2067]:X2067=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2067,X2066),X2066), inference(variable_rename,[status(thm)],[fact_diff__add__inverse2])). 1.16/1.44 fof(c_0_2095, plain, ![X2287, X2288]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2288,X2287),X2288), inference(variable_rename,[status(thm)],[fact_div__le__dividend])). 1.16/1.44 fof(c_0_2096, plain, ![X1646, X1647]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1647,X1646),X1647), inference(variable_rename,[status(thm)],[fact_diff__le__self])). 1.16/1.44 fof(c_0_2097, plain, ![X810, X811]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X811,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X811,X810)), inference(variable_rename,[status(thm)],[fact_le__add1])). 1.16/1.44 fof(c_0_2098, plain, ![X767, X768]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X768,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X767,X768)), inference(variable_rename,[status(thm)],[fact_le__add2])). 1.16/1.44 fof(c_0_2099, plain, ![X2856]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2856)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X2856)))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X2856))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2856))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])])). 1.16/1.44 fof(c_0_2100, plain, ![X1782]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1782),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1782,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))&(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1782,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1782),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one])])). 1.16/1.44 fof(c_0_2101, plain, ![X1387, X1388]:((~c_Orderings_Oord__class_Oless(X1388,c_Groups_Ozero__class_Ozero(X1388),c_Groups_Oabs__class_Oabs(X1388,X1387))|X1387!=c_Groups_Ozero__class_Ozero(X1388)|~class_Groups_Oordered__ab__group__add__abs(X1388))&(X1387=c_Groups_Ozero__class_Ozero(X1388)|c_Orderings_Oord__class_Oless(X1388,c_Groups_Ozero__class_Ozero(X1388),c_Groups_Oabs__class_Oabs(X1388,X1387))|~class_Groups_Oordered__ab__group__add__abs(X1388))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__abs__iff])])])])). 1.16/1.44 cnf(c_0_2102, plain, (c_Nat_OSuc(esk26_1(X1))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1361])). 1.16/1.44 fof(c_0_2103, plain, ![X506, X507]:c_Divides_Odiv__class_Odiv(tc_Int_Oint,X507,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X506))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X507),X506), inference(variable_rename,[status(thm)],[fact_zdiv__zminus2])). 1.16/1.44 fof(c_0_2104, plain, ![X387, X388]:c_Divides_Odiv__class_Odiv(tc_Int_Oint,X388,X387)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X388),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X387)), inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus])). 1.16/1.44 fof(c_0_2105, plain, ![X829]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X829)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X829))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__gt__zero])])). 1.16/1.44 fof(c_0_2106, plain, ![X2245]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2245)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X2245))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__ge__zero])])). 1.16/1.44 fof(c_0_2107, plain, ![X1880, X1881, X1882]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1882),X1880)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1882),X1881)|(X1880=X1881|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1882))&((X1880!=X1881|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1882),X1880)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1882),X1881))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1882|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1882),X1880)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1882),X1881)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])])). 1.16/1.44 fof(c_0_2108, plain, ![X1220, X1221, X1222]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1222),X1221)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1222),X1220)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1222|X1221=X1220))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1222|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1222),X1221)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1222),X1220))&(X1221!=X1220|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1222),X1221)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1222),X1220)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])])). 1.16/1.44 fof(c_0_2109, plain, ![X2900, X2901, X2902]:(((X2901!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2900),X2901)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2902),X2901))&(X2900!=X2902|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2900),X2901)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2902),X2901)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2900),X2901)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2902),X2901)|(X2901=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2900=X2902))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])])). 1.16/1.44 fof(c_0_2110, plain, ![X2761, X2762, X2763]:((X2762!=X2761|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2762),X2763)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2761),X2763)|X2763=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2762),X2763)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2761),X2763)|X2762=X2761|X2763=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__mult__right__cancel])])])])). 1.16/1.44 fof(c_0_2111, plain, ![X2272, X2273, X2274]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2274),X2273)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2274),X2272)|X2273=X2272|X2274=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))&(X2273!=X2272|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2274),X2273)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2274),X2272)|X2274=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__mult__left__cancel])])])])). 1.16/1.44 fof(c_0_2112, plain, ![X340, X341]:((~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X341,X340)|c_Groups_Ominus__class_Ominus(tc_Int_Oint,X340,X341)=c_Nat__Transfer_Otsub(X340,X341))&(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X341,X340)|c_Nat__Transfer_Otsub(X340,X341)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tsub__def])])])). 1.16/1.44 fof(c_0_2113, plain, ![X1527, X1528]:(~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1528,X1527)|c_Nat__Transfer_Otsub(X1527,X1528)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1527,X1528)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tsub__eq])])])). 1.16/1.44 fof(c_0_2114, plain, ![X1439, X1440, X1441]:(((X1440!=X1439|~c_Orderings_Oord__class_Oless(X1441,X1440,X1439)|~class_Orderings_Oorder(X1441))&(c_Orderings_Oord__class_Oless__eq(X1441,X1440,X1439)|~c_Orderings_Oord__class_Oless(X1441,X1440,X1439)|~class_Orderings_Oorder(X1441)))&(X1440=X1439|~c_Orderings_Oord__class_Oless__eq(X1441,X1440,X1439)|c_Orderings_Oord__class_Oless(X1441,X1440,X1439)|~class_Orderings_Oorder(X1441))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__le])])])])). 1.16/1.44 fof(c_0_2115, plain, ![X1025, X1026, X1027]:((X1025!=X1026|c_Orderings_Oord__class_Oless__eq(X1027,X1026,X1025)|c_Orderings_Oord__class_Oless(X1027,X1026,X1025)|~class_Orderings_Olinorder(X1027))&(~c_Orderings_Oord__class_Oless__eq(X1027,X1026,X1025)|X1025=X1026|c_Orderings_Oord__class_Oless(X1027,X1026,X1025)|~class_Orderings_Olinorder(X1027))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1])])])])). 1.16/1.44 fof(c_0_2116, plain, ![X2342, X2343, X2344]:(~class_Orderings_Oorder(X2344)|(~c_Orderings_Oord__class_Oless__eq(X2344,X2343,X2342)|(X2342=X2343|c_Orderings_Oord__class_Oless(X2344,X2343,X2342)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__le__imp__less__or__eq])])])). 1.16/1.44 fof(c_0_2117, plain, ![X2090, X2091, X2092]:(((~c_Orderings_Oord__class_Oless(X2092,X2091,X2090)|c_Orderings_Oord__class_Oless__eq(X2092,X2091,X2090)|~class_Orderings_Oorder(X2092))&(X2090!=X2091|c_Orderings_Oord__class_Oless__eq(X2092,X2091,X2090)|~class_Orderings_Oorder(X2092)))&(~c_Orderings_Oord__class_Oless__eq(X2092,X2091,X2090)|(c_Orderings_Oord__class_Oless(X2092,X2091,X2090)|X2090=X2091)|~class_Orderings_Oorder(X2092))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__le__less])])])])). 1.16/1.44 fof(c_0_2118, plain, ![X153, X154, X155]:(~class_Orderings_Oorder(X155)|(~c_Orderings_Oord__class_Oless__eq(X155,X154,X153)|(X154=X153|c_Orderings_Oord__class_Oless(X155,X154,X153)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])])). 1.16/1.44 fof(c_0_2119, plain, ![X116, X117, X118]:(~class_Orderings_Oorder(X118)|(~c_Orderings_Oord__class_Oless__eq(X118,X117,X116)|(X117=X116|c_Orderings_Oord__class_Oless(X118,X117,X116)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__le__neq__trans])])])). 1.16/1.44 fof(c_0_2120, plain, ![X2807, X2808, X2809]:(~class_Orderings_Oorder(X2809)|(X2808=X2807|(~c_Orderings_Oord__class_Oless__eq(X2809,X2807,X2808)|c_Orderings_Oord__class_Oless(X2809,X2807,X2808)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I12_J])])])). 1.16/1.44 fof(c_0_2121, plain, ![X2682, X2683, X2684]:(~class_Orderings_Oorder(X2684)|(X2682=X2683|(~c_Orderings_Oord__class_Oless__eq(X2684,X2683,X2682)|c_Orderings_Oord__class_Oless(X2684,X2683,X2682)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__neq__le__trans])])])). 1.16/1.44 fof(c_0_2122, plain, ![X1205, X1206]:(~class_Rings_Ocomm__ring__1(X1206)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1206),c_Groups_Ouminus__class_Ouminus(X1206,c_Groups_Oone__class_Oone(X1206))),X1205)=c_Groups_Ouminus__class_Ouminus(X1206,X1205)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])])). 1.16/1.44 fof(c_0_2123, plain, ![X1228, X1229]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1229,X1228)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1229),c_RComplete_Onatfloor(X1228))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_natfloor__mono])])])). 1.16/1.44 fof(c_0_2124, plain, ![X2385, X2386]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2386,X2385)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X2386),c_RComplete_Onatceiling(X2385))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__mono])])). 1.16/1.44 fof(c_0_2125, plain, ![X939, X940]:((~c_Orderings_Oord__class_Oless__eq(X940,c_Groups_Oabs__class_Oabs(X940,X939),c_Groups_Ozero__class_Ozero(X940))|X939=c_Groups_Ozero__class_Ozero(X940)|~class_Groups_Oordered__ab__group__add__abs(X940))&(X939!=c_Groups_Ozero__class_Ozero(X940)|c_Orderings_Oord__class_Oless__eq(X940,c_Groups_Oabs__class_Oabs(X940,X939),c_Groups_Ozero__class_Ozero(X940))|~class_Groups_Oordered__ab__group__add__abs(X940))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])])). 1.16/1.44 fof(c_0_2126, plain, ![X240, X241, X242]:(~class_Orderings_Opreorder(X242)|(~c_Orderings_Oord__class_Oless(X242,X241,X240)|c_Orderings_Oord__class_Oless__eq(X242,X241,X240))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__imp__le])])])). 1.16/1.44 fof(c_0_2127, plain, ![X2838]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2838)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X2838),X2838)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__less__self])])). 1.16/1.44 cnf(c_0_2128, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|c_Nat_OSuc(X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_1361])). 1.16/1.44 fof(c_0_2129, plain, ![X2556, X2557]:(~class_Groups_Oordered__ab__group__add__abs(X2557)|c_Orderings_Oord__class_Oless__eq(X2557,c_Groups_Ouminus__class_Ouminus(X2557,c_Groups_Oabs__class_Oabs(X2557,X2556)),c_Groups_Ozero__class_Ozero(X2557))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])])). 1.16/1.44 fof(c_0_2130, plain, ![X1173]:((~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1173)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1173))&(~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1173)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1173))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])])). 1.16/1.44 fof(c_0_2131, plain, ![X2292, X2293]:((c_Groups_Ozero__class_Ozero(X2293)=X2292|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2293,X2292))|~class_RealVector_Oreal__normed__vector(X2293))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2293,X2292))|c_Groups_Ozero__class_Ozero(X2293)!=X2292|~class_RealVector_Oreal__normed__vector(X2293))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__norm__iff])])])])). 1.16/1.44 fof(c_0_2132, plain, ![X1539]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1539)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1539)), inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod])). 1.16/1.44 fof(c_0_2133, plain, ![X538, X539]:(~class_Groups_Oordered__ab__group__add__abs(X539)|~c_Orderings_Oord__class_Oless(X539,c_Groups_Oabs__class_Oabs(X539,X538),c_Groups_Ozero__class_Ozero(X539))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero])])])). 1.16/1.44 fof(c_0_2134, plain, ![X2123]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2123),X2123)), inference(variable_rename,[status(thm)],[fact_le__square])). 1.16/1.44 fof(c_0_2135, plain, ![X826, X827, X828]:(~class_Groups_Oab__group__add(X828)|c_Groups_Oplus__class_Oplus(X828,X827,c_Groups_Ouminus__class_Ouminus(X828,X826))=c_Groups_Ominus__class_Ominus(X828,X827,X826)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ab__diff__minus])])])). 1.16/1.44 fof(c_0_2136, plain, ![X1442, X1443, X1444]:(~class_Rings_Ocomm__ring__1(X1444)|c_Groups_Oplus__class_Oplus(X1444,X1443,c_Groups_Ouminus__class_Ouminus(X1444,X1442))=c_Groups_Ominus__class_Ominus(X1444,X1443,X1442)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])])])). 1.16/1.44 fof(c_0_2137, plain, ![X1846, X1847, X1848]:(~class_Groups_Ogroup__add(X1848)|c_Groups_Oplus__class_Oplus(X1848,X1847,c_Groups_Ouminus__class_Ouminus(X1848,X1846))=c_Groups_Ominus__class_Ominus(X1848,X1847,X1846)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])])). 1.16/1.44 fof(c_0_2138, plain, ![X2333, X2334, X2335]:(~class_Groups_Ogroup__add(X2335)|c_Groups_Oplus__class_Oplus(X2335,X2334,X2333)=c_Groups_Ominus__class_Ominus(X2335,X2334,c_Groups_Ouminus__class_Ouminus(X2335,X2333))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])])). 1.16/1.44 fof(c_0_2139, plain, ![X2727, X2728]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2728,X2727),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(X2728)=X2727|~class_RealVector_Oreal__normed__vector(X2728))&(c_Groups_Ozero__class_Ozero(X2728)!=X2727|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2728,X2727),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~class_RealVector_Oreal__normed__vector(X2728))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])])). 1.16/1.44 fof(c_0_2140, plain, ![X2222, X2223]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2223,X2222)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2223,X2222))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2223,X2222)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2223,X2222))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])])). 1.16/1.44 fof(c_0_2141, plain, ![X1969, X1970]:(((X1970!=X1969|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1970,X1969))&(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1970,X1969)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1970,X1969)))&(X1970=X1969|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1970,X1969)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1970,X1969))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])])). 1.16/1.44 fof(c_0_2142, plain, ![X1799, X1800]:(((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1800,X1799)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1800,X1799))&(X1800!=X1799|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1800,X1799)))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1800,X1799)|(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1800,X1799)|X1800=X1799))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])])). 1.16/1.44 fof(c_0_2143, plain, ![X1373, X1374]:((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1374,X1373)|X1374=X1373|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1374,X1373))&((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1374,X1373)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1374,X1373))&(X1374!=X1373|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1374,X1373)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])])). 1.16/1.44 fof(c_0_2144, plain, ![X830, X831]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X831,X830)|(X830=X831|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X831,X830))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])])). 1.16/1.44 fof(c_0_2145, plain, ![X2846, X2847]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2847,X2846)|(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2847,X2846)|X2846=X2847))&((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2847,X2846)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2847,X2846))&(X2846!=X2847|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2847,X2846)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])])). 1.16/1.44 fof(c_0_2146, plain, ![X1369, X1370]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1370,X1369)|X1370=X1369|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1370,X1369))&((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1370,X1369)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1370,X1369))&(X1370!=X1369|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1370,X1369)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])])). 1.16/1.44 fof(c_0_2147, plain, ![X759, X760]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X760,X759)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X760,X759)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__less])])])). 1.16/1.44 fof(c_0_2148, plain, ![X2819, X2820]:(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2820,X2819)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2820,X2819)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__is__0__eq_H])])])). 1.16/1.44 fof(c_0_2149, plain, ![X2590, X2591, X2592, X2593]:(~class_Groups_Ouminus(X2593)|c_Groups_Ouminus__class_Ouminus(X2593,hAPP(X2591,X2590))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2592,X2593),X2591),X2590)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_uminus__apply])])])). 1.16/1.44 fof(c_0_2150, plain, ![X1323, X1324]:(~class_Rings_Olinordered__idom(X1324)|X1323=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1324),c_Groups_Osgn__class_Osgn(X1324,X1323)),c_Groups_Oabs__class_Oabs(X1324,X1323))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])])). 1.16/1.44 fof(c_0_2151, plain, ![X1896, X1897]:((~c_Orderings_Oord__class_Oless(X1897,X1896,c_Groups_Ozero__class_Ozero(X1897))|c_Groups_Osgn__class_Osgn(X1897,X1896)=c_Groups_Ouminus__class_Ouminus(X1897,c_Groups_Oone__class_Oone(X1897))|~class_Rings_Olinordered__idom(X1897))&(c_Groups_Osgn__class_Osgn(X1897,X1896)!=c_Groups_Ouminus__class_Ouminus(X1897,c_Groups_Oone__class_Oone(X1897))|c_Orderings_Oord__class_Oless(X1897,X1896,c_Groups_Ozero__class_Ozero(X1897))|~class_Rings_Olinordered__idom(X1897))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__1__neg])])])])). 1.16/1.44 fof(c_0_2152, plain, ![X894, X895]:(~class_Rings_Olinordered__idom(X895)|(~c_Orderings_Oord__class_Oless(X895,X894,c_Groups_Ozero__class_Ozero(X895))|c_Groups_Osgn__class_Osgn(X895,X894)=c_Groups_Ouminus__class_Ouminus(X895,c_Groups_Oone__class_Oone(X895)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__neg])])])). 1.16/1.44 fof(c_0_2153, plain, ![X2851, X2852]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2852,X2851)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2852,X2851)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_termination__basic__simps_I5_J])])])). 1.16/1.44 fof(c_0_2154, plain, ![X2615, X2616]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2616,X2615)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2616,X2615)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])])). 1.16/1.44 fof(c_0_2155, plain, ![X1692, X1693]:((X1692!=X1693|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1693,X1692))&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1693,X1692)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1693,X1692))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__or__eq__imp__le])])])])). 1.16/1.44 fof(c_0_2156, plain, ![X1762, X1763]:(~class_RealVector_Oreal__normed__vector(X1763)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1763,X1762),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero])])])). 1.16/1.44 fof(c_0_2157, plain, ![X838, X839]:((~c_Orderings_Oord__class_Oless(X839,X838,c_Groups_Ozero__class_Ozero(X839))|c_Groups_Oabs__class_Oabs(X839,X838)=c_Groups_Ouminus__class_Ouminus(X839,X838)|~class_Groups_Oabs__if(X839))&(c_Orderings_Oord__class_Oless(X839,X838,c_Groups_Ozero__class_Ozero(X839))|X838=c_Groups_Oabs__class_Oabs(X839,X838)|~class_Groups_Oabs__if(X839))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__if])])])])). 1.16/1.44 fof(c_0_2158, plain, ![X620, X621]:(~class_Groups_Oordered__ab__group__add__abs(X621)|(~c_Orderings_Oord__class_Oless(X621,X620,c_Groups_Ozero__class_Ozero(X621))|c_Groups_Ouminus__class_Ouminus(X621,X620)=c_Groups_Oabs__class_Oabs(X621,X620))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__neg])])])). 1.16/1.44 fof(c_0_2159, plain, ![X2468, X2469]:(~class_Groups_Oordered__ab__group__add__abs(X2469)|(~c_Orderings_Oord__class_Oless__eq(X2469,X2468,c_Groups_Ozero__class_Ozero(X2469))|c_Groups_Ouminus__class_Ouminus(X2469,X2468)=c_Groups_Oabs__class_Oabs(X2469,X2468))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])])). 1.16/1.44 cnf(c_0_2160, plain, (c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[fact_real__of__nat__one])). 1.16/1.44 fof(c_0_2161, plain, ![X2805, X2806]:(~class_Rings_Ocomm__semiring__0(X2806)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2806)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2806))),X2805)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2806))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__poly__0__left])])])). 1.16/1.44 fof(c_0_2162, plain, ![X1883, X1884]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1884,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1883))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1884,X1883), inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric])). 1.16/1.44 fof(c_0_2163, plain, ![X1285, X1286]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1286,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1285))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1286,X1285), inference(variable_rename,[status(thm)],[fact_diff__int__def])). 1.16/1.44 fof(c_0_2164, plain, ![X385, X386]:c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X386,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X385))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X386,X385), inference(variable_rename,[status(thm)],[fact_real__diff__def])). 1.16/1.44 fof(c_0_2165, plain, ![X754, X755]:c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X755,X754)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X755,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X754)), inference(variable_rename,[status(thm)],[fact_minus__real__def])). 1.16/1.44 fof(c_0_2166, plain, ![X1371, X1372]:c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1372,X1371)=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1372,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1371)), inference(variable_rename,[status(thm)],[fact_complex__diff__def])). 1.16/1.44 fof(c_0_2167, plain, ![X2897]:((~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2897),c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2897)&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X2897|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2897),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff])])). 1.16/1.44 fof(c_0_2168, plain, ![X1918]:((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1918),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1918)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1918|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1918),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__zero__cancel__iff])])). 1.16/1.44 fof(c_0_2169, plain, ![X2134, X2135]:(hAPP(X2134,esk62_2(X2134,X2135))!=hAPP(X2135,esk62_2(X2134,X2135))|X2134=X2135), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ext])])])])). 1.16/1.44 fof(c_0_2170, plain, ![X2503, X2504]:(((c_Orderings_Oord__class_Oless(X2504,c_Groups_Ozero__class_Ozero(X2504),X2503)|c_Groups_Osgn__class_Osgn(X2504,X2503)=c_Groups_Ouminus__class_Ouminus(X2504,c_Groups_Oone__class_Oone(X2504))|X2503=c_Groups_Ozero__class_Ozero(X2504)|~class_Groups_Osgn__if(X2504))&(~c_Orderings_Oord__class_Oless(X2504,c_Groups_Ozero__class_Ozero(X2504),X2503)|c_Groups_Oone__class_Oone(X2504)=c_Groups_Osgn__class_Osgn(X2504,X2503)|X2503=c_Groups_Ozero__class_Ozero(X2504)|~class_Groups_Osgn__if(X2504)))&(X2503!=c_Groups_Ozero__class_Ozero(X2504)|c_Groups_Osgn__class_Osgn(X2504,X2503)=c_Groups_Ozero__class_Ozero(X2504)|~class_Groups_Osgn__if(X2504))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__if])])])])). 1.16/1.44 fof(c_0_2171, plain, ![X2112, X2113]:((c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2113,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2112))|X2113=X2112)&(X2113!=X2112|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2113,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2112)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff])])). 1.16/1.44 fof(c_0_2172, plain, ![X2271]:~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2271),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__real__of__nat__less__zero])])). 1.16/1.44 fof(c_0_2173, plain, ![X1849, X1850, X1851]:((c_Groups_Ozero__class_Ozero(X1851)!=X1850|X1849=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X1851),X1850),X1849)=c_Groups_Ozero__class_Ozero(X1851)|(~class_Rings_Omult__zero(X1851)|~class_Rings_Ozero__neq__one(X1851)|~class_Rings_Ono__zero__divisors(X1851)|~class_Power_Opower(X1851)))&((c_Groups_Ozero__class_Ozero(X1851)=X1850|hAPP(hAPP(c_Power_Opower__class_Opower(X1851),X1850),X1849)!=c_Groups_Ozero__class_Ozero(X1851)|(~class_Rings_Omult__zero(X1851)|~class_Rings_Ozero__neq__one(X1851)|~class_Rings_Ono__zero__divisors(X1851)|~class_Power_Opower(X1851)))&(X1849!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X1851),X1850),X1849)!=c_Groups_Ozero__class_Ozero(X1851)|(~class_Rings_Omult__zero(X1851)|~class_Rings_Ozero__neq__one(X1851)|~class_Rings_Ono__zero__divisors(X1851)|~class_Power_Opower(X1851))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__eq__0__iff])])])])). 1.16/1.44 fof(c_0_2174, plain, ![X171, X172]:(((X171!=c_Groups_Oone__class_Oone(X172)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X172),X171),X171)=c_Groups_Oone__class_Oone(X172)|~class_Rings_Oring__1__no__zero__divisors(X172))&(c_Groups_Ouminus__class_Ouminus(X172,c_Groups_Oone__class_Oone(X172))!=X171|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X172),X171),X171)=c_Groups_Oone__class_Oone(X172)|~class_Rings_Oring__1__no__zero__divisors(X172)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X172),X171),X171)!=c_Groups_Oone__class_Oone(X172)|(X171=c_Groups_Oone__class_Oone(X172)|c_Groups_Ouminus__class_Ouminus(X172,c_Groups_Oone__class_Oone(X172))=X171)|~class_Rings_Oring__1__no__zero__divisors(X172))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_square__eq__1__iff])])])])). 1.16/1.44 fof(c_0_2175, plain, ![X2110, X2111]:((c_Groups_Osgn__class_Osgn(X2111,X2110)!=c_Groups_Oone__class_Oone(X2111)|c_Orderings_Oord__class_Oless(X2111,c_Groups_Ozero__class_Ozero(X2111),X2110)|~class_Rings_Olinordered__idom(X2111))&(~c_Orderings_Oord__class_Oless(X2111,c_Groups_Ozero__class_Ozero(X2111),X2110)|c_Groups_Osgn__class_Osgn(X2111,X2110)=c_Groups_Oone__class_Oone(X2111)|~class_Rings_Olinordered__idom(X2111))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])])). 1.16/1.44 fof(c_0_2176, plain, ![X1111, X1112]:(~class_Rings_Olinordered__idom(X1112)|(~c_Orderings_Oord__class_Oless(X1112,c_Groups_Ozero__class_Ozero(X1112),X1111)|c_Groups_Osgn__class_Osgn(X1112,X1111)=c_Groups_Oone__class_Oone(X1112))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])])). 1.16/1.44 fof(c_0_2177, plain, ![X2185, X2186, X2187]:(((~c_Orderings_Oord__class_Oless(X2187,X2185,X2186)|X2186!=X2185|~class_Orderings_Olinorder(X2187))&(~c_Orderings_Oord__class_Oless(X2187,X2186,X2185)|X2186!=X2185|~class_Orderings_Olinorder(X2187)))&(X2186=X2185|(c_Orderings_Oord__class_Oless(X2187,X2185,X2186)|c_Orderings_Oord__class_Oless(X2187,X2186,X2185))|~class_Orderings_Olinorder(X2187))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neq__iff])])])])). 1.16/1.44 fof(c_0_2178, plain, ![X2485, X2486, X2487]:(~class_Rings_Olinordered__idom(X2487)|(X2486=X2485|(c_Orderings_Oord__class_Oless(X2487,X2486,X2485)|c_Orderings_Oord__class_Oless(X2487,X2485,X2486)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom])])])). 1.16/1.44 fof(c_0_2179, plain, ![X1533, X1534, X1535]:(~class_Orderings_Olinorder(X1535)|(X1533=X1534|(c_Orderings_Oord__class_Oless(X1535,X1534,X1533)|c_Orderings_Oord__class_Oless(X1535,X1533,X1534)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE])])])). 1.16/1.44 fof(c_0_2180, plain, ![X1329, X1330, X1331]:(~class_Orderings_Olinorder(X1331)|(c_Orderings_Oord__class_Oless(X1331,X1330,X1329)|(X1329=X1330|c_Orderings_Oord__class_Oless(X1331,X1329,X1330)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__cases])])])). 1.16/1.44 fof(c_0_2181, plain, ![X773, X774, X775]:(~class_Orderings_Olinorder(X775)|(c_Orderings_Oord__class_Oless(X775,X773,X774)|X773=X774|c_Orderings_Oord__class_Oless(X775,X774,X773))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])])). 1.16/1.44 fof(c_0_2182, plain, ![X237, X238, X239]:((c_Orderings_Oord__class_Oless(X239,X237,X238)|X237=X238|c_Orderings_Oord__class_Oless(X239,X238,X237)|~class_Orderings_Olinorder(X239))&(X237!=X238|~c_Orderings_Oord__class_Oless(X239,X237,X238)|c_Orderings_Oord__class_Oless(X239,X238,X237)|~class_Orderings_Olinorder(X239))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3])])])])). 1.16/1.44 fof(c_0_2183, plain, ![X2817, X2818]:(~class_Groups_Oordered__ab__group__add__abs(X2818)|(~c_Orderings_Oord__class_Oless(X2818,c_Groups_Ozero__class_Ozero(X2818),X2817)|X2817=c_Groups_Oabs__class_Oabs(X2818,X2817))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__pos])])])). 1.16/1.44 fof(c_0_2184, plain, ![X1976, X1977]:(~class_Groups_Oordered__ab__group__add__abs(X1977)|(~c_Orderings_Oord__class_Oless__eq(X1977,c_Groups_Ozero__class_Ozero(X1977),X1976)|X1976=c_Groups_Oabs__class_Oabs(X1977,X1976))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__nonneg])])])). 1.16/1.44 fof(c_0_2185, plain, ![X1877, X1878, X1879]:(~class_Orderings_Olinorder(X1879)|(c_Orderings_Oord__class_Oless__eq(X1879,X1878,X1877)|c_Orderings_Oord__class_Oless(X1879,X1877,X1878))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])])). 1.16/1.44 fof(c_0_2186, plain, ![X397, X398, X399]:(~class_Orderings_Olinorder(X399)|(c_Orderings_Oord__class_Oless__eq(X399,X398,X397)|c_Orderings_Oord__class_Oless(X399,X397,X398))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__leE])])])). 1.16/1.44 fof(c_0_2187, plain, ![X191, X192, X193]:(~class_Orderings_Olinorder(X193)|(c_Orderings_Oord__class_Oless(X193,X192,X191)|c_Orderings_Oord__class_Oless__eq(X193,X191,X192))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_leI])])])). 1.16/1.44 fof(c_0_2188, plain, ![X1459, X1460, X1461]:(~class_Orderings_Olinorder(X1461)|(c_Orderings_Oord__class_Oless__eq(X1461,X1460,X1459)|c_Orderings_Oord__class_Oless__eq(X1461,X1459,X1460))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__le__cases])])])). 1.16/1.44 fof(c_0_2189, plain, ![X710, X711, X712]:(~class_Orderings_Olinorder(X712)|(c_Orderings_Oord__class_Oless__eq(X712,X710,X711)|c_Orderings_Oord__class_Oless__eq(X712,X711,X710))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__linear])])])). 1.16/1.44 fof(c_0_2190, plain, ![X139, X140, X141]:(~class_Rings_Ocomm__semiring__1(X141)|c_Groups_Oplus__class_Oplus(X141,X140,X139)=c_Groups_Oplus__class_Oplus(X141,X139,X140)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])])). 1.16/1.44 fof(c_0_2191, plain, ![X136, X137, X138]:(~class_Groups_Ogroup__add(X138)|(c_Groups_Ozero__class_Ozero(X138)!=c_Groups_Oplus__class_Oplus(X138,X137,X136)|c_Groups_Ouminus__class_Ouminus(X138,X137)=X136)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__unique])])])). 1.16/1.44 fof(c_0_2192, plain, ![X1726, X1727, X1728]:((X1727!=c_Groups_Ouminus__class_Ouminus(X1728,X1726)|c_Groups_Oplus__class_Oplus(X1728,X1727,X1726)=c_Groups_Ozero__class_Ozero(X1728)|~class_Groups_Ogroup__add(X1728))&(c_Groups_Oplus__class_Oplus(X1728,X1727,X1726)!=c_Groups_Ozero__class_Ozero(X1728)|X1727=c_Groups_Ouminus__class_Ouminus(X1728,X1726)|~class_Groups_Ogroup__add(X1728))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])])). 1.16/1.44 fof(c_0_2193, plain, ![X2074, X2075, X2076]:((c_Groups_Ozero__class_Ozero(X2076)!=c_Groups_Oplus__class_Oplus(X2076,X2075,X2074)|X2074=c_Groups_Ouminus__class_Ouminus(X2076,X2075)|~class_Groups_Ogroup__add(X2076))&(X2074!=c_Groups_Ouminus__class_Ouminus(X2076,X2075)|c_Groups_Ozero__class_Ozero(X2076)=c_Groups_Oplus__class_Oplus(X2076,X2075,X2074)|~class_Groups_Ogroup__add(X2076))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__eq__0__iff])])])])). 1.16/1.44 fof(c_0_2194, plain, ![X2108, X2109]:(~class_Groups_Oordered__ab__group__add__abs(X2109)|c_Orderings_Oord__class_Oless__eq(X2109,c_Groups_Ouminus__class_Ouminus(X2109,X2108),c_Groups_Oabs__class_Oabs(X2109,X2108))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__ge__minus__self])])])). 1.16/1.44 fof(c_0_2195, plain, ![X2692]:((~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2692,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2692)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2692))&(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2692,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2692)=X2692)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zabs__def])])])). 1.16/1.44 fof(c_0_2196, plain, ![X2154]:((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2154,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2154)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2154))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2154,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|X2154=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2154))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__abs__def])])])). 1.16/1.44 fof(c_0_2197, plain, ![X1425]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1425,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1425)=X1425)&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1425,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1425)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1425))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__real__def])])])). 1.16/1.44 fof(c_0_2198, plain, ![X1015]:(~class_Rings_Olinordered__semidom(X1015)|~c_Orderings_Oord__class_Oless(X1015,c_Groups_Oone__class_Oone(X1015),c_Groups_Ozero__class_Ozero(X1015))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__one__less__zero])])])). 1.16/1.44 fof(c_0_2199, plain, ![X801]:(~class_Rings_Olinordered__semidom(X801)|~c_Orderings_Oord__class_Oless__eq(X801,c_Groups_Oone__class_Oone(X801),c_Groups_Ozero__class_Ozero(X801))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__one__le__zero])])])). 1.16/1.44 fof(c_0_2200, plain, ![X614, X615]:(~class_Rings_Ocomm__semiring__0(X615)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X615)),X614),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X615)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X615))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__poly__0__right])])])). 1.16/1.44 cnf(c_0_2201, plain, (c_Nat_OSuc(X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1362])). 1.16/1.44 fof(c_0_2202, plain, ![X1641, X1642, X1643]:(~class_Rings_Ocomm__semiring__1(X1643)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1643),X1641),X1642)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1643),X1642),X1641)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])). 1.16/1.44 cnf(c_0_2203, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_1352])). 1.16/1.44 fof(c_0_2204, plain, ![X1210, X1211]:(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1211,X1210)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1210,X1211)|X1211=X1210), inference(variable_rename,[status(thm)],[fact_zless__linear])). 1.16/1.44 fof(c_0_2205, plain, ![X2546, X2547]:(X2546=X2547|(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2547,X2546)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2546,X2547))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat])])])). 1.16/1.44 fof(c_0_2206, plain, ![X1248, X1249]:(((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1249,X1248)|X1249!=X1248)&(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1248,X1249)|X1249!=X1248))&(X1249=X1248|(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1249,X1248)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1248,X1249)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])])). 1.16/1.44 fof(c_0_2207, plain, ![X2679]:((X2679!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X2679)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))&((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2679)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X2679)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X2679)&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2679)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X2679)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X2679))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__sgn__def])])])])). 1.16/1.44 fof(c_0_2208, plain, ![X822]:((c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X822|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X822))&((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X822)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X822)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X822)&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X822)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X822)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X822))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__real__def])])])])). 1.16/1.44 fof(c_0_2209, plain, ![X2059]:(((~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2059)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2059)=c_Groups_Oone__class_Oone(tc_Int_Oint)|X2059=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2059)|c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2059)|X2059=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(X2059!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2059)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zsgn__def])])])])). 1.16/1.44 fof(c_0_2210, plain, ![X765, X766]:(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X766,X765)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X765,X766)), inference(variable_rename,[status(thm)],[fact_zle__linear])). 1.16/1.44 fof(c_0_2211, plain, ![X819, X820]:(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X820,X819)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X819,X820)), inference(variable_rename,[status(thm)],[fact_nat__le__linear])). 1.16/1.44 fof(c_0_2212, plain, ![X646, X647]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X646,X647)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X647,X646)), inference(variable_rename,[status(thm)],[fact_real__le__linear])). 1.16/1.44 fof(c_0_2213, plain, ![X2311, X2312, X2313]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2313),X2312),X2311)!=c_Groups_Ozero__class_Ozero(X2313)|(c_Groups_Ozero__class_Ozero(X2313)=X2312|c_Groups_Ozero__class_Ozero(X2313)=X2311)|~class_Rings_Oring__no__zero__divisors(X2313))&((c_Groups_Ozero__class_Ozero(X2313)!=X2312|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2313),X2312),X2311)=c_Groups_Ozero__class_Ozero(X2313)|~class_Rings_Oring__no__zero__divisors(X2313))&(c_Groups_Ozero__class_Ozero(X2313)!=X2311|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2313),X2312),X2311)=c_Groups_Ozero__class_Ozero(X2313)|~class_Rings_Oring__no__zero__divisors(X2313)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])])). 1.16/1.44 fof(c_0_2214, plain, ![X358, X359, X360]:(~class_Rings_Ono__zero__divisors(X360)|(c_Groups_Ozero__class_Ozero(X360)=X359|(c_Groups_Ozero__class_Ozero(X360)=X358|c_Groups_Ozero__class_Ozero(X360)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X360),X359),X358)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_no__zero__divisors])])])). 1.16/1.44 fof(c_0_2215, plain, ![X865, X866, X867]:(~class_Rings_Ono__zero__divisors(X867)|(c_Groups_Ozero__class_Ozero(X867)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X867),X866),X865)|(c_Groups_Ozero__class_Ozero(X867)=X865|X866=c_Groups_Ozero__class_Ozero(X867)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divisors__zero])])])). 1.16/1.44 fof(c_0_2216, plain, ![X300, X301]:(~class_Groups_Oab__group__add(X301)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X301),X300)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X301),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X301)),X300)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__poly__code_I1_J])])])). 1.16/1.44 fof(c_0_2217, plain, ![X1277, X1278]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1277,X1278)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1278,X1277), inference(variable_rename,[status(thm)],[fact_zadd__commute])). 1.16/1.44 fof(c_0_2218, plain, ![X2680, X2681]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2680,X2681)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2681,X2680), inference(variable_rename,[status(thm)],[fact_nat__add__commute])). 1.16/1.44 fof(c_0_2219, plain, ![X2378, X2379]:((c_Groups_Ozero__class_Ozero(X2379)!=X2378|c_Groups_Oplus__class_Oplus(X2379,X2378,X2378)=c_Groups_Ozero__class_Ozero(X2379)|~class_Groups_Olinordered__ab__group__add(X2379))&(c_Groups_Oplus__class_Oplus(X2379,X2378,X2378)!=c_Groups_Ozero__class_Ozero(X2379)|c_Groups_Ozero__class_Ozero(X2379)=X2378|~class_Groups_Olinordered__ab__group__add(X2379))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])])). 1.16/1.44 fof(c_0_2220, plain, ![X2505, X2506]:((c_Groups_Ozero__class_Ozero(X2506)!=c_Groups_Oplus__class_Oplus(X2506,X2505,X2505)|X2505=c_Groups_Ozero__class_Ozero(X2506)|~class_Groups_Olinordered__ab__group__add(X2506))&(X2505!=c_Groups_Ozero__class_Ozero(X2506)|c_Groups_Ozero__class_Ozero(X2506)=c_Groups_Oplus__class_Oplus(X2506,X2505,X2505)|~class_Groups_Olinordered__ab__group__add(X2506))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])])). 1.16/1.44 fof(c_0_2221, plain, ![X1989]:(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1989)|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1989)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_real__sgn__pos])])])). 1.16/1.44 fof(c_0_2222, plain, ![X2239]:((c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=X2239|c_Transcendental_Oln(X2239)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2239))&(c_Transcendental_Oln(X2239)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=X2239|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2239))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ln__eq__zero__iff])])])])). 1.16/1.44 fof(c_0_2223, plain, ![X2452, X2453, X2454]:((X2453!=X2452|c_Groups_Ozero__class_Ozero(X2454)=c_Groups_Ominus__class_Ominus(X2454,X2453,X2452)|~class_Groups_Oab__group__add(X2454))&(c_Groups_Ozero__class_Ozero(X2454)!=c_Groups_Ominus__class_Ominus(X2454,X2453,X2452)|X2453=X2452|~class_Groups_Oab__group__add(X2454))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__iff__diff__eq__0])])])])). 1.16/1.44 fof(c_0_2224, plain, ![X1620, X1621, X1622]:((X1620!=X1621|c_Groups_Ozero__class_Ozero(X1622)=c_Groups_Ominus__class_Ominus(X1622,X1621,X1620)|~class_Groups_Ogroup__add(X1622))&(c_Groups_Ozero__class_Ozero(X1622)!=c_Groups_Ominus__class_Ominus(X1622,X1621,X1620)|X1620=X1621|~class_Groups_Ogroup__add(X1622))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_right__minus__eq])])])])). 1.16/1.44 fof(c_0_2225, plain, ![X2401, X2402, X2403]:(~class_Rings_Oring__1__no__zero__divisors(X2403)|(c_Groups_Ozero__class_Ozero(X2403)=X2402|hAPP(hAPP(c_Power_Opower__class_Opower(X2403),X2402),X2401)!=c_Groups_Ozero__class_Ozero(X2403))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_field__power__not__zero])])])). 1.16/1.44 fof(c_0_2226, plain, ![X107, X108]:((c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X108)!=X107|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X108,X107))&(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X108,X107)|c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X108)=X107)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__eq__0__iff])])). 1.16/1.44 fof(c_0_2227, plain, ![X2729, X2730, X2731]:((X2730!=c_Groups_Oplus__class_Oplus(X2731,X2730,X2729)|c_Groups_Ozero__class_Ozero(X2731)=X2729|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2731))&(c_Groups_Ozero__class_Ozero(X2731)!=X2729|X2730=c_Groups_Oplus__class_Oplus(X2731,X2730,X2729)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2731))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__0__iff])])])])). 1.16/1.44 fof(c_0_2228, plain, ![X2304, X2305]:(~class_Rings_Olinordered__idom(X2305)|c_Groups_Oabs__class_Oabs(X2305,X2304)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2305),X2304),c_Groups_Osgn__class_Osgn(X2305,X2304))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])])). 1.16/1.44 fof(c_0_2229, plain, ![X2836, X2837]:((c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2837))!=X2836|c_Polynomial_Opoly(X2837,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2837)))=c_Polynomial_Opoly(X2837,X2836)|(~class_Int_Oring__char__0(X2837)|~class_Rings_Oidom(X2837)))&(c_Polynomial_Opoly(X2837,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2837)))!=c_Polynomial_Opoly(X2837,X2836)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2837))=X2836|(~class_Int_Oring__char__0(X2837)|~class_Rings_Oidom(X2837)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__zero])])])). 1.16/1.44 fof(c_0_2230, plain, ![X2640, X2641, X2642]:(~class_Orderings_Oorder(X2642)|(~c_Orderings_Oord__class_Oless(X2642,X2641,X2640)|X2640!=X2641)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__eq2])])])). 1.16/1.44 fof(c_0_2231, plain, ![X2204, X2205, X2206]:(~class_Orderings_Oorder(X2206)|(~c_Orderings_Oord__class_Oless(X2206,X2205,X2204)|X2205!=X2204)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__imp__neq])])])). 1.16/1.44 fof(c_0_2232, plain, ![X659, X660, X661]:(~class_Orderings_Oorder(X661)|(~c_Orderings_Oord__class_Oless(X661,X660,X659)|X660!=X659)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__eq])])])). 1.16/1.44 fof(c_0_2233, plain, ![X1648]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1648,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_RComplete_Onatfloor(X1648)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__neg])])). 1.16/1.44 fof(c_0_2234, plain, ![X1598]:(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1598,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_RComplete_Onatceiling(X1598)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__neg])])). 1.16/1.44 fof(c_0_2235, plain, ![X2025]:((~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2025)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2025)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2025|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2025))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])])). 1.16/1.44 fof(c_0_2236, plain, ![X1925, X1926]:(~class_Groups_Oordered__ab__group__add__abs(X1926)|c_Orderings_Oord__class_Oless__eq(X1926,c_Groups_Ozero__class_Ozero(X1926),c_Groups_Oabs__class_Oabs(X1926,X1925))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__ge__zero])])])). 1.16/1.44 fof(c_0_2237, plain, ![X2127, X2128]:((X2127=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(X2128)=hAPP(c_Polynomial_Ocoeff(X2128,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2128))),X2127)|~class_Rings_Ocomm__semiring__1(X2128))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2127|hAPP(c_Polynomial_Ocoeff(X2128,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2128))),X2127)=c_Groups_Oone__class_Oone(X2128)|~class_Rings_Ocomm__semiring__1(X2128))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__1])])])). 1.16/1.44 fof(c_0_2238, plain, ![X2588, X2589]:(~class_Orderings_Opreorder(X2589)|~c_Orderings_Oord__class_Oless(X2589,X2588,X2588)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__irrefl])])])). 1.16/1.44 fof(c_0_2239, plain, ![X1207]:((X1207!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1207,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1207,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1207=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])])). 1.16/1.44 cnf(c_0_2240, plain, (c_Nat_OSuc(X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_1363])). 1.16/1.44 cnf(c_0_2241, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X1)), inference(split_conjunct,[status(thm)],[c_0_1364])). 1.16/1.44 cnf(c_0_2242, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X1)), inference(split_conjunct,[status(thm)],[c_0_1365])). 1.16/1.44 cnf(c_0_2243, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X1)), inference(split_conjunct,[status(thm)],[c_0_1366])). 1.16/1.44 cnf(c_0_2244, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X1)), inference(split_conjunct,[status(thm)],[c_0_1367])). 1.16/1.44 cnf(c_0_2245, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(X1)), inference(split_conjunct,[status(thm)],[c_0_1368])). 1.16/1.44 fof(c_0_2246, plain, ![X1864, X1865]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1865),X1864)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1864),X1865), inference(variable_rename,[status(thm)],[fact_zmult__commute])). 1.16/1.44 fof(c_0_2247, plain, ![X148, X149]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X149),X148)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X148),X149), inference(variable_rename,[status(thm)],[fact_nat__mult__commute])). 1.16/1.44 fof(c_0_2248, plain, ![X466, X467]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X466),X467)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X467),X466), inference(variable_rename,[status(thm)],[fact_real__mult__commute])). 1.16/1.44 fof(c_0_2249, plain, ![X2787, X2788]:(~class_Groups_Oab__group__add(X2788)|c_Groups_Oplus__class_Oplus(X2788,c_Groups_Ouminus__class_Ouminus(X2788,X2787),X2787)=c_Groups_Ozero__class_Ozero(X2788)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])])). 1.16/1.44 fof(c_0_2250, plain, ![X211, X212]:(~class_Groups_Ogroup__add(X212)|c_Groups_Ozero__class_Ozero(X212)=c_Groups_Oplus__class_Oplus(X212,c_Groups_Ouminus__class_Ouminus(X212,X211),X211)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_left__minus])])])). 1.16/1.44 fof(c_0_2251, plain, ![X123, X124]:(~class_Groups_Ogroup__add(X124)|c_Groups_Ozero__class_Ozero(X124)=c_Groups_Oplus__class_Oplus(X124,X123,c_Groups_Ouminus__class_Ouminus(X124,X123))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_right__minus])])])). 1.16/1.44 fof(c_0_2252, plain, ![X1235, X1236]:(((X1235=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1236,X1235)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1236|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1236,X1235)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X1235!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1236|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1236,X1235)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])])). 1.16/1.44 fof(c_0_2253, plain, ![X356, X357]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X357,X356)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X356), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_gr__implies__not0])])])). 1.16/1.44 cnf(c_0_2254, plain, (X1!=c_Nat_OSuc(X1)), inference(split_conjunct,[status(thm)],[c_0_1369])). 1.16/1.44 cnf(c_0_2255, plain, (X1!=c_Nat_OSuc(X1)), inference(split_conjunct,[status(thm)],[c_0_1370])). 1.16/1.44 fof(c_0_2256, plain, ![X1852, X1853]:(~class_RealVector_Oreal__normed__vector(X1853)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1853,X1852))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__ge__zero])])])). 1.16/1.44 fof(c_0_2257, plain, ![X1531, X1532]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1531|hAPP(hAPP(c_Power_Opower__class_Opower(X1532),c_Groups_Ozero__class_Ozero(X1532)),X1531)=c_Groups_Oone__class_Oone(X1532)|(~class_Rings_Osemiring__0(X1532)|~class_Power_Opower(X1532)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1531|hAPP(hAPP(c_Power_Opower__class_Opower(X1532),c_Groups_Ozero__class_Ozero(X1532)),X1531)=c_Groups_Ozero__class_Ozero(X1532)|(~class_Rings_Osemiring__0(X1532)|~class_Power_Opower(X1532)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__0__left])])])])). 1.16/1.44 fof(c_0_2258, plain, ![X1603, X1604]:(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1604,X1603)!=X1604|X1603=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])). 1.16/1.44 fof(c_0_2259, plain, ![X1801]:~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1801,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code])])). 1.16/1.44 fof(c_0_2260, plain, ![X1478]:~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1478,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less0])])). 1.16/1.44 fof(c_0_2261, plain, ![X769]:~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X769,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__zeroE])])). 1.16/1.44 fof(c_0_2262, plain, ![X2345]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2345,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X2345))), inference(variable_rename,[status(thm)],[fact_real__natceiling__ge])). 1.16/1.44 fof(c_0_2263, plain, ![X1709, X1710]:(~class_Groups_Ozero(X1710)|hAPP(c_Polynomial_Ocoeff(X1710,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1710))),X1709)=c_Groups_Ozero__class_Ozero(X1710)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__0])])). 1.16/1.44 fof(c_0_2264, plain, ![X1321, X1322]:(~class_Rings_Ocomm__semiring__0(X1322)|hAPP(c_Polynomial_Opoly(X1322,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1322))),X1321)=c_Groups_Ozero__class_Ozero(X1322)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])])). 1.16/1.44 fof(c_0_2265, plain, ![X702, X703]:(~class_Rings_Ocomm__semiring__1(X703)|c_Groups_Oone__class_Oone(X703)=hAPP(c_Polynomial_Opoly(X703,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X703))),X702)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__1])])). 1.16/1.44 fof(c_0_2266, plain, ![X1140, X1141]:(~class_Groups_Oordered__ab__group__add__abs(X1141)|c_Orderings_Oord__class_Oless__eq(X1141,X1140,c_Groups_Oabs__class_Oabs(X1141,X1140))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__ge__self])])])). 1.16/1.44 fof(c_0_2267, plain, ![X1927, X1928]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1928,X1927)|X1927!=X1928), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__not__refl2])])])). 1.16/1.44 fof(c_0_2268, plain, ![X436, X437]:(~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X437,X436)|X437!=X436), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])])). 1.16/1.44 fof(c_0_2269, plain, ![X2701, X2702]:(~class_RealVector_Oreal__normed__vector(X2702)|c_Groups_Osgn__class_Osgn(X2702,c_Groups_Ouminus__class_Ouminus(X2702,X2701))=c_Groups_Ouminus__class_Ouminus(X2702,c_Groups_Osgn__class_Osgn(X2702,X2701))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__minus])])])). 1.16/1.44 fof(c_0_2270, plain, ![X733, X734]:(~class_Groups_Ocomm__monoid__add(X734)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X734),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X734)),X733)=X733), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__poly__code_I1_J])])])). 1.16/1.44 fof(c_0_2271, plain, ![X509, X510]:(~class_Groups_Oab__group__add(X510)|X509=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X510),X509,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X510)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__poly__code_I2_J])])])). 1.16/1.44 fof(c_0_2272, plain, ![X977, X978]:(~class_Groups_Ocomm__monoid__add(X978)|X977=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X978),X977,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X978)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__poly__code_I2_J])])])). 1.16/1.44 fof(c_0_2273, plain, ![X477, X478]:(~class_Rings_Olinordered__idom(X478)|(c_Polynomial_Opos__poly(X478,X477)|c_Polynomial_Opos__poly(X478,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X478),X477))|X477=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X478)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__poly__total])])])). 1.16/1.44 fof(c_0_2274, plain, ![X1326, X1327]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1327|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1327),X1326))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1326|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1327),X1326)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1327),X1326)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1327|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1326))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])])). 1.16/1.44 fof(c_0_2275, plain, ![X2824]:~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2824,X2824), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__not__refl])])). 1.16/1.44 fof(c_0_2276, plain, ![X821]:~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X821,X821), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat])])). 1.16/1.44 fof(c_0_2277, plain, ![X475, X476]:(X476!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X476),X475)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X476|c_Groups_Oone__class_Oone(tc_Nat_Onat)=X475)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10])])). 1.16/1.44 fof(c_0_2278, plain, ![X1046, X1047]:(~class_Groups_Ogroup__add(X1047)|c_Groups_Ominus__class_Ominus(X1047,c_Groups_Ozero__class_Ozero(X1047),X1046)=c_Groups_Ouminus__class_Ouminus(X1047,X1046)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__0])])])). 1.16/1.44 fof(c_0_2279, plain, ![X1415, X1416]:((X1415!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=X1416|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1416),X1415)=c_Groups_Oone__class_Oone(tc_Nat_Onat))&((X1415=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1416),X1415)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1416|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1416),X1415)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])])). 1.16/1.44 fof(c_0_2280, plain, ![X1044, X1045]:(((X1044=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1045),X1044))&(X1045=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1045),X1044)))&(X1044!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1045!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1045),X1044))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])])). 1.16/1.44 fof(c_0_2281, plain, ![X713]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X713)), inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero])). 1.16/1.44 fof(c_0_2282, plain, ![X1819]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1819),X1819), inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2])). 1.16/1.44 fof(c_0_2283, plain, ![X1863]:(~class_Power_Opower(X1863)|c_Power_Opower_Opower(X1863,c_Groups_Oone__class_Oone(X1863),c_Groups_Otimes__class_Otimes(X1863))=c_Power_Opower__class_Opower(X1863)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])])). 1.16/1.44 fof(c_0_2284, plain, ![X1435, X1436]:(~class_Rings_Ocomm__semiring__1(X1436)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1436),c_Groups_Ozero__class_Ozero(X1436)),X1435)=c_Groups_Ozero__class_Ozero(X1436)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])])). 1.16/1.44 fof(c_0_2285, plain, ![X2137, X2138]:(~class_RealVector_Oreal__normed__algebra(X2138)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2138),c_Groups_Ozero__class_Ozero(X2138)),X2137)=c_Groups_Ozero__class_Ozero(X2138)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult_Ozero__left])])])). 1.16/1.44 fof(c_0_2286, plain, ![X2383, X2384]:(~class_Rings_Omult__zero(X2384)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2384),c_Groups_Ozero__class_Ozero(X2384)),X2383)=c_Groups_Ozero__class_Ozero(X2384)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__zero__left])])])). 1.16/1.44 fof(c_0_2287, plain, ![X1040, X1041]:(~class_Groups_Omonoid__mult(X1041)|c_Groups_Oone__class_Oone(X1041)=hAPP(hAPP(c_Power_Opower__class_Opower(X1041),c_Groups_Oone__class_Oone(X1041)),X1040)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__one])])])). 1.16/1.44 fof(c_0_2288, plain, ![X2581, X2582]:(~class_RealVector_Oreal__normed__algebra(X2582)|c_Groups_Ozero__class_Ozero(X2582)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2582),c_Groups_Ozero__class_Ozero(X2582)),X2581)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left_Ozero])])])). 1.16/1.44 fof(c_0_2289, plain, ![X511]:(~class_Rings_Olinordered__semidom(X511)|c_Orderings_Oord__class_Oless(X511,c_Groups_Ozero__class_Ozero(X511),c_Groups_Oone__class_Oone(X511))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__one])])])). 1.16/1.44 fof(c_0_2290, plain, ![X2685]:(~class_Rings_Olinordered__semidom(X2685)|c_Orderings_Oord__class_Oless__eq(X2685,c_Groups_Ozero__class_Ozero(X2685),c_Groups_Oone__class_Oone(X2685))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__one])])])). 1.16/1.44 fof(c_0_2291, plain, ![X924, X925]:(~class_Groups_Ocomm__monoid__mult(X925)|X924=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X925),c_Groups_Oone__class_Oone(X925)),X924)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__1])])])). 1.16/1.44 fof(c_0_2292, plain, ![X590, X591]:(~class_Groups_Omonoid__mult(X591)|X590=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X591),c_Groups_Oone__class_Oone(X591)),X590)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__1__left])])])). 1.16/1.44 fof(c_0_2293, plain, ![X1836, X1837]:(~class_Rings_Ocomm__semiring__1(X1837)|X1836=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1837),c_Groups_Oone__class_Oone(X1837)),X1836)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])])])). 1.16/1.44 fof(c_0_2294, plain, ![X788, X789]:(~class_Divides_Osemiring__div(X789)|c_Divides_Odiv__class_Odiv(X789,c_Groups_Ozero__class_Ozero(X789),X788)=c_Groups_Ozero__class_Ozero(X789)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__0])])])). 1.16/1.44 fof(c_0_2295, plain, ![X1275, X1276]:(~class_Divides_Osemiring__div(X1276)|c_Divides_Odiv__class_Odiv(X1276,X1275,c_Groups_Ozero__class_Ozero(X1276))=c_Groups_Ozero__class_Ozero(X1276)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])])). 1.16/1.44 fof(c_0_2296, plain, ![X2655, X2656]:(~class_Divides_Osemiring__div(X2656)|(c_Groups_Ozero__class_Ozero(X2656)=X2655|c_Divides_Odiv__class_Odiv(X2656,X2655,X2655)=c_Groups_Oone__class_Oone(X2656))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__self])])])). 1.16/1.44 fof(c_0_2297, plain, ![X662, X663]:(~class_Rings_Ocomm__semiring__1(X663)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X663),X662),c_Groups_Ozero__class_Ozero(X663))=c_Groups_Ozero__class_Ozero(X663)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])])). 1.16/1.44 fof(c_0_2298, plain, ![X1450, X1451]:(~class_RealVector_Oreal__normed__algebra(X1451)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1451),X1450),c_Groups_Ozero__class_Ozero(X1451))=c_Groups_Ozero__class_Ozero(X1451)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right_Ozero])])])). 1.16/1.44 fof(c_0_2299, plain, ![X2349, X2350]:(~class_RealVector_Oreal__normed__algebra(X2350)|c_Groups_Ozero__class_Ozero(X2350)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2350),X2349),c_Groups_Ozero__class_Ozero(X2350))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult_Ozero__right])])])). 1.16/1.44 fof(c_0_2300, plain, ![X2235, X2236]:(~class_Rings_Omult__zero(X2236)|c_Groups_Ozero__class_Ozero(X2236)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2236),X2235),c_Groups_Ozero__class_Ozero(X2236))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__zero__right])])])). 1.16/1.44 fof(c_0_2301, plain, ![X1593, X1594]:(~class_Groups_Ocomm__monoid__add(X1594)|c_Groups_Oplus__class_Oplus(X1594,c_Groups_Ozero__class_Ozero(X1594),X1593)=X1593), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])])). 1.16/1.44 fof(c_0_2302, plain, ![X714, X715]:(~class_Rings_Ocomm__semiring__1(X715)|c_Groups_Oplus__class_Oplus(X715,c_Groups_Ozero__class_Ozero(X715),X714)=X714), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])])). 1.16/1.44 fof(c_0_2303, plain, ![X278, X279]:(~class_Groups_Ocomm__monoid__add(X279)|c_Groups_Oplus__class_Oplus(X279,X278,c_Groups_Ozero__class_Ozero(X279))=X278), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add_Ocomm__neutral])])])). 1.16/1.44 fof(c_0_2304, plain, ![X2197, X2198]:(~class_Groups_Omonoid__add(X2198)|X2197=c_Groups_Oplus__class_Oplus(X2198,c_Groups_Ozero__class_Ozero(X2198),X2197)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__0__left])])])). 1.16/1.44 fof(c_0_2305, plain, ![X2747, X2748]:(~class_Divides_Osemiring__div(X2748)|X2747=c_Divides_Odiv__class_Odiv(X2748,X2747,c_Groups_Oone__class_Oone(X2748))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])])). 1.16/1.44 fof(c_0_2306, plain, ![X2441, X2442]:(~class_Groups_Ogroup__add(X2442)|X2441=c_Groups_Ominus__class_Ominus(X2442,X2441,c_Groups_Ozero__class_Ozero(X2442))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__0__right])])])). 1.16/1.44 fof(c_0_2307, plain, ![X2352, X2353]:(~class_Groups_Omonoid__add(X2353)|X2352=c_Groups_Oplus__class_Oplus(X2353,X2352,c_Groups_Ozero__class_Ozero(X2353))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])])). 1.16/1.44 fof(c_0_2308, plain, ![X1187, X1188]:(~class_Rings_Ocomm__semiring__1(X1188)|X1187=c_Groups_Oplus__class_Oplus(X1188,X1187,c_Groups_Ozero__class_Ozero(X1188))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])])). 1.16/1.44 fof(c_0_2309, plain, ![X309, X310]:(~class_Power_Opower(X310)|hAPP(hAPP(c_Power_Opower__class_Opower(X310),X309),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X310)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])])). 1.16/1.44 fof(c_0_2310, plain, ![X365, X366]:(~class_Rings_Ocomm__semiring__1(X366)|c_Groups_Oone__class_Oone(X366)=hAPP(hAPP(c_Power_Opower__class_Opower(X366),X365),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])])). 1.16/1.44 fof(c_0_2311, plain, ![X1569, X1570]:(~class_Groups_Omonoid__mult(X1570)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1570),X1569),c_Groups_Oone__class_Oone(X1570))=X1569), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__1__right])])])). 1.16/1.44 fof(c_0_2312, plain, ![X1213, X1214]:(~class_Groups_Ocomm__monoid__mult(X1214)|X1213=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1214),X1213),c_Groups_Oone__class_Oone(X1214))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult_Ocomm__neutral])])])). 1.16/1.44 fof(c_0_2313, plain, ![X1256, X1257]:(~class_Rings_Ocomm__semiring__1(X1257)|X1256=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1257),X1256),c_Groups_Oone__class_Oone(X1257))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])])])). 1.16/1.44 fof(c_0_2314, plain, ![X1919, X1920]:(~class_Groups_Ogroup__add(X1920)|c_Groups_Ominus__class_Ominus(X1920,X1919,X1919)=c_Groups_Ozero__class_Ozero(X1920)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__self])])])). 1.16/1.44 fof(c_0_2315, plain, ![X179, X180, X181]:(~class_Orderings_Opreorder(X181)|(X179!=X180|c_Orderings_Oord__class_Oless__eq(X181,X180,X179))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__eq__refl])])])). 1.16/1.44 fof(c_0_2316, plain, ![X763, X764]:(~class_Groups_Omonoid__mult(X764)|hAPP(hAPP(c_Power_Opower__class_Opower(X764),X763),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X763), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__one__right])])])). 1.16/1.44 fof(c_0_2317, plain, ![X2165, X2166]:(~class_Rings_Ocomm__semiring__1(X2166)|X2165=hAPP(hAPP(c_Power_Opower__class_Opower(X2166),X2165),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])])). 1.16/1.44 fof(c_0_2318, plain, ![X1994]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X1994)), inference(variable_rename,[status(thm)],[fact_zero__le__natfloor])). 1.16/1.44 fof(c_0_2319, plain, ![X1946]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X1946)), inference(variable_rename,[status(thm)],[fact_zero__le__natceiling])). 1.16/1.44 fof(c_0_2320, plain, ![X1797, X1798]:(~class_Orderings_Opreorder(X1798)|c_Orderings_Oord__class_Oless__eq(X1798,X1797,X1797)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__refl])])])). 1.16/1.44 cnf(c_0_2321, plain, (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_One__nat__def])). 1.16/1.44 fof(c_0_2322, plain, ![X565, X566]:(~class_Groups_Oordered__ab__group__add__abs(X566)|c_Groups_Oabs__class_Oabs(X566,c_Groups_Ouminus__class_Ouminus(X566,X565))=c_Groups_Oabs__class_Oabs(X566,X565)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])])). 1.16/1.44 fof(c_0_2323, plain, ![X2161, X2162]:(~class_Rings_Olinordered__idom(X2162)|c_Groups_Osgn__class_Osgn(X2162,c_Groups_Osgn__class_Osgn(X2162,X2161))=c_Groups_Osgn__class_Osgn(X2162,X2161)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])])). 1.16/1.44 fof(c_0_2324, plain, ![X2167, X2168]:(~class_Groups_Oordered__ab__group__add__abs(X2168)|c_Groups_Oabs__class_Oabs(X2168,X2167)=c_Groups_Oabs__class_Oabs(X2168,c_Groups_Oabs__class_Oabs(X2168,X2167))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])])). 1.16/1.44 fof(c_0_2325, plain, ![X2511, X2512]:(~class_RealVector_Oreal__normed__vector(X2512)|c_RealVector_Onorm__class_Onorm(X2512,X2511)=c_RealVector_Onorm__class_Onorm(X2512,c_Groups_Ouminus__class_Ouminus(X2512,X2511))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__minus__cancel])])])). 1.16/1.44 fof(c_0_2326, plain, ![X2794, X2795, X2796]:((c_Polynomial_Opoly(X2796,X2794)!=c_Polynomial_Opoly(X2796,X2795)|X2794=X2795|(~class_Int_Oring__char__0(X2796)|~class_Rings_Oidom(X2796)))&(X2794!=X2795|c_Polynomial_Opoly(X2796,X2794)=c_Polynomial_Opoly(X2796,X2795)|(~class_Int_Oring__char__0(X2796)|~class_Rings_Oidom(X2796)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_poly__eq__iff])])])])). 1.16/1.44 fof(c_0_2327, plain, ![X2460, X2461]:(~class_Lattices_Oab__semigroup__idem__mult(X2461)|X2460=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2461),X2460),X2460)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_times_Oidem])])])). 1.16/1.44 fof(c_0_2328, plain, ![X2023, X2024]:(~class_Lattices_Oab__semigroup__idem__mult(X2024)|X2023=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2024),X2023),X2023)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__idem])])])). 1.16/1.44 fof(c_0_2329, plain, ![X1729]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1729|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1729)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_gr0I])])])). 1.16/1.44 fof(c_0_2330, plain, ![X2212, X2213]:(~class_RealVector_Oreal__normed__vector(X2213)|c_RealVector_Onorm__class_Onorm(X2213,X2212)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2213,X2212))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__norm__cancel])])])). 1.16/1.44 fof(c_0_2331, plain, ![X1691]:(X1691=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1691,X1691)=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__self])])])). 1.16/1.44 fof(c_0_2332, plain, ![X2061]:(~class_Rings_Olinordered__idom(X2061)|~c_Polynomial_Opos__poly(X2061,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2061)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__pos__poly__0])])])). 1.16/1.44 fof(c_0_2333, plain, ![X2314]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2314), inference(variable_rename,[status(thm)],[fact_zdiv__zero])). 1.16/1.44 fof(c_0_2334, plain, ![X1404]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1404), inference(variable_rename,[status(thm)],[fact_diff__0__eq__0])). 1.16/1.44 fof(c_0_2335, plain, ![X174, X175]:((X174=c_Groups_Ozero__class_Ozero(X175)|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(X175,c_Groups_Osgn__class_Osgn(X175,X174))|~class_RealVector_Oreal__normed__vector(X175))&(X174!=c_Groups_Ozero__class_Ozero(X175)|c_RealVector_Onorm__class_Onorm(X175,c_Groups_Osgn__class_Osgn(X175,X174))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~class_RealVector_Oreal__normed__vector(X175))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__sgn])])])])). 1.16/1.44 fof(c_0_2336, plain, ![X106]:c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X106)=X106, inference(variable_rename,[status(thm)],[fact_zadd__0])). 1.16/1.44 fof(c_0_2337, plain, ![X1343]:c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1343)=X1343, inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0])). 1.16/1.44 fof(c_0_2338, plain, ![X1039]:X1039=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1039,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0])). 1.16/1.44 fof(c_0_2339, plain, ![X2240]:X2240=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2240,c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(variable_rename,[status(thm)],[fact_zadd__0__right])). 1.16/1.44 fof(c_0_2340, plain, ![X236]:X236=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X236,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right])). 1.16/1.44 fof(c_0_2341, plain, ![X2117, X2118]:(X2117!=X2118|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2118,X2117)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])])). 1.16/1.44 fof(c_0_2342, plain, ![X577]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X577), inference(variable_rename,[status(thm)],[fact_le0])). 1.16/1.44 fof(c_0_2343, plain, ![X243]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X243), inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J])). 1.16/1.44 fof(c_0_2344, plain, ![X1031]:(~class_Groups_Oab__group__add(X1031)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1031))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1031),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1031)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J])])). 1.16/1.44 fof(c_0_2345, plain, ![X258]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X258,X258), inference(variable_rename,[status(thm)],[fact_diff__self__eq__0])). 1.16/1.44 fof(c_0_2346, plain, ![X2234]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2234)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_mult__0])). 1.16/1.44 fof(c_0_2347, plain, ![X2457, X2458, X2459]:((c_Polynomial_Ocoeff(X2459,X2457)!=c_Polynomial_Ocoeff(X2459,X2458)|X2458=X2457|~class_Groups_Ozero(X2459))&(X2458!=X2457|c_Polynomial_Ocoeff(X2459,X2457)=c_Polynomial_Ocoeff(X2459,X2458)|~class_Groups_Ozero(X2459))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_coeff__inject])])])])). 1.16/1.44 fof(c_0_2348, plain, ![X2848, X2849, X2850]:((X2848!=X2849|c_Groups_Ouminus__class_Ouminus(X2850,X2848)=c_Groups_Ouminus__class_Ouminus(X2850,X2849)|~class_Lattices_Oboolean__algebra(X2850))&(c_Groups_Ouminus__class_Ouminus(X2850,X2848)!=c_Groups_Ouminus__class_Ouminus(X2850,X2849)|X2848=X2849|~class_Lattices_Oboolean__algebra(X2850))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])])). 1.16/1.44 fof(c_0_2349, plain, ![X1951, X1952, X1953]:((c_Groups_Ouminus__class_Ouminus(X1953,X1951)!=c_Groups_Ouminus__class_Ouminus(X1953,X1952)|X1951=X1952|~class_Groups_Ogroup__add(X1953))&(X1951!=X1952|c_Groups_Ouminus__class_Ouminus(X1953,X1951)=c_Groups_Ouminus__class_Ouminus(X1953,X1952)|~class_Groups_Ogroup__add(X1953))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__equal__iff__equal])])])])). 1.16/1.44 fof(c_0_2350, plain, ![X1592]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1592)=X1592, inference(variable_rename,[status(thm)],[fact_real__mult__1])). 1.16/1.44 fof(c_0_2351, plain, ![X131]:X131=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X131), inference(variable_rename,[status(thm)],[fact_zmult__1])). 1.16/1.44 fof(c_0_2352, plain, ![X1954]:X1954=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1954), inference(variable_rename,[status(thm)],[fact_nat__mult__1])). 1.16/1.44 fof(c_0_2353, plain, ![X2286]:c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2286,X2286), inference(variable_rename,[status(thm)],[fact_zle__refl])). 1.16/1.44 fof(c_0_2354, plain, ![X2188]:c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2188,X2188), inference(variable_rename,[status(thm)],[fact_le__refl])). 1.16/1.44 fof(c_0_2355, plain, ![X468]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X468,X468), inference(variable_rename,[status(thm)],[fact_real__le__refl])). 1.16/1.44 fof(c_0_2356, plain, ![X1307]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1307),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_mult__0__right])). 1.16/1.44 fof(c_0_2357, plain, ![X2394]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2394),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2394, inference(variable_rename,[status(thm)],[fact_nat__mult__1__right])). 1.16/1.44 fof(c_0_2358, plain, ![X389]:X389=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X389),c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(variable_rename,[status(thm)],[fact_zmult__1__right])). 1.16/1.44 fof(c_0_2359, plain, ![X2597, X2598]:(~class_Lattices_Oboolean__algebra(X2598)|c_Groups_Ouminus__class_Ouminus(X2598,c_Groups_Ouminus__class_Ouminus(X2598,X2597))=X2597), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])])). 1.16/1.44 fof(c_0_2360, plain, ![X741, X742]:(~class_Groups_Ogroup__add(X742)|X741=c_Groups_Ouminus__class_Ouminus(X742,c_Groups_Ouminus__class_Ouminus(X742,X741))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])])). 1.16/1.44 fof(c_0_2361, plain, ![X595]:c_RealDef_Oreal(tc_Nat_Onat,X595)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X595)), inference(variable_rename,[status(thm)],[fact_abs__real__of__nat__cancel])). 1.16/1.44 fof(c_0_2362, plain, ![X1452, X1453, X1454]:((X1453!=c_Groups_Ouminus__class_Ouminus(X1454,X1452)|c_Groups_Ouminus__class_Ouminus(X1454,X1453)=X1452|~class_Groups_Ogroup__add(X1454))&(c_Groups_Ouminus__class_Ouminus(X1454,X1453)!=X1452|X1453=c_Groups_Ouminus__class_Ouminus(X1454,X1452)|~class_Groups_Ogroup__add(X1454))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equation__minus__iff])])])])). 1.16/1.44 fof(c_0_2363, plain, ![X1202, X1203, X1204]:((X1202!=c_Groups_Ouminus__class_Ouminus(X1204,X1203)|X1203=c_Groups_Ouminus__class_Ouminus(X1204,X1202)|~class_Groups_Ogroup__add(X1204))&(X1203!=c_Groups_Ouminus__class_Ouminus(X1204,X1202)|X1202=c_Groups_Ouminus__class_Ouminus(X1204,X1203)|~class_Groups_Ogroup__add(X1204))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])])). 1.16/1.44 fof(c_0_2364, plain, ![X2064, X2065]:((X2064!=X2065|c_RealDef_Oreal(tc_Nat_Onat,X2064)=c_RealDef_Oreal(tc_Nat_Onat,X2065))&(c_RealDef_Oreal(tc_Nat_Onat,X2064)!=c_RealDef_Oreal(tc_Nat_Onat,X2065)|X2064=X2065)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject])])). 1.16/1.44 fof(c_0_2365, plain, ![X1981, X1982]:((c_Groups_Ozero__class_Ozero(X1982)!=X1981|c_Groups_Ozero__class_Ozero(X1982)=c_Groups_Osgn__class_Osgn(X1982,X1981)|~class_Rings_Olinordered__idom(X1982))&(c_Groups_Ozero__class_Ozero(X1982)!=c_Groups_Osgn__class_Osgn(X1982,X1981)|c_Groups_Ozero__class_Ozero(X1982)=X1981|~class_Rings_Olinordered__idom(X1982))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])])). 1.16/1.44 fof(c_0_2366, plain, ![X808, X809]:((c_Groups_Ozero__class_Ozero(X809)!=X808|c_Groups_Ozero__class_Ozero(X809)=c_Groups_Osgn__class_Osgn(X809,X808)|~class_RealVector_Oreal__normed__vector(X809))&(c_Groups_Ozero__class_Ozero(X809)!=c_Groups_Osgn__class_Osgn(X809,X808)|c_Groups_Ozero__class_Ozero(X809)=X808|~class_RealVector_Oreal__normed__vector(X809))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__zero__iff])])])])). 1.16/1.44 fof(c_0_2367, plain, ![X990, X991]:((c_Groups_Ouminus__class_Ouminus(X991,X990)!=c_Groups_Ozero__class_Ozero(X991)|X990=c_Groups_Ozero__class_Ozero(X991)|~class_Groups_Ogroup__add(X991))&(X990!=c_Groups_Ozero__class_Ozero(X991)|c_Groups_Ouminus__class_Ouminus(X991,X990)=c_Groups_Ozero__class_Ozero(X991)|~class_Groups_Ogroup__add(X991))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])])). 1.16/1.44 fof(c_0_2368, plain, ![X681, X682]:((X681!=c_Groups_Ozero__class_Ozero(X682)|c_Groups_Ouminus__class_Ouminus(X682,X681)=c_Groups_Ozero__class_Ozero(X682)|~class_Groups_Ogroup__add(X682))&(c_Groups_Ouminus__class_Ouminus(X682,X681)!=c_Groups_Ozero__class_Ozero(X682)|X681=c_Groups_Ozero__class_Ozero(X682)|~class_Groups_Ogroup__add(X682))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__0__equal__iff__equal])])])])). 1.16/1.44 fof(c_0_2369, plain, ![X1905, X1906]:((X1905!=c_Groups_Ozero__class_Ozero(X1906)|c_Groups_Ozero__class_Ozero(X1906)=c_Groups_Oabs__class_Oabs(X1906,X1905)|~class_Groups_Oordered__ab__group__add__abs(X1906))&(c_Groups_Ozero__class_Ozero(X1906)!=c_Groups_Oabs__class_Oabs(X1906,X1905)|X1905=c_Groups_Ozero__class_Ozero(X1906)|~class_Groups_Oordered__ab__group__add__abs(X1906))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])])). 1.16/1.44 fof(c_0_2370, plain, ![X1260, X1261]:((c_RealVector_Onorm__class_Onorm(X1261,X1260)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(X1261)=X1260|~class_RealVector_Oreal__normed__vector(X1261))&(c_Groups_Ozero__class_Ozero(X1261)!=X1260|c_RealVector_Onorm__class_Onorm(X1261,X1260)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~class_RealVector_Oreal__normed__vector(X1261))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])])). 1.16/1.44 fof(c_0_2371, plain, ![X1892, X1893]:(~class_Lattices_Oboolean__algebra(X1893)|class_Lattices_Oboolean__algebra(tc_fun(X1892,X1893))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])])). 1.16/1.44 fof(c_0_2372, plain, ![X453, X454]:(~class_Orderings_Oord(X454)|class_Orderings_Oord(tc_fun(X453,X454))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])])). 1.16/1.44 fof(c_0_2373, plain, ![X1660, X1661]:(~class_Groups_Ominus(X1661)|class_Groups_Ominus(tc_fun(X1660,X1661))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])])). 1.16/1.44 fof(c_0_2374, plain, ![X988, X989]:(~class_Groups_Ouminus(X989)|class_Groups_Ouminus(tc_fun(X988,X989))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Groups_Ouminus])])])). 1.16/1.44 fof(c_0_2375, plain, ![X2030, X2031]:(~class_Orderings_Opreorder(X2031)|class_Orderings_Opreorder(tc_fun(X2030,X2031))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])])). 1.16/1.44 fof(c_0_2376, plain, ![X1265, X1266]:(~class_Orderings_Oorder(X1266)|class_Orderings_Oorder(tc_fun(X1265,X1266))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Oorder])])])). 1.16/1.44 fof(c_0_2377, plain, ![X1614]:c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1614))=X1614, inference(variable_rename,[status(thm)],[fact_zminus__zminus])). 1.16/1.44 fof(c_0_2378, plain, ![X2163, X2164]:((X2163!=c_Groups_Ouminus__class_Ouminus(X2164,X2163)|X2163=c_Groups_Ozero__class_Ozero(X2164)|~class_Groups_Olinordered__ab__group__add(X2164))&(X2163!=c_Groups_Ozero__class_Ozero(X2164)|X2163=c_Groups_Ouminus__class_Ouminus(X2164,X2163)|~class_Groups_Olinordered__ab__group__add(X2164))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equal__neg__zero])])])])). 1.16/1.44 fof(c_0_2379, plain, ![X882, X883]:((X882!=c_Groups_Ouminus__class_Ouminus(X883,X882)|X882=c_Groups_Ozero__class_Ozero(X883)|~class_Groups_Olinordered__ab__group__add(X883))&(X882!=c_Groups_Ozero__class_Ozero(X883)|X882=c_Groups_Ouminus__class_Ouminus(X883,X882)|~class_Groups_Olinordered__ab__group__add(X883))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__equal__zero])])])])). 1.16/1.44 fof(c_0_2380, plain, ![X1759]:(~class_Rings_Olinordered__idom(X1759)|c_Groups_Oabs__class_Oabs(X1759,c_Groups_Oone__class_Oone(X1759))=c_Groups_Oone__class_Oone(X1759)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__one])])])). 1.16/1.44 fof(c_0_2381, plain, ![X651]:(~class_RealVector_Oreal__normed__algebra__1(X651)|c_Groups_Osgn__class_Osgn(X651,c_Groups_Oone__class_Oone(X651))=c_Groups_Oone__class_Oone(X651)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__one])])])). 1.16/1.44 fof(c_0_2382, plain, ![X156]:(~class_RealVector_Oreal__normed__vector(X156)|c_Groups_Osgn__class_Osgn(X156,c_Groups_Ozero__class_Ozero(X156))=c_Groups_Ozero__class_Ozero(X156)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__zero])])])). 1.16/1.44 fof(c_0_2383, plain, ![X2466]:(~class_Groups_Oordered__ab__group__add__abs(X2466)|c_Groups_Ozero__class_Ozero(X2466)=c_Groups_Oabs__class_Oabs(X2466,c_Groups_Ozero__class_Ozero(X2466))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])])). 1.16/1.44 fof(c_0_2384, plain, ![X1644]:(~class_Groups_Osgn__if(X1644)|c_Groups_Ozero__class_Ozero(X1644)=c_Groups_Osgn__class_Osgn(X1644,c_Groups_Ozero__class_Ozero(X1644))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])])). 1.16/1.44 fof(c_0_2385, plain, ![X1623]:(~class_Groups_Ogroup__add(X1623)|c_Groups_Ozero__class_Ozero(X1623)=c_Groups_Ouminus__class_Ouminus(X1623,c_Groups_Ozero__class_Ozero(X1623))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])])). 1.16/1.44 fof(c_0_2386, plain, ![X508]:(~class_RealVector_Oreal__normed__vector(X508)|c_RealVector_Onorm__class_Onorm(X508,c_Groups_Ozero__class_Ozero(X508))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__zero])])). 1.16/1.44 fof(c_0_2387, plain, ![X2476]:(~class_RealVector_Oreal__normed__algebra__1(X2476)|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(X2476,c_Groups_Oone__class_Oone(X2476))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__one])])). 1.16/1.44 fof(c_0_2388, plain, ![X1697]:c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1697))=X1697, inference(variable_rename,[status(thm)],[fact_natfloor__real__of__nat])). 1.16/1.44 fof(c_0_2389, plain, ![X1924]:c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1924))=X1924, inference(variable_rename,[status(thm)],[fact_natceiling__real__of__nat])). 1.16/1.44 fof(c_0_2390, plain, ![X2839]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2839|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_RealDef_Oreal(tc_Nat_Onat,X2839))&(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_RealDef_Oreal(tc_Nat_Onat,X2839)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2839)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero__iff])])). 1.16/1.44 fof(c_0_2391, plain, ![X1255]:c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1255)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1255), inference(variable_rename,[status(thm)],[fact_real__norm__def])). 1.16/1.44 fof(c_0_2392, plain, ![X1325]:(~class_Rings_Ozero__neq__one(X1325)|c_Groups_Ozero__class_Ozero(X1325)!=c_Groups_Oone__class_Oone(X1325)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__neq__zero])])])). 1.16/1.44 fof(c_0_2393, plain, ![X1122]:(~class_Rings_Ozero__neq__one(X1122)|c_Groups_Ozero__class_Ozero(X1122)!=c_Groups_Oone__class_Oone(X1122)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])])). 1.16/1.44 fof(c_0_2394, plain, ![X1132]:(~class_Rings_Olinordered__idom(X1132)|class_Groups_Osgn__if(tc_Polynomial_Opoly(X1132))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Osgn__if])])])). 1.16/1.44 fof(c_0_2395, plain, ![X1788]:(~class_Rings_Ocomm__semiring__1(X1788)|class_Groups_Oone(tc_Polynomial_Opoly(X1788))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone])])). 1.16/1.44 fof(c_0_2396, plain, ![X2257]:(~class_Rings_Olinordered__idom(X2257)|class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X2257))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring])])])). 1.16/1.44 fof(c_0_2397, plain, ![X2651]:(~class_Rings_Ocomm__semiring__0(X2651)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X2651))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring])])])). 1.16/1.44 fof(c_0_2398, plain, ![X2751]:(~class_Rings_Olinordered__idom(X2751)|class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X2751))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring])])). 1.16/1.44 fof(c_0_2399, plain, ![X2840]:(~class_Rings_Ocomm__semiring__1(X2840)|class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X2840))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one])])). 1.16/1.44 fof(c_0_2400, plain, ![X1240]:(~class_Groups_Ozero(X1240)|class_Groups_Ozero(tc_Polynomial_Opoly(X1240))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero])])). 1.16/1.44 fof(c_0_2401, plain, ![X2793]:(~class_Rings_Oidom(X2793)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X2793))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])])). 1.16/1.44 fof(c_0_2402, plain, ![X1011]:(~class_Rings_Olinordered__idom(X1011)|class_Groups_Oabs__if(tc_Polynomial_Opoly(X1011))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oabs__if])])). 1.16/1.44 fof(c_0_2403, plain, ![X1993]:(~class_Rings_Ocomm__semiring__1(X1993)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1993))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult])])])). 1.16/1.44 fof(c_0_2404, plain, ![X2789]:(~class_Rings_Ocomm__ring__1(X2789)|class_Rings_Oring__1(tc_Polynomial_Opoly(X2789))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1])])])). 1.16/1.44 fof(c_0_2405, plain, ![X1107]:(~class_Rings_Olinordered__idom(X1107)|class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1107))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict])])). 1.16/1.44 fof(c_0_2406, plain, ![X607]:(~class_Rings_Olinordered__idom(X607)|class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X607))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring])])])). 1.16/1.44 fof(c_0_2407, plain, ![X906]:(~class_Rings_Olinordered__idom(X906)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X906))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add])])])). 1.16/1.44 fof(c_0_2408, plain, ![X2650]:(~class_Rings_Olinordered__idom(X2650)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X2650))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le])])). 1.16/1.44 fof(c_0_2409, plain, ![X613]:(~class_Rings_Olinordered__idom(X613)|class_Int_Oring__char__0(tc_Polynomial_Opoly(X613))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0])])). 1.16/1.44 fof(c_0_2410, plain, ![X474]:(~class_Rings_Ocomm__semiring__0(X474)|class_Rings_Osemiring(tc_Polynomial_Opoly(X474))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring])])])). 1.16/1.44 fof(c_0_2411, plain, ![X462]:(~class_Rings_Olinordered__idom(X462)|class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X462))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1])])). 1.16/1.44 fof(c_0_2412, plain, ![X442]:(~class_Groups_Ocancel__comm__monoid__add(X442)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X442))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add])])])). 1.16/1.44 fof(c_0_2413, plain, ![X2678]:(~class_Rings_Olinordered__idom(X2678)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X2678))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict])])])). 1.16/1.44 fof(c_0_2414, plain, ![X2696]:(~class_Rings_Olinordered__idom(X2696)|class_Rings_Oordered__ring(tc_Polynomial_Opoly(X2696))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring])])])). 1.16/1.44 fof(c_0_2415, plain, ![X2244]:(~class_Rings_Olinordered__idom(X2244)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X2244))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict])])])). 1.16/1.44 fof(c_0_2416, plain, ![X418]:(~class_Rings_Olinordered__idom(X418)|class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X418))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring])])])). 1.16/1.44 fof(c_0_2417, plain, ![X2060]:(~class_Groups_Ocomm__monoid__add(X2060)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(X2060))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add])])). 1.16/1.44 fof(c_0_2418, plain, ![X394]:(~class_Rings_Oidom(X394)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X394))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors])])). 1.16/1.44 fof(c_0_2419, plain, ![X2310]:(~class_Groups_Ocancel__comm__monoid__add(X2310)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X2310))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add])])])). 1.16/1.44 fof(c_0_2420, plain, ![X1975]:(~class_Rings_Olinordered__idom(X1975)|class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1975))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring__abs])])). 1.16/1.44 fof(c_0_2421, plain, ![X2243]:(~class_Rings_Oidom(X2243)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X2243))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors])])])). 1.16/1.44 fof(c_0_2422, plain, ![X2017]:(~class_Rings_Ocomm__semiring__1(X2017)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X2017))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult])])])). 1.16/1.44 fof(c_0_2423, plain, ![X573]:(~class_Rings_Olinordered__idom(X573)|class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X573))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add])])])). 1.16/1.44 fof(c_0_2424, plain, ![X616]:(~class_Rings_Olinordered__idom(X616)|class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X616))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring])])])). 1.16/1.44 fof(c_0_2425, plain, ![X2740]:(~class_Groups_Oab__group__add(X2740)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(X2740))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add])])). 1.16/1.44 fof(c_0_2426, plain, ![X346]:(~class_Rings_Olinordered__idom(X346)|class_Orderings_Oord(tc_Polynomial_Opoly(X346))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord])])])). 1.16/1.44 fof(c_0_2427, plain, ![X1244]:(~class_Groups_Oab__group__add(X1244)|class_Groups_Ominus(tc_Polynomial_Opoly(X1244))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus])])). 1.16/1.44 fof(c_0_2428, plain, ![X349]:(~class_Groups_Ocomm__monoid__add(X349)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X349))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add])])])). 1.16/1.44 fof(c_0_2429, plain, ![X1270]:(~class_Fields_Ofield(X1270)|class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1270))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Osemiring__div])])). 1.16/1.44 fof(c_0_2430, plain, ![X2812]:(~class_Groups_Ocancel__comm__monoid__add(X2812)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X2812))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add])])). 1.16/1.44 fof(c_0_2431, plain, ![X1397]:(~class_Rings_Ocomm__ring(X1397)|class_Rings_Oring(tc_Polynomial_Opoly(X1397))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring])])])). 1.16/1.44 fof(c_0_2432, plain, ![X1561]:(~class_Rings_Olinordered__idom(X1561)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1561))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add])])])). 1.16/1.44 fof(c_0_2433, plain, ![X2280]:(~class_Groups_Oab__group__add(X2280)|class_Groups_Ouminus(tc_Polynomial_Opoly(X2280))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus])])). 1.16/1.44 fof(c_0_2434, plain, ![X2016]:(~class_Rings_Ocomm__semiring__1(X2016)|class_Power_Opower(tc_Polynomial_Opoly(X2016))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower])])). 1.16/1.44 fof(c_0_2435, plain, ![X2746]:(~class_Rings_Olinordered__idom(X2746)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X2746))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom])])). 1.16/1.44 fof(c_0_2436, plain, ![X2395]:(~class_Rings_Ocomm__semiring__0(X2395)|class_Rings_Osemiring__0(tc_Polynomial_Opoly(X2395))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0])])). 1.16/1.44 fof(c_0_2437, plain, ![X2119]:(~class_Rings_Olinordered__idom(X2119)|class_Orderings_Olinorder(tc_Polynomial_Opoly(X2119))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder])])). 1.16/1.44 fof(c_0_2438, plain, ![X931]:(~class_Rings_Olinordered__idom(X931)|class_Orderings_Opreorder(tc_Polynomial_Opoly(X931))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder])])])). 1.16/1.44 fof(c_0_2439, plain, ![X2351]:(~class_Rings_Olinordered__idom(X2351)|class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X2351))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs])])). 1.16/1.44 fof(c_0_2440, plain, ![X697]:(~class_Rings_Ocomm__ring__1(X697)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X697))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1])])])). 1.16/1.44 fof(c_0_2441, plain, ![X1328]:(~class_Rings_Oidom(X1328)|class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1328))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors])])). 1.16/1.44 fof(c_0_2442, plain, ![X1825]:(~class_Rings_Olinordered__idom(X1825)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1825))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add])])). 1.16/1.44 fof(c_0_2443, plain, ![X319]:(~class_Rings_Olinordered__idom(X319)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X319))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict])])])). 1.16/1.44 fof(c_0_2444, plain, ![X377]:(~class_Groups_Ocomm__monoid__add(X377)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X377))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add])])])). 1.16/1.44 fof(c_0_2445, plain, ![X2089]:(~class_Rings_Ocomm__semiring__1(X2089)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X2089))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])])). 1.16/1.44 fof(c_0_2446, plain, ![X666]:(~class_Groups_Oab__group__add(X666)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(X666))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])])])). 1.16/1.44 fof(c_0_2447, plain, ![X952]:(~class_Rings_Ocomm__semiring__0(X952)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X952))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])])). 1.16/1.44 fof(c_0_2448, plain, ![X323]:(~class_Rings_Olinordered__idom(X323)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X323))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add])])). 1.16/1.44 fof(c_0_2449, plain, ![X2811]:(~class_Rings_Olinordered__idom(X2811)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X2811))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom])])])). 1.16/1.44 fof(c_0_2450, plain, ![X1378]:(~class_Rings_Olinordered__idom(X1378)|class_Orderings_Oorder(tc_Polynomial_Opoly(X1378))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder])])])). 1.16/1.44 fof(c_0_2451, plain, ![X1833]:(~class_Rings_Ocomm__semiring__0(X1833)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1833))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult])])])). 1.16/1.44 fof(c_0_2452, plain, ![X95]:(~class_Rings_Oidom(X95)|class_Rings_Oidom(tc_Polynomial_Opoly(X95))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom])])])). 1.16/1.44 fof(c_0_2453, plain, ![X1284]:(~class_Rings_Ocomm__semiring__0(X1284)|class_Rings_Omult__zero(tc_Polynomial_Opoly(X1284))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero])])). 1.16/1.44 fof(c_0_2454, plain, ![X369]:(~class_Rings_Ocomm__ring(X369)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X369))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring])])])). 1.16/1.44 cnf(c_0_2455, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(X2,X3),hAPP(X2,esk70_4(X2,X3,X4,X1)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(X4,X3,X5)|~class_Orderings_Oord(X4)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1371]), ['final']). 1.16/1.44 cnf(c_0_2456, plain, (c_SEQ_OBseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,esk12_4(X2,X1,X3,X4)),c_Groups_Ouminus__class_Ouminus(X1,hAPP(X2,X4)))),X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1372]), ['final']). 1.16/1.44 cnf(c_0_2457, plain, (c_SEQ_OBseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,esk2_4(X2,X1,X3,X4)),c_Groups_Ouminus__class_Ouminus(X1,X4))),X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1373]), ['final']). 1.16/1.44 cnf(c_0_2458, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk39_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk38_3(X1,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk38_3(X1,X2,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1374]), ['final']). 1.16/1.44 cnf(c_0_2459, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk6_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_3(X1,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk5_3(X1,X2,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1375]), ['final']). 1.16/1.44 cnf(c_0_2460, plain, (X1=hAPP(X2,esk39_3(X1,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk38_3(X1,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk38_3(X1,X2,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1374]), ['final']). 1.16/1.44 cnf(c_0_2461, plain, (X1=hAPP(X2,esk6_3(X1,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_3(X1,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk5_3(X1,X2,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1375]), ['final']). 1.16/1.44 cnf(c_0_2462, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_1376]), ['final']). 1.16/1.44 cnf(c_0_2463, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_1377]), ['final']). 1.16/1.44 cnf(c_0_2464, plain, (c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk56_4(X3,X2,X4,X1)),hAPP(X3,esk56_4(X3,X2,X4,X1)))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_1378]), ['final']). 1.16/1.44 cnf(c_0_2465, plain, (c_SEQ_OBseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk54_4(X3,X2,X4,X1))),X3)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1379]), ['final']). 1.16/1.44 cnf(c_0_2466, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1380]), ['final']). 1.16/1.44 cnf(c_0_2467, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)))))), inference(split_conjunct,[status(thm)],[c_0_1381]), ['final']). 1.16/1.44 cnf(c_0_2468, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1382]), ['final']). 1.16/1.44 cnf(c_0_2469, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1383]), ['final']). 1.16/1.44 cnf(c_0_2470, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1384]), ['final']). 1.16/1.44 cnf(c_0_2471, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1385]), ['final']). 1.16/1.44 cnf(c_0_2472, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1386]), ['final']). 1.16/1.44 cnf(c_0_2473, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1387]), ['final']). 1.16/1.44 cnf(c_0_2474, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_1388]), ['final']). 1.16/1.44 cnf(c_0_2475, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_1389]), ['final']). 1.16/1.44 cnf(c_0_2476, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1382]), ['final']). 1.16/1.44 cnf(c_0_2477, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1383]), ['final']). 1.16/1.44 cnf(c_0_2478, plain, (c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1384]), ['final']). 1.16/1.44 cnf(c_0_2479, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1385]), ['final']). 1.16/1.44 cnf(c_0_2480, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1)), inference(split_conjunct,[status(thm)],[c_0_1386]), ['final']). 1.16/1.44 cnf(c_0_2481, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1)), inference(split_conjunct,[status(thm)],[c_0_1387]), ['final']). 1.16/1.44 cnf(c_0_2482, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_1388]), ['final']). 1.16/1.44 cnf(c_0_2483, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_1389]), ['final']). 1.16/1.44 cnf(c_0_2484, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1390]), ['final']). 1.16/1.44 cnf(c_0_2485, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1391]), ['final']). 1.16/1.44 cnf(c_0_2486, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,X2,X3))=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Rings_Ocomm__ring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1392, c_0_1393]), c_0_1393]), c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2487, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1394]), ['final']). 1.16/1.44 cnf(c_0_2488, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1395]), ['final']). 1.16/1.44 cnf(c_0_2489, plain, (hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,esk20_3(X2,X1,X3),X3)))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~hBOOL(hAPP(X1,X4))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)), inference(split_conjunct,[status(thm)],[c_0_1396]), ['final']). 1.16/1.44 cnf(c_0_2490, plain, (hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,esk65_3(X2,X1,X3),X3)))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~hBOOL(hAPP(X1,X4))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)), inference(split_conjunct,[status(thm)],[c_0_1397]), ['final']). 1.16/1.44 cnf(c_0_2491, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1398, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2492, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1399, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2493, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk1_2(X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(rw,[status(thm)],[c_0_1400, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2494, plain, (c_Polynomial_Opoly__rec(X4,X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))=X2|~class_Groups_Ozero(X1)|X2!=hAPP(hAPP(hAPP(X3,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2)), inference(split_conjunct,[status(thm)],[c_0_1401]), ['final']). 1.16/1.44 cnf(c_0_2495, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk60_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk59_3(X2,X1,X3))),X3)), inference(rw,[status(thm)],[c_0_1402, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2496, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk30_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk29_3(X2,X1,X3))),X3)), inference(rw,[status(thm)],[c_0_1403, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2497, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk58_2(X2,X1))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk57_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[c_0_1404, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2498, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk28_2(X2,X1))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk27_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[c_0_1405, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2499, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_1406]), ['final']). 1.16/1.44 cnf(c_0_2500, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1)), inference(split_conjunct,[status(thm)],[c_0_1407]), ['final']). 1.16/1.44 cnf(c_0_2501, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk47_1(X1)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1408]), ['final']). 1.16/1.44 cnf(c_0_2502, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk32_1(X1)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1409]), ['final']). 1.16/1.44 cnf(c_0_2503, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk7_1(X1)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1410]), ['final']). 1.16/1.44 cnf(c_0_2504, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk58_2(X1,X2))|~class_RealVector_Oreal__normed__vector(X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk57_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[c_0_1411, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2505, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk28_2(X1,X2))|~class_RealVector_Oreal__normed__vector(X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk27_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[c_0_1412, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2506, negated_conjecture, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))), inference(split_conjunct,[status(thm)],[c_0_1413]), ['final']). 1.16/1.44 cnf(c_0_2507, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X1)), inference(split_conjunct,[status(thm)],[c_0_1414]), ['final']). 1.16/1.44 cnf(c_0_2508, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X5)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_1415]), ['final']). 1.16/1.44 cnf(c_0_2509, plain, (c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk71_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[c_0_1416, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2510, plain, (c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk35_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[c_0_1417, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2511, plain, (X2=X3|c_Groups_Ouminus__class_Ouminus(X1,X3)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Oidom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1418, c_0_1393]), c_0_1393]), c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2512, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1419, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2513, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4)!=X5|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1420]), ['final']). 1.16/1.44 cnf(c_0_2514, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_1421]), ['final']). 1.16/1.44 cnf(c_0_2515, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5)=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5)!=X6|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_1422]), ['final']). 1.16/1.44 cnf(c_0_2516, plain, (c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5),X1)=c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5),X6)|X1!=c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X3,X4)),X5),X6)|~class_Rings_Oring(X2)), inference(split_conjunct,[status(thm)],[c_0_1423]), ['final']). 1.16/1.44 cnf(c_0_2517, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2518, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1425, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2519, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1426, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2520, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,X3),c_Groups_Ouminus__class_Ouminus(X1,hAPP(X2,esk11_2(X2,X1))))),esk10_2(X2,X1))|~c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1372]), ['final']). 1.16/1.44 cnf(c_0_2521, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X2,X3)),esk43_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2522, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X4))=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X4))|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_1427]), ['final']). 1.16/1.44 cnf(c_0_2523, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1428]), ['final']). 1.16/1.44 cnf(c_0_2524, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2525, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2526, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))),X4)|~class_Groups_Omonoid__mult(X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)), inference(rw,[status(thm)],[c_0_1429, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2527, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3)=X5|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1)), inference(split_conjunct,[status(thm)],[c_0_1420]), ['final']). 1.16/1.44 cnf(c_0_2528, plain, (X3=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_1421]), ['final']). 1.16/1.44 cnf(c_0_2529, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk42_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2530, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X3,X2)),esk43_3(X1,X3,X2))=X3|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2531, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4)=X6|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)!=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_1422]), ['final']). 1.16/1.44 cnf(c_0_2532, plain, (X4=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)!=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_1423]), ['final']). 1.16/1.44 cnf(c_0_2533, plain, (hBOOL(hAPP(X1,esk65_3(X2,X1,X3)))|hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~hBOOL(hAPP(X1,X4))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)), inference(split_conjunct,[status(thm)],[c_0_1397]), ['final']). 1.16/1.44 cnf(c_0_2534, plain, (hBOOL(hAPP(X1,esk20_3(X2,X1,X3)))|hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~hBOOL(hAPP(X1,X4))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)), inference(split_conjunct,[status(thm)],[c_0_1396]), ['final']). 1.16/1.44 cnf(c_0_2535, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2536, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5))=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3),X5)|~class_Rings_Osemiring(X1)), inference(split_conjunct,[status(thm)],[c_0_1430]), ['final']). 1.16/1.44 cnf(c_0_2537, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,esk70_4(X3,X2,X1,X4))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(X3,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,hAPP(X3,X2))))|~c_Orderings_Oord__class_Oless__eq(X1,X2,X5)|~class_Orderings_Oord(X1)|~class_RealVector_Oreal__normed__vector(X4)), inference(split_conjunct,[status(thm)],[c_0_1371]), ['final']). 1.16/1.44 cnf(c_0_2538, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4)),X3)|~class_Rings_Olinordered__semiring__1__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X5)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)|c_Groups_Oone__class_Oone(X1)!=c_Groups_Oplus__class_Oplus(X1,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_1431]), ['final']). 1.16/1.44 cnf(c_0_2539, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4)),X3)|~class_Rings_Olinordered__semiring__1(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X5)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)|c_Groups_Oone__class_Oone(X1)!=c_Groups_Oplus__class_Oplus(X1,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_1432]), ['final']). 1.16/1.44 cnf(c_0_2540, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2)))|~hBOOL(hAPP(X2,esk42_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2541, plain, (c_SEQ_OBseq(X1,X3)|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X3,esk63_3(X3,X2,X1))),X2)), inference(split_conjunct,[status(thm)],[c_0_1433]), ['final']). 1.16/1.44 cnf(c_0_2542, plain, (c_SEQ_OBseq(X2,X3)|~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,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk51_3(X3,X2,X1))),X1)|~class_RealVector_Oreal__normed__vector(X2)), inference(split_conjunct,[status(thm)],[c_0_1434]), ['final']). 1.16/1.44 cnf(c_0_2543, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X4))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_1435]), ['final']). 1.16/1.44 cnf(c_0_2544, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk33_3(X2,X3,X1)),X3),X2)|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_1436]), ['final']). 1.16/1.44 cnf(c_0_2545, plain, (~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))|X3!=c_Groups_Ozero__class_Ozero(X1)|X2!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1437]), ['final']). 1.16/1.44 cnf(c_0_2546, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1438]), ['final']). 1.16/1.44 cnf(c_0_2547, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2548, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2549, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2550, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2551, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),c_Groups_Ozero__class_Ozero(X2))|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_1439]), ['final']). 1.16/1.44 cnf(c_0_2552, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),c_Groups_Ozero__class_Ozero(X2))|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_1439]), ['final']). 1.16/1.44 cnf(c_0_2553, plain, (~class_Rings_Olinordered__ring(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1440]), ['final']). 1.16/1.44 cnf(c_0_2554, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5))), inference(rw,[status(thm)],[c_0_1441, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2555, plain, (hBOOL(hAPP(X5,X3))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),X2)!=X4|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2556, plain, (hBOOL(hAPP(X5,X2))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3)!=X4|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2557, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2558, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X2,X3)),esk43_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2559, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X2,X3)),esk43_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2560, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2561, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3)|~class_Groups_Omonoid__mult(X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1442]), ['final']). 1.16/1.44 cnf(c_0_2562, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2563, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2564, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2565, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2566, plain, (X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1443, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2567, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2)),esk8_3(X4,X3,X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X4)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_1444]), ['final']). 1.16/1.44 cnf(c_0_2568, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X1)),esk8_3(X2,X3,X4))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_1444]), ['final']). 1.16/1.44 cnf(c_0_2569, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2)),esk15_3(X4,X3,X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X4)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_1445]), ['final']). 1.16/1.44 cnf(c_0_2570, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X1)),esk15_3(X2,X3,X4))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_1445]), ['final']). 1.16/1.44 cnf(c_0_2571, plain, (X1=X2|X3=X4|c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3))!=c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)), inference(split_conjunct,[status(thm)],[c_0_1446]), ['final']). 1.16/1.44 cnf(c_0_2572, plain, (X5=X3|X4=X2|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))!=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(split_conjunct,[status(thm)],[c_0_1447]), ['final']). 1.16/1.44 cnf(c_0_2573, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Groups_Ouminus__class_Ouminus(X1,X2)!=X3|~class_Rings_Oidom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1448, c_0_1393]), c_0_1393]), c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2574, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2575, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2576, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1449]), ['final']). 1.16/1.44 cnf(c_0_2577, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1450, c_0_1393]), c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2578, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1451, c_0_1393]), c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2579, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X3,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2580, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk42_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2581, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk42_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2582, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X3,X2))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2583, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1452]), ['final']). 1.16/1.44 cnf(c_0_2584, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_1453]), ['final']). 1.16/1.44 cnf(c_0_2585, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,X3),c_Groups_Ouminus__class_Ouminus(X1,esk4_2(X2,X1)))),esk3_2(X2,X1))|~c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1373]), ['final']). 1.16/1.44 cnf(c_0_2586, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_1454]), ['final']). 1.16/1.44 cnf(c_0_2587, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X2,X3)),esk43_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2588, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2589, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk66_3(X2,X3,X1)),esk67_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_1455]), ['final']). 1.16/1.44 cnf(c_0_2590, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1456]), ['final']). 1.16/1.44 cnf(c_0_2591, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1457]), ['final']). 1.16/1.44 cnf(c_0_2592, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2593, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2594, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1458]), ['final']). 1.16/1.44 cnf(c_0_2595, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1459]), ['final']). 1.16/1.44 cnf(c_0_2596, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1460, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2597, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1461, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2598, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X5,X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X2)!=X4|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4,X1)))), inference(split_conjunct,[status(thm)],[c_0_1455]), ['final']). 1.16/1.44 cnf(c_0_2599, plain, (X2=X4|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1462, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2600, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk66_3(X1,X2,X3)),esk67_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1455]), ['final']). 1.16/1.44 cnf(c_0_2601, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(rw,[status(thm)],[c_0_1463, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2602, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))), inference(split_conjunct,[status(thm)],[c_0_1464]), ['final']). 1.16/1.44 cnf(c_0_2603, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)))), inference(split_conjunct,[status(thm)],[c_0_1465]), ['final']). 1.16/1.44 cnf(c_0_2604, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1466, c_0_1393]), c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2605, plain, (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X4)),X3)|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_1467]), ['final']). 1.16/1.44 cnf(c_0_2606, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk42_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2607, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2608, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk66_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1455]), ['final']). 1.16/1.44 cnf(c_0_2609, plain, (hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk68_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1468]), ['final']). 1.16/1.44 cnf(c_0_2610, plain, (hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,esk23_3(X2,X3,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_1469]), ['final']). 1.16/1.44 cnf(c_0_2611, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X4),X5)), inference(split_conjunct,[status(thm)],[c_0_1470]), ['final']). 1.16/1.44 cnf(c_0_2612, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1471, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2613, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1472, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2614, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))|~hBOOL(hAPP(X3,esk68_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_1468]), ['final']). 1.16/1.44 cnf(c_0_2615, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)|hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,esk23_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1469]), ['final']). 1.16/1.44 cnf(c_0_2616, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_1473]), ['final']). 1.16/1.44 cnf(c_0_2617, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1474]), ['final']). 1.16/1.44 cnf(c_0_2618, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X5))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5)), inference(split_conjunct,[status(thm)],[c_0_1475]), ['final']). 1.16/1.44 cnf(c_0_2619, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,esk14_3(X3,X2,X1)))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_1476]), ['final']). 1.16/1.44 cnf(c_0_2620, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1477, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2621, plain, (hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4))|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_1478]), ['final']). 1.16/1.44 cnf(c_0_2622, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1479]), ['final']). 1.16/1.44 cnf(c_0_2623, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1449]), ['final']). 1.16/1.44 cnf(c_0_2624, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1449]), ['final']). 1.16/1.44 cnf(c_0_2625, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1480]), ['final']). 1.16/1.44 cnf(c_0_2626, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1481]), ['final']). 1.16/1.44 cnf(c_0_2627, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X5)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1482]), ['final']). 1.16/1.44 cnf(c_0_2628, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1483]), ['final']). 1.16/1.44 cnf(c_0_2629, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X5)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1484]), ['final']). 1.16/1.44 cnf(c_0_2630, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1485]), ['final']). 1.16/1.44 cnf(c_0_2631, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Oordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1486]), ['final']). 1.16/1.44 cnf(c_0_2632, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Oordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1487]), ['final']). 1.16/1.44 cnf(c_0_2633, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X5))|~class_RealVector_Oreal__normed__algebra(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5)), inference(split_conjunct,[status(thm)],[c_0_1488]), ['final']). 1.16/1.44 cnf(c_0_2634, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)=X4|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_1489]), ['final']). 1.16/1.44 cnf(c_0_2635, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)))|~hBOOL(hAPP(X2,esk66_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_1455]), ['final']). 1.16/1.44 cnf(c_0_2636, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1490]), ['final']). 1.16/1.44 cnf(c_0_2637, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_1491]), ['final']). 1.16/1.44 cnf(c_0_2638, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2639, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk1_2(X1,X2))),X2),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(split_conjunct,[status(thm)],[c_0_1269]), ['final']). 1.16/1.44 cnf(c_0_2640, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2641, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2642, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2643, plain, (c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),c_Groups_Ozero__class_Ozero(X2))|X1!=c_Groups_Ozero__class_Ozero(X2)|X3!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_1439]), ['final']). 1.16/1.44 cnf(c_0_2644, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)))|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_1437]), ['final']). 1.16/1.44 cnf(c_0_2645, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)))|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_1437]), ['final']). 1.16/1.44 cnf(c_0_2646, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))|~class_Rings_Olinordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1492]), ['final']). 1.16/1.44 cnf(c_0_2647, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(rw,[status(thm)],[c_0_1493, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2648, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk39_3(X1,X2,X3),X3)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk38_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_1374]), ['final']). 1.16/1.44 cnf(c_0_2649, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk6_3(X1,X2,X3),X3)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk5_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_1375]), ['final']). 1.16/1.44 cnf(c_0_2650, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Oone__class_Oone(X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1)))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1494]), ['final']). 1.16/1.44 cnf(c_0_2651, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1495, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2652, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1496, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2653, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(rw,[status(thm)],[c_0_1497, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2654, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2655, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk54_4(X2,X3,X1,X4))|c_SEQ_OBseq(X4,X3)|~class_RealVector_Oreal__normed__vector(X4)), inference(split_conjunct,[status(thm)],[c_0_1379]), ['final']). 1.16/1.44 cnf(c_0_2656, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1498]), ['final']). 1.16/1.44 cnf(c_0_2657, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Rings_Olinordered__semiring(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1499]), ['final']). 1.16/1.44 cnf(c_0_2658, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1500]), ['final']). 1.16/1.44 cnf(c_0_2659, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1501]), ['final']). 1.16/1.44 cnf(c_0_2660, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Rings_Olinordered__semiring(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1502]), ['final']). 1.16/1.44 cnf(c_0_2661, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1503]), ['final']). 1.16/1.44 cnf(c_0_2662, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1504]), ['final']). 1.16/1.44 cnf(c_0_2663, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1505]), ['final']). 1.16/1.44 cnf(c_0_2664, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1506]), ['final']). 1.16/1.44 cnf(c_0_2665, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1507]), ['final']). 1.16/1.44 cnf(c_0_2666, plain, (c_Orderings_Oord__class_Oless(X1,X4,X3)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1508]), ['final']). 1.16/1.44 cnf(c_0_2667, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,X3)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1509]), ['final']). 1.16/1.44 cnf(c_0_2668, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2669, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2670, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_1510]), ['final']). 1.16/1.44 cnf(c_0_2671, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_1511]), ['final']). 1.16/1.44 cnf(c_0_2672, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_1512]), ['final']). 1.16/1.44 cnf(c_0_2673, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_1513]), ['final']). 1.16/1.44 cnf(c_0_2674, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_1514, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2675, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(rw,[status(thm)],[c_0_1515, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2676, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2677, plain, (hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),X2),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1516]), ['final']). 1.16/1.44 cnf(c_0_2678, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)=X4|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_1489]), ['final']). 1.16/1.44 cnf(c_0_2679, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(split_conjunct,[status(thm)],[c_0_1517]), ['final']). 1.16/1.44 cnf(c_0_2680, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ominus__class_Ominus(X1,X4,X5))=c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1518]), ['final']). 1.16/1.44 cnf(c_0_2681, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1519]), ['final']). 1.16/1.44 cnf(c_0_2682, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_1520]), ['final']). 1.16/1.44 cnf(c_0_2683, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_1521]), ['final']). 1.16/1.44 cnf(c_0_2684, plain, (X1=hAPP(X2,esk39_3(X1,X2,X3))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk38_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_1374]), ['final']). 1.16/1.44 cnf(c_0_2685, plain, (X1=hAPP(X2,esk6_3(X1,X2,X3))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk5_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_1375]), ['final']). 1.16/1.44 cnf(c_0_2686, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,X3,c_Divides_Odiv__class_Odiv(X1,X4,X2))=c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_1522]), ['final']). 1.16/1.44 cnf(c_0_2687, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,X3,c_Divides_Odiv__class_Odiv(X1,X4,X2))=c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_1523]), ['final']). 1.16/1.44 cnf(c_0_2688, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)), inference(split_conjunct,[status(thm)],[c_0_1524]), ['final']). 1.16/1.44 cnf(c_0_2689, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1525]), ['final']). 1.16/1.44 cnf(c_0_2690, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1526]), ['final']). 1.16/1.44 cnf(c_0_2691, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk61_2(X3,X1)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1527]), ['final']). 1.16/1.44 cnf(c_0_2692, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk46_2(X3,X1)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1528]), ['final']). 1.16/1.44 cnf(c_0_2693, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk17_2(X3,X1)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1529]), ['final']). 1.16/1.44 cnf(c_0_2694, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1530]), ['final']). 1.16/1.44 cnf(c_0_2695, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk55_2(X2,X1)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1531]), ['final']). 1.16/1.44 cnf(c_0_2696, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk52_2(X2,X1)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1532]), ['final']). 1.16/1.44 cnf(c_0_2697, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk24_2(X2,X1)))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1533]), ['final']). 1.16/1.44 cnf(c_0_2698, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1534]), ['final']). 1.16/1.44 cnf(c_0_2699, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3)|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1535]), ['final']). 1.16/1.44 cnf(c_0_2700, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1536]), ['final']). 1.16/1.44 cnf(c_0_2701, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1537]), ['final']). 1.16/1.44 cnf(c_0_2702, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Ocomm__semiring(X1)), inference(split_conjunct,[status(thm)],[c_0_1538]), ['final']). 1.16/1.44 cnf(c_0_2703, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1539]), ['final']). 1.16/1.44 cnf(c_0_2704, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1540]), ['final']). 1.16/1.44 cnf(c_0_2705, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk21_2(X1,X2))),X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1541]), ['final']). 1.16/1.44 cnf(c_0_2706, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1526]), ['final']). 1.16/1.44 cnf(c_0_2707, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1525]), ['final']). 1.16/1.44 cnf(c_0_2708, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1525]), ['final']). 1.16/1.44 cnf(c_0_2709, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1526]), ['final']). 1.16/1.44 cnf(c_0_2710, plain, (c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5))=c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4))|X1!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)), inference(split_conjunct,[status(thm)],[c_0_1447]), ['final']). 1.16/1.44 cnf(c_0_2711, plain, (c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5))=c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4))|X1!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)), inference(split_conjunct,[status(thm)],[c_0_1446]), ['final']). 1.16/1.44 cnf(c_0_2712, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1542, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2713, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1526]), ['final']). 1.16/1.44 cnf(c_0_2714, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1525]), ['final']). 1.16/1.44 cnf(c_0_2715, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1543]), ['final']). 1.16/1.44 cnf(c_0_2716, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1544]), ['final']). 1.16/1.44 cnf(c_0_2717, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1545]), ['final']). 1.16/1.44 cnf(c_0_2718, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_1546]), ['final']). 1.16/1.44 cnf(c_0_2719, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1547]), ['final']). 1.16/1.44 cnf(c_0_2720, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2721, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2722, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)=X4|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_1489]), ['final']). 1.16/1.44 cnf(c_0_2723, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)), inference(split_conjunct,[status(thm)],[c_0_1480]), ['final']). 1.16/1.44 cnf(c_0_2724, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)), inference(split_conjunct,[status(thm)],[c_0_1481]), ['final']). 1.16/1.44 cnf(c_0_2725, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2726, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2727, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1548]), ['final']). 1.16/1.44 cnf(c_0_2728, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1549]), ['final']). 1.16/1.44 cnf(c_0_2729, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1550]), ['final']). 1.16/1.44 cnf(c_0_2730, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1551]), ['final']). 1.16/1.44 cnf(c_0_2731, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X5=X6|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)|X3!=X4|c_Groups_Oplus__class_Oplus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X6))!=c_Groups_Oplus__class_Oplus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5))), inference(split_conjunct,[status(thm)],[c_0_1552]), ['final']). 1.16/1.44 cnf(c_0_2732, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_1553]), ['final']). 1.16/1.44 cnf(c_0_2733, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1554]), ['final']). 1.16/1.44 cnf(c_0_2734, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(split_conjunct,[status(thm)],[c_0_1555]), ['final']). 1.16/1.44 cnf(c_0_2735, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1556]), ['final']). 1.16/1.44 cnf(c_0_2736, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1557]), ['final']). 1.16/1.44 cnf(c_0_2737, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1558]), ['final']). 1.16/1.44 cnf(c_0_2738, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(split_conjunct,[status(thm)],[c_0_1559]), ['final']). 1.16/1.44 cnf(c_0_2739, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1560]), ['final']). 1.16/1.44 cnf(c_0_2740, plain, (c_RComplete_Onatceiling(X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), inference(split_conjunct,[status(thm)],[c_0_1561]), ['final']). 1.16/1.44 cnf(c_0_2741, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1562]), ['final']). 1.16/1.44 cnf(c_0_2742, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1563]), ['final']). 1.16/1.44 cnf(c_0_2743, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1564]), ['final']). 1.16/1.44 cnf(c_0_2744, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1565]), ['final']). 1.16/1.44 cnf(c_0_2745, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk72_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_RealVector_Oreal__normed__vector(X1)|~c_SEQ_OBseq(X1,X2)), inference(rw,[status(thm)],[c_0_1566, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2746, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk34_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_RealVector_Oreal__normed__vector(X1)|~c_SEQ_OBseq(X1,X2)), inference(rw,[status(thm)],[c_0_1567, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2747, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3),hAPP(c_Polynomial_Opoly(X1,X4),X3))=hAPP(c_Polynomial_Opoly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X4)),X3)|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_1568]), ['final']). 1.16/1.44 cnf(c_0_2748, plain, (hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4)=c_Groups_Ominus__class_Ominus(X1,hAPP(c_Polynomial_Ocoeff(X1,X2),X4),hAPP(c_Polynomial_Ocoeff(X1,X3),X4))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1569]), ['final']). 1.16/1.44 cnf(c_0_2749, plain, (hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4)=c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Ocoeff(X1,X2),X4),hAPP(c_Polynomial_Ocoeff(X1,X3),X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1570]), ['final']). 1.16/1.44 cnf(c_0_2750, plain, (hAPP(c_Polynomial_Opoly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4)=c_Groups_Ominus__class_Ominus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))|~class_Rings_Ocomm__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1571]), ['final']). 1.16/1.44 cnf(c_0_2751, plain, (hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_1468]), ['final']). 1.16/1.44 cnf(c_0_2752, plain, (hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_1469]), ['final']). 1.16/1.44 cnf(c_0_2753, plain, (hBOOL(hAPP(X1,X2))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)!=X4|~hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X3)))), inference(split_conjunct,[status(thm)],[c_0_1469]), ['final']). 1.16/1.44 cnf(c_0_2754, plain, (hBOOL(hAPP(X4,X3))|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)|~hBOOL(hAPP(X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_1468]), ['final']). 1.16/1.44 cnf(c_0_2755, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_1572]), ['final']). 1.16/1.44 cnf(c_0_2756, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1572]), ['final']). 1.16/1.44 cnf(c_0_2757, plain, (c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_1573]), ['final']). 1.16/1.44 cnf(c_0_2758, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_1574]), ['final']). 1.16/1.44 cnf(c_0_2759, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_1575]), ['final']). 1.16/1.44 cnf(c_0_2760, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_1576]), ['final']). 1.16/1.44 cnf(c_0_2761, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_1577]), ['final']). 1.16/1.44 cnf(c_0_2762, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)), inference(rw,[status(thm)],[c_0_1578, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2763, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3))|~class_RealVector_Oreal__normed__algebra__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1579]), ['final']). 1.16/1.44 cnf(c_0_2764, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))), inference(split_conjunct,[status(thm)],[c_0_1580]), ['final']). 1.16/1.44 cnf(c_0_2765, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_1581]), ['final']). 1.16/1.44 cnf(c_0_2766, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_1582]), ['final']). 1.16/1.44 cnf(c_0_2767, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_1583]), ['final']). 1.16/1.44 cnf(c_0_2768, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))), inference(split_conjunct,[status(thm)],[c_0_1584]), ['final']). 1.16/1.44 cnf(c_0_2769, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_1585]), ['final']). 1.16/1.44 cnf(c_0_2770, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_1586]), ['final']). 1.16/1.44 cnf(c_0_2771, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_1587]), ['final']). 1.16/1.44 cnf(c_0_2772, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1588, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2773, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1589, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2774, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1590, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2775, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1591, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2776, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_1592]), ['final']). 1.16/1.44 cnf(c_0_2777, plain, (X2=X3|hAPP(c_Polynomial_Ocoeff(X1,X2),esk48_3(X2,X3,X1))!=hAPP(c_Polynomial_Ocoeff(X1,X3),esk48_3(X2,X3,X1))|~class_Groups_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_1593]), ['final']). 1.16/1.44 cnf(c_0_2778, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1594]), ['final']). 1.16/1.44 cnf(c_0_2779, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1474]), ['final']). 1.16/1.44 cnf(c_0_2780, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_1595]), ['final']). 1.16/1.44 cnf(c_0_2781, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_1596, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2782, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_1597]), ['final']). 1.16/1.44 cnf(c_0_2783, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_1598]), ['final']). 1.16/1.44 cnf(c_0_2784, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2785, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3))|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2786, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Oone__class_Oone(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))!=X1|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1599]), ['final']). 1.16/1.44 cnf(c_0_2787, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2788, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2789, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk23_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_1469]), ['final']). 1.16/1.44 cnf(c_0_2790, plain, (X2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk68_3(X3,X2,X1))|hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_1468]), ['final']). 1.16/1.44 cnf(c_0_2791, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk67_3(X2,X3,X1),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_1455]), ['final']). 1.16/1.44 cnf(c_0_2792, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))!=X1|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1600]), ['final']). 1.16/1.44 cnf(c_0_2793, plain, (X2=X4|~class_Rings_Olinordered__semidom(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)), inference(split_conjunct,[status(thm)],[c_0_1601]), ['final']). 1.16/1.44 cnf(c_0_2794, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1602]), ['final']). 1.16/1.44 cnf(c_0_2795, plain, (c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1603]), ['final']). 1.16/1.44 cnf(c_0_2796, plain, (c_RComplete_Onatfloor(X2)=X1|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), inference(split_conjunct,[status(thm)],[c_0_1604]), ['final']). 1.16/1.44 cnf(c_0_2797, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk23_3(X1,X2,X3))=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1469]), ['final']). 1.16/1.44 cnf(c_0_2798, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk68_3(X2,X1,X3))|hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_1468]), ['final']). 1.16/1.44 cnf(c_0_2799, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_1605]), ['final']). 1.16/1.44 cnf(c_0_2800, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_1606]), ['final']). 1.16/1.44 cnf(c_0_2801, plain, (c_Groups_Ozero__class_Ozero(X1)=X3|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_RealVector_Onorm__class_Onorm(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_1607]), ['final']). 1.16/1.44 cnf(c_0_2802, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1525]), ['final']). 1.16/1.44 cnf(c_0_2803, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1526]), ['final']). 1.16/1.44 cnf(c_0_2804, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1608]), ['final']). 1.16/1.44 cnf(c_0_2805, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1503]), ['final']). 1.16/1.44 cnf(c_0_2806, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Olinordered__comm__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1609]), ['final']). 1.16/1.44 cnf(c_0_2807, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1610]), ['final']). 1.16/1.44 cnf(c_0_2808, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1611]), ['final']). 1.16/1.44 cnf(c_0_2809, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Oordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1612]), ['final']). 1.16/1.44 cnf(c_0_2810, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Oordered__comm__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1613]), ['final']). 1.16/1.44 cnf(c_0_2811, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1506]), ['final']). 1.16/1.44 cnf(c_0_2812, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Oordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1614]), ['final']). 1.16/1.44 cnf(c_0_2813, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1525]), ['final']). 1.16/1.44 cnf(c_0_2814, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1615]), ['final']). 1.16/1.44 cnf(c_0_2815, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1526]), ['final']). 1.16/1.44 cnf(c_0_2816, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1508]), ['final']). 1.16/1.44 cnf(c_0_2817, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1616]), ['final']). 1.16/1.44 cnf(c_0_2818, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1617]), ['final']). 1.16/1.44 cnf(c_0_2819, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1509]), ['final']). 1.16/1.44 cnf(c_0_2820, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1618]), ['final']). 1.16/1.44 cnf(c_0_2821, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1619]), ['final']). 1.16/1.44 cnf(c_0_2822, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_1620]), ['final']). 1.16/1.44 cnf(c_0_2823, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_1621]), ['final']). 1.16/1.44 cnf(c_0_2824, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_1622]), ['final']). 1.16/1.44 cnf(c_0_2825, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oordered__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_1623]), ['final']). 1.16/1.44 cnf(c_0_2826, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1624]), ['final']). 1.16/1.44 cnf(c_0_2827, plain, (c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)|~class_Rings_Olinordered__semidom(X3)), inference(split_conjunct,[status(thm)],[c_0_1511]), ['final']). 1.16/1.44 cnf(c_0_2828, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_1625]), ['final']). 1.16/1.44 cnf(c_0_2829, plain, (c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)|~class_Rings_Olinordered__semidom(X3)), inference(split_conjunct,[status(thm)],[c_0_1513]), ['final']). 1.16/1.44 cnf(c_0_2830, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1626]), ['final']). 1.16/1.44 cnf(c_0_2831, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1626]), ['final']). 1.16/1.44 cnf(c_0_2832, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1626]), ['final']). 1.16/1.44 cnf(c_0_2833, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1626]), ['final']). 1.16/1.44 cnf(c_0_2834, plain, (hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk49_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_1627]), ['final']). 1.16/1.44 cnf(c_0_2835, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_1628]), ['final']). 1.16/1.44 cnf(c_0_2836, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_1629, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2837, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)), inference(split_conjunct,[status(thm)],[c_0_1630]), ['final']). 1.16/1.44 cnf(c_0_2838, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1631]), ['final']). 1.16/1.44 cnf(c_0_2839, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1632]), ['final']). 1.16/1.44 cnf(c_0_2840, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X4))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1633]), ['final']). 1.16/1.44 cnf(c_0_2841, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)), inference(split_conjunct,[status(thm)],[c_0_1634]), ['final']). 1.16/1.44 cnf(c_0_2842, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_1635]), ['final']). 1.16/1.44 cnf(c_0_2843, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1636]), ['final']). 1.16/1.44 cnf(c_0_2844, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1637]), ['final']). 1.16/1.44 cnf(c_0_2845, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1638]), ['final']). 1.16/1.44 cnf(c_0_2846, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1638]), ['final']). 1.16/1.44 cnf(c_0_2847, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[c_0_1639, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2848, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[c_0_1640, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2849, plain, (X2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3)))), inference(split_conjunct,[status(thm)],[c_0_1641]), ['final']). 1.16/1.44 cnf(c_0_2850, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1642]), ['final']). 1.16/1.44 cnf(c_0_2851, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1643]), ['final']). 1.16/1.44 cnf(c_0_2852, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1644]), ['final']). 1.16/1.44 cnf(c_0_2853, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1645]), ['final']). 1.16/1.44 cnf(c_0_2854, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1646]), ['final']). 1.16/1.44 cnf(c_0_2855, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_1647]), ['final']). 1.16/1.44 cnf(c_0_2856, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_1648]), ['final']). 1.16/1.44 cnf(c_0_2857, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1649]), ['final']). 1.16/1.44 cnf(c_0_2858, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1650]), ['final']). 1.16/1.44 cnf(c_0_2859, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1651]), ['final']). 1.16/1.44 cnf(c_0_2860, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_1648]), ['final']). 1.16/1.44 cnf(c_0_2861, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_1647]), ['final']). 1.16/1.44 cnf(c_0_2862, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_1652]), ['final']). 1.16/1.44 cnf(c_0_2863, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1653]), ['final']). 1.16/1.44 cnf(c_0_2864, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1654]), ['final']). 1.16/1.44 cnf(c_0_2865, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)|~class_Groups_Oab__semigroup__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_1655]), ['final']). 1.16/1.44 cnf(c_0_2866, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2))), inference(split_conjunct,[status(thm)],[c_0_1656]), ['final']). 1.16/1.44 cnf(c_0_2867, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), inference(split_conjunct,[status(thm)],[c_0_1657]), ['final']). 1.16/1.44 cnf(c_0_2868, plain, (hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2869, plain, (hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1455]), ['final']). 1.16/1.44 cnf(c_0_2870, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk64_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1658]), ['final']). 1.16/1.44 cnf(c_0_2871, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk36_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(rw,[status(thm)],[c_0_1659, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2872, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_1660, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2873, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2874, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1661, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2875, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_1662]), ['final']). 1.16/1.44 cnf(c_0_2876, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1663]), ['final']). 1.16/1.44 cnf(c_0_2877, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)), inference(split_conjunct,[status(thm)],[c_0_1664]), ['final']). 1.16/1.44 cnf(c_0_2878, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1647]), ['final']). 1.16/1.44 cnf(c_0_2879, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)), inference(split_conjunct,[status(thm)],[c_0_1665]), ['final']). 1.16/1.44 cnf(c_0_2880, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1648]), ['final']). 1.16/1.44 cnf(c_0_2881, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)), inference(split_conjunct,[status(thm)],[c_0_1666]), ['final']). 1.16/1.44 cnf(c_0_2882, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)), inference(split_conjunct,[status(thm)],[c_0_1554]), ['final']). 1.16/1.44 cnf(c_0_2883, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1667]), ['final']). 1.16/1.44 cnf(c_0_2884, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)), inference(split_conjunct,[status(thm)],[c_0_1555]), ['final']). 1.16/1.44 cnf(c_0_2885, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)), inference(split_conjunct,[status(thm)],[c_0_1558]), ['final']). 1.16/1.44 cnf(c_0_2886, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)), inference(split_conjunct,[status(thm)],[c_0_1559]), ['final']). 1.16/1.44 cnf(c_0_2887, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)), inference(split_conjunct,[status(thm)],[c_0_1560]), ['final']). 1.16/1.44 cnf(c_0_2888, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(split_conjunct,[status(thm)],[c_0_1668]), ['final']). 1.16/1.44 cnf(c_0_2889, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_1669]), ['final']). 1.16/1.44 cnf(c_0_2890, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_1670]), ['final']). 1.16/1.44 cnf(c_0_2891, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_1669]), ['final']). 1.16/1.44 cnf(c_0_2892, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_1670]), ['final']). 1.16/1.44 cnf(c_0_2893, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk67_3(X1,X2,X3),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_1455]), ['final']). 1.16/1.44 cnf(c_0_2894, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1671]), ['final']). 1.16/1.44 cnf(c_0_2895, plain, (c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3),X4)=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_1672]), ['final']). 1.16/1.44 cnf(c_0_2896, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1673]), ['final']). 1.16/1.44 cnf(c_0_2897, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1674]), ['final']). 1.16/1.44 cnf(c_0_2898, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1675]), ['final']). 1.16/1.44 cnf(c_0_2899, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1676]), ['final']). 1.16/1.44 cnf(c_0_2900, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1677]), ['final']). 1.16/1.44 cnf(c_0_2901, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1649]), ['final']). 1.16/1.44 cnf(c_0_2902, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1678]), ['final']). 1.16/1.44 cnf(c_0_2903, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1679]), ['final']). 1.16/1.44 cnf(c_0_2904, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1680]), ['final']). 1.16/1.44 cnf(c_0_2905, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1681]), ['final']). 1.16/1.44 cnf(c_0_2906, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1649]), ['final']). 1.16/1.44 cnf(c_0_2907, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1682]), ['final']). 1.16/1.44 cnf(c_0_2908, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),X1)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_1683]), ['final']). 1.16/1.44 cnf(c_0_2909, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1684]), ['final']). 1.16/1.44 cnf(c_0_2910, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1684]), ['final']). 1.16/1.44 cnf(c_0_2911, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1684]), ['final']). 1.16/1.44 cnf(c_0_2912, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1685]), ['final']). 1.16/1.44 cnf(c_0_2913, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1685]), ['final']). 1.16/1.44 cnf(c_0_2914, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1685]), ['final']). 1.16/1.44 cnf(c_0_2915, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1685]), ['final']). 1.16/1.44 cnf(c_0_2916, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1684]), ['final']). 1.16/1.44 cnf(c_0_2917, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_1686]), ['final']). 1.16/1.44 cnf(c_0_2918, plain, (c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_1687]), ['final']). 1.16/1.44 cnf(c_0_2919, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_1688]), ['final']). 1.16/1.44 cnf(c_0_2920, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_1689]), ['final']). 1.16/1.44 cnf(c_0_2921, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_1690]), ['final']). 1.16/1.44 cnf(c_0_2922, plain, (c_Groups_Oplus__class_Oplus(X1,X2,X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1691]), ['final']). 1.16/1.44 cnf(c_0_2923, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1692]), ['final']). 1.16/1.44 cnf(c_0_2924, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[c_0_1693]), ['final']). 1.16/1.44 cnf(c_0_2925, plain, (X1=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[c_0_1693]), ['final']). 1.16/1.44 cnf(c_0_2926, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1694, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2927, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1695, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2928, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1696]), ['final']). 1.16/1.44 cnf(c_0_2929, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1697, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2930, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1698, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2931, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1699]), ['final']). 1.16/1.44 cnf(c_0_2932, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1700]), ['final']). 1.16/1.44 cnf(c_0_2933, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1701]), ['final']). 1.16/1.44 cnf(c_0_2934, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1702]), ['final']). 1.16/1.44 cnf(c_0_2935, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1703]), ['final']). 1.16/1.44 cnf(c_0_2936, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1704]), ['final']). 1.16/1.44 cnf(c_0_2937, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1705]), ['final']). 1.16/1.44 cnf(c_0_2938, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1706]), ['final']). 1.16/1.44 cnf(c_0_2939, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_1707]), ['final']). 1.16/1.44 cnf(c_0_2940, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_1708]), ['final']). 1.16/1.44 cnf(c_0_2941, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_1709]), ['final']). 1.16/1.44 cnf(c_0_2942, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_1710]), ['final']). 1.16/1.44 cnf(c_0_2943, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_1711]), ['final']). 1.16/1.44 cnf(c_0_2944, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1712]), ['final']). 1.16/1.44 cnf(c_0_2945, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1713]), ['final']). 1.16/1.44 cnf(c_0_2946, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1714]), ['final']). 1.16/1.44 cnf(c_0_2947, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~class_Rings_Oordered__cancel__semiring(X1)), inference(split_conjunct,[status(thm)],[c_0_1715]), ['final']). 1.16/1.44 cnf(c_0_2948, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1716]), ['final']). 1.16/1.44 cnf(c_0_2949, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__cancel__semiring(X1)), inference(split_conjunct,[status(thm)],[c_0_1715]), ['final']). 1.16/1.44 cnf(c_0_2950, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1717]), ['final']). 1.16/1.44 cnf(c_0_2951, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1684]), ['final']). 1.16/1.44 cnf(c_0_2952, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1718]), ['final']). 1.16/1.44 cnf(c_0_2953, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1684]), ['final']). 1.16/1.44 cnf(c_0_2954, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1719]), ['final']). 1.16/1.44 cnf(c_0_2955, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1720]), ['final']). 1.16/1.44 cnf(c_0_2956, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_1721]), ['final']). 1.16/1.44 cnf(c_0_2957, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1722]), ['final']). 1.16/1.44 cnf(c_0_2958, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1685]), ['final']). 1.16/1.44 cnf(c_0_2959, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1723]), ['final']). 1.16/1.44 cnf(c_0_2960, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1722]), ['final']). 1.16/1.44 cnf(c_0_2961, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1724]), ['final']). 1.16/1.44 cnf(c_0_2962, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1685]), ['final']). 1.16/1.44 cnf(c_0_2963, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1725]), ['final']). 1.16/1.44 cnf(c_0_2964, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_1581]), ['final']). 1.16/1.44 cnf(c_0_2965, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1726]), ['final']). 1.16/1.44 cnf(c_0_2966, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_1582]), ['final']). 1.16/1.44 cnf(c_0_2967, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_1585]), ['final']). 1.16/1.44 cnf(c_0_2968, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Groups_Oordered__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1727]), ['final']). 1.16/1.44 cnf(c_0_2969, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_1587]), ['final']). 1.16/1.44 cnf(c_0_2970, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~class_Groups_Oordered__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1728]), ['final']). 1.16/1.44 cnf(c_0_2971, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1729, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2972, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1730, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2973, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1731, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2974, plain, (X1=esk9_2(X2,X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|X2!=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)), inference(split_conjunct,[status(thm)],[c_0_1732]), ['final']). 1.16/1.44 cnf(c_0_2975, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)), inference(split_conjunct,[status(thm)],[c_0_1733]), ['final']). 1.16/1.44 cnf(c_0_2976, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_1424]), ['final']). 1.16/1.44 cnf(c_0_2977, plain, (c_SEQ_Oincseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk40_2(X2,X1)),hAPP(X2,esk41_2(X2,X1)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_1734]), ['final']). 1.16/1.44 cnf(c_0_2978, plain, (c_SEQ_Odecseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk19_2(X2,X1)),hAPP(X2,esk18_2(X2,X1)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_1735]), ['final']). 1.16/1.44 cnf(c_0_2979, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)), inference(split_conjunct,[status(thm)],[c_0_1736]), ['final']). 1.16/1.44 cnf(c_0_2980, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1737]), ['final']). 1.16/1.44 cnf(c_0_2981, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1738]), ['final']). 1.16/1.44 cnf(c_0_2982, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1739]), ['final']). 1.16/1.44 cnf(c_0_2983, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1740]), ['final']). 1.16/1.44 cnf(c_0_2984, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,X2))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1741]), ['final']). 1.16/1.44 cnf(c_0_2985, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2))), inference(split_conjunct,[status(thm)],[c_0_1742]), ['final']). 1.16/1.44 cnf(c_0_2986, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1743]), ['final']). 1.16/1.44 cnf(c_0_2987, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1744]), ['final']). 1.16/1.44 cnf(c_0_2988, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1597]), ['final']). 1.16/1.44 cnf(c_0_2989, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1745]), ['final']). 1.16/1.44 cnf(c_0_2990, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1746]), ['final']). 1.16/1.44 cnf(c_0_2991, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1747]), ['final']). 1.16/1.44 cnf(c_0_2992, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1748]), ['final']). 1.16/1.44 cnf(c_0_2993, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1749]), ['final']). 1.16/1.44 cnf(c_0_2994, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1598]), ['final']). 1.16/1.44 cnf(c_0_2995, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1750]), ['final']). 1.16/1.44 cnf(c_0_2996, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3))=c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1751]), ['final']). 1.16/1.44 cnf(c_0_2997, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk25_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1752, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2998, plain, (X1=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1753, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_2999, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Groups_Oone__class_Oone(X1))=c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_1754]), ['final']). 1.16/1.44 cnf(c_0_3000, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Groups_Oone__class_Oone(X1))=c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X3,X2),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_1755]), ['final']). 1.16/1.44 cnf(c_0_3001, plain, (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)), inference(rw,[status(thm)],[c_0_1756, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3002, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1757, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3003, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk25_2(X1,X2),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1758, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3004, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1759]), ['final']). 1.16/1.44 cnf(c_0_3005, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1680]), ['final']). 1.16/1.44 cnf(c_0_3006, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1760]), ['final']). 1.16/1.44 cnf(c_0_3007, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1679]), ['final']). 1.16/1.44 cnf(c_0_3008, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1761]), ['final']). 1.16/1.44 cnf(c_0_3009, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1762]), ['final']). 1.16/1.44 cnf(c_0_3010, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1678]), ['final']). 1.16/1.44 cnf(c_0_3011, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1763]), ['final']). 1.16/1.44 cnf(c_0_3012, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1764]), ['final']). 1.16/1.44 cnf(c_0_3013, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1681]), ['final']). 1.16/1.44 cnf(c_0_3014, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1765, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3015, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X3!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1766, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3016, plain, (c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(split_conjunct,[status(thm)],[c_0_1767]), ['final']). 1.16/1.44 cnf(c_0_3017, plain, (X1=X3|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1768]), ['final']). 1.16/1.44 cnf(c_0_3018, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1769]), ['final']). 1.16/1.44 cnf(c_0_3019, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1770]), ['final']). 1.16/1.44 cnf(c_0_3020, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1771]), ['final']). 1.16/1.44 cnf(c_0_3021, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1772]), ['final']). 1.16/1.44 cnf(c_0_3022, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1773]), ['final']). 1.16/1.44 cnf(c_0_3023, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_1682]), ['final']). 1.16/1.44 cnf(c_0_3024, plain, (c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X2),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1774]), ['final']). 1.16/1.44 cnf(c_0_3025, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X2),X1)=c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1)))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1775]), ['final']). 1.16/1.44 cnf(c_0_3026, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1776]), ['final']). 1.16/1.44 cnf(c_0_3027, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1777]), ['final']). 1.16/1.44 cnf(c_0_3028, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1778]), ['final']). 1.16/1.44 cnf(c_0_3029, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1779]), ['final']). 1.16/1.44 cnf(c_0_3030, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1780]), ['final']). 1.16/1.44 cnf(c_0_3031, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1781, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3032, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk15_3(X1,X2,X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_1445]), ['final']). 1.16/1.44 cnf(c_0_3033, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_3(X1,X2,X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_1444]), ['final']). 1.16/1.44 cnf(c_0_3034, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1782]), ['final']). 1.16/1.44 cnf(c_0_3035, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)|~class_Groups_Oab__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1783]), ['final']). 1.16/1.44 cnf(c_0_3036, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1784]), ['final']). 1.16/1.44 cnf(c_0_3037, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1785]), ['final']). 1.16/1.44 cnf(c_0_3038, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))=c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1786]), ['final']). 1.16/1.44 cnf(c_0_3039, plain, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)), inference(split_conjunct,[status(thm)],[c_0_1787]), ['final']). 1.16/1.44 cnf(c_0_3040, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_1788]), ['final']). 1.16/1.44 cnf(c_0_3041, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_1789]), ['final']). 1.16/1.44 cnf(c_0_3042, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_1790]), ['final']). 1.16/1.44 cnf(c_0_3043, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_1791]), ['final']). 1.16/1.44 cnf(c_0_3044, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1772]), ['final']). 1.16/1.44 cnf(c_0_3045, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1773]), ['final']). 1.16/1.44 cnf(c_0_3046, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))=c_Divides_Odiv__class_Odiv(X1,X3,X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_1792]), ['final']). 1.16/1.44 cnf(c_0_3047, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=c_Divides_Odiv__class_Odiv(X1,X3,X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_1793]), ['final']). 1.16/1.44 cnf(c_0_3048, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Divides_Odiv__class_Odiv(X2,X3,X4)=c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))|~class_Divides_Osemiring__div(X2)), inference(split_conjunct,[status(thm)],[c_0_1794]), ['final']). 1.16/1.44 cnf(c_0_3049, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1795]), ['final']). 1.16/1.44 cnf(c_0_3050, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1796]), ['final']). 1.16/1.44 cnf(c_0_3051, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1797, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3052, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1798, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3053, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1799, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3054, plain, (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)))), inference(split_conjunct,[status(thm)],[c_0_1800]), ['final']). 1.16/1.44 cnf(c_0_3055, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1801]), ['final']). 1.16/1.44 cnf(c_0_3056, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(split_conjunct,[status(thm)],[c_0_1802]), ['final']). 1.16/1.44 cnf(c_0_3057, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1803]), ['final']). 1.16/1.44 cnf(c_0_3058, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[c_0_1804, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3059, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[c_0_1805, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3060, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Power_Opower(X1)), inference(rw,[status(thm)],[c_0_1806, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3061, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),X2)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1807]), ['final']). 1.16/1.44 cnf(c_0_3062, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),esk53_0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)), inference(split_conjunct,[status(thm)],[c_0_1808]), ['final']). 1.16/1.44 cnf(c_0_3063, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),esk31_0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)), inference(split_conjunct,[status(thm)],[c_0_1809]), ['final']). 1.16/1.44 cnf(c_0_3064, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),v_m____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)), inference(split_conjunct,[status(thm)],[c_0_1810]), ['final']). 1.16/1.44 cnf(c_0_3065, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)))), inference(split_conjunct,[status(thm)],[c_0_1811]), ['final']). 1.16/1.44 cnf(c_0_3066, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1812, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3067, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1813, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3068, plain, (c_Orderings_Oord__class_Oless(X1,X4,X5)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Groups_Ominus__class_Ominus(X1,X4,X5)!=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1814]), ['final']). 1.16/1.44 cnf(c_0_3069, plain, (c_Orderings_Oord__class_Oless(X1,X4,X5)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Groups_Ominus__class_Ominus(X1,X2,X3)!=c_Groups_Ominus__class_Ominus(X1,X4,X5)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1814]), ['final']). 1.16/1.44 cnf(c_0_3070, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Groups_Ominus__class_Ominus(X1,X4,X5)!=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1815]), ['final']). 1.16/1.44 cnf(c_0_3071, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Groups_Ominus__class_Ominus(X1,X2,X3)!=c_Groups_Ominus__class_Ominus(X1,X4,X5)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1815]), ['final']). 1.16/1.44 cnf(c_0_3072, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1816]), ['final']). 1.16/1.44 cnf(c_0_3073, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1556]), ['final']). 1.16/1.44 cnf(c_0_3074, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1557]), ['final']). 1.16/1.44 cnf(c_0_3075, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1817]), ['final']). 1.16/1.44 cnf(c_0_3076, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_1818]), ['final']). 1.16/1.44 cnf(c_0_3077, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1656]), ['final']). 1.16/1.44 cnf(c_0_3078, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1657]), ['final']). 1.16/1.44 cnf(c_0_3079, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1819]), ['final']). 1.16/1.44 cnf(c_0_3080, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_1820]), ['final']). 1.16/1.44 cnf(c_0_3081, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_1821]), ['final']). 1.16/1.44 cnf(c_0_3082, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_1822]), ['final']). 1.16/1.44 cnf(c_0_3083, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_1823]), ['final']). 1.16/1.44 cnf(c_0_3084, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_1824]), ['final']). 1.16/1.44 cnf(c_0_3085, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_1825]), ['final']). 1.16/1.44 cnf(c_0_3086, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_1826]), ['final']). 1.16/1.44 cnf(c_0_3087, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|X2=X1|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1827]), ['final']). 1.16/1.44 cnf(c_0_3088, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1828, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3089, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1829, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3090, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1830, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3091, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1831, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3092, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)), inference(split_conjunct,[status(thm)],[c_0_1832]), ['final']). 1.16/1.44 cnf(c_0_3093, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)), inference(rw,[status(thm)],[c_0_1833, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3094, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)), inference(rw,[status(thm)],[c_0_1834, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3095, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)), inference(rw,[status(thm)],[c_0_1835, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3096, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)), inference(rw,[status(thm)],[c_0_1836, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3097, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)), inference(rw,[status(thm)],[c_0_1837, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3098, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1838]), ['final']). 1.16/1.44 cnf(c_0_3099, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_1839]), ['final']). 1.16/1.44 cnf(c_0_3100, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1840, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3101, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X3), inference(rw,[status(thm)],[c_0_1841, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3102, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1842]), ['final']). 1.16/1.44 cnf(c_0_3103, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_1843]), ['final']). 1.16/1.44 cnf(c_0_3104, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_1844]), ['final']). 1.16/1.44 cnf(c_0_3105, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1845, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3106, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_1846]), ['final']). 1.16/1.44 cnf(c_0_3107, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2), inference(split_conjunct,[status(thm)],[c_0_1455]), ['final']). 1.16/1.44 cnf(c_0_3108, plain, (c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1847]), ['final']). 1.16/1.44 cnf(c_0_3109, plain, (c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1848]), ['final']). 1.16/1.44 cnf(c_0_3110, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1849]), ['final']). 1.16/1.44 cnf(c_0_3111, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1850]), ['final']). 1.16/1.44 cnf(c_0_3112, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_1851]), ['final']). 1.16/1.44 cnf(c_0_3113, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_1852]), ['final']). 1.16/1.44 cnf(c_0_3114, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_1853]), ['final']). 1.16/1.44 cnf(c_0_3115, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1853]), ['final']). 1.16/1.44 cnf(c_0_3116, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_1854]), ['final']). 1.16/1.44 cnf(c_0_3117, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_1855]), ['final']). 1.16/1.44 cnf(c_0_3118, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X3)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_1856]), ['final']). 1.16/1.44 cnf(c_0_3119, plain, (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_RealDef_Oreal(tc_Nat_Onat,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1857]), ['final']). 1.16/1.44 cnf(c_0_3120, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1858, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3121, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[c_0_1859, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3122, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1860, c_0_1393]), c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3123, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1861, c_0_1393]), c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3124, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk16_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1862, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3125, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Ozero__class_Ozero(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Oordered__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1863]), ['final']). 1.16/1.44 cnf(c_0_3126, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Oplus__class_Oplus(X2,X3,X1)!=c_Groups_Ozero__class_Ozero(X2)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)|~class_Groups_Oordered__comm__monoid__add(X2)), inference(split_conjunct,[status(thm)],[c_0_1863]), ['final']). 1.16/1.44 cnf(c_0_3127, plain, (c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X4,X3)|c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)|~class_Orderings_Oord(X2)), inference(split_conjunct,[status(thm)],[c_0_1864]), ['final']). 1.16/1.44 cnf(c_0_3128, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|X2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1865, c_0_1393]), c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3129, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_1866]), ['final']). 1.16/1.44 cnf(c_0_3130, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_1867]), ['final']). 1.16/1.44 cnf(c_0_3131, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_1557]), ['final']). 1.16/1.44 cnf(c_0_3132, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_1556]), ['final']). 1.16/1.44 cnf(c_0_3133, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_1868]), ['final']). 1.16/1.44 cnf(c_0_3134, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|c_Groups_Ozero__class_Ozero(X1)!=X3|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_1638]), ['final']). 1.16/1.44 cnf(c_0_3135, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_1801]), ['final']). 1.16/1.44 cnf(c_0_3136, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_1801]), ['final']). 1.16/1.44 cnf(c_0_3137, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(X2,X3),hAPP(X4,X3))=hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,X1),X2,X4),X3)|~class_Groups_Ominus(X1)), inference(split_conjunct,[status(thm)],[c_0_1869]), ['final']). 1.16/1.44 cnf(c_0_3138, plain, (c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1870]), ['final']). 1.16/1.44 cnf(c_0_3139, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_1871]), ['final']). 1.16/1.44 cnf(c_0_3140, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))), inference(split_conjunct,[status(thm)],[c_0_1790]), ['final']). 1.16/1.44 cnf(c_0_3141, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))), inference(split_conjunct,[status(thm)],[c_0_1791]), ['final']). 1.16/1.44 cnf(c_0_3142, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1788]), ['final']). 1.16/1.44 cnf(c_0_3143, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1789]), ['final']). 1.16/1.44 cnf(c_0_3144, plain, (c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Divides_Osemiring__div(X2)), inference(split_conjunct,[status(thm)],[c_0_1794]), ['final']). 1.16/1.44 cnf(c_0_3145, plain, (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X3,X2)|~c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1872]), ['final']). 1.16/1.44 cnf(c_0_3146, plain, (c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2)|~c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1873]), ['final']). 1.16/1.44 cnf(c_0_3147, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk22_2(X1,X2)),X2)=X1|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1874]), ['final']). 1.16/1.44 cnf(c_0_3148, plain, (X1=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk9_2(X1,X2)),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1732]), ['final']). 1.16/1.44 cnf(c_0_3149, plain, (c_Groups_Oplus__class_Oplus(X2,X3,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ozero__class_Ozero(X2)!=X3|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)|~class_Groups_Oordered__comm__monoid__add(X2)), inference(split_conjunct,[status(thm)],[c_0_1863]), ['final']). 1.16/1.44 cnf(c_0_3150, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1875]), ['final']). 1.16/1.44 cnf(c_0_3151, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1778]), ['final']). 1.16/1.44 cnf(c_0_3152, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1779]), ['final']). 1.16/1.44 cnf(c_0_3153, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1780]), ['final']). 1.16/1.44 cnf(c_0_3154, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1776]), ['final']). 1.16/1.44 cnf(c_0_3155, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1777]), ['final']). 1.16/1.44 cnf(c_0_3156, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1876, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3157, plain, (X4=X3|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_1877]), ['final']). 1.16/1.44 cnf(c_0_3158, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))), inference(split_conjunct,[status(thm)],[c_0_1878]), ['final']). 1.16/1.44 cnf(c_0_3159, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1879]), ['final']). 1.16/1.44 cnf(c_0_3160, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(split_conjunct,[status(thm)],[c_0_1880]), ['final']). 1.16/1.44 cnf(c_0_3161, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1881, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3162, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1882]), ['final']). 1.16/1.44 cnf(c_0_3163, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1883]), ['final']). 1.16/1.44 cnf(c_0_3164, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1884]), ['final']). 1.16/1.44 cnf(c_0_3165, plain, (c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1885]), ['final']). 1.16/1.44 cnf(c_0_3166, plain, (c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1886]), ['final']). 1.16/1.44 cnf(c_0_3167, plain, (~class_Rings_Olinordered__ring(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_1887]), ['final']). 1.16/1.44 cnf(c_0_3168, plain, (~c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)|~c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X4,X3)|~class_Orderings_Oord(X2)), inference(split_conjunct,[status(thm)],[c_0_1864]), ['final']). 1.16/1.44 cnf(c_0_3169, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1795]), ['final']). 1.16/1.44 cnf(c_0_3170, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1796]), ['final']). 1.16/1.44 cnf(c_0_3171, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)), inference(split_conjunct,[status(thm)],[c_0_1888]), ['final']). 1.16/1.44 cnf(c_0_3172, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk22_2(X1,X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1874]), ['final']). 1.16/1.44 cnf(c_0_3173, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk9_2(X1,X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1732]), ['final']). 1.16/1.44 cnf(c_0_3174, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_1889]), ['final']). 1.16/1.44 cnf(c_0_3175, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)), inference(split_conjunct,[status(thm)],[c_0_1880]), ['final']). 1.16/1.44 cnf(c_0_3176, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1879]), ['final']). 1.16/1.44 cnf(c_0_3177, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2), inference(split_conjunct,[status(thm)],[c_0_1890]), ['final']). 1.16/1.44 cnf(c_0_3178, plain, (hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk49_2(X2,X3))|~hBOOL(hAPP(X3,X1))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_1627]), ['final']). 1.16/1.44 cnf(c_0_3179, plain, (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(rw,[status(thm)],[c_0_1891, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3180, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_1892, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3181, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_1893, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3182, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_1894]), ['final']). 1.16/1.44 cnf(c_0_3183, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1895]), ['final']). 1.16/1.44 cnf(c_0_3184, plain, (c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))|~class_RealVector_Oreal__normed__div__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1896]), ['final']). 1.16/1.44 cnf(c_0_3185, plain, (c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1897]), ['final']). 1.16/1.44 cnf(c_0_3186, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1898, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3187, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X1!=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(rw,[status(thm)],[c_0_1899, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3188, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))=c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1900]), ['final']). 1.16/1.44 cnf(c_0_3189, plain, (c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))=c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1901]), ['final']). 1.16/1.44 cnf(c_0_3190, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1707]), ['final']). 1.16/1.44 cnf(c_0_3191, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1707]), ['final']). 1.16/1.44 cnf(c_0_3192, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|X1!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X2), inference(split_conjunct,[status(thm)],[c_0_1693]), ['final']). 1.16/1.44 cnf(c_0_3193, plain, (c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))|~class_RealVector_Oreal__normed__div__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1902]), ['final']). 1.16/1.44 cnf(c_0_3194, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1903]), ['final']). 1.16/1.44 cnf(c_0_3195, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1832]), ['final']). 1.16/1.44 cnf(c_0_3196, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1904, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3197, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1905, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3198, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1906, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3199, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1827]), ['final']). 1.16/1.44 cnf(c_0_3200, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1839]), ['final']). 1.16/1.44 cnf(c_0_3201, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1907, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3202, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1908, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3203, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1909, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3204, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1910, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3205, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1838]), ['final']). 1.16/1.44 cnf(c_0_3206, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1911, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3207, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_1912, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3208, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_1913]), ['final']). 1.16/1.44 cnf(c_0_3209, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_1914]), ['final']). 1.16/1.44 cnf(c_0_3210, plain, (c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2),X3)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_1915]), ['final']). 1.16/1.44 cnf(c_0_3211, plain, (c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3))=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_1916]), ['final']). 1.16/1.44 cnf(c_0_3212, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1842]), ['final']). 1.16/1.44 cnf(c_0_3213, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1843]), ['final']). 1.16/1.44 cnf(c_0_3214, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1844]), ['final']). 1.16/1.44 cnf(c_0_3215, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2)),X1))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_1686]), ['final']). 1.16/1.44 cnf(c_0_3216, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1917]), ['final']). 1.16/1.44 cnf(c_0_3217, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1918]), ['final']). 1.16/1.44 cnf(c_0_3218, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1919]), ['final']). 1.16/1.44 cnf(c_0_3219, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1920]), ['final']). 1.16/1.44 cnf(c_0_3220, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1921]), ['final']). 1.16/1.44 cnf(c_0_3221, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1)=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1922]), ['final']). 1.16/1.44 cnf(c_0_3222, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))=X1|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1923]), ['final']). 1.16/1.44 cnf(c_0_3223, plain, (X2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1924]), ['final']). 1.16/1.44 cnf(c_0_3224, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_1686]), ['final']). 1.16/1.44 cnf(c_0_3225, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_1868]), ['final']). 1.16/1.44 cnf(c_0_3226, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))|~class_Orderings_Oord(X1)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1925]), ['final']). 1.16/1.44 cnf(c_0_3227, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))|~class_Orderings_Oord(X1)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1926]), ['final']). 1.16/1.44 cnf(c_0_3228, plain, (c_Orderings_Oord__class_Oless__eq(X2,hAPP(X3,X5),hAPP(X4,X5))|~c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)|~class_Orderings_Oord(X2)), inference(split_conjunct,[status(thm)],[c_0_1378]), ['final']). 1.16/1.44 cnf(c_0_3229, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1927]), ['final']). 1.16/1.44 cnf(c_0_3230, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1928]), ['final']). 1.16/1.44 cnf(c_0_3231, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1929]), ['final']). 1.16/1.44 cnf(c_0_3232, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1930]), ['final']). 1.16/1.44 cnf(c_0_3233, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1931]), ['final']). 1.16/1.44 cnf(c_0_3234, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1932]), ['final']). 1.16/1.44 cnf(c_0_3235, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1933]), ['final']). 1.16/1.44 cnf(c_0_3236, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1934]), ['final']). 1.16/1.44 cnf(c_0_3237, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1935]), ['final']). 1.16/1.44 cnf(c_0_3238, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))), inference(split_conjunct,[status(thm)],[fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096]), ['final']). 1.16/1.44 cnf(c_0_3239, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1936, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3240, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1937, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3241, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1938, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3242, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1939, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3243, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1917]), ['final']). 1.16/1.44 cnf(c_0_3244, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1920]), ['final']). 1.16/1.44 cnf(c_0_3245, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_1940]), ['final']). 1.16/1.44 cnf(c_0_3246, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1921]), ['final']). 1.16/1.44 cnf(c_0_3247, plain, (c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2))|X3=X2|~c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1873]), ['final']). 1.16/1.44 cnf(c_0_3248, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_1941]), ['final']). 1.16/1.44 cnf(c_0_3249, plain, (c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2))|~c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,X3)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1872]), ['final']). 1.16/1.44 cnf(c_0_3250, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X1|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_1942]), ['final']). 1.16/1.44 cnf(c_0_3251, plain, (X3=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1943]), ['final']). 1.16/1.44 cnf(c_0_3252, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1867]), ['final']). 1.16/1.44 cnf(c_0_3253, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1866]), ['final']). 1.16/1.44 cnf(c_0_3254, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_1944]), ['final']). 1.16/1.44 cnf(c_0_3255, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1945]), ['final']). 1.16/1.44 cnf(c_0_3256, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1946]), ['final']). 1.16/1.44 cnf(c_0_3257, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1947]), ['final']). 1.16/1.44 cnf(c_0_3258, plain, (c_Orderings_Oord__class_Oless(X1,X4,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_1948]), ['final']). 1.16/1.44 cnf(c_0_3259, plain, (c_Orderings_Oord__class_Oless(X1,X4,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_1949]), ['final']). 1.16/1.44 cnf(c_0_3260, plain, (c_Orderings_Oord__class_Oless(X1,X4,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_1950]), ['final']). 1.16/1.44 cnf(c_0_3261, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_1951]), ['final']). 1.16/1.44 cnf(c_0_3262, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_1952]), ['final']). 1.16/1.44 cnf(c_0_3263, plain, (c_Groups_Ominus__class_Ominus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1953]), ['final']). 1.16/1.44 cnf(c_0_3264, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X3,X2))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1954]), ['final']). 1.16/1.44 cnf(c_0_3265, plain, (c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3))=c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1955]), ['final']). 1.16/1.44 cnf(c_0_3266, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), inference(split_conjunct,[status(thm)],[c_0_1956]), ['final']). 1.16/1.44 cnf(c_0_3267, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1)=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1957]), ['final']). 1.16/1.44 cnf(c_0_3268, plain, (X2=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_1958]), ['final']). 1.16/1.44 cnf(c_0_3269, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_SMT_Oz3div(X2,X1)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)))), inference(split_conjunct,[status(thm)],[c_0_1959]), ['final']). 1.16/1.44 cnf(c_0_3270, plain, (c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1960]), ['final']). 1.16/1.44 cnf(c_0_3271, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1961]), ['final']). 1.16/1.44 cnf(c_0_3272, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1962]), ['final']). 1.16/1.44 cnf(c_0_3273, plain, (c_Orderings_Oord__class_Oless(X1,esk33_3(X2,X3,X1),c_Groups_Oone__class_Oone(X1))|c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_1436]), ['final']). 1.16/1.44 cnf(c_0_3274, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),esk33_3(X2,X3,X1))|c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_1436]), ['final']). 1.16/1.44 cnf(c_0_3275, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),esk14_3(X2,X3,X1))|c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_1476]), ['final']). 1.16/1.44 cnf(c_0_3276, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1963, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3277, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1964]), ['final']). 1.16/1.44 cnf(c_0_3278, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1965]), ['final']). 1.16/1.44 cnf(c_0_3279, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_1964]), ['final']). 1.16/1.44 cnf(c_0_3280, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_1966]), ['final']). 1.16/1.44 cnf(c_0_3281, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_1293]), ['final']). 1.16/1.44 cnf(c_0_3282, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)=c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1967]), ['final']). 1.16/1.44 cnf(c_0_3283, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1968]), ['final']). 1.16/1.44 cnf(c_0_3284, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_1969]), ['final']). 1.16/1.44 cnf(c_0_3285, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1970]), ['final']). 1.16/1.44 cnf(c_0_3286, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1971, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3287, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1972, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3288, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)=X2|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)), inference(split_conjunct,[status(thm)],[c_0_1973]), ['final']). 1.16/1.44 cnf(c_0_3289, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)!=X3|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_1973]), ['final']). 1.16/1.44 cnf(c_0_3290, plain, (c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3)|~class_RealVector_Oreal__normed__div__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1974]), ['final']). 1.16/1.44 cnf(c_0_3291, plain, (X2=c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1975]), ['final']). 1.16/1.44 cnf(c_0_3292, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1976]), ['final']). 1.16/1.44 cnf(c_0_3293, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1977]), ['final']). 1.16/1.44 cnf(c_0_3294, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_1978]), ['final']). 1.16/1.44 cnf(c_0_3295, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X2,X4))|~c_SEQ_Oincseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_1734]), ['final']). 1.16/1.44 cnf(c_0_3296, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4),hAPP(X2,X3))|~c_SEQ_Odecseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_1735]), ['final']). 1.16/1.44 cnf(c_0_3297, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X1!=X2), inference(rw,[status(thm)],[c_0_1979, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3298, plain, (c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))|~class_Rings_Olinordered__idom(X1)|~c_Polynomial_Opos__poly(X1,X2)|~c_Polynomial_Opos__poly(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_1980]), ['final']). 1.16/1.44 cnf(c_0_3299, plain, (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))), inference(split_conjunct,[status(thm)],[c_0_1981]), ['final']). 1.16/1.44 cnf(c_0_3300, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(rw,[status(thm)],[c_0_1982, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3301, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_1983, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3302, plain, (hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3)=c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Ocoeff(X1,X2),X3))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1984]), ['final']). 1.16/1.44 cnf(c_0_3303, plain, (hAPP(c_Polynomial_Opoly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3)=c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3))|~class_Rings_Ocomm__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_1985]), ['final']). 1.16/1.44 cnf(c_0_3304, plain, (c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)|~c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)|~class_Orderings_Oord(X2)), inference(split_conjunct,[status(thm)],[c_0_1864]), ['final']). 1.16/1.44 cnf(c_0_3305, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1849]), ['final']). 1.16/1.44 cnf(c_0_3306, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1986]), ['final']). 1.16/1.44 cnf(c_0_3307, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1986]), ['final']). 1.16/1.44 cnf(c_0_3308, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1850]), ['final']). 1.16/1.44 cnf(c_0_3309, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_1987]), ['final']). 1.16/1.44 cnf(c_0_3310, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1988]), ['final']). 1.16/1.44 cnf(c_0_3311, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1988]), ['final']). 1.16/1.44 cnf(c_0_3312, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1989]), ['final']). 1.16/1.44 cnf(c_0_3313, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1989]), ['final']). 1.16/1.44 cnf(c_0_3314, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1990]), ['final']). 1.16/1.44 cnf(c_0_3315, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1990]), ['final']). 1.16/1.44 cnf(c_0_3316, plain, (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))), inference(split_conjunct,[status(thm)],[c_0_1991]), ['final']). 1.16/1.44 cnf(c_0_3317, plain, (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))), inference(split_conjunct,[status(thm)],[c_0_1992]), ['final']). 1.16/1.44 cnf(c_0_3318, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Lattices_Oab__semigroup__idem__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_1993]), ['final']). 1.16/1.44 cnf(c_0_3319, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1994, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3320, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1995, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3321, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1996, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3322, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1997, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3323, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)))), inference(split_conjunct,[status(thm)],[c_0_1998]), ['final']). 1.16/1.44 cnf(c_0_3324, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))=X1), inference(split_conjunct,[status(thm)],[c_0_1999]), ['final']). 1.16/1.44 cnf(c_0_3325, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))), inference(split_conjunct,[status(thm)],[c_0_2000]), ['final']). 1.16/1.44 cnf(c_0_3326, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))), inference(split_conjunct,[status(thm)],[c_0_2001]), ['final']). 1.16/1.44 cnf(c_0_3327, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2002]), ['final']). 1.16/1.44 cnf(c_0_3328, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2003]), ['final']). 1.16/1.44 cnf(c_0_3329, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2004]), ['final']). 1.16/1.44 cnf(c_0_3330, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2005]), ['final']). 1.16/1.44 cnf(c_0_3331, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2006]), ['final']). 1.16/1.44 cnf(c_0_3332, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2007]), ['final']). 1.16/1.44 cnf(c_0_3333, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_1964]), ['final']). 1.16/1.44 cnf(c_0_3334, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2008]), ['final']). 1.16/1.44 cnf(c_0_3335, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_2009]), ['final']). 1.16/1.44 cnf(c_0_3336, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_2010]), ['final']). 1.16/1.44 cnf(c_0_3337, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_2011]), ['final']). 1.16/1.44 cnf(c_0_3338, plain, (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), inference(rw,[status(thm)],[c_0_2012, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3339, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_1964]), ['final']). 1.16/1.44 cnf(c_0_3340, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_1964]), ['final']). 1.16/1.44 cnf(c_0_3341, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1960]), ['final']). 1.16/1.44 cnf(c_0_3342, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1961]), ['final']). 1.16/1.44 cnf(c_0_3343, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Lattices_Oboolean__algebra(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_2013]), ['final']). 1.16/1.44 cnf(c_0_3344, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_1962]), ['final']). 1.16/1.44 cnf(c_0_3345, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_2014]), ['final']). 1.16/1.44 cnf(c_0_3346, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_2015, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3347, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2016]), ['final']). 1.16/1.44 cnf(c_0_3348, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)))), inference(split_conjunct,[status(thm)],[c_0_2017]), ['final']). 1.16/1.44 cnf(c_0_3349, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_1964]), ['final']). 1.16/1.44 cnf(c_0_3350, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_1871]), ['final']). 1.16/1.44 cnf(c_0_3351, plain, (X2=c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Oplus__class_Oplus(X1,X3,X2))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2018]), ['final']). 1.16/1.44 cnf(c_0_3352, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2019]), ['final']). 1.16/1.44 cnf(c_0_3353, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2020]), ['final']). 1.16/1.44 cnf(c_0_3354, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2021]), ['final']). 1.16/1.44 cnf(c_0_3355, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2022]), ['final']). 1.16/1.44 cnf(c_0_3356, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_2023]), ['final']). 1.16/1.44 cnf(c_0_3357, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_2024]), ['final']). 1.16/1.44 cnf(c_0_3358, plain, (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_2025]), ['final']). 1.16/1.44 cnf(c_0_3359, plain, (X1=X2|c_Transcendental_Oln(X1)!=c_Transcendental_Oln(X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2026]), ['final']). 1.16/1.44 cnf(c_0_3360, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__0(X1)|~class_Power_Opower(X1)), inference(rw,[status(thm)],[c_0_2027, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3361, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|hBOOL(hAPP(hAPP(X3,X1),X2))|X2=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2028]), ['final']). 1.16/1.44 cnf(c_0_3362, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2002]), ['final']). 1.16/1.44 cnf(c_0_3363, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2003]), ['final']). 1.16/1.44 cnf(c_0_3364, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2005]), ['final']). 1.16/1.44 cnf(c_0_3365, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X2))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2004]), ['final']). 1.16/1.44 cnf(c_0_3366, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2006]), ['final']). 1.16/1.44 cnf(c_0_3367, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2007]), ['final']). 1.16/1.44 cnf(c_0_3368, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2029]), ['final']). 1.16/1.44 cnf(c_0_3369, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_2030]), ['final']). 1.16/1.44 cnf(c_0_3370, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_2031]), ['final']). 1.16/1.44 cnf(c_0_3371, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_1849]), ['final']). 1.16/1.44 cnf(c_0_3372, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_1850]), ['final']). 1.16/1.44 cnf(c_0_3373, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_2032]), ['final']). 1.16/1.44 cnf(c_0_3374, plain, (X2=c_Groups_Ouminus__class_Ouminus(X1,X3)|X3=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2033]), ['final']). 1.16/1.44 cnf(c_0_3375, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk50_2(X2,X1))|~c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_1434]), ['final']). 1.16/1.44 cnf(c_0_3376, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk37_2(X2,X1))|~c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2034]), ['final']). 1.16/1.44 cnf(c_0_3377, plain, (c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))|~class_Rings_Olinordered__idom(X1)|~c_Polynomial_Opos__poly(X1,X2)|~c_Polynomial_Opos__poly(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_2035]), ['final']). 1.16/1.44 cnf(c_0_3378, plain, (X3=X4|X1!=X2|c_Groups_Ominus__class_Ominus(X5,X4,X3)!=c_Groups_Ominus__class_Ominus(X5,X1,X2)|~class_Groups_Oab__group__add(X5)), inference(split_conjunct,[status(thm)],[c_0_2036]), ['final']). 1.16/1.44 cnf(c_0_3379, plain, (X3=X4|X1!=X2|c_Groups_Ominus__class_Ominus(X5,X2,X1)!=c_Groups_Ominus__class_Ominus(X5,X3,X4)|~class_Groups_Oab__group__add(X5)), inference(split_conjunct,[status(thm)],[c_0_2036]), ['final']). 1.16/1.44 cnf(c_0_3380, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2019]), ['final']). 1.16/1.44 cnf(c_0_3381, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2020]), ['final']). 1.16/1.44 cnf(c_0_3382, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2021]), ['final']). 1.16/1.44 cnf(c_0_3383, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2022]), ['final']). 1.16/1.44 cnf(c_0_3384, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_2037, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3385, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_2038, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3386, plain, (c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)|X1!=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))), inference(split_conjunct,[status(thm)],[c_0_2039]), ['final']). 1.16/1.44 cnf(c_0_3387, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(X3,X2,X1)|~c_Orderings_Oord__class_Oless__eq(X3,X2,X1)|~class_Orderings_Olinorder(X3)), inference(split_conjunct,[status(thm)],[c_0_2040]), ['final']). 1.16/1.44 cnf(c_0_3388, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2000]), ['final']). 1.16/1.44 cnf(c_0_3389, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2001]), ['final']). 1.16/1.44 cnf(c_0_3390, plain, (c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))=c_Groups_Ominus__class_Ominus(X1,X3,X2)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2041]), ['final']). 1.16/1.44 cnf(c_0_3391, plain, (X2=X3|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2042]), ['final']). 1.16/1.44 cnf(c_0_3392, plain, (X3=X2|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2043]), ['final']). 1.16/1.44 cnf(c_0_3393, plain, (X2=X3|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2044]), ['final']). 1.16/1.44 cnf(c_0_3394, plain, (X2=X3|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2045]), ['final']). 1.16/1.44 cnf(c_0_3395, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1))), inference(split_conjunct,[status(thm)],[c_0_2046]), ['final']). 1.16/1.44 cnf(c_0_3396, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2047]), ['final']). 1.16/1.44 cnf(c_0_3397, plain, (X4=X2|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X4,X3)|~class_Groups_Ocancel__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2048]), ['final']). 1.16/1.44 cnf(c_0_3398, plain, (X4=X2|~class_Groups_Ocancel__semigroup__add(X1)|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_2049]), ['final']). 1.16/1.44 cnf(c_0_3399, plain, (X3=X4|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X2,X4)|~class_Groups_Ocancel__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2050]), ['final']). 1.16/1.44 cnf(c_0_3400, plain, (X4=X3|~class_Groups_Ocancel__semigroup__add(X1)|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_2051]), ['final']). 1.16/1.44 cnf(c_0_3401, plain, (X4=X3|~class_Groups_Ocancel__ab__semigroup__add(X1)|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_2052]), ['final']). 1.16/1.44 cnf(c_0_3402, plain, (c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_2053]), ['final']). 1.16/1.44 cnf(c_0_3403, plain, (~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2054]), ['final']). 1.16/1.44 cnf(c_0_3404, plain, (~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2055]), ['final']). 1.16/1.44 cnf(c_0_3405, plain, (~class_Orderings_Olinorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2056]), ['final']). 1.16/1.44 cnf(c_0_3406, plain, (~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2057]), ['final']). 1.16/1.44 cnf(c_0_3407, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2058]), ['final']). 1.16/1.44 cnf(c_0_3408, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2059]), ['final']). 1.16/1.44 cnf(c_0_3409, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2060]), ['final']). 1.16/1.44 cnf(c_0_3410, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2061]), ['final']). 1.16/1.44 cnf(c_0_3411, plain, (~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2008]), ['final']). 1.16/1.44 cnf(c_0_3412, plain, (~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2062]), ['final']). 1.16/1.44 cnf(c_0_3413, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))), inference(split_conjunct,[status(thm)],[c_0_2063]), ['final']). 1.16/1.44 cnf(c_0_3414, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_2064]), ['final']). 1.16/1.44 cnf(c_0_3415, plain, (X1=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_2065, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3416, plain, (X1=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_2066, c_0_1393]), c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3417, plain, (c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))=X2|c_Groups_Ozero__class_Ozero(X1)!=hAPP(c_Polynomial_Opoly(X1,X2),X3)|c_Polynomial_Oorder(X1,X3,X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2067]), ['final']). 1.16/1.44 cnf(c_0_3418, plain, (X1=X2|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2068]), ['final']). 1.16/1.44 cnf(c_0_3419, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,esk36_1(X1)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1304]), ['final']). 1.16/1.44 cnf(c_0_3420, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2069]), ['final']). 1.16/1.44 cnf(c_0_3421, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,esk64_1(X1)))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_1658]), ['final']). 1.16/1.44 cnf(c_0_3422, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(rw,[status(thm)],[c_0_2070, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3423, plain, (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))=c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))=X2|~c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2071]), ['final']). 1.16/1.44 cnf(c_0_3424, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_1871]), ['final']). 1.16/1.44 cnf(c_0_3425, plain, (c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)=c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2072]), ['final']). 1.16/1.44 cnf(c_0_3426, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_2073]), ['final']). 1.16/1.44 cnf(c_0_3427, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|X3=c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_2074]), ['final']). 1.16/1.44 cnf(c_0_3428, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))|~class_Rings_Olinordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_2075]), ['final']). 1.16/1.44 cnf(c_0_3429, plain, (X2=X1|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2076]), ['final']). 1.16/1.44 cnf(c_0_3430, plain, (X1=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2077]), ['final']). 1.16/1.44 cnf(c_0_3431, plain, (X1=X2|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2078]), ['final']). 1.16/1.44 cnf(c_0_3432, plain, (X1=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_2079, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3433, plain, (X2=c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2080]), ['final']). 1.16/1.44 cnf(c_0_3434, plain, (X2=c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2081]), ['final']). 1.16/1.44 cnf(c_0_3435, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_2082]), ['final']). 1.16/1.44 cnf(c_0_3436, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_2082]), ['final']). 1.16/1.44 cnf(c_0_3437, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(rw,[status(thm)],[c_0_2083, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3438, plain, (X1=X3|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2084]), ['final']). 1.16/1.44 cnf(c_0_3439, plain, (X3=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_2085]), ['final']). 1.16/1.44 cnf(c_0_3440, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_2046]), ['final']). 1.16/1.44 cnf(c_0_3441, plain, (X1=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_2086, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3442, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_1827]), ['final']). 1.16/1.44 cnf(c_0_3443, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X1!=X2), inference(rw,[status(thm)],[c_0_2087, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3444, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_2088, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3445, plain, (X2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk69_2(X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2089]), ['final']). 1.16/1.44 cnf(c_0_3446, plain, (X2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk13_2(X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2090]), ['final']). 1.16/1.44 cnf(c_0_3447, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk49_2(X1,X2),X1)|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_1627]), ['final']). 1.16/1.44 cnf(c_0_3448, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_2091, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3449, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2092]), ['final']). 1.16/1.44 cnf(c_0_3450, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1)=X2), inference(split_conjunct,[status(thm)],[c_0_2093]), ['final']). 1.16/1.44 cnf(c_0_3451, plain, (X1=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_2094]), ['final']). 1.16/1.44 cnf(c_0_3452, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_2095]), ['final']). 1.16/1.44 cnf(c_0_3453, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_2096]), ['final']). 1.16/1.44 cnf(c_0_3454, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_2097]), ['final']). 1.16/1.44 cnf(c_0_3455, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_2098]), ['final']). 1.16/1.44 cnf(c_0_3456, plain, (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)))=c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))=X2|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2071]), ['final']). 1.16/1.44 cnf(c_0_3457, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)=c_SMT_Oz3div(X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_1959]), ['final']). 1.16/1.44 cnf(c_0_3458, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1))), inference(split_conjunct,[status(thm)],[c_0_2099]), ['final']). 1.16/1.44 cnf(c_0_3459, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_2100]), ['final']). 1.16/1.44 cnf(c_0_3460, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_1866]), ['final']). 1.16/1.44 cnf(c_0_3461, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_1867]), ['final']). 1.16/1.44 cnf(c_0_3462, plain, (~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2))|X2!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2101]), ['final']). 1.16/1.44 cnf(c_0_3463, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk26_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_2102, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3464, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_2103]), ['final']). 1.16/1.44 cnf(c_0_3465, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))), inference(split_conjunct,[status(thm)],[c_0_2104]), ['final']). 1.16/1.44 cnf(c_0_3466, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2105]), ['final']). 1.16/1.44 cnf(c_0_3467, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2099]), ['final']). 1.16/1.44 cnf(c_0_3468, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2106]), ['final']). 1.16/1.44 cnf(c_0_3469, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_2100]), ['final']). 1.16/1.44 cnf(c_0_3470, plain, (X2=X3|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_2107]), ['final']). 1.16/1.44 cnf(c_0_3471, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_2108]), ['final']). 1.16/1.44 cnf(c_0_3472, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_2109]), ['final']). 1.16/1.44 cnf(c_0_3473, plain, (X1=X3|X2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_2110]), ['final']). 1.16/1.44 cnf(c_0_3474, plain, (X2=X3|X1=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_2111]), ['final']). 1.16/1.44 cnf(c_0_3475, plain, (c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)=c_Nat__Transfer_Otsub(X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2112]), ['final']). 1.16/1.44 cnf(c_0_3476, plain, (c_Nat__Transfer_Otsub(X2,X1)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2113]), ['final']). 1.16/1.44 cnf(c_0_3477, plain, (X1=X2|c_Orderings_Oord__class_Oless(X3,X1,X2)|~c_Orderings_Oord__class_Oless__eq(X3,X1,X2)|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_2114]), ['final']). 1.16/1.44 cnf(c_0_3478, plain, (X3=X2|c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2115]), ['final']). 1.16/1.44 cnf(c_0_3479, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|X3=X2|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2040]), ['final']). 1.16/1.44 cnf(c_0_3480, plain, (X3=X2|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_2116]), ['final']). 1.16/1.44 cnf(c_0_3481, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|X3=X2|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2117]), ['final']). 1.16/1.44 cnf(c_0_3482, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_2118]), ['final']). 1.16/1.44 cnf(c_0_3483, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_2119]), ['final']). 1.16/1.44 cnf(c_0_3484, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2120]), ['final']). 1.16/1.44 cnf(c_0_3485, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_2121]), ['final']). 1.16/1.44 cnf(c_0_3486, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1), inference(split_conjunct,[status(thm)],[c_0_1942]), ['final']). 1.16/1.44 cnf(c_0_3487, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2)=c_Groups_Ouminus__class_Ouminus(X1,X2)|~class_Rings_Ocomm__ring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2122]), ['final']). 1.16/1.44 cnf(c_0_3488, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)|X1!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=X2|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_2082]), ['final']). 1.16/1.44 cnf(c_0_3489, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2123]), ['final']). 1.16/1.44 cnf(c_0_3490, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2124]), ['final']). 1.16/1.44 cnf(c_0_3491, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2125]), ['final']). 1.16/1.44 cnf(c_0_3492, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2008]), ['final']). 1.16/1.44 cnf(c_0_3493, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_2126]), ['final']). 1.16/1.44 cnf(c_0_3494, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2117]), ['final']). 1.16/1.44 cnf(c_0_3495, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2114]), ['final']). 1.16/1.44 cnf(c_0_3496, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2127]), ['final']). 1.16/1.44 cnf(c_0_3497, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X2), inference(rw,[status(thm)],[c_0_2128, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3498, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2129]), ['final']). 1.16/1.44 cnf(c_0_3499, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_2130]), ['final']). 1.16/1.44 cnf(c_0_3500, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_2130]), ['final']). 1.16/1.44 cnf(c_0_3501, plain, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2131]), ['final']). 1.16/1.44 cnf(c_0_3502, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))), inference(split_conjunct,[status(thm)],[c_0_2132]), ['final']). 1.16/1.44 cnf(c_0_3503, plain, (~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_2133]), ['final']). 1.16/1.44 cnf(c_0_3504, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_2134]), ['final']). 1.16/1.44 cnf(c_0_3505, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2135]), ['final']). 1.16/1.44 cnf(c_0_3506, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Rings_Ocomm__ring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2136]), ['final']). 1.16/1.44 cnf(c_0_3507, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2137]), ['final']). 1.16/1.44 cnf(c_0_3508, plain, (c_Groups_Oplus__class_Oplus(X1,X2,X3)=c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2138]), ['final']). 1.16/1.44 cnf(c_0_3509, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2139]), ['final']). 1.16/1.44 cnf(c_0_3510, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2140]), ['final']). 1.16/1.44 cnf(c_0_3511, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2141]), ['final']). 1.16/1.44 cnf(c_0_3512, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X1=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2142]), ['final']). 1.16/1.44 cnf(c_0_3513, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2143]), ['final']). 1.16/1.44 cnf(c_0_3514, plain, (X2=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2144]), ['final']). 1.16/1.44 cnf(c_0_3515, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|X2=X1|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2145]), ['final']). 1.16/1.44 cnf(c_0_3516, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2146]), ['final']). 1.16/1.44 cnf(c_0_3517, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2147]), ['final']). 1.16/1.44 cnf(c_0_3518, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2148]), ['final']). 1.16/1.44 cnf(c_0_3519, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2140]), ['final']). 1.16/1.44 cnf(c_0_3520, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(X2,X3))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,X1),X2),X3)|~class_Groups_Ouminus(X1)), inference(split_conjunct,[status(thm)],[c_0_2149]), ['final']). 1.16/1.44 cnf(c_0_3521, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_2089]), ['final']). 1.16/1.44 cnf(c_0_3522, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_2090]), ['final']). 1.16/1.44 cnf(c_0_3523, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2150]), ['final']). 1.16/1.44 cnf(c_0_3524, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2151]), ['final']). 1.16/1.44 cnf(c_0_3525, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_2152]), ['final']). 1.16/1.44 cnf(c_0_3526, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2141]), ['final']). 1.16/1.44 cnf(c_0_3527, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2153]), ['final']). 1.16/1.44 cnf(c_0_3528, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2154]), ['final']). 1.16/1.44 cnf(c_0_3529, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2142]), ['final']). 1.16/1.44 cnf(c_0_3530, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2155]), ['final']). 1.16/1.44 cnf(c_0_3531, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2143]), ['final']). 1.16/1.44 cnf(c_0_3532, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2145]), ['final']). 1.16/1.44 cnf(c_0_3533, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2146]), ['final']). 1.16/1.44 cnf(c_0_3534, plain, (~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_2156]), ['final']). 1.16/1.44 cnf(c_0_3535, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Rings_Oidom(X2)), inference(split_conjunct,[status(thm)],[c_0_2033]), ['final']). 1.16/1.44 cnf(c_0_3536, plain, (c_Groups_Oabs__class_Oabs(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,X2)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oabs__if(X1)), inference(split_conjunct,[status(thm)],[c_0_2157]), ['final']). 1.16/1.44 cnf(c_0_3537, plain, (c_Groups_Ouminus__class_Ouminus(X1,X2)=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_2158]), ['final']). 1.16/1.44 cnf(c_0_3538, plain, (c_Groups_Ouminus__class_Ouminus(X1,X2)=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_2159]), ['final']). 1.16/1.44 cnf(c_0_3539, plain, (c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_2160, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3540, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_2161]), ['final']). 1.16/1.44 cnf(c_0_3541, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2162]), ['final']). 1.16/1.44 cnf(c_0_3542, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2163]), ['final']). 1.16/1.44 cnf(c_0_3543, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2164]), ['final']). 1.16/1.44 cnf(c_0_3544, plain, (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))), inference(split_conjunct,[status(thm)],[c_0_2165]), ['final']). 1.16/1.44 cnf(c_0_3545, plain, (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))), inference(split_conjunct,[status(thm)],[c_0_2166]), ['final']). 1.16/1.44 cnf(c_0_3546, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_2167]), ['final']). 1.16/1.44 cnf(c_0_3547, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_2168]), ['final']). 1.16/1.44 cnf(c_0_3548, plain, (X1=X2|hAPP(X1,esk62_2(X1,X2))!=hAPP(X2,esk62_2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_2169]), ['final']). 1.16/1.44 cnf(c_0_3549, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk40_2(X1,X2),esk41_2(X1,X2))|c_SEQ_Oincseq(X2,X1)|~class_Orderings_Oorder(X2)), inference(split_conjunct,[status(thm)],[c_0_1734]), ['final']). 1.16/1.44 cnf(c_0_3550, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk18_2(X1,X2),esk19_2(X1,X2))|c_SEQ_Odecseq(X2,X1)|~class_Orderings_Oorder(X2)), inference(split_conjunct,[status(thm)],[c_0_1735]), ['final']). 1.16/1.44 cnf(c_0_3551, plain, (c_Groups_Oone__class_Oone(X1)=c_Groups_Osgn__class_Osgn(X1,X2)|X2=c_Groups_Ozero__class_Ozero(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_2170]), ['final']). 1.16/1.44 cnf(c_0_3552, plain, (X1=X2|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))), inference(split_conjunct,[status(thm)],[c_0_2171]), ['final']). 1.16/1.44 cnf(c_0_3553, plain, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_2172]), ['final']). 1.16/1.44 cnf(c_0_3554, plain, (X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Omult__zero(X2)|~class_Rings_Ozero__neq__one(X2)|~class_Rings_Ono__zero__divisors(X2)|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_2173]), ['final']). 1.16/1.44 cnf(c_0_3555, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_2173]), ['final']). 1.16/1.44 cnf(c_0_3556, plain, (X2=c_Groups_Oone__class_Oone(X1)|c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_2174]), ['final']). 1.16/1.44 cnf(c_0_3557, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2151]), ['final']). 1.16/1.44 cnf(c_0_3558, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2175]), ['final']). 1.16/1.44 cnf(c_0_3559, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_2176]), ['final']). 1.16/1.44 cnf(c_0_3560, plain, (c_Orderings_Oord__class_Oless__eq(X3,X2,X1)|c_Orderings_Oord__class_Oless(X3,X2,X1)|X1!=X2|~class_Orderings_Olinorder(X3)), inference(split_conjunct,[status(thm)],[c_0_2115]), ['final']). 1.16/1.44 cnf(c_0_3561, plain, (X1=X2|c_Orderings_Oord__class_Oless(X3,X2,X1)|c_Orderings_Oord__class_Oless(X3,X1,X2)|~class_Orderings_Olinorder(X3)), inference(split_conjunct,[status(thm)],[c_0_2177]), ['final']). 1.16/1.44 cnf(c_0_3562, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2178]), ['final']). 1.16/1.44 cnf(c_0_3563, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2179]), ['final']). 1.16/1.44 cnf(c_0_3564, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|X3=X2|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2180]), ['final']). 1.16/1.44 cnf(c_0_3565, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2181]), ['final']). 1.16/1.44 cnf(c_0_3566, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2054]), ['final']). 1.16/1.44 cnf(c_0_3567, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2182]), ['final']). 1.16/1.44 cnf(c_0_3568, plain, (X2=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_2183]), ['final']). 1.16/1.44 cnf(c_0_3569, plain, (X2=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_2184]), ['final']). 1.16/1.44 cnf(c_0_3570, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2185]), ['final']). 1.16/1.44 cnf(c_0_3571, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2057]), ['final']). 1.16/1.44 cnf(c_0_3572, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2186]), ['final']). 1.16/1.44 cnf(c_0_3573, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2055]), ['final']). 1.16/1.44 cnf(c_0_3574, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2187]), ['final']). 1.16/1.44 cnf(c_0_3575, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2188]), ['final']). 1.16/1.44 cnf(c_0_3576, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2189]), ['final']). 1.16/1.44 cnf(c_0_3577, plain, (c_Groups_Oplus__class_Oplus(X1,X2,X3)=c_Groups_Oplus__class_Oplus(X1,X3,X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2190]), ['final']). 1.16/1.44 cnf(c_0_3578, plain, (c_Groups_Ouminus__class_Ouminus(X1,X2)=X3|~class_Groups_Ogroup__add(X1)|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Oplus__class_Oplus(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_2191]), ['final']). 1.16/1.44 cnf(c_0_3579, plain, (X2=c_Groups_Ouminus__class_Ouminus(X1,X3)|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2192]), ['final']). 1.16/1.44 cnf(c_0_3580, plain, (X3=c_Groups_Ouminus__class_Ouminus(X1,X2)|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Oplus__class_Oplus(X1,X2,X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2193]), ['final']). 1.16/1.44 cnf(c_0_3581, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oabs__class_Oabs(X1,X2))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2194]), ['final']). 1.16/1.44 cnf(c_0_3582, plain, (c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_2195]), ['final']). 1.16/1.44 cnf(c_0_3583, plain, (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_2196]), ['final']). 1.16/1.44 cnf(c_0_3584, plain, (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_2197]), ['final']). 1.16/1.44 cnf(c_0_3585, plain, (~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_2198]), ['final']). 1.16/1.44 cnf(c_0_3586, plain, (~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))), inference(split_conjunct,[status(thm)],[c_0_2199]), ['final']). 1.16/1.44 cnf(c_0_3587, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_2200]), ['final']). 1.16/1.44 cnf(c_0_3588, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk50_2(X1,X2))|~c_SEQ_OBseq(X2,X1)|~class_RealVector_Oreal__normed__vector(X2)), inference(split_conjunct,[status(thm)],[c_0_1434]), ['final']). 1.16/1.44 cnf(c_0_3589, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk37_2(X1,X2))|~c_SEQ_OBseq(X2,X1)|~class_RealVector_Oreal__normed__vector(X2)), inference(split_conjunct,[status(thm)],[c_0_2034]), ['final']). 1.16/1.44 cnf(c_0_3590, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk10_2(X1,X2))|~c_SEQ_OBseq(X2,X1)|~class_RealVector_Oreal__normed__vector(X2)), inference(split_conjunct,[status(thm)],[c_0_1372]), ['final']). 1.16/1.44 cnf(c_0_3591, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_2(X1,X2))|~c_SEQ_OBseq(X2,X1)|~class_RealVector_Oreal__normed__vector(X2)), inference(split_conjunct,[status(thm)],[c_0_1373]), ['final']). 1.16/1.44 cnf(c_0_3592, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_2201, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3593, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2202]), ['final']). 1.16/1.44 cnf(c_0_3594, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(rw,[status(thm)],[c_0_2203, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3595, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|X1=X2), inference(split_conjunct,[status(thm)],[c_0_2204]), ['final']). 1.16/1.44 cnf(c_0_3596, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2205]), ['final']). 1.16/1.44 cnf(c_0_3597, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2206]), ['final']). 1.16/1.44 cnf(c_0_3598, plain, (c_Polynomial_Oorder(X1,X2,X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(X1)=hAPP(c_Polynomial_Opoly(X1,X3),X2)|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2067]), ['final']). 1.16/1.44 cnf(c_0_3599, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_2170]), ['final']). 1.16/1.44 cnf(c_0_3600, plain, (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))|X2=c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X1),X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2072]), ['final']). 1.16/1.44 cnf(c_0_3601, plain, (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2207]), ['final']). 1.16/1.44 cnf(c_0_3602, plain, (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2208]), ['final']). 1.16/1.44 cnf(c_0_3603, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_2209]), ['final']). 1.16/1.44 cnf(c_0_3604, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2210]), ['final']). 1.16/1.44 cnf(c_0_3605, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2211]), ['final']). 1.16/1.44 cnf(c_0_3606, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2212]), ['final']). 1.16/1.44 cnf(c_0_3607, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_2213]), ['final']). 1.16/1.44 cnf(c_0_3608, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Rings_Ono__zero__divisors(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_2214]), ['final']). 1.16/1.44 cnf(c_0_3609, plain, (c_Groups_Ozero__class_Ozero(X1)=X3|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ono__zero__divisors(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_2215]), ['final']). 1.16/1.44 cnf(c_0_3610, plain, (c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2216]), ['final']). 1.16/1.44 cnf(c_0_3611, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2217]), ['final']). 1.16/1.44 cnf(c_0_3612, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_2218]), ['final']). 1.16/1.44 cnf(c_0_3613, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,X2,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2219]), ['final']). 1.16/1.44 cnf(c_0_3614, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Oplus__class_Oplus(X1,X2,X2)|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2220]), ['final']). 1.16/1.44 cnf(c_0_3615, plain, (c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2221]), ['final']). 1.16/1.44 cnf(c_0_3616, plain, (c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=X1|c_Transcendental_Oln(X1)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2222]), ['final']). 1.16/1.44 cnf(c_0_3617, plain, (c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Ozero__class_Ozero(X2))|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__ab__group__add__abs(X2)), inference(split_conjunct,[status(thm)],[c_0_2125]), ['final']). 1.16/1.44 cnf(c_0_3618, plain, (X2=X3|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2223]), ['final']). 1.16/1.44 cnf(c_0_3619, plain, (X3=X2|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2224]), ['final']). 1.16/1.44 cnf(c_0_3620, plain, (c_Transcendental_Oln(X1)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=X1|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)), inference(split_conjunct,[status(thm)],[c_0_2222]), ['final']). 1.16/1.44 cnf(c_0_3621, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~class_Rings_Oring__1__no__zero__divisors(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_2225]), ['final']). 1.16/1.44 cnf(c_0_3622, plain, (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)=X2|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2226]), ['final']). 1.16/1.44 cnf(c_0_3623, plain, (c_Groups_Ozero__class_Ozero(X2)=X3|X1!=c_Groups_Oplus__class_Oplus(X2,X1,X3)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)), inference(split_conjunct,[status(thm)],[c_0_2227]), ['final']). 1.16/1.44 cnf(c_0_3624, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oabs__class_Oabs(X2,X1))|~class_Groups_Oordered__ab__group__add__abs(X2)), inference(split_conjunct,[status(thm)],[c_0_2101]), ['final']). 1.16/1.44 cnf(c_0_3625, plain, (c_Groups_Oabs__class_Oabs(X1,X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2228]), ['final']). 1.16/1.44 cnf(c_0_3626, plain, (c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))=X2|c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))!=c_Polynomial_Opoly(X1,X2)|~class_Int_Oring__char__0(X1)|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2229]), ['final']). 1.16/1.44 cnf(c_0_3627, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_2107]), ['final']). 1.16/1.44 cnf(c_0_3628, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_2108]), ['final']). 1.16/1.44 cnf(c_0_3629, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2109]), ['final']). 1.16/1.44 cnf(c_0_3630, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2139]), ['final']). 1.16/1.44 cnf(c_0_3631, plain, (X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Omult__zero(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_2173]), ['final']). 1.16/1.44 cnf(c_0_3632, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))!=X2|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_2174]), ['final']). 1.16/1.44 cnf(c_0_3633, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(X3,X1,X2)|~class_Orderings_Olinorder(X3)), inference(split_conjunct,[status(thm)],[c_0_2054]), ['final']). 1.16/1.44 cnf(c_0_3634, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(X3,X1,X2)|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_2114]), ['final']). 1.16/1.44 cnf(c_0_3635, plain, (~c_Orderings_Oord__class_Oless(X1,X2,X3)|X3!=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2177]), ['final']). 1.16/1.44 cnf(c_0_3636, plain, (~c_Orderings_Oord__class_Oless(X1,X2,X3)|X2!=X3|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2177]), ['final']). 1.16/1.44 cnf(c_0_3637, plain, (~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|X3!=X2), inference(split_conjunct,[status(thm)],[c_0_2230]), ['final']). 1.16/1.44 cnf(c_0_3638, plain, (~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|X2!=X3), inference(split_conjunct,[status(thm)],[c_0_2231]), ['final']). 1.16/1.44 cnf(c_0_3639, plain, (~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|X2!=X3), inference(split_conjunct,[status(thm)],[c_0_2232]), ['final']). 1.16/1.44 cnf(c_0_3640, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2175]), ['final']). 1.16/1.44 cnf(c_0_3641, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_RComplete_Onatfloor(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_2233]), ['final']). 1.16/1.44 cnf(c_0_3642, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_RComplete_Onatceiling(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[c_0_2234]), ['final']). 1.16/1.44 cnf(c_0_3643, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2131]), ['final']). 1.16/1.44 cnf(c_0_3644, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_2235]), ['final']). 1.16/1.44 cnf(c_0_3645, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2236]), ['final']). 1.16/1.44 cnf(c_0_3646, plain, (hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2))),X1)=c_Groups_Oone__class_Oone(X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~class_Rings_Ocomm__semiring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_2237]), ['final']). 1.16/1.44 cnf(c_0_3647, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X2)), inference(split_conjunct,[status(thm)],[c_0_2238]), ['final']). 1.16/1.44 cnf(c_0_3648, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_2239]), ['final']). 1.16/1.44 cnf(c_0_3649, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_2240, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3650, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_2241, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3651, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_2242, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3652, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_2243, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3653, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_2244, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3654, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_2245, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3655, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_2246]), ['final']). 1.16/1.44 cnf(c_0_3656, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_2247]), ['final']). 1.16/1.44 cnf(c_0_3657, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_2248]), ['final']). 1.16/1.44 cnf(c_0_3658, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(X2)=hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2))),X1)|~class_Rings_Ocomm__semiring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_2237]), ['final']). 1.16/1.44 cnf(c_0_3659, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2249]), ['final']). 1.16/1.44 cnf(c_0_3660, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2250]), ['final']). 1.16/1.44 cnf(c_0_3661, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2251]), ['final']). 1.16/1.44 cnf(c_0_3662, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2252]), ['final']). 1.16/1.44 cnf(c_0_3663, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2252]), ['final']). 1.16/1.44 cnf(c_0_3664, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2), inference(split_conjunct,[status(thm)],[c_0_2253]), ['final']). 1.16/1.44 cnf(c_0_3665, plain, (X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_2254, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3666, plain, (X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_2255, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3667, plain, (c_Groups_Oplus__class_Oplus(X2,X1,X3)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2192]), ['final']). 1.16/1.44 cnf(c_0_3668, plain, (c_Groups_Ozero__class_Ozero(X2)=c_Groups_Oplus__class_Oplus(X2,X3,X1)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2193]), ['final']). 1.16/1.44 cnf(c_0_3669, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk52_2(X1,X2))|~class_RealVector_Oreal__normed__algebra(X2)), inference(split_conjunct,[status(thm)],[c_0_1532]), ['final']). 1.16/1.44 cnf(c_0_3670, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk17_2(X1,X2))|~class_RealVector_Oreal__normed__algebra(X2)), inference(split_conjunct,[status(thm)],[c_0_1529]), ['final']). 1.16/1.44 cnf(c_0_3671, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk55_2(X1,X2))|~class_RealVector_Oreal__normed__algebra(X2)), inference(split_conjunct,[status(thm)],[c_0_1531]), ['final']). 1.16/1.44 cnf(c_0_3672, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk46_2(X1,X2))|~class_RealVector_Oreal__normed__algebra(X2)), inference(split_conjunct,[status(thm)],[c_0_1528]), ['final']). 1.16/1.44 cnf(c_0_3673, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2256]), ['final']). 1.16/1.44 cnf(c_0_3674, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1)=c_Groups_Oone__class_Oone(X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~class_Rings_Osemiring__0(X2)|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_2257]), ['final']). 1.16/1.44 cnf(c_0_3675, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_2258]), ['final']). 1.16/1.44 cnf(c_0_3676, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_2259]), ['final']). 1.16/1.44 cnf(c_0_3677, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_2260]), ['final']). 1.16/1.44 cnf(c_0_3678, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_2261]), ['final']). 1.16/1.44 cnf(c_0_3679, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1), inference(split_conjunct,[status(thm)],[c_0_2207]), ['final']). 1.16/1.44 cnf(c_0_3680, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1), inference(split_conjunct,[status(thm)],[c_0_2208]), ['final']). 1.16/1.44 cnf(c_0_3681, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_2209]), ['final']). 1.16/1.44 cnf(c_0_3682, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1)))), inference(split_conjunct,[status(thm)],[c_0_2262]), ['final']). 1.16/1.44 cnf(c_0_3683, plain, (hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_2263]), ['final']). 1.16/1.44 cnf(c_0_3684, plain, (hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_2264]), ['final']). 1.16/1.44 cnf(c_0_3685, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2265]), ['final']). 1.16/1.44 cnf(c_0_3686, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oabs__class_Oabs(X1,X2))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2266]), ['final']). 1.16/1.44 cnf(c_0_3687, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2141]), ['final']). 1.16/1.44 cnf(c_0_3688, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X2!=X1), inference(split_conjunct,[status(thm)],[c_0_2267]), ['final']). 1.16/1.44 cnf(c_0_3689, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2143]), ['final']). 1.16/1.44 cnf(c_0_3690, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_2206]), ['final']). 1.16/1.44 cnf(c_0_3691, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X2!=X1), inference(split_conjunct,[status(thm)],[c_0_2206]), ['final']). 1.16/1.44 cnf(c_0_3692, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_2268]), ['final']). 1.16/1.44 cnf(c_0_3693, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_2146]), ['final']). 1.16/1.44 cnf(c_0_3694, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Osgn__class_Osgn(X1,X2))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2269]), ['final']). 1.16/1.44 cnf(c_0_3695, plain, (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)=X2|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2270]), ['final']). 1.16/1.44 cnf(c_0_3696, plain, (X2=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2271]), ['final']). 1.16/1.44 cnf(c_0_3697, plain, (X2=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2272]), ['final']). 1.16/1.44 cnf(c_0_3698, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1)=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Osemiring__0(X2)|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_2257]), ['final']). 1.16/1.44 cnf(c_0_3699, plain, (c_Polynomial_Opos__poly(X1,X2)|c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2))|X2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2273]), ['final']). 1.16/1.44 cnf(c_0_3700, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_2167]), ['final']). 1.16/1.44 cnf(c_0_3701, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_2168]), ['final']). 1.16/1.44 cnf(c_0_3702, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_2274]), ['final']). 1.16/1.44 cnf(c_0_3703, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1)), inference(split_conjunct,[status(thm)],[c_0_2275]), ['final']). 1.16/1.44 cnf(c_0_3704, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1)), inference(split_conjunct,[status(thm)],[c_0_2276]), ['final']). 1.16/1.44 cnf(c_0_3705, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|X2=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oabs__if(X1)), inference(split_conjunct,[status(thm)],[c_0_2157]), ['final']). 1.16/1.44 cnf(c_0_3706, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_2171]), ['final']). 1.16/1.44 cnf(c_0_3707, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oone__class_Oone(tc_Nat_Onat)=X2|X1!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_2277]), ['final']). 1.16/1.44 cnf(c_0_3708, plain, (c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2)=c_Groups_Ouminus__class_Ouminus(X1,X2)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2278]), ['final']). 1.16/1.44 cnf(c_0_3709, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2279]), ['final']). 1.16/1.44 cnf(c_0_3710, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2279]), ['final']). 1.16/1.44 cnf(c_0_3711, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_2280]), ['final']). 1.16/1.44 cnf(c_0_3712, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_2280]), ['final']). 1.16/1.44 cnf(c_0_3713, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1))), inference(split_conjunct,[status(thm)],[c_0_2281]), ['final']). 1.16/1.44 cnf(c_0_3714, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1)), inference(split_conjunct,[status(thm)],[c_0_2282]), ['final']). 1.16/1.44 cnf(c_0_3715, plain, (c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))=c_Power_Opower__class_Opower(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_2283]), ['final']). 1.16/1.44 cnf(c_0_3716, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)|c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_2226]), ['final']). 1.16/1.44 cnf(c_0_3717, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))), inference(split_conjunct,[status(thm)],[fact__0960_A_060_061_Acmod_Ac_096]), ['final']). 1.16/1.44 cnf(c_0_3718, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2284]), ['final']). 1.16/1.44 cnf(c_0_3719, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_2285]), ['final']). 1.16/1.44 cnf(c_0_3720, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_2286]), ['final']). 1.16/1.44 cnf(c_0_3721, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_2287]), ['final']). 1.16/1.44 cnf(c_0_3722, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_2288]), ['final']). 1.16/1.44 cnf(c_0_3723, plain, (c_Groups_Oplus__class_Oplus(X1,X2,X2)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2219]), ['final']). 1.16/1.44 cnf(c_0_3724, plain, (c_Groups_Ozero__class_Ozero(X2)=c_Groups_Oplus__class_Oplus(X2,X1,X1)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Olinordered__ab__group__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2220]), ['final']). 1.16/1.44 cnf(c_0_3725, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2289]), ['final']). 1.16/1.44 cnf(c_0_3726, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2290]), ['final']). 1.16/1.44 cnf(c_0_3727, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_2291]), ['final']). 1.16/1.44 cnf(c_0_3728, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_2292]), ['final']). 1.16/1.44 cnf(c_0_3729, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2293]), ['final']). 1.16/1.44 cnf(c_0_3730, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_2213]), ['final']). 1.16/1.44 cnf(c_0_3731, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_2213]), ['final']). 1.16/1.44 cnf(c_0_3732, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)=c_Groups_Oone__class_Oone(X2)|X1!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(split_conjunct,[status(thm)],[c_0_2174]), ['final']). 1.16/1.44 cnf(c_0_3733, plain, (c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_2294]), ['final']). 1.16/1.44 cnf(c_0_3734, plain, (c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_2295]), ['final']). 1.16/1.44 cnf(c_0_3735, plain, (c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X3),X2,X1)|X1!=X2|~class_Rings_Olinordered__idom(X3)), inference(split_conjunct,[status(thm)],[c_0_1873]), ['final']). 1.16/1.44 cnf(c_0_3736, plain, (X3=c_Groups_Oplus__class_Oplus(X1,X3,X2)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(split_conjunct,[status(thm)],[c_0_2227]), ['final']). 1.16/1.44 cnf(c_0_3737, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Divides_Odiv__class_Odiv(X1,X2,X2)=c_Groups_Oone__class_Oone(X1)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_2296]), ['final']). 1.16/1.44 cnf(c_0_3738, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)=X1), inference(split_conjunct,[status(thm)],[c_0_2195]), ['final']). 1.16/1.44 cnf(c_0_3739, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)=X1), inference(split_conjunct,[status(thm)],[c_0_2197]), ['final']). 1.16/1.44 cnf(c_0_3740, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|X1=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)), inference(split_conjunct,[status(thm)],[c_0_2196]), ['final']). 1.16/1.44 cnf(c_0_3741, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|c_Nat__Transfer_Otsub(X2,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_2112]), ['final']). 1.16/1.44 cnf(c_0_3742, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2297]), ['final']). 1.16/1.44 cnf(c_0_3743, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_2298]), ['final']). 1.16/1.44 cnf(c_0_3744, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_2299]), ['final']). 1.16/1.44 cnf(c_0_3745, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Omult__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_2300]), ['final']). 1.16/1.44 cnf(c_0_3746, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk47_1(X1))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1408]), ['final']). 1.16/1.44 cnf(c_0_3747, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_1(X1))|~class_RealVector_Oreal__normed__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_1410]), ['final']). 1.16/1.44 cnf(c_0_3748, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)=c_Groups_Oone__class_Oone(X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_1628]), ['final']). 1.16/1.44 cnf(c_0_3749, plain, (c_Groups_Ozero__class_Ozero(X3)=c_Groups_Ominus__class_Ominus(X3,X1,X2)|X1!=X2|~class_Groups_Oab__group__add(X3)), inference(split_conjunct,[status(thm)],[c_0_2223]), ['final']). 1.16/1.44 cnf(c_0_3750, plain, (c_Groups_Ozero__class_Ozero(X3)=c_Groups_Ominus__class_Ominus(X3,X2,X1)|X1!=X2|~class_Groups_Ogroup__add(X3)), inference(split_conjunct,[status(thm)],[c_0_2224]), ['final']). 1.16/1.44 cnf(c_0_3751, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(c_Polynomial_Opoly(X1,X2),X3)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))!=X2|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2067]), ['final']). 1.16/1.44 cnf(c_0_3752, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2)=X2|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2301]), ['final']). 1.16/1.44 cnf(c_0_3753, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2)=X2|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2302]), ['final']). 1.16/1.44 cnf(c_0_3754, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2303]), ['final']). 1.16/1.44 cnf(c_0_3755, plain, (X2=c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2304]), ['final']). 1.16/1.44 cnf(c_0_3756, plain, (X2=c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_2305]), ['final']). 1.16/1.44 cnf(c_0_3757, plain, (X2=c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2306]), ['final']). 1.16/1.44 cnf(c_0_3758, plain, (X2=c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2307]), ['final']). 1.16/1.44 cnf(c_0_3759, plain, (X2=c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2308]), ['final']). 1.16/1.44 cnf(c_0_3760, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2), inference(split_conjunct,[status(thm)],[c_0_2252]), ['final']). 1.16/1.44 cnf(c_0_3761, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_2309]), ['final']). 1.16/1.44 cnf(c_0_3762, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2310]), ['final']). 1.16/1.44 cnf(c_0_3763, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_2311]), ['final']). 1.16/1.44 cnf(c_0_3764, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_2312]), ['final']). 1.16/1.44 cnf(c_0_3765, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2313]), ['final']). 1.16/1.44 cnf(c_0_3766, plain, (c_Groups_Ominus__class_Ominus(X1,X2,X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2314]), ['final']). 1.16/1.44 cnf(c_0_3767, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|X2!=X3|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2042]), ['final']). 1.16/1.44 cnf(c_0_3768, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|X3!=X2|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2042]), ['final']). 1.16/1.44 cnf(c_0_3769, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Orderings_Opreorder(X1)|X2!=X3), inference(split_conjunct,[status(thm)],[c_0_2315]), ['final']). 1.16/1.44 cnf(c_0_3770, plain, (c_Orderings_Oord__class_Oless__eq(X3,X2,X1)|X1!=X2|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_2117]), ['final']). 1.16/1.44 cnf(c_0_3771, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_2316]), ['final']). 1.16/1.44 cnf(c_0_3772, plain, (X2=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2317]), ['final']). 1.16/1.44 cnf(c_0_3773, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X1))), inference(split_conjunct,[status(thm)],[c_0_2318]), ['final']). 1.16/1.44 cnf(c_0_3774, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X1))), inference(split_conjunct,[status(thm)],[c_0_2319]), ['final']). 1.16/1.44 cnf(c_0_3775, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2239]), ['final']). 1.16/1.44 cnf(c_0_3776, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X2)|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2320]), ['final']). 1.16/1.44 cnf(c_0_3777, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_2321, c_0_1393]), ['final']). 1.16/1.44 cnf(c_0_3778, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_1964]), ['final']). 1.16/1.44 cnf(c_0_3779, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2322]), ['final']). 1.16/1.44 cnf(c_0_3780, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2))=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2323]), ['final']). 1.16/1.44 cnf(c_0_3781, plain, (c_Groups_Oabs__class_Oabs(X1,X2)=c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2324]), ['final']). 1.16/1.44 cnf(c_0_3782, plain, (c_RealVector_Onorm__class_Onorm(X1,X2)=c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2325]), ['final']). 1.16/1.44 cnf(c_0_3783, plain, (X2=X3|c_Polynomial_Opoly(X1,X2)!=c_Polynomial_Opoly(X1,X3)|~class_Int_Oring__char__0(X1)|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2326]), ['final']). 1.16/1.44 cnf(c_0_3784, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=X2), inference(split_conjunct,[status(thm)],[c_0_2279]), ['final']). 1.16/1.44 cnf(c_0_3785, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)|X1!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2280]), ['final']). 1.16/1.44 cnf(c_0_3786, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Lattices_Oab__semigroup__idem__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_2327]), ['final']). 1.16/1.44 cnf(c_0_3787, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Lattices_Oab__semigroup__idem__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_2328]), ['final']). 1.16/1.44 cnf(c_0_3788, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_2235]), ['final']). 1.16/1.44 cnf(c_0_3789, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_2329]), ['final']). 1.16/1.44 cnf(c_0_3790, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_1301]), ['final']). 1.16/1.44 cnf(c_0_3791, plain, (c_RealVector_Onorm__class_Onorm(X1,X2)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2330]), ['final']). 1.16/1.44 cnf(c_0_3792, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_2331]), ['final']). 1.16/1.44 cnf(c_0_3793, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_int__0__less__1]), ['final']). 1.16/1.44 cnf(c_0_3794, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]), ['final']). 1.16/1.44 cnf(c_0_3795, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]), ['final']). 1.16/1.44 cnf(c_0_3796, plain, (~class_Rings_Olinordered__idom(X1)|~c_Polynomial_Opos__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))), inference(split_conjunct,[status(thm)],[c_0_2332]), ['final']). 1.16/1.44 cnf(c_0_3797, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_2333]), ['final']). 1.16/1.44 cnf(c_0_3798, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_2334]), ['final']). 1.16/1.44 cnf(c_0_3799, plain, (c_RealVector_Onorm__class_Onorm(X2,c_Groups_Osgn__class_Osgn(X2,X1))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_RealVector_Oreal__normed__vector(X2)), inference(split_conjunct,[status(thm)],[c_0_2335]), ['final']). 1.16/1.44 cnf(c_0_3800, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_2336]), ['final']). 1.16/1.44 cnf(c_0_3801, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_2337]), ['final']). 1.16/1.44 cnf(c_0_3802, plain, (X1=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_2338]), ['final']). 1.16/1.44 cnf(c_0_3803, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_2339]), ['final']). 1.16/1.44 cnf(c_0_3804, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_2340]), ['final']). 1.16/1.44 cnf(c_0_3805, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_2142]), ['final']). 1.16/1.44 cnf(c_0_3806, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_2341]), ['final']). 1.16/1.44 cnf(c_0_3807, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_2155]), ['final']). 1.16/1.44 cnf(c_0_3808, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_2145]), ['final']). 1.16/1.44 cnf(c_0_3809, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_2342]), ['final']). 1.16/1.44 cnf(c_0_3810, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_2343]), ['final']). 1.16/1.44 cnf(c_0_3811, plain, (c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2344]), ['final']). 1.16/1.44 cnf(c_0_3812, plain, (c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))!=X2|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2071]), ['final']). 1.16/1.44 cnf(c_0_3813, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)), inference(split_conjunct,[status(thm)],[c_0_2345]), ['final']). 1.16/1.44 cnf(c_0_3814, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(X2,c_Groups_Osgn__class_Osgn(X2,X1))|~class_RealVector_Oreal__normed__vector(X2)), inference(split_conjunct,[status(thm)],[c_0_2335]), ['final']). 1.16/1.44 cnf(c_0_3815, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_2346]), ['final']). 1.16/1.44 cnf(c_0_3816, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk31_0)), inference(split_conjunct,[status(thm)],[c_0_1809]), ['final']). 1.16/1.44 cnf(c_0_3817, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_1479]), ['final']). 1.16/1.44 cnf(c_0_3818, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_1668]), ['final']). 1.16/1.44 cnf(c_0_3819, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_2274]), ['final']). 1.16/1.45 cnf(c_0_3820, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_2274]), ['final']). 1.16/1.45 cnf(c_0_3821, plain, (X3=X2|c_Polynomial_Ocoeff(X1,X2)!=c_Polynomial_Ocoeff(X1,X3)|~class_Groups_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_2347]), ['final']). 1.16/1.45 cnf(c_0_3822, plain, (X2=X3|c_Groups_Ouminus__class_Ouminus(X1,X2)!=c_Groups_Ouminus__class_Ouminus(X1,X3)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_2348]), ['final']). 1.16/1.45 cnf(c_0_3823, plain, (X2=X3|c_Groups_Ouminus__class_Ouminus(X1,X2)!=c_Groups_Ouminus__class_Ouminus(X1,X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2349]), ['final']). 1.16/1.45 cnf(c_0_3824, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_2350]), ['final']). 1.16/1.45 cnf(c_0_3825, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)), inference(split_conjunct,[status(thm)],[c_0_2351]), ['final']). 1.16/1.45 cnf(c_0_3826, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_2352]), ['final']). 1.16/1.45 cnf(c_0_3827, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1)), inference(split_conjunct,[status(thm)],[c_0_2353]), ['final']). 1.16/1.45 cnf(c_0_3828, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)), inference(split_conjunct,[status(thm)],[c_0_2354]), ['final']). 1.16/1.45 cnf(c_0_3829, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1)), inference(split_conjunct,[status(thm)],[c_0_2355]), ['final']). 1.16/1.45 cnf(c_0_3830, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_2356]), ['final']). 1.16/1.45 cnf(c_0_3831, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1), inference(split_conjunct,[status(thm)],[c_0_2357]), ['final']). 1.16/1.45 cnf(c_0_3832, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_2358]), ['final']). 1.16/1.45 cnf(c_0_3833, plain, (c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=X2|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_2359]), ['final']). 1.16/1.45 cnf(c_0_3834, plain, (X2=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2360]), ['final']). 1.16/1.45 cnf(c_0_3835, plain, (c_RealDef_Oreal(tc_Nat_Onat,X1)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1))), inference(split_conjunct,[status(thm)],[c_0_2361]), ['final']). 1.16/1.45 cnf(c_0_3836, plain, (c_Groups_Ouminus__class_Ouminus(X2,X1)=X3|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2362]), ['final']). 1.16/1.45 cnf(c_0_3837, plain, (X2=c_Groups_Ouminus__class_Ouminus(X1,X3)|c_Groups_Ouminus__class_Ouminus(X1,X2)!=X3|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2362]), ['final']). 1.16/1.45 cnf(c_0_3838, plain, (X3=c_Groups_Ouminus__class_Ouminus(X2,X1)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2363]), ['final']). 1.16/1.45 cnf(c_0_3839, plain, (X3=c_Groups_Ouminus__class_Ouminus(X2,X1)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2363]), ['final']). 1.16/1.45 cnf(c_0_3840, plain, (X1=X2|c_RealDef_Oreal(tc_Nat_Onat,X1)!=c_RealDef_Oreal(tc_Nat_Onat,X2)), inference(split_conjunct,[status(thm)],[c_0_2364]), ['final']). 1.16/1.45 cnf(c_0_3841, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2365]), ['final']). 1.16/1.45 cnf(c_0_3842, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Osgn__class_Osgn(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2366]), ['final']). 1.16/1.45 cnf(c_0_3843, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ouminus__class_Ouminus(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2367]), ['final']). 1.16/1.45 cnf(c_0_3844, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ouminus__class_Ouminus(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2368]), ['final']). 1.16/1.45 cnf(c_0_3845, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2369]), ['final']). 1.16/1.45 cnf(c_0_3846, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_RealVector_Onorm__class_Onorm(X1,X2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2370]), ['final']). 1.16/1.45 cnf(c_0_3847, plain, (class_Lattices_Oboolean__algebra(tc_fun(X2,X1))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_2371]), ['final']). 1.16/1.45 cnf(c_0_3848, plain, (class_Orderings_Oord(tc_fun(X2,X1))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_2372]), ['final']). 1.16/1.45 cnf(c_0_3849, plain, (class_Groups_Ominus(tc_fun(X2,X1))|~class_Groups_Ominus(X1)), inference(split_conjunct,[status(thm)],[c_0_2373]), ['final']). 1.16/1.45 cnf(c_0_3850, plain, (class_Groups_Ouminus(tc_fun(X2,X1))|~class_Groups_Ouminus(X1)), inference(split_conjunct,[status(thm)],[c_0_2374]), ['final']). 1.16/1.45 cnf(c_0_3851, plain, (class_Orderings_Opreorder(tc_fun(X2,X1))|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2375]), ['final']). 1.16/1.45 cnf(c_0_3852, plain, (class_Orderings_Oorder(tc_fun(X2,X1))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_2376]), ['final']). 1.16/1.45 cnf(c_0_3853, plain, (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))=X1), inference(split_conjunct,[status(thm)],[c_0_2377]), ['final']). 1.16/1.45 cnf(c_0_3854, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X1)|~class_Groups_Olinordered__ab__group__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2378]), ['final']). 1.16/1.45 cnf(c_0_3855, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X1)|~class_Groups_Olinordered__ab__group__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2379]), ['final']). 1.16/1.45 cnf(c_0_3856, plain, (c_Groups_Osgn__class_Osgn(X2,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Osgn__if(X2)), inference(split_conjunct,[status(thm)],[c_0_2170]), ['final']). 1.16/1.45 cnf(c_0_3857, plain, (c_Groups_Ouminus__class_Ouminus(X2,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2367]), ['final']). 1.16/1.45 cnf(c_0_3858, plain, (c_Groups_Ouminus__class_Ouminus(X2,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2368]), ['final']). 1.16/1.45 cnf(c_0_3859, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Groups_Osgn__class_Osgn(X1,X2)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2365]), ['final']). 1.16/1.45 cnf(c_0_3860, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Groups_Osgn__class_Osgn(X1,X2)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2366]), ['final']). 1.16/1.45 cnf(c_0_3861, plain, (c_Groups_Ozero__class_Ozero(X2)=c_Groups_Oabs__class_Oabs(X2,X1)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__ab__group__add__abs(X2)), inference(split_conjunct,[status(thm)],[c_0_2369]), ['final']). 1.16/1.45 cnf(c_0_3862, plain, (c_RealVector_Onorm__class_Onorm(X1,X2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2370]), ['final']). 1.16/1.45 cnf(c_0_3863, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2380]), ['final']). 1.16/1.45 cnf(c_0_3864, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(X1)|~class_RealVector_Oreal__normed__algebra__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2381]), ['final']). 1.16/1.45 cnf(c_0_3865, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2382]), ['final']). 1.16/1.45 cnf(c_0_3866, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_2383]), ['final']). 1.16/1.45 cnf(c_0_3867, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_2384]), ['final']). 1.16/1.45 cnf(c_0_3868, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2385]), ['final']). 1.16/1.45 cnf(c_0_3869, plain, (X1=c_Groups_Ouminus__class_Ouminus(X2,X1)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Olinordered__ab__group__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2378]), ['final']). 1.16/1.45 cnf(c_0_3870, plain, (X1=c_Groups_Ouminus__class_Ouminus(X2,X1)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Olinordered__ab__group__add(X2)), inference(split_conjunct,[status(thm)],[c_0_2379]), ['final']). 1.16/1.45 cnf(c_0_3871, plain, (c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~class_RealVector_Oreal__normed__vector(X1)), inference(split_conjunct,[status(thm)],[c_0_2386]), ['final']). 1.16/1.45 cnf(c_0_3872, plain, (c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1))|~class_RealVector_Oreal__normed__algebra__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2387]), ['final']). 1.16/1.45 cnf(c_0_3873, plain, (c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1))=X1), inference(split_conjunct,[status(thm)],[c_0_2388]), ['final']). 1.16/1.45 cnf(c_0_3874, plain, (c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1))=X1), inference(split_conjunct,[status(thm)],[c_0_2389]), ['final']). 1.16/1.45 cnf(c_0_3875, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_RealDef_Oreal(tc_Nat_Onat,X1)), inference(split_conjunct,[status(thm)],[c_0_2390]), ['final']). 1.16/1.45 cnf(c_0_3876, plain, (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)), inference(split_conjunct,[status(thm)],[c_0_2391]), ['final']). 1.16/1.45 cnf(c_0_3877, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_2209]), ['final']). 1.16/1.45 cnf(c_0_3878, plain, (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|X1!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[c_0_2207]), ['final']). 1.16/1.45 cnf(c_0_3879, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X1), inference(split_conjunct,[status(thm)],[c_0_2208]), ['final']). 1.16/1.45 cnf(c_0_3880, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_RealDef_Oreal(tc_Nat_Onat,X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_2390]), ['final']). 1.16/1.45 cnf(c_0_3881, plain, (~class_Rings_Ozero__neq__one(X1)|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Oone__class_Oone(X1)), inference(split_conjunct,[status(thm)],[c_0_2392]), ['final']). 1.16/1.45 cnf(c_0_3882, plain, (~class_Rings_Ozero__neq__one(X1)|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Oone__class_Oone(X1)), inference(split_conjunct,[status(thm)],[c_0_2393]), ['final']). 1.16/1.45 cnf(c_0_3883, plain, (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[fact_real__of__nat__1]), ['final']). 1.16/1.45 cnf(c_0_3884, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_zminus__0]), ['final']). 1.16/1.45 cnf(c_0_3885, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_real__of__nat__zero]), ['final']). 1.16/1.45 cnf(c_0_3886, plain, (class_Groups_Osgn__if(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2394]), ['final']). 1.16/1.45 cnf(c_0_3887, plain, (class_Groups_Oone(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2395]), ['final']). 1.16/1.45 cnf(c_0_3888, plain, (class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2396]), ['final']). 1.16/1.45 cnf(c_0_3889, plain, (class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_2397]), ['final']). 1.16/1.45 cnf(c_0_3890, plain, (class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2398]), ['final']). 1.16/1.45 cnf(c_0_3891, plain, (class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2399]), ['final']). 1.16/1.45 cnf(c_0_3892, plain, (class_Groups_Ozero(tc_Polynomial_Opoly(X1))|~class_Groups_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_2400]), ['final']). 1.16/1.45 cnf(c_0_3893, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2401]), ['final']). 1.16/1.45 cnf(c_0_3894, plain, (class_Groups_Oabs__if(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2402]), ['final']). 1.16/1.45 cnf(c_0_3895, plain, (class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2403]), ['final']). 1.16/1.45 cnf(c_0_3896, plain, (class_Rings_Oring__1(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__ring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2404]), ['final']). 1.16/1.45 cnf(c_0_3897, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2405]), ['final']). 1.16/1.45 cnf(c_0_3898, plain, (class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2406]), ['final']). 1.16/1.45 cnf(c_0_3899, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2407]), ['final']). 1.16/1.45 cnf(c_0_3900, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2408]), ['final']). 1.16/1.45 cnf(c_0_3901, plain, (class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2409]), ['final']). 1.16/1.45 cnf(c_0_3902, plain, (class_Rings_Osemiring(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_2410]), ['final']). 1.16/1.45 cnf(c_0_3903, plain, (class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2411]), ['final']). 1.16/1.45 cnf(c_0_3904, plain, (class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocancel__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2412]), ['final']). 1.16/1.45 cnf(c_0_3905, plain, (class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2413]), ['final']). 1.16/1.45 cnf(c_0_3906, plain, (class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2414]), ['final']). 1.16/1.45 cnf(c_0_3907, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2415]), ['final']). 1.16/1.45 cnf(c_0_3908, plain, (class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2416]), ['final']). 1.16/1.45 cnf(c_0_3909, plain, (class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2417]), ['final']). 1.16/1.45 cnf(c_0_3910, plain, (class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2418]), ['final']). 1.16/1.45 cnf(c_0_3911, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocancel__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2419]), ['final']). 1.16/1.45 cnf(c_0_3912, plain, (class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2420]), ['final']). 1.16/1.45 cnf(c_0_3913, plain, (class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2421]), ['final']). 1.16/1.45 cnf(c_0_3914, plain, (class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2422]), ['final']). 1.16/1.45 cnf(c_0_3915, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2423]), ['final']). 1.16/1.45 cnf(c_0_3916, plain, (class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2424]), ['final']). 1.16/1.45 cnf(c_0_3917, plain, (class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2425]), ['final']). 1.16/1.45 cnf(c_0_3918, plain, (class_Orderings_Oord(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2426]), ['final']). 1.16/1.45 cnf(c_0_3919, plain, (class_Groups_Ominus(tc_Polynomial_Opoly(X1))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2427]), ['final']). 1.16/1.45 cnf(c_0_3920, plain, (class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2428]), ['final']). 1.16/1.45 cnf(c_0_3921, plain, (class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_2429]), ['final']). 1.16/1.45 cnf(c_0_3922, plain, (class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocancel__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2430]), ['final']). 1.16/1.45 cnf(c_0_3923, plain, (class_Rings_Oring(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_2431]), ['final']). 1.16/1.45 cnf(c_0_3924, plain, (class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2432]), ['final']). 1.16/1.45 cnf(c_0_3925, plain, (class_Groups_Ouminus(tc_Polynomial_Opoly(X1))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2433]), ['final']). 1.16/1.45 cnf(c_0_3926, plain, (class_Power_Opower(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2434]), ['final']). 1.16/1.45 cnf(c_0_3927, plain, (class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2435]), ['final']). 1.16/1.45 cnf(c_0_3928, plain, (class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_2436]), ['final']). 1.16/1.45 cnf(c_0_3929, plain, (class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2437]), ['final']). 1.16/1.45 cnf(c_0_3930, plain, (class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2438]), ['final']). 1.16/1.45 cnf(c_0_3931, plain, (class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2439]), ['final']). 1.16/1.45 cnf(c_0_3932, plain, (class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__ring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2440]), ['final']). 1.16/1.45 cnf(c_0_3933, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2441]), ['final']). 1.16/1.45 cnf(c_0_3934, plain, (class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2442]), ['final']). 1.16/1.45 cnf(c_0_3935, plain, (class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2443]), ['final']). 1.16/1.45 cnf(c_0_3936, plain, (class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2444]), ['final']). 1.16/1.45 cnf(c_0_3937, plain, (class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_2445]), ['final']). 1.16/1.45 cnf(c_0_3938, plain, (class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_2446]), ['final']). 1.16/1.45 cnf(c_0_3939, plain, (class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_2447]), ['final']). 1.16/1.45 cnf(c_0_3940, plain, (class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2448]), ['final']). 1.16/1.45 cnf(c_0_3941, plain, (class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2449]), ['final']). 1.16/1.45 cnf(c_0_3942, plain, (class_Orderings_Oorder(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_2450]), ['final']). 1.16/1.45 cnf(c_0_3943, plain, (class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_2451]), ['final']). 1.16/1.45 cnf(c_0_3944, plain, (class_Rings_Oidom(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_2452]), ['final']). 1.16/1.45 cnf(c_0_3945, plain, (class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_2453]), ['final']). 1.16/1.45 cnf(c_0_3946, plain, (class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_2454]), ['final']). 1.16/1.45 cnf(c_0_3947, plain, (c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_natfloor__zero]), ['final']). 1.16/1.45 cnf(c_0_3948, plain, (c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_natceiling__one]), ['final']). 1.16/1.45 cnf(c_0_3949, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[fact_natfloor__one]), ['final']). 1.16/1.45 cnf(c_0_3950, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[fact_natceiling__zero]), ['final']). 1.16/1.45 cnf(c_0_3951, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), inference(split_conjunct,[status(thm)],[fact_ln__one]), ['final']). 1.16/1.45 cnf(c_0_3952, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[fact_int__0__neq__1]), ['final']). 1.16/1.45 cnf(c_0_3953, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[fact_real__zero__not__eq__one]), ['final']). 1.16/1.45 cnf(c_0_3954, plain, (class_Fields_Ofield(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]), ['final']). 1.16/1.45 cnf(c_0_3955, plain, (class_Fields_Ofield(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]), ['final']). 1.16/1.45 cnf(c_0_3956, plain, (class_Groups_Osgn__if(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]), ['final']). 1.16/1.45 cnf(c_0_3957, plain, (class_Groups_Osgn__if(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]), ['final']). 1.16/1.45 cnf(c_0_3958, plain, (class_Lattices_Oboolean__algebra(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]), ['final']). 1.16/1.45 cnf(c_0_3959, plain, (class_Groups_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]), ['final']). 1.16/1.45 cnf(c_0_3960, plain, (class_Groups_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]), ['final']). 1.16/1.45 cnf(c_0_3961, plain, (class_Groups_Oone(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]), ['final']). 1.16/1.45 cnf(c_0_3962, plain, (class_Groups_Oone(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]), ['final']). 1.16/1.45 cnf(c_0_3963, plain, (class_Rings_Oordered__comm__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]), ['final']). 1.16/1.45 cnf(c_0_3964, plain, (class_Rings_Oordered__comm__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]), ['final']). 1.16/1.45 cnf(c_0_3965, plain, (class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]), ['final']). 1.16/1.45 cnf(c_0_3966, plain, (class_Rings_Ocomm__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]), ['final']). 1.16/1.45 cnf(c_0_3967, plain, (class_Rings_Ocomm__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]), ['final']). 1.16/1.45 cnf(c_0_3968, plain, (class_Rings_Ocomm__semiring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]), ['final']). 1.16/1.45 cnf(c_0_3969, plain, (class_Rings_Ocomm__semiring(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]), ['final']). 1.16/1.45 cnf(c_0_3970, plain, (class_Rings_Oordered__cancel__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]), ['final']). 1.16/1.45 cnf(c_0_3971, plain, (class_Rings_Oordered__cancel__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]), ['final']). 1.16/1.45 cnf(c_0_3972, plain, (class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]), ['final']). 1.16/1.45 cnf(c_0_3973, plain, (class_Rings_Ozero__neq__one(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]), ['final']). 1.16/1.45 cnf(c_0_3974, plain, (class_Rings_Ozero__neq__one(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]), ['final']). 1.16/1.45 cnf(c_0_3975, plain, (class_Rings_Ozero__neq__one(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]), ['final']). 1.16/1.45 cnf(c_0_3976, plain, (class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]), ['final']). 1.16/1.45 cnf(c_0_3977, plain, (class_Groups_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]), ['final']). 1.16/1.45 cnf(c_0_3978, plain, (class_Groups_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]), ['final']). 1.16/1.45 cnf(c_0_3979, plain, (class_Groups_Ozero(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]), ['final']). 1.16/1.45 cnf(c_0_3980, plain, (class_Groups_Ozero(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]), ['final']). 1.16/1.45 cnf(c_0_3981, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]), ['final']). 1.16/1.45 cnf(c_0_3982, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]), ['final']). 1.16/1.45 cnf(c_0_3983, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]), ['final']). 1.16/1.45 cnf(c_0_3984, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]), ['final']). 1.16/1.45 cnf(c_0_3985, plain, (class_Groups_Oabs__if(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]), ['final']). 1.16/1.45 cnf(c_0_3986, plain, (class_Groups_Oabs__if(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]), ['final']). 1.16/1.45 cnf(c_0_3987, plain, (class_Groups_Ocomm__monoid__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]), ['final']). 1.16/1.45 cnf(c_0_3988, plain, (class_Groups_Ocomm__monoid__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]), ['final']). 1.16/1.45 cnf(c_0_3989, plain, (class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]), ['final']). 1.16/1.45 cnf(c_0_3990, plain, (class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]), ['final']). 1.16/1.45 cnf(c_0_3991, plain, (class_Rings_Oring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]), ['final']). 1.16/1.45 cnf(c_0_3992, plain, (class_Rings_Oring__1(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]), ['final']). 1.16/1.45 cnf(c_0_3993, plain, (class_Rings_Oring__1(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]), ['final']). 1.16/1.45 cnf(c_0_3994, plain, (class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]), ['final']). 1.16/1.45 cnf(c_0_3995, plain, (class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra]), ['final']). 1.16/1.45 cnf(c_0_3996, plain, (class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]), ['final']). 1.16/1.45 cnf(c_0_3997, plain, (class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]), ['final']). 1.16/1.45 cnf(c_0_3998, plain, (class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]), ['final']). 1.16/1.45 cnf(c_0_3999, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]), ['final']). 1.16/1.45 cnf(c_0_4000, plain, (class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict]), ['final']). 1.16/1.45 cnf(c_0_4001, plain, (class_Rings_Olinordered__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]), ['final']). 1.16/1.45 cnf(c_0_4002, plain, (class_Rings_Olinordered__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]), ['final']). 1.16/1.45 cnf(c_0_4003, plain, (class_Rings_Olinordered__semiring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]), ['final']). 1.16/1.45 cnf(c_0_4004, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4005, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4006, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4007, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]), ['final']). 1.16/1.45 cnf(c_0_4008, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]), ['final']). 1.16/1.45 cnf(c_0_4009, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]), ['final']). 1.16/1.45 cnf(c_0_4010, plain, (class_Int_Oring__char__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]), ['final']). 1.16/1.45 cnf(c_0_4011, plain, (class_Int_Oring__char__0(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]), ['final']). 1.16/1.45 cnf(c_0_4012, plain, (class_Int_Oring__char__0(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]), ['final']). 1.16/1.45 cnf(c_0_4013, plain, (class_Rings_Osemiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]), ['final']). 1.16/1.45 cnf(c_0_4014, plain, (class_Rings_Osemiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]), ['final']). 1.16/1.45 cnf(c_0_4015, plain, (class_Rings_Osemiring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]), ['final']). 1.16/1.45 cnf(c_0_4016, plain, (class_Rings_Osemiring(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]), ['final']). 1.16/1.45 cnf(c_0_4017, plain, (class_Rings_Olinordered__semiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]), ['final']). 1.16/1.45 cnf(c_0_4018, plain, (class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]), ['final']). 1.16/1.45 cnf(c_0_4019, plain, (class_Groups_Ocancel__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4020, plain, (class_Groups_Ocancel__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4021, plain, (class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4022, plain, (class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4023, plain, (class_Rings_Olinordered__ring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]), ['final']). 1.16/1.45 cnf(c_0_4024, plain, (class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]), ['final']). 1.16/1.45 cnf(c_0_4025, plain, (class_Rings_Oordered__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]), ['final']). 1.16/1.45 cnf(c_0_4026, plain, (class_Rings_Oordered__ring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]), ['final']). 1.16/1.45 cnf(c_0_4027, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]), ['final']). 1.16/1.45 cnf(c_0_4028, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]), ['final']). 1.16/1.45 cnf(c_0_4029, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict]), ['final']). 1.16/1.45 cnf(c_0_4030, plain, (class_Fields_Olinordered__field(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]), ['final']). 1.16/1.45 cnf(c_0_4031, plain, (class_Rings_Oordered__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]), ['final']). 1.16/1.45 cnf(c_0_4032, plain, (class_Rings_Oordered__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]), ['final']). 1.16/1.45 cnf(c_0_4033, plain, (class_Rings_Oordered__semiring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]), ['final']). 1.16/1.45 cnf(c_0_4034, plain, (class_Groups_Omonoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]), ['final']). 1.16/1.45 cnf(c_0_4035, plain, (class_Groups_Omonoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]), ['final']). 1.16/1.45 cnf(c_0_4036, plain, (class_Groups_Omonoid__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]), ['final']). 1.16/1.45 cnf(c_0_4037, plain, (class_Groups_Omonoid__add(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]), ['final']). 1.16/1.45 cnf(c_0_4038, plain, (class_Rings_Oring__no__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4039, plain, (class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__no__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4040, plain, (class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4041, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4042, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4043, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4044, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4045, plain, (class_Rings_Oordered__ring__abs(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]), ['final']). 1.16/1.45 cnf(c_0_4046, plain, (class_Rings_Oordered__ring__abs(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]), ['final']). 1.16/1.45 cnf(c_0_4047, plain, (class_Rings_Ono__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4048, plain, (class_Rings_Ono__zero__divisors(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4049, plain, (class_Rings_Ono__zero__divisors(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4050, plain, (class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4051, plain, (class_Groups_Omonoid__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]), ['final']). 1.16/1.45 cnf(c_0_4052, plain, (class_Groups_Omonoid__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]), ['final']). 1.16/1.45 cnf(c_0_4053, plain, (class_Groups_Omonoid__mult(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]), ['final']). 1.16/1.45 cnf(c_0_4054, plain, (class_Groups_Omonoid__mult(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]), ['final']). 1.16/1.45 cnf(c_0_4055, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4056, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4057, plain, (class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4058, plain, (class_Rings_Olinordered__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]), ['final']). 1.16/1.45 cnf(c_0_4059, plain, (class_Rings_Olinordered__ring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]), ['final']). 1.16/1.45 cnf(c_0_4060, plain, (class_Groups_Oab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]), ['final']). 1.16/1.45 cnf(c_0_4061, plain, (class_Groups_Oab__group__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]), ['final']). 1.16/1.45 cnf(c_0_4062, plain, (class_Groups_Oab__group__add(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]), ['final']). 1.16/1.45 cnf(c_0_4063, plain, (class_Orderings_Oord(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]), ['final']). 1.16/1.45 cnf(c_0_4064, plain, (class_Orderings_Oord(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]), ['final']). 1.16/1.45 cnf(c_0_4065, plain, (class_Orderings_Oord(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]), ['final']). 1.16/1.45 cnf(c_0_4066, plain, (class_Orderings_Oord(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]), ['final']). 1.16/1.45 cnf(c_0_4067, plain, (class_Groups_Ominus(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]), ['final']). 1.16/1.45 cnf(c_0_4068, plain, (class_Groups_Ominus(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]), ['final']). 1.16/1.45 cnf(c_0_4069, plain, (class_Groups_Ominus(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]), ['final']). 1.16/1.45 cnf(c_0_4070, plain, (class_Groups_Ominus(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ominus]), ['final']). 1.16/1.45 cnf(c_0_4071, plain, (class_Groups_Ominus(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ominus]), ['final']). 1.16/1.45 cnf(c_0_4072, plain, (class_Groups_Ocomm__monoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4073, plain, (class_Groups_Ocomm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4074, plain, (class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4075, plain, (class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4076, plain, (class_Divides_Osemiring__div(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]), ['final']). 1.16/1.45 cnf(c_0_4077, plain, (class_Divides_Osemiring__div(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]), ['final']). 1.16/1.45 cnf(c_0_4078, plain, (class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__comm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4079, plain, (class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__comm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4080, plain, (class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4081, plain, (class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4082, plain, (class_Rings_Oring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]), ['final']). 1.16/1.45 cnf(c_0_4083, plain, (class_Rings_Oring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]), ['final']). 1.16/1.45 cnf(c_0_4084, plain, (class_Rings_Oring(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]), ['final']). 1.16/1.45 cnf(c_0_4085, plain, (class_Groups_Olinordered__ab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]), ['final']). 1.16/1.45 cnf(c_0_4086, plain, (class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]), ['final']). 1.16/1.45 cnf(c_0_4087, plain, (class_Groups_Ouminus(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]), ['final']). 1.16/1.45 cnf(c_0_4088, plain, (class_Groups_Ouminus(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]), ['final']). 1.16/1.45 cnf(c_0_4089, plain, (class_Groups_Ouminus(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]), ['final']). 1.16/1.45 cnf(c_0_4090, plain, (class_Groups_Ouminus(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]), ['final']). 1.16/1.45 cnf(c_0_4091, plain, (class_Power_Opower(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]), ['final']). 1.16/1.45 cnf(c_0_4092, plain, (class_Power_Opower(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]), ['final']). 1.16/1.45 cnf(c_0_4093, plain, (class_Power_Opower(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]), ['final']). 1.16/1.45 cnf(c_0_4094, plain, (class_Power_Opower(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]), ['final']). 1.16/1.45 cnf(c_0_4095, plain, (class_Rings_Olinordered__idom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]), ['final']). 1.16/1.45 cnf(c_0_4096, plain, (class_Rings_Olinordered__idom(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]), ['final']). 1.16/1.45 cnf(c_0_4097, plain, (class_Rings_Osemiring__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]), ['final']). 1.16/1.45 cnf(c_0_4098, plain, (class_Rings_Osemiring__0(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]), ['final']). 1.16/1.45 cnf(c_0_4099, plain, (class_Rings_Osemiring__0(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]), ['final']). 1.16/1.45 cnf(c_0_4100, plain, (class_Rings_Osemiring__0(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]), ['final']). 1.16/1.45 cnf(c_0_4101, plain, (class_Orderings_Olinorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]), ['final']). 1.16/1.45 cnf(c_0_4102, plain, (class_Orderings_Olinorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]), ['final']). 1.16/1.45 cnf(c_0_4103, plain, (class_Orderings_Olinorder(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]), ['final']). 1.16/1.45 cnf(c_0_4104, plain, (class_Orderings_Opreorder(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]), ['final']). 1.16/1.45 cnf(c_0_4105, plain, (class_Orderings_Opreorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]), ['final']). 1.16/1.45 cnf(c_0_4106, plain, (class_Orderings_Opreorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]), ['final']). 1.16/1.45 cnf(c_0_4107, plain, (class_Orderings_Opreorder(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]), ['final']). 1.16/1.45 cnf(c_0_4108, plain, (class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]), ['final']). 1.16/1.45 cnf(c_0_4109, plain, (class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]), ['final']). 1.16/1.45 cnf(c_0_4110, plain, (class_Rings_Ocomm__ring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]), ['final']). 1.16/1.45 cnf(c_0_4111, plain, (class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]), ['final']). 1.16/1.45 cnf(c_0_4112, plain, (class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]), ['final']). 1.16/1.45 cnf(c_0_4113, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4114, plain, (class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4115, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors]), ['final']). 1.16/1.45 cnf(c_0_4116, plain, (class_Groups_Oordered__comm__monoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4117, plain, (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4118, plain, (class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]), ['final']). 1.16/1.45 cnf(c_0_4119, plain, (class_Rings_Olinordered__semiring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]), ['final']). 1.16/1.45 cnf(c_0_4120, plain, (class_Rings_Olinordered__semiring__strict(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]), ['final']). 1.16/1.45 cnf(c_0_4121, plain, (class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]), ['final']). 1.16/1.45 cnf(c_0_4122, plain, (class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]), ['final']). 1.16/1.45 cnf(c_0_4123, plain, (class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]), ['final']). 1.16/1.45 cnf(c_0_4124, plain, (class_Groups_Oab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4125, plain, (class_Groups_Oab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4126, plain, (class_Groups_Oab__semigroup__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4127, plain, (class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]), ['final']). 1.16/1.45 cnf(c_0_4128, plain, (class_Rings_Ocomm__semiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]), ['final']). 1.16/1.45 cnf(c_0_4129, plain, (class_Rings_Ocomm__semiring__1(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]), ['final']). 1.16/1.45 cnf(c_0_4130, plain, (class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]), ['final']). 1.16/1.45 cnf(c_0_4131, plain, (class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]), ['final']). 1.16/1.45 cnf(c_0_4132, plain, (class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]), ['final']). 1.16/1.45 cnf(c_0_4133, plain, (class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]), ['final']). 1.16/1.45 cnf(c_0_4134, plain, (class_Groups_Ogroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]), ['final']). 1.16/1.45 cnf(c_0_4135, plain, (class_Groups_Ogroup__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]), ['final']). 1.16/1.45 cnf(c_0_4136, plain, (class_Groups_Ogroup__add(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]), ['final']). 1.16/1.45 cnf(c_0_4137, plain, (class_Rings_Ocomm__semiring__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]), ['final']). 1.16/1.45 cnf(c_0_4138, plain, (class_Rings_Ocomm__semiring__0(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]), ['final']). 1.16/1.45 cnf(c_0_4139, plain, (class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__0]), ['final']). 1.16/1.45 cnf(c_0_4140, plain, (class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]), ['final']). 1.16/1.45 cnf(c_0_4141, plain, (class_Groups_Oordered__ab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]), ['final']). 1.16/1.45 cnf(c_0_4142, plain, (class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]), ['final']). 1.16/1.45 cnf(c_0_4143, plain, (class_Rings_Olinordered__semidom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]), ['final']). 1.16/1.45 cnf(c_0_4144, plain, (class_Rings_Olinordered__semidom(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]), ['final']). 1.16/1.45 cnf(c_0_4145, plain, (class_Rings_Olinordered__semidom(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]), ['final']). 1.16/1.45 cnf(c_0_4146, plain, (class_Orderings_Oorder(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]), ['final']). 1.16/1.45 cnf(c_0_4147, plain, (class_Orderings_Oorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]), ['final']). 1.16/1.45 cnf(c_0_4148, plain, (class_Orderings_Oorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]), ['final']). 1.16/1.45 cnf(c_0_4149, plain, (class_Orderings_Oorder(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]), ['final']). 1.16/1.45 cnf(c_0_4150, plain, (class_Groups_Oab__semigroup__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]), ['final']). 1.16/1.45 cnf(c_0_4151, plain, (class_Groups_Oab__semigroup__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]), ['final']). 1.16/1.45 cnf(c_0_4152, plain, (class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]), ['final']). 1.16/1.45 cnf(c_0_4153, plain, (class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]), ['final']). 1.16/1.45 cnf(c_0_4154, plain, (class_Rings_Oidom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]), ['final']). 1.16/1.45 cnf(c_0_4155, plain, (class_Rings_Oidom(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]), ['final']). 1.16/1.45 cnf(c_0_4156, plain, (class_Rings_Oidom(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]), ['final']). 1.16/1.45 cnf(c_0_4157, plain, (class_Rings_Omult__zero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]), ['final']). 1.16/1.45 cnf(c_0_4158, plain, (class_Rings_Omult__zero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]), ['final']). 1.16/1.45 cnf(c_0_4159, plain, (class_Rings_Omult__zero(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]), ['final']). 1.16/1.45 cnf(c_0_4160, plain, (class_Rings_Omult__zero(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]), ['final']). 1.16/1.45 cnf(c_0_4161, plain, (class_Rings_Ocomm__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]), ['final']). 1.16/1.45 cnf(c_0_4162, plain, (class_Rings_Ocomm__ring(tc_RealDef_Oreal)), inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]), ['final']). 1.16/1.45 cnf(c_0_4163, plain, (class_Rings_Ocomm__ring(tc_Complex_Ocomplex)), inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]), ['final']). 1.16/1.45 1.16/1.45 # End clausification derivation 1.16/1.45 # Begin listing active clauses obtained from FOF to CNF conversion 1.16/1.45 cnf(i_0_1, plain, (class_Rings_Ocomm__ring(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1104, plain, (class_Rings_Ocomm__ring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_934, plain, (class_Rings_Ocomm__ring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_2, plain, (class_Rings_Omult__zero(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1578, plain, (class_Rings_Omult__zero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_390, plain, (class_Rings_Omult__zero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1275, plain, (class_Rings_Omult__zero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_587, plain, (class_Rings_Oidom(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_355, plain, (class_Rings_Oidom(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_253, plain, (class_Rings_Oidom(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1274, plain, (class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_4, plain, (class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1099, plain, (class_Groups_Oab__semigroup__mult(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_300, plain, (class_Groups_Oab__semigroup__mult(tc_Int_Oint))). 1.16/1.45 cnf(i_0_938, plain, (class_Orderings_Oorder(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_183, plain, (class_Orderings_Oorder(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_965, plain, (class_Orderings_Oorder(tc_Int_Oint))). 1.16/1.45 cnf(i_0_509, plain, (class_Orderings_Oorder(tc_HOL_Obool))). 1.16/1.45 cnf(i_0_455, plain, (class_Rings_Olinordered__semidom(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_252, plain, (class_Rings_Olinordered__semidom(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_474, plain, (class_Rings_Olinordered__semidom(tc_Int_Oint))). 1.16/1.45 cnf(i_0_774, plain, (class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1138, plain, (class_Groups_Oordered__ab__group__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_266, plain, (class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_588, plain, (class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1430, plain, (class_Rings_Ocomm__semiring__0(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_580, plain, (class_Rings_Ocomm__semiring__0(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1338, plain, (class_Groups_Ogroup__add(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1404, plain, (class_Groups_Ogroup__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_50, plain, (class_Groups_Ogroup__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_908, plain, (class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1348, plain, (class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1425, plain, (class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_233, plain, (class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_526, plain, (class_Rings_Ocomm__semiring__1(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1579, plain, (class_Rings_Ocomm__semiring__1(tc_Int_Oint))). 1.16/1.45 cnf(i_0_31, plain, (class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1432, plain, (class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1639, plain, (class_Groups_Oab__semigroup__add(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1097, plain, (class_Groups_Oab__semigroup__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_70, plain, (class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1302, plain, (class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1633, plain, (class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1009, plain, (class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1119, plain, (class_Rings_Olinordered__semiring__strict(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1644, plain, (class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_43, plain, (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_729, plain, (class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1515, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_635, plain, (class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_395, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))). 1.16/1.45 cnf(i_0_53, plain, (class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1120, plain, (class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1609, plain, (class_Rings_Ocomm__ring__1(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1402, plain, (class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1310, plain, (class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))). 1.16/1.45 cnf(i_0_925, plain, (class_Orderings_Opreorder(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_932, plain, (class_Orderings_Opreorder(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_637, plain, (class_Orderings_Opreorder(tc_Int_Oint))). 1.16/1.45 cnf(i_0_352, plain, (class_Orderings_Opreorder(tc_HOL_Obool))). 1.16/1.45 cnf(i_0_65, plain, (class_Orderings_Olinorder(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_308, plain, (class_Orderings_Olinorder(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1118, plain, (class_Orderings_Olinorder(tc_Int_Oint))). 1.16/1.45 cnf(i_0_590, plain, (class_Rings_Osemiring__0(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_67, plain, (class_Rings_Osemiring__0(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_86, plain, (class_Rings_Osemiring__0(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_821, plain, (class_Rings_Osemiring__0(tc_Int_Oint))). 1.16/1.45 cnf(i_0_222, plain, (class_Rings_Olinordered__idom(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1346, plain, (class_Rings_Olinordered__idom(tc_Int_Oint))). 1.16/1.45 cnf(i_0_681, plain, (class_Power_Opower(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_74, plain, (class_Power_Opower(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1358, plain, (class_Power_Opower(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1239, plain, (class_Power_Opower(tc_Int_Oint))). 1.16/1.45 cnf(i_0_81, plain, (class_Groups_Ouminus(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_80, plain, (class_Groups_Ouminus(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_433, plain, (class_Groups_Ouminus(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1361, plain, (class_Groups_Ouminus(tc_HOL_Obool))). 1.16/1.45 cnf(i_0_1743, plain, (class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_835, plain, (class_Groups_Olinordered__ab__group__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1377, plain, (class_Rings_Oring(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_107, plain, (class_Rings_Oring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1652, plain, (class_Rings_Oring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_306, plain, (class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_175, plain, (class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_112, plain, (class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_221, plain, (class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_967, plain, (class_Divides_Osemiring__div(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1479, plain, (class_Divides_Osemiring__div(tc_Int_Oint))). 1.16/1.45 cnf(i_0_591, plain, (class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1210, plain, (class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1741, plain, (class_Groups_Ocomm__monoid__add(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_746, plain, (class_Groups_Ocomm__monoid__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_924, plain, (class_Groups_Ominus(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1690, plain, (class_Groups_Ominus(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_117, plain, (class_Groups_Ominus(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_217, plain, (class_Groups_Ominus(tc_Int_Oint))). 1.16/1.45 cnf(i_0_346, plain, (class_Groups_Ominus(tc_HOL_Obool))). 1.16/1.45 cnf(i_0_1661, plain, (class_Orderings_Oord(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_820, plain, (class_Orderings_Oord(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_641, plain, (class_Orderings_Oord(tc_Int_Oint))). 1.16/1.45 cnf(i_0_956, plain, (class_Orderings_Oord(tc_HOL_Obool))). 1.16/1.45 cnf(i_0_240, plain, (class_Groups_Oab__group__add(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1133, plain, (class_Groups_Oab__group__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1299, plain, (class_Groups_Oab__group__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_128, plain, (class_Rings_Olinordered__ring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_805, plain, (class_Rings_Olinordered__ring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_414, plain, (class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_616, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_230, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1347, plain, (class_Groups_Omonoid__mult(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_150, plain, (class_Groups_Omonoid__mult(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_506, plain, (class_Groups_Omonoid__mult(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1495, plain, (class_Groups_Omonoid__mult(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1065, plain, (class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_695, plain, (class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_718, plain, (class_Rings_Ono__zero__divisors(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1440, plain, (class_Rings_Ono__zero__divisors(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1508, plain, (class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1255, plain, (class_Rings_Oordered__ring__abs(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1110, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1441, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_176, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1078, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_708, plain, (class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_672, plain, (class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_750, plain, (class_Rings_Oring__no__zero__divisors(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1450, plain, (class_Groups_Omonoid__add(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_738, plain, (class_Groups_Omonoid__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_193, plain, (class_Groups_Omonoid__add(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_515, plain, (class_Groups_Omonoid__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1748, plain, (class_Rings_Oordered__semiring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_401, plain, (class_Rings_Oordered__semiring(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_420, plain, (class_Rings_Oordered__semiring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1683, plain, (class_Fields_Olinordered__field(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_203, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_311, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1108, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1698, plain, (class_Rings_Oordered__ring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1602, plain, (class_Rings_Oordered__ring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_207, plain, (class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_649, plain, (class_Rings_Olinordered__ring__strict(tc_Int_Oint))). 1.16/1.45 cnf(i_0_209, plain, (class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_975, plain, (class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_289, plain, (class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1397, plain, (class_Groups_Ocancel__semigroup__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1064, plain, (class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_817, plain, (class_Rings_Olinordered__semiring__1(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1202, plain, (class_Rings_Osemiring(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_964, plain, (class_Rings_Osemiring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1399, plain, (class_Rings_Osemiring(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_640, plain, (class_Rings_Osemiring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_394, plain, (class_Int_Oring__char__0(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_698, plain, (class_Int_Oring__char__0(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_285, plain, (class_Int_Oring__char__0(tc_Int_Oint))). 1.16/1.45 cnf(i_0_290, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_809, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1619, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))). 1.16/1.45 cnf(i_0_565, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_727, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1638, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))). 1.16/1.45 cnf(i_0_541, plain, (class_Rings_Olinordered__semiring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_468, plain, (class_Rings_Olinordered__semiring(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_409, plain, (class_Rings_Olinordered__semiring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1269, plain, (class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_327, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))). 1.16/1.45 cnf(i_0_357, plain, (class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_631, plain, (class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_972, plain, (class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_402, plain, (class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_342, plain, (class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1032, plain, (class_Rings_Oring__1(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1354, plain, (class_Rings_Oring__1(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1201, plain, (class_Rings_Oring__1(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1124, plain, (class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_408, plain, (class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1484, plain, (class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_624, plain, (class_Groups_Ocomm__monoid__mult(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1557, plain, (class_Groups_Oabs__if(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1259, plain, (class_Groups_Oabs__if(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1172, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1382, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1728, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1437, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1457, plain, (class_Groups_Ozero(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_507, plain, (class_Groups_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1568, plain, (class_Groups_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1562, plain, (class_Groups_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_517, plain, (class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_736, plain, (class_Rings_Ozero__neq__one(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_715, plain, (class_Rings_Ozero__neq__one(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1567, plain, (class_Rings_Ozero__neq__one(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1500, plain, (class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1295, plain, (class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1209, plain, (class_Rings_Oordered__cancel__semiring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_536, plain, (class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_535, plain, (class_Rings_Ocomm__semiring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1674, plain, (class_Rings_Ocomm__semiring(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1574, plain, (class_Rings_Ocomm__semiring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_585, plain, (class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1556, plain, (class_Rings_Oordered__comm__semiring(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_749, plain, (class_Rings_Oordered__comm__semiring(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1279, plain, (class_Groups_Oone(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_586, plain, (class_Groups_Oone(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1150, plain, (class_Groups_Oone(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1393, plain, (class_Groups_Oone(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1418, plain, (class_Lattices_Oboolean__algebra(tc_HOL_Obool))). 1.16/1.45 cnf(i_0_1452, plain, (class_Groups_Osgn__if(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1426, plain, (class_Groups_Osgn__if(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1143, plain, (class_Fields_Ofield(tc_Complex_Ocomplex))). 1.16/1.45 cnf(i_0_1052, plain, (class_Fields_Ofield(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1189, plain, (c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1198, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_625, plain, (c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_460, plain, (c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1355, plain, (c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_174, plain, (c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1412, plain, (c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_162, plain, (class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__ring(X1))). 1.16/1.45 cnf(i_0_707, plain, (class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_3, plain, (class_Rings_Oidom(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_1100, plain, (class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_779, plain, (class_Orderings_Oorder(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1702, plain, (class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_137, plain, (class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_497, plain, (class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_339, plain, (class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_1254, plain, (class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_168, plain, (class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocomm__monoid__add(X1))). 1.16/1.45 cnf(i_0_135, plain, (class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1093, plain, (class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_735, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_358, plain, (class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__ring__1(X1))). 1.16/1.45 cnf(i_0_1428, plain, (class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_488, plain, (class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1276, plain, (class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1456, plain, (class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_1665, plain, (class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1213, plain, (class_Power_Opower(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1386, plain, (class_Groups_Ouminus(tc_Polynomial_Opoly(X1))|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_937, plain, (class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_787, plain, (class_Rings_Oring(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__ring(X1))). 1.16/1.45 cnf(i_0_1703, plain, (class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocancel__comm__monoid__add(X1))). 1.16/1.45 cnf(i_0_699, plain, (class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))|~class_Fields_Ofield(X1))). 1.16/1.45 cnf(i_0_153, plain, (class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocomm__monoid__add(X1))). 1.16/1.45 cnf(i_0_673, plain, (class_Groups_Ominus(tc_Polynomial_Opoly(X1))|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_149, plain, (class_Orderings_Oord(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1660, plain, (class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_310, plain, (class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_282, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1214, plain, (class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1365, plain, (class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_1190, plain, (class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1403, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocancel__comm__monoid__add(X1))). 1.16/1.45 cnf(i_0_182, plain, (class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_1233, plain, (class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocomm__monoid__add(X1))). 1.16/1.45 cnf(i_0_198, plain, (class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1366, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1634, plain, (class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1620, plain, (class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_211, plain, (class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Groups_Ocancel__comm__monoid__add(X1))). 1.16/1.45 cnf(i_0_227, plain, (class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_236, plain, (class_Rings_Osemiring(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_307, plain, (class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1605, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_478, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_304, plain, (class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_592, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1689, plain, (class_Rings_Oring__1(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__ring__1(X1))). 1.16/1.45 cnf(i_0_1200, plain, (class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_531, plain, (class_Groups_Oabs__if(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1693, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_670, plain, (class_Groups_Ozero(tc_Polynomial_Opoly(X1))|~class_Groups_Ozero(X1))). 1.16/1.45 cnf(i_0_1720, plain, (class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1670, plain, (class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1606, plain, (class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_1373, plain, (class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1073, plain, (class_Groups_Oone(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_606, plain, (class_Groups_Osgn__if(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1265, plain, (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1559, plain, (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_807, plain, (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_602, plain, (c_Groups_Oone__class_Oone(X1)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ozero__neq__one(X1))). 1.16/1.45 cnf(i_0_731, plain, (c_Groups_Oone__class_Oone(X1)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ozero__neq__one(X1))). 1.16/1.45 cnf(i_0_1719, plain, (c_RealDef_Oreal(tc_Nat_Onat,X1)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_437, plain, (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X1)). 1.16/1.45 cnf(i_0_1623, plain, (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|X1!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1230, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_688, plain, (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))). 1.16/1.45 cnf(i_0_1718, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_RealDef_Oreal(tc_Nat_Onat,X1)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1158, plain, (c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1))=X1)). 1.16/1.45 cnf(i_0_1018, plain, (c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1))=X1)). 1.16/1.45 cnf(i_0_1507, plain, (c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~class_RealVector_Oreal__normed__algebra__1(X1))). 1.16/1.45 cnf(i_0_254, plain, (c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_466, plain, (c_Groups_Ouminus__class_Ouminus(X2,X1)=X1|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Olinordered__ab__group__add(X2))). 1.16/1.45 cnf(i_0_1303, plain, (c_Groups_Ouminus__class_Ouminus(X2,X1)=X1|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Olinordered__ab__group__add(X2))). 1.16/1.45 cnf(i_0_979, plain, (c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_986, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Osgn__if(X1))). 1.16/1.45 cnf(i_0_1498, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_38, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_333, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(X1)|~class_RealVector_Oreal__normed__algebra__1(X1))). 1.16/1.45 cnf(i_0_1058, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_691, plain, (c_RealVector_Onorm__class_Onorm(X1,X2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1148, plain, (c_Groups_Oabs__class_Oabs(X2,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__ab__group__add__abs(X2))). 1.16/1.45 cnf(i_0_428, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1194, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_348, plain, (c_Groups_Ouminus__class_Ouminus(X2,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ogroup__add(X2))). 1.16/1.45 cnf(i_0_518, plain, (c_Groups_Ouminus__class_Ouminus(X2,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ogroup__add(X2))). 1.16/1.45 cnf(i_0_1524, plain, (c_Groups_Osgn__class_Osgn(X2,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Osgn__if(X2))). 1.16/1.45 cnf(i_0_467, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ouminus__class_Ouminus(X2,X1)!=X1|~class_Groups_Olinordered__ab__group__add(X2))). 1.16/1.45 cnf(i_0_1304, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ouminus__class_Ouminus(X2,X1)!=X1|~class_Groups_Olinordered__ab__group__add(X2))). 1.16/1.45 cnf(i_0_971, plain, (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))=X1)). 1.16/1.45 cnf(i_0_694, plain, (class_Orderings_Oorder(tc_fun(X2,X1))|~class_Orderings_Oorder(X1))). 1.16/1.45 cnf(i_0_1221, plain, (class_Orderings_Opreorder(tc_fun(X2,X1))|~class_Orderings_Opreorder(X1))). 1.16/1.45 cnf(i_0_516, plain, (class_Groups_Ouminus(tc_fun(X2,X1))|~class_Groups_Ouminus(X1))). 1.16/1.45 cnf(i_0_993, plain, (class_Groups_Ominus(tc_fun(X2,X1))|~class_Groups_Ominus(X1))). 1.16/1.45 cnf(i_0_223, plain, (class_Orderings_Oord(tc_fun(X2,X1))|~class_Orderings_Oord(X1))). 1.16/1.45 cnf(i_0_1139, plain, (class_Lattices_Oboolean__algebra(tc_fun(X2,X1))|~class_Lattices_Oboolean__algebra(X1))). 1.16/1.45 cnf(i_0_692, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_RealVector_Onorm__class_Onorm(X1,X2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1147, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Oabs__class_Oabs(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_347, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ouminus__class_Ouminus(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_519, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ouminus__class_Ouminus(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_427, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1193, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1237, plain, (X1=X2|c_RealDef_Oreal(tc_Nat_Onat,X1)!=c_RealDef_Oreal(tc_Nat_Onat,X2))). 1.16/1.45 cnf(i_0_642, plain, (X3=c_Groups_Ouminus__class_Ouminus(X2,X1)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2))). 1.16/1.45 cnf(i_0_643, plain, (X3=c_Groups_Ouminus__class_Ouminus(X2,X1)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2))). 1.16/1.45 cnf(i_0_831, plain, (X2=c_Groups_Ouminus__class_Ouminus(X1,X3)|c_Groups_Ouminus__class_Ouminus(X1,X2)!=X3|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_832, plain, (c_Groups_Ouminus__class_Ouminus(X2,X1)=X3|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2))). 1.16/1.45 cnf(i_0_298, plain, (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1))=c_RealDef_Oreal(tc_Nat_Onat,X1))). 1.16/1.45 cnf(i_0_376, plain, (c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=X2|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1580, plain, (c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=X2|~class_Lattices_Oboolean__algebra(X1))). 1.16/1.45 cnf(i_0_173, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=X1)). 1.16/1.45 cnf(i_0_1455, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 1.16/1.45 cnf(i_0_722, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_232, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1))). 1.16/1.45 cnf(i_0_1321, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1))). 1.16/1.45 cnf(i_0_1388, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1))). 1.16/1.45 cnf(i_0_1175, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=X1)). 1.16/1.45 cnf(i_0_25, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)=X1)). 1.16/1.45 cnf(i_0_954, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)=X1)). 1.16/1.45 cnf(i_0_1174, plain, (X2=X3|c_Groups_Ouminus__class_Ouminus(X1,X2)!=c_Groups_Ouminus__class_Ouminus(X1,X3)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1726, plain, (X2=X3|c_Groups_Ouminus__class_Ouminus(X1,X2)!=c_Groups_Ouminus__class_Ouminus(X1,X3)|~class_Lattices_Oboolean__algebra(X1))). 1.16/1.45 cnf(i_0_1493, plain, (X2=X3|c_Polynomial_Ocoeff(X1,X2)!=c_Polynomial_Ocoeff(X1,X3)|~class_Groups_Ozero(X1))). 1.16/1.45 cnf(i_0_733, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_734, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_1616, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_1612, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_527, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk31_0))). 1.16/1.45 cnf(i_0_1353, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_52, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_RealVector_Onorm__class_Onorm(X2,c_Groups_Osgn__class_Osgn(X2,X1))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~class_RealVector_Oreal__normed__vector(X2))). 1.16/1.45 cnf(i_0_104, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1572, plain, (c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))!=X2|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_545, plain, (c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_97, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_284, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1723, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)|X1!=X2)). 1.16/1.45 cnf(i_0_1012, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|X1!=X2)). 1.16/1.45 cnf(i_0_1273, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|X1!=X2)). 1.16/1.45 cnf(i_0_1080, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|X1!=X2)). 1.16/1.45 cnf(i_0_93, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 1.16/1.45 cnf(i_0_1362, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 1.16/1.45 cnf(i_0_549, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 1.16/1.45 cnf(i_0_747, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)=X1)). 1.16/1.45 cnf(i_0_12, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=X1)). 1.16/1.45 cnf(i_0_51, plain, (c_RealVector_Onorm__class_Onorm(X2,c_Groups_Osgn__class_Osgn(X2,X1))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_RealVector_Oreal__normed__vector(X2))). 1.16/1.45 cnf(i_0_791, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1408, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1234, plain, (~class_Rings_Olinordered__idom(X1)|~c_Polynomial_Opos__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))). 1.16/1.45 cnf(i_0_495, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_589, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_1642, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_1010, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1)=c_Groups_Oone__class_Oone(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1333, plain, (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))=c_RealVector_Onorm__class_Onorm(X1,X2)|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_218, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_1039, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1218, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1217, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=X2|~class_Lattices_Oab__semigroup__idem__mult(X1))). 1.16/1.45 cnf(i_0_1494, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=X2|~class_Lattices_Oab__semigroup__idem__mult(X1))). 1.16/1.45 cnf(i_0_553, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_804, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=X2)). 1.16/1.45 cnf(i_0_1695, plain, (X2=X3|c_Polynomial_Opoly(X1,X2)!=c_Polynomial_Opoly(X1,X3)|~class_Rings_Oidom(X1)|~class_Int_Oring__char__0(X1))). 1.16/1.45 cnf(i_0_1530, plain, (c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=c_RealVector_Onorm__class_Onorm(X1,X2)|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1306, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2))=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_1301, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2))=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_279, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_383, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1)). 1.16/1.45 cnf(i_0_1368, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1077, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X2)|~class_Orderings_Opreorder(X1))). 1.16/1.45 cnf(i_0_646, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1170, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X1)))). 1.16/1.45 cnf(i_0_1203, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X1)))). 1.16/1.45 cnf(i_0_1305, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_398, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~class_Groups_Omonoid__mult(X1))). 1.16/1.45 cnf(i_0_1257, plain, (c_Orderings_Oord__class_Oless__eq(X3,X2,X1)|X1!=X2|~class_Orderings_Oorder(X3))). 1.16/1.45 cnf(i_0_55, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|X2!=X3|~class_Orderings_Opreorder(X1))). 1.16/1.45 cnf(i_0_1178, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|X2!=X3|~class_Orderings_Oorder(X1))). 1.16/1.45 cnf(i_0_1179, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|X2!=X3|~class_Orderings_Oorder(X1))). 1.16/1.45 cnf(i_0_1156, plain, (c_Groups_Ominus__class_Ominus(X1,X2,X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_689, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_651, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Ocomm__monoid__mult(X1))). 1.16/1.45 cnf(i_0_943, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Omonoid__mult(X1))). 1.16/1.45 cnf(i_0_160, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_130, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Power_Opower(X1))). 1.16/1.45 cnf(i_0_665, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2)). 1.16/1.45 cnf(i_0_632, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1429, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Omonoid__add(X1))). 1.16/1.45 cnf(i_0_1480, plain, (c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1666, plain, (c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1))=X2|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_1325, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2)=X2|~class_Groups_Omonoid__add(X1))). 1.16/1.45 cnf(i_0_116, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ocomm__monoid__add(X1))). 1.16/1.45 cnf(i_0_365, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2)=X2|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_955, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2)=X2|~class_Groups_Ocomm__monoid__add(X1))). 1.16/1.45 cnf(i_0_9, plain, (hAPP(c_Polynomial_Opoly(X1,X2),X3)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))!=X2|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_978, plain, (c_Groups_Ominus__class_Ominus(X3,X2,X1)=c_Groups_Ozero__class_Ozero(X3)|X1!=X2|~class_Groups_Ogroup__add(X3))). 1.16/1.45 cnf(i_0_1489, plain, (c_Groups_Ominus__class_Ominus(X3,X1,X2)=c_Groups_Ozero__class_Ozero(X3)|X1!=X2|~class_Groups_Oab__group__add(X3))). 1.16/1.45 cnf(i_0_1261, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)=c_Groups_Oone__class_Oone(X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~class_Power_Opower(X2))). 1.16/1.45 cnf(i_0_101, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_1(X1))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_995, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk47_1(X1))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1356, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1))). 1.16/1.45 cnf(i_0_1427, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_830, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_337, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_146, plain, (c_Nat__Transfer_Otsub(X2,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1296, plain, (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)=X1|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_812, plain, (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)=X1|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1629, plain, (c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_1608, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Divides_Odiv__class_Odiv(X1,X2,X2)=c_Groups_Oone__class_Oone(X1)|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_1656, plain, (c_Groups_Oplus__class_Oplus(X1,X3,X2)=X3|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 1.16/1.45 cnf(i_0_595, plain, (c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X3),X2,X1)|X1!=X2|~class_Rings_Olinordered__idom(X3))). 1.16/1.45 cnf(i_0_702, plain, (c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_413, plain, (c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_47, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)=c_Groups_Oone__class_Oone(X2)|X1!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2))). 1.16/1.45 cnf(i_0_1405, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__no__zero__divisors(X1))). 1.16/1.45 cnf(i_0_1406, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__no__zero__divisors(X1))). 1.16/1.45 cnf(i_0_1103, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_295, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Omonoid__mult(X1))). 1.16/1.45 cnf(i_0_485, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Ocomm__monoid__mult(X1))). 1.16/1.45 cnf(i_0_1626, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__semidom(X1))). 1.16/1.45 cnf(i_0_256, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__semidom(X1))). 1.16/1.45 cnf(i_0_1527, plain, (c_Groups_Oplus__class_Oplus(X2,X1,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Olinordered__ab__group__add(X2))). 1.16/1.45 cnf(i_0_1444, plain, (c_Groups_Oplus__class_Oplus(X1,X2,X2)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Groups_Olinordered__ab__group__add(X1))). 1.16/1.45 cnf(i_0_1569, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_550, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2)=c_Groups_Oone__class_Oone(X1)|~class_Groups_Omonoid__mult(X1))). 1.16/1.45 cnf(i_0_1448, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1))). 1.16/1.45 cnf(i_0_1286, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_822, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1595, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))). 1.16/1.45 cnf(i_0_14, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)!=X2)). 1.16/1.45 cnf(i_0_1121, plain, (c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))=c_Power_Opower__class_Opower(X1)|~class_Power_Opower(X1))). 1.16/1.45 cnf(i_0_1090, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_364, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)))). 1.16/1.45 cnf(i_0_555, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_554, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_803, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_802, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_556, plain, (c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2)=c_Groups_Ouminus__class_Ouminus(X1,X2)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_237, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oone__class_Oone(tc_Nat_Onat)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=X1)). 1.16/1.45 cnf(i_0_1270, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|X1!=X2)). 1.16/1.45 cnf(i_0_446, plain, (c_Groups_Oabs__class_Oabs(X1,X2)=X2|c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oabs__if(X1))). 1.16/1.45 cnf(i_0_434, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1))). 1.16/1.45 cnf(i_0_1709, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1))). 1.16/1.45 cnf(i_0_732, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1154, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_1754, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1)). 1.16/1.45 cnf(i_0_238, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))|c_Polynomial_Opos__poly(X1,X2)|c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_917, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1)=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Osemiring__0(X2)|~class_Power_Opower(X2))). 1.16/1.45 cnf(i_0_508, plain, (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))=X2|~class_Groups_Ocomm__monoid__add(X1))). 1.16/1.45 cnf(i_0_255, plain, (c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))=X2|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_373, plain, (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)=X2|~class_Groups_Ocomm__monoid__add(X1))). 1.16/1.45 cnf(i_0_1636, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Osgn__class_Osgn(X1,X2))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_770, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_208, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_677, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_678, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_775, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1160, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1186, plain, (X1!=X2|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_609, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oabs__class_Oabs(X1,X2))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_360, plain, (hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X2)=c_Groups_Oone__class_Oone(X1)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_728, plain, (hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_1026, plain, (hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ozero(X1))). 1.16/1.45 cnf(i_0_1423, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1))))). 1.16/1.45 cnf(i_0_1231, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_435, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1621, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_403, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_843, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_1082, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_966, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=X1)). 1.16/1.45 cnf(i_0_918, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1)=c_Groups_Oone__class_Oone(X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~class_Rings_Osemiring__0(X2)|~class_Power_Opower(X2))). 1.16/1.45 cnf(i_0_1114, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_906, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk46_2(X1,X2))|~class_RealVector_Oreal__normed__algebra(X2))). 1.16/1.45 cnf(i_0_1188, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk55_2(X1,X2))|~class_RealVector_Oreal__normed__algebra(X2))). 1.16/1.45 cnf(i_0_260, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk17_2(X1,X2))|~class_RealVector_Oreal__normed__algebra(X2))). 1.16/1.45 cnf(i_0_1066, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk52_2(X1,X2))|~class_RealVector_Oreal__normed__algebra(X2))). 1.16/1.45 cnf(i_0_1248, plain, (c_Groups_Oplus__class_Oplus(X2,X3,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2))). 1.16/1.45 cnf(i_0_1038, plain, (c_Groups_Oplus__class_Oplus(X2,X1,X3)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Groups_Ogroup__add(X2))). 1.16/1.45 cnf(i_0_1312, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X1)). 1.16/1.45 cnf(i_0_1371, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X1)). 1.16/1.45 cnf(i_0_157, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_667, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_666, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_21, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_77, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1688, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_1283, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2))),X1)=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Ocomm__semiring__1(X2))). 1.16/1.45 cnf(i_0_231, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1))). 1.16/1.45 cnf(i_0_34, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))). 1.16/1.45 cnf(i_0_1122, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1))). 1.16/1.45 cnf(i_0_106, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_664, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_766, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1394, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1545, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1019, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_645, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_1575, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X2))). 1.16/1.45 cnf(i_0_1282, plain, (hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2))),X1)=c_Groups_Oone__class_Oone(X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~class_Rings_Ocomm__semiring__1(X2))). 1.16/1.45 cnf(i_0_1159, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_1219, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1392, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_959, plain, (c_RComplete_Onatceiling(X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_989, plain, (c_RComplete_Onatfloor(X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1268, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_336, plain, (X2!=X3|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1330, plain, (X2!=X3|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1600, plain, (X2!=X3|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1319, plain, (X2!=X3|~class_Orderings_Olinorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1320, plain, (X2!=X3|~class_Orderings_Olinorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_826, plain, (X1!=X2|~class_Orderings_Oorder(X3)|~c_Orderings_Oord__class_Oless(X3,X1,X2))). 1.16/1.45 cnf(i_0_387, plain, (X1!=X2|~class_Orderings_Olinorder(X3)|~c_Orderings_Oord__class_Oless(X3,X1,X2))). 1.16/1.45 cnf(i_0_46, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))!=X2|~class_Rings_Oring__1__no__zero__divisors(X1))). 1.16/1.45 cnf(i_0_1113, plain, (X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Omult__zero(X1)|~class_Power_Opower(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1))). 1.16/1.45 cnf(i_0_1654, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1759, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_658, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_1130, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_1715, plain, (c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))=X2|c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))!=c_Polynomial_Opoly(X1,X2)|~class_Rings_Oidom(X1)|~class_Int_Oring__char__0(X1))). 1.16/1.45 cnf(i_0_1400, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_782, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oabs__class_Oabs(X2,X1))|~class_Groups_Oordered__ab__group__add__abs(X2))). 1.16/1.45 cnf(i_0_1657, plain, (c_Groups_Ozero__class_Ozero(X2)=X3|c_Groups_Oplus__class_Oplus(X2,X1,X3)!=X1|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2))). 1.16/1.45 cnf(i_0_13, plain, (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)=X2|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1460, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 1.16/1.45 cnf(i_0_1360, plain, (c_Transcendental_Oln(X1)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=X1|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_977, plain, (X2=X3|c_Groups_Ominus__class_Ominus(X1,X2,X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1488, plain, (X2=X3|c_Groups_Ominus__class_Ominus(X1,X2,X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_491, plain, (c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Ozero__class_Ozero(X2))|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__ab__group__add__abs(X2))). 1.16/1.45 cnf(i_0_1359, plain, (c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=X1|c_Transcendental_Oln(X1)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1197, plain, (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1528, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Oplus__class_Oplus(X1,X2,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1))). 1.16/1.45 cnf(i_0_1443, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,X2,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1))). 1.16/1.45 cnf(i_0_1624, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))). 1.16/1.45 cnf(i_0_703, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))). 1.16/1.45 cnf(i_0_126, plain, (c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_461, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ono__zero__divisors(X1))). 1.16/1.45 cnf(i_0_158, plain, (c_Groups_Ozero__class_Ozero(X1)=X3|c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ono__zero__divisors(X1))). 1.16/1.45 cnf(i_0_1407, plain, (c_Groups_Ozero__class_Ozero(X1)=X3|c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1))). 1.16/1.45 cnf(i_0_330, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_432, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_399, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1232, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_436, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1622, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_680, plain, (c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X1),X2)=X2|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1526, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Osgn__if(X1))). 1.16/1.45 cnf(i_0_10, plain, (c_Polynomial_Oorder(X1,X2,X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Opoly(X1,X3),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_676, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1551, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_648, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1344, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_985, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1322, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_39, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_2(X1,X2))|~class_RealVector_Oreal__normed__vector(X2)|~c_SEQ_OBseq(X2,X1))). 1.16/1.45 cnf(i_0_191, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk10_2(X1,X2))|~class_RealVector_Oreal__normed__vector(X2)|~c_SEQ_OBseq(X2,X1))). 1.16/1.45 cnf(i_0_741, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk37_2(X1,X2))|~class_RealVector_Oreal__normed__vector(X2)|~c_SEQ_OBseq(X2,X1))). 1.16/1.45 cnf(i_0_1042, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk50_2(X1,X2))|~class_RealVector_Oreal__normed__vector(X2)|~c_SEQ_OBseq(X2,X1))). 1.16/1.45 cnf(i_0_309, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_421, plain, (~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_533, plain, (~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_811, plain, (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1297, plain, (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1630, plain, (c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_1266, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oabs__class_Oabs(X1,X2))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_1249, plain, (X3=c_Groups_Ouminus__class_Ouminus(X1,X2)|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1037, plain, (X2=c_Groups_Ouminus__class_Ouminus(X1,X3)|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_29, plain, (c_Groups_Ouminus__class_Ouminus(X1,X2)=X3|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_30, plain, (c_Groups_Oplus__class_Oplus(X1,X2,X3)=c_Groups_Oplus__class_Oplus(X1,X3,X2)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_363, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_834, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_61, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_1692, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_186, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_204, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_1129, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_1191, plain, (c_Groups_Oabs__class_Oabs(X1,X2)=X2|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1705, plain, (c_Groups_Oabs__class_Oabs(X1,X2)=X2|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_95, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_388, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_405, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_737, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_919, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1))). 1.16/1.45 cnf(i_0_1516, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1318, plain, (X1=X2|c_Orderings_Oord__class_Oless(X3,X2,X1)|c_Orderings_Oord__class_Oless(X3,X1,X2)|~class_Orderings_Olinorder(X3))). 1.16/1.45 cnf(i_0_540, plain, (c_Orderings_Oord__class_Oless__eq(X3,X2,X1)|c_Orderings_Oord__class_Oless(X3,X2,X1)|X1!=X2|~class_Orderings_Olinorder(X3))). 1.16/1.45 cnf(i_0_594, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1267, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1141, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_45, plain, (X2=c_Groups_Oone__class_Oone(X1)|c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 1.16/1.45 cnf(i_0_1112, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1)|~class_Power_Opower(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1))). 1.16/1.45 cnf(i_0_1111, plain, (X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Omult__zero(X2)|~class_Power_Opower(X2)|~class_Rings_Ono__zero__divisors(X2)|~class_Rings_Ozero__neq__one(X2))). 1.16/1.45 cnf(i_0_1381, plain, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1271, plain, (X1=X2|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1525, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|~class_Groups_Osgn__if(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_263, plain, (c_SEQ_Odecseq(X2,X1)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk18_2(X1,X2),esk19_2(X1,X2))|~class_Orderings_Oorder(X2))). 1.16/1.45 cnf(i_0_762, plain, (c_SEQ_Oincseq(X2,X1)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk40_2(X1,X2),esk41_2(X1,X2))|~class_Orderings_Oorder(X2))). 1.16/1.45 cnf(i_0_1285, plain, (X1=X2|hAPP(X1,esk62_2(X1,X2))!=hAPP(X2,esk62_2(X1,X2)))). 1.16/1.45 cnf(i_0_1155, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1755, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_773, plain, (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))=c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2))). 1.16/1.45 cnf(i_0_389, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_171, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_709, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1134, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1699, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_302, plain, (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1501, plain, (c_Groups_Oabs__class_Oabs(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_314, plain, (c_Groups_Oabs__class_Oabs(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_447, plain, (c_Groups_Oabs__class_Oabs(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,X2)|~class_Groups_Oabs__if(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_656, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)|X1!=c_Groups_Ouminus__class_Ouminus(X2,X3)|~class_Rings_Oidom(X2))). 1.16/1.45 cnf(i_0_1060, plain, (~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_771, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_1724, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_776, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1011, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1081, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1588, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1729, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1185, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_472, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1142, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_730, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2))=X2|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_197, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))). 1.16/1.45 cnf(i_0_1522, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))). 1.16/1.45 cnf(i_0_1576, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,X1),X2),X3)=c_Groups_Ouminus__class_Ouminus(X1,hAPP(X2,X3))|~class_Groups_Ouminus(X1))). 1.16/1.45 cnf(i_0_1341, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1706, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_393, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_772, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_1725, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_441, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_777, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1079, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1184, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1342, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_1655, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1417, plain, (c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Oplus__class_Oplus(X1,X2,X3)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1109, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_827, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Rings_Ocomm__ring__1(X1))). 1.16/1.45 cnf(i_0_439, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ominus__class_Ominus(X1,X2,X3)|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_1280, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)))). 1.16/1.45 cnf(i_0_270, plain, (~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_921, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)))). 1.16/1.45 cnf(i_0_1391, plain, (c_Groups_Ozero__class_Ozero(X1)!=X2|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)))). 1.16/1.45 cnf(i_0_622, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_623, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_1554, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_476, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X2)). 1.16/1.45 cnf(i_0_1717, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_825, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1258, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_96, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_542, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_492, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1449, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_662, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_940, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|X1!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=X2|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_644, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2)=c_Groups_Ouminus__class_Ouminus(X1,X2)|~class_Rings_Ocomm__ring__1(X1))). 1.16/1.45 cnf(i_0_639, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)))). 1.16/1.45 cnf(i_0_1625, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2))). 1.16/1.45 cnf(i_0_1700, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2))). 1.16/1.45 cnf(i_0_19, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_37, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_1256, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_1422, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_215, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_539, plain, (X2=X3|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_824, plain, (X1=X2|c_Orderings_Oord__class_Oless(X3,X1,X2)|~class_Orderings_Oorder(X3)|~c_Orderings_Oord__class_Oless__eq(X3,X1,X2))). 1.16/1.45 cnf(i_0_914, plain, (c_Nat__Transfer_Otsub(X2,X1)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_147, plain, (c_Nat__Transfer_Otsub(X2,X1)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1384, plain, (X2=X3|X1=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))). 1.16/1.45 cnf(i_0_1675, plain, (X1=X3|X2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))). 1.16/1.45 cnf(i_0_1757, plain, (X1=X3|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))). 1.16/1.45 cnf(i_0_659, plain, (X2=X3|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))). 1.16/1.45 cnf(i_0_1132, plain, (X2=X3|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))). 1.16/1.45 cnf(i_0_1069, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1367, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1733, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_440, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_172, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_251, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)))). 1.16/1.45 cnf(i_0_475, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk26_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_783, plain, (X2!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2)))). 1.16/1.45 cnf(i_0_1328, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_815, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_1070, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_1732, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1)))). 1.16/1.45 cnf(i_0_459, plain, (c_SMT_Oz3div(X2,X1)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_1570, plain, (c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))=X2|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)))=c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2)|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_400, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)))). 1.16/1.45 cnf(i_0_429, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))). 1.16/1.45 cnf(i_0_988, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1))). 1.16/1.45 cnf(i_0_1389, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X1))). 1.16/1.45 cnf(i_0_1240, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)=X1)). 1.16/1.45 cnf(i_0_1290, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1)=X2)). 1.16/1.45 cnf(i_0_1087, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_22, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1035, plain, (hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk49_2(X1,X2),X1)|~hBOOL(hAPP(X2,X1)))). 1.16/1.45 cnf(i_0_196, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk13_2(X2,X1))=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1521, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk69_2(X2,X1))=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_75, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1647, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X1!=X2)). 1.16/1.45 cnf(i_0_179, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))|X1!=X2)). 1.16/1.45 cnf(i_0_1055, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 1.16/1.45 cnf(i_0_89, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_560, plain, (X2=X3|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))). 1.16/1.45 cnf(i_0_1707, plain, (X1=X3|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))). 1.16/1.45 cnf(i_0_443, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_942, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_941, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_1208, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3)=X2|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1151, plain, (c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3)=X2|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1738, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X1)). 1.16/1.45 cnf(i_0_813, plain, (X1=X2|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_767, plain, (X1=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1395, plain, (X1=X2|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_234, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))|~class_Rings_Olinordered__ring(X1))). 1.16/1.45 cnf(i_0_1653, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2)=X3|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_1226, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)=X3|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_679, plain, (c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X1),X2)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))). 1.16/1.45 cnf(i_0_214, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2))). 1.16/1.45 cnf(i_0_1571, plain, (c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))=X2|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2))). 1.16/1.45 cnf(i_0_27, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_1336, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,esk64_1(X1)))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_99, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_710, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,esk36_1(X1)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_122, plain, (X1=X2|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_11, plain, (c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))=X2|c_Polynomial_Oorder(X1,X3,X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Opoly(X1,X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_567, plain, (X1=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_982, plain, (X1=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_1546, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2))). 1.16/1.45 cnf(i_0_1062, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)))). 1.16/1.45 cnf(i_0_933, plain, (~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_543, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2))). 1.16/1.45 cnf(i_0_271, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_362, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_712, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1372, plain, (~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_205, plain, (~class_Orderings_Olinorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1584, plain, (~class_Orderings_Olinorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2))). 1.16/1.45 cnf(i_0_1691, plain, (~class_Orderings_Olinorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X2))). 1.16/1.45 cnf(i_0_386, plain, (~class_Orderings_Olinorder(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X2)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_968, plain, (c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 1.16/1.45 cnf(i_0_948, plain, (X3=X4|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X2,X4)|~class_Groups_Ocancel__ab__semigroup__add(X1))). 1.16/1.45 cnf(i_0_808, plain, (X3=X4|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X2,X4)|~class_Groups_Ocancel__semigroup__add(X1))). 1.16/1.45 cnf(i_0_1672, plain, (X3=X4|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X2,X4)|~class_Groups_Ocancel__semigroup__add(X1))). 1.16/1.45 cnf(i_0_210, plain, (X2=X4|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X4,X3)|~class_Groups_Ocancel__semigroup__add(X1))). 1.16/1.45 cnf(i_0_1021, plain, (X2=X4|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Oplus__class_Oplus(X1,X4,X3)|~class_Groups_Ocancel__semigroup__add(X1))). 1.16/1.45 cnf(i_0_169, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1))). 1.16/1.45 cnf(i_0_90, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)))). 1.16/1.45 cnf(i_0_7, plain, (X2=X3|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_456, plain, (X2=X3|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_671, plain, (X2=X3|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_1180, plain, (X2=X3|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_947, plain, (c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))=c_Groups_Ominus__class_Ominus(X1,X3,X2)|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_946, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1293, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_216, plain, (X1!=X2|~class_Orderings_Olinorder(X3)|~c_Orderings_Oord__class_Oless__eq(X3,X2,X1)|~c_Orderings_Oord__class_Oless(X3,X2,X1))). 1.16/1.45 cnf(i_0_1074, plain, (c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)|c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))!=X1)). 1.16/1.45 cnf(i_0_1246, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_796, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_1747, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1378, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1339, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_799, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_487, plain, (X3=X4|X1!=X2|c_Groups_Ominus__class_Ominus(X5,X2,X1)!=c_Groups_Ominus__class_Ominus(X5,X3,X4)|~class_Groups_Oab__group__add(X5))). 1.16/1.45 cnf(i_0_486, plain, (X3=X4|X1!=X2|c_Groups_Ominus__class_Ominus(X5,X1,X2)!=c_Groups_Ominus__class_Ominus(X5,X4,X3)|~class_Groups_Oab__group__add(X5))). 1.16/1.45 cnf(i_0_1215, plain, (c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))|~class_Rings_Olinordered__idom(X1)|~c_Polynomial_Opos__poly(X1,X3)|~c_Polynomial_Opos__poly(X1,X2))). 1.16/1.45 cnf(i_0_740, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk37_2(X2,X1))|~class_RealVector_Oreal__normed__vector(X1)|~c_SEQ_OBseq(X1,X2))). 1.16/1.45 cnf(i_0_1041, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk50_2(X2,X1))|~class_RealVector_Oreal__normed__vector(X1)|~c_SEQ_OBseq(X1,X2))). 1.16/1.45 cnf(i_0_654, plain, (X2=X3|X2=c_Groups_Ouminus__class_Ouminus(X1,X3)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_1025, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3))). 1.16/1.45 cnf(i_0_1503, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3))). 1.16/1.45 cnf(i_0_111, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3))). 1.16/1.45 cnf(i_0_1601, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|~class_Rings_Oring(X1))). 1.16/1.45 cnf(i_0_278, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Rings_Oring(X1))). 1.16/1.45 cnf(i_0_1300, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1712, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_963, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1169, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X2))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1649, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1686, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1590, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_759, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|hBOOL(hAPP(hAPP(X3,X1),X2)))). 1.16/1.45 cnf(i_0_1710, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__0(X1)|~class_Power_Opower(X1))). 1.16/1.45 cnf(i_0_1056, plain, (X1=X2|c_Transcendental_Oln(X1)!=c_Transcendental_Oln(X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_250, plain, (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X2))). 1.16/1.45 cnf(i_0_739, plain, (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2))). 1.16/1.45 cnf(i_0_829, plain, (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2))). 1.16/1.45 cnf(i_0_1746, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)))). 1.16/1.45 cnf(i_0_1379, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)))). 1.16/1.45 cnf(i_0_1340, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2))). 1.16/1.45 cnf(i_0_800, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2))). 1.16/1.45 cnf(i_0_1607, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Oplus__class_Oplus(X1,X3,X2))=X2|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_213, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),X1))). 1.16/1.45 cnf(i_0_381, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1211, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))))). 1.16/1.45 cnf(i_0_898, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1))). 1.16/1.45 cnf(i_0_1343, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_131, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_953, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_605, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Lattices_Oboolean__algebra(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_1505, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Lattices_Oboolean__algebra(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_155, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_379, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_382, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_449, plain, (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_23, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_991, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1287, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))|~class_Rings_Oring(X1))). 1.16/1.45 cnf(i_0_544, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2))). 1.16/1.45 cnf(i_0_380, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_1711, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)))). 1.16/1.45 cnf(i_0_962, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)))). 1.16/1.45 cnf(i_0_1650, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1168, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X2)))). 1.16/1.45 cnf(i_0_1687, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1589, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_945, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))). 1.16/1.45 cnf(i_0_1294, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))). 1.16/1.45 cnf(i_0_1409, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_482, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))))). 1.16/1.45 cnf(i_0_792, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_793, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X2)). 1.16/1.45 cnf(i_0_1241, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_1242, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X2)). 1.16/1.45 cnf(i_0_1292, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|~class_Lattices_Oab__semigroup__idem__mult(X1))). 1.16/1.45 cnf(i_0_615, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)))). 1.16/1.45 cnf(i_0_1721, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))=c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))). 1.16/1.45 cnf(i_0_768, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)))). 1.16/1.45 cnf(i_0_769, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)))). 1.16/1.45 cnf(i_0_668, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)))). 1.16/1.45 cnf(i_0_669, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)))). 1.16/1.45 cnf(i_0_331, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3))). 1.16/1.45 cnf(i_0_332, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3))). 1.16/1.45 cnf(i_0_1459, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3))). 1.16/1.45 cnf(i_0_1502, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3))). 1.16/1.45 cnf(i_0_1482, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3))). 1.16/1.45 cnf(i_0_1483, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3))). 1.16/1.45 cnf(i_0_110, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3))). 1.16/1.45 cnf(i_0_1095, plain, (c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)|~class_Orderings_Oord(X2)|~c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4))). 1.16/1.45 cnf(i_0_28, plain, (hAPP(c_Polynomial_Opoly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3)=c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3))|~class_Rings_Ocomm__ring(X1))). 1.16/1.45 cnf(i_0_578, plain, (hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3)=c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Ocoeff(X1,X2),X3))|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_151, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_269, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_276, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 1.16/1.45 cnf(i_0_1697, plain, (c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))|~class_Rings_Olinordered__idom(X1)|~c_Polynomial_Opos__poly(X1,X3)|~c_Polynomial_Opos__poly(X1,X2))). 1.16/1.45 cnf(i_0_1161, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X1!=X2)). 1.16/1.45 cnf(i_0_261, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4),hAPP(X2,X3))|~class_Orderings_Oorder(X1)|~c_SEQ_Odecseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4))). 1.16/1.45 cnf(i_0_763, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X2,X4))|~class_Orderings_Oorder(X1)|~c_SEQ_Oincseq(X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4))). 1.16/1.45 cnf(i_0_1596, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_1750, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_577, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_909, plain, (c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2))=X2|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_341, plain, (c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3)|~class_RealVector_Oreal__normed__div__algebra(X1))). 1.16/1.45 cnf(i_0_997, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)!=X3|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1))). 1.16/1.45 cnf(i_0_998, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)=X2|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1))). 1.16/1.45 cnf(i_0_62, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_63, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_220, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_607, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)|~class_Rings_Oring(X1))). 1.16/1.45 cnf(i_0_534, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_523, plain, (c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_719, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))). 1.16/1.45 cnf(i_0_1737, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_385, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_647, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_384, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_1345, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_202, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),esk14_3(X2,X3,X1))|~class_Fields_Olinordered__field(X1))). 1.16/1.45 cnf(i_0_612, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),esk33_3(X2,X3,X1))|~class_Fields_Olinordered__field__inverse__zero(X1))). 1.16/1.45 cnf(i_0_611, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,esk33_3(X2,X3,X1),c_Groups_Oone__class_Oone(X1))|~class_Fields_Olinordered__field__inverse__zero(X1))). 1.16/1.45 cnf(i_0_952, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)))). 1.16/1.45 cnf(i_0_1506, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Lattices_Oboolean__algebra(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)))). 1.16/1.45 cnf(i_0_154, plain, (c_Orderings_Oord__class_Oless(X1,X3,X2)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)))). 1.16/1.45 cnf(i_0_458, plain, (c_SMT_Oz3div(X2,X1)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_161, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1)=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1544, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1)=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1086, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))). 1.16/1.45 cnf(i_0_156, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_1454, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X3,X2))|~class_Groups_Ogroup__add(X1))). 1.16/1.45 cnf(i_0_1658, plain, (c_Groups_Ominus__class_Ominus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))=c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_1435, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X2)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_1704, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_340, plain, (c_Orderings_Oord__class_Oless(X1,X4,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X2)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1220, plain, (c_Orderings_Oord__class_Oless(X1,X4,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X2))). 1.16/1.45 cnf(i_0_105, plain, (c_Orderings_Oord__class_Oless(X1,X4,X3)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless(X1,X4,X2)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1685, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_98, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X3,X4))). 1.16/1.45 cnf(i_0_56, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1183, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_816, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1327, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_696, plain, (X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_638, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X1|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)))). 1.16/1.45 cnf(i_0_297, plain, (c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,X3))). 1.16/1.45 cnf(i_0_1648, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)))). 1.16/1.45 cnf(i_0_597, plain, (X2=X3|c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3))). 1.16/1.45 cnf(i_0_49, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1753, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_189, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1007, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1245, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))). 1.16/1.45 cnf(i_0_794, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_1244, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_797, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_422, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))). 1.16/1.45 cnf(i_0_108, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_660, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1005, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1135, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_356, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1565, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_100, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_936, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_120, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1196, plain, (c_Orderings_Oord__class_Oless__eq(X2,hAPP(X3,X5),hAPP(X4,X5))|~class_Orderings_Oord(X2)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4))). 1.16/1.45 cnf(i_0_457, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))|~class_Orderings_Oord(X1)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4))). 1.16/1.45 cnf(i_0_1385, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))|~class_Orderings_Oord(X1)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4))). 1.16/1.45 cnf(i_0_1084, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1)). 1.16/1.45 cnf(i_0_424, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)))). 1.16/1.45 cnf(i_0_1357, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_84, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))=X1|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1216, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1)=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_48, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_188, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1)))). 1.16/1.45 cnf(i_0_650, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1)))). 1.16/1.45 cnf(i_0_520, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1)))). 1.16/1.45 cnf(i_0_1008, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(X1)))). 1.16/1.45 cnf(i_0_425, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2)),X1))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 1.16/1.45 cnf(i_0_630, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_294, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_1350, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1145, plain, (c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3))|~class_Fields_Ofield(X1))). 1.16/1.45 cnf(i_0_1722, plain, (c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2),X3)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3))|~class_Fields_Ofield(X1))). 1.16/1.45 cnf(i_0_473, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2))). 1.16/1.45 cnf(i_0_785, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1))). 1.16/1.45 cnf(i_0_548, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1668, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_915, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_286, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1307, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_806, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1646, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_839, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_180, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_552, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_653, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_818, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_764, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1523, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1628, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))=c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_RealVector_Oreal__normed__div__algebra(X1))). 1.16/1.45 cnf(i_0_1015, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|X1!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X2)). 1.16/1.45 cnf(i_0_1029, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1030, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_44, plain, (c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))=c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1566, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))=c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_927, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X1!=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1))). 1.16/1.45 cnf(i_0_1667, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X2)). 1.16/1.45 cnf(i_0_582, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))=c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1329, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))=c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_RealVector_Oreal__normed__div__algebra(X1))). 1.16/1.45 cnf(i_0_78, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))=c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1597, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_987, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1451, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1072, plain, (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_1033, plain, (hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(X3,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk49_2(X2,X3)))). 1.16/1.45 cnf(i_0_431, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 1.16/1.45 cnf(i_0_367, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1420, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2))). 1.16/1.45 cnf(i_0_1375, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_144, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk9_2(X1,X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))). 1.16/1.45 cnf(i_0_312, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk22_2(X1,X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))). 1.16/1.45 cnf(i_0_1166, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 1.16/1.45 cnf(i_0_18, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_1176, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1094, plain, (~class_Orderings_Oord(X2)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)|~c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X4,X3))). 1.16/1.45 cnf(i_0_1036, plain, (~class_Rings_Olinordered__ring(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1313, plain, (c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1581, plain, (c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1481, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1651, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2))). 1.16/1.45 cnf(i_0_406, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_503, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1419, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2))). 1.16/1.45 cnf(i_0_366, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)))). 1.16/1.45 cnf(i_0_1439, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)))). 1.16/1.45 cnf(i_0_417, plain, (X3=X4|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2))). 1.16/1.45 cnf(i_0_26, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_961, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_177, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_349, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_72, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_82, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_990, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_902, plain, (c_Groups_Oplus__class_Oplus(X2,X3,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ozero__class_Ozero(X2)!=X3|~class_Groups_Oordered__comm__monoid__add(X2)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1))). 1.16/1.45 cnf(i_0_143, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk9_2(X1,X2)),X2)=X1|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))). 1.16/1.45 cnf(i_0_313, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk22_2(X1,X2)),X2)=X1|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))). 1.16/1.45 cnf(i_0_596, plain, (c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2)|~class_Rings_Olinordered__idom(X1)|~c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)))). 1.16/1.45 cnf(i_0_296, plain, (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X3,X2)|~class_Rings_Olinordered__idom(X1)|~c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)))). 1.16/1.45 cnf(i_0_1474, plain, (c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Divides_Osemiring__div(X2))). 1.16/1.45 cnf(i_0_1662, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2))). 1.16/1.45 cnf(i_0_1490, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2))). 1.16/1.45 cnf(i_0_511, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)))). 1.16/1.45 cnf(i_0_1101, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)))). 1.16/1.45 cnf(i_0_212, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2),X1))). 1.16/1.45 cnf(i_0_1518, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Transcendental_Oln(X1))=c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1475, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(X2,X3),hAPP(X4,X3))=hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,X1),X2,X4),X3)|~class_Groups_Ominus(X1))). 1.16/1.45 cnf(i_0_1001, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))). 1.16/1.45 cnf(i_0_1002, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 1.16/1.45 cnf(i_0_321, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X3|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Olinordered__ring__strict(X1))). 1.16/1.45 cnf(i_0_1085, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))). 1.16/1.45 cnf(i_0_1534, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))). 1.16/1.45 cnf(i_0_1447, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))). 1.16/1.45 cnf(i_0_1326, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))). 1.16/1.45 cnf(i_0_814, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))). 1.16/1.45 cnf(i_0_64, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|X2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X1)). 1.16/1.45 cnf(i_0_1096, plain, (c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X4,X3)|c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)|~class_Orderings_Oord(X2)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4))). 1.16/1.45 cnf(i_0_904, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Oplus__class_Oplus(X2,X3,X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__comm__monoid__add(X2)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1))). 1.16/1.45 cnf(i_0_903, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,X2,X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_247, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk16_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_795, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_1243, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))). 1.16/1.45 cnf(i_0_345, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 1.16/1.45 cnf(i_0_823, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1146, plain, (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_RealDef_Oreal(tc_Nat_Onat,X1))=c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_935, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X3))). 1.16/1.45 cnf(i_0_292, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3))). 1.16/1.45 cnf(i_0_1682, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3))). 1.16/1.45 cnf(i_0_325, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2))). 1.16/1.45 cnf(i_0_326, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2))). 1.16/1.45 cnf(i_0_1061, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3))). 1.16/1.45 cnf(i_0_54, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3))). 1.16/1.45 cnf(i_0_1504, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3))). 1.16/1.45 cnf(i_0_109, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3))). 1.16/1.45 cnf(i_0_1585, plain, (c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_91, plain, (c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1467, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1401, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X4)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_481, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_629, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))). 1.16/1.45 cnf(i_0_293, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1349, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_248, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X3)). 1.16/1.45 cnf(i_0_1308, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_838, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_916, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_1477, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))). 1.16/1.45 cnf(i_0_551, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))). 1.16/1.45 cnf(i_0_652, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))). 1.16/1.45 cnf(i_0_1756, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))). 1.16/1.45 cnf(i_0_1144, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))). 1.16/1.45 cnf(i_0_765, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))). 1.16/1.45 cnf(i_0_1088, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1162, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1253, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1645, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_181, plain, (X1=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_1532, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))). 1.16/1.45 cnf(i_0_633, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)))). 1.16/1.45 cnf(i_0_976, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)))). 1.16/1.45 cnf(i_0_1476, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)))). 1.16/1.45 cnf(i_0_324, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)))). 1.16/1.45 cnf(i_0_471, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2))). 1.16/1.45 cnf(i_0_1438, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))). 1.16/1.45 cnf(i_0_249, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))). 1.16/1.45 cnf(i_0_195, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_288, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1635, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_693, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1446, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1533, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1577, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1163, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|c_Groups_Ominus__class_Ominus(X1,X2,X3)!=c_Groups_Ominus__class_Ominus(X1,X4,X5)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_1164, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|c_Groups_Ominus__class_Ominus(X1,X2,X3)!=c_Groups_Ominus__class_Ominus(X1,X4,X5)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_583, plain, (c_Orderings_Oord__class_Oless(X1,X4,X5)|c_Groups_Ominus__class_Ominus(X1,X2,X3)!=c_Groups_Ominus__class_Ominus(X1,X4,X5)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_584, plain, (c_Orderings_Oord__class_Oless(X1,X4,X5)|c_Groups_Ominus__class_Ominus(X1,X2,X3)!=c_Groups_Ominus__class_Ominus(X1,X4,X5)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_524, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_145, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_187, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))))). 1.16/1.45 cnf(i_0_407, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),v_m____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r))). 1.16/1.45 cnf(i_0_528, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),esk31_0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r))). 1.16/1.45 cnf(i_0_1076, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),esk53_0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r))). 1.16/1.45 cnf(i_0_132, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),X2)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_118, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Power_Opower(X1))). 1.16/1.45 cnf(i_0_1424, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1677, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1051, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_410, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1000, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_726, plain, (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))))). 1.16/1.45 cnf(i_0_1745, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_103, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_76, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_17, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1177, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1473, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))=c_Divides_Odiv__class_Odiv(X2,X3,X4)|~class_Divides_Osemiring__div(X2))). 1.16/1.45 cnf(i_0_628, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=c_Divides_Odiv__class_Odiv(X1,X3,X4)|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_113, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))=c_Divides_Odiv__class_Odiv(X1,X3,X4)|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_1315, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1236, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_510, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1102, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). 1.16/1.45 cnf(i_0_1663, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)))). 1.16/1.45 cnf(i_0_1491, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)))). 1.16/1.45 cnf(i_0_115, plain, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))). 1.16/1.45 cnf(i_0_1376, plain, (c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))=c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_301, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)=c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1552, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)=c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_246, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)=c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Groups_Oab__semigroup__add(X1))). 1.16/1.45 cnf(i_0_1223, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_141, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_3(X1,X2,X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1))). 1.16/1.45 cnf(i_0_244, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk15_3(X1,X2,X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1))). 1.16/1.45 cnf(i_0_361, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_350, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_73, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_83, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_960, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)))). 1.16/1.45 cnf(i_0_178, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Olinordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)))). 1.16/1.45 cnf(i_0_1181, plain, (c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X2),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2))). 1.16/1.45 cnf(i_0_1049, plain, (c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X2),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2))). 1.16/1.45 cnf(i_0_396, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_1314, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~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,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2)))). 1.16/1.45 cnf(i_0_1235, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2)))). 1.16/1.45 cnf(i_0_1751, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_690, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1641, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_68, plain, (X1=X3|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1))). 1.16/1.45 cnf(i_0_900, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))=c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_442, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X3!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_8, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 1.16/1.45 cnf(i_0_1289, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_1587, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_1472, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_134, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_1583, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_121, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_185, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_661, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_1364, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_1149, plain, (c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_445, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk25_2(X1,X2),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_152, plain, (~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_268, plain, (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))). 1.16/1.45 cnf(i_0_790, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Groups_Oone__class_Oone(X1))=c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X3,X2),X2)|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_1351, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Groups_Oone__class_Oone(X1))=c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2)|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_926, plain, (X1=X2|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_444, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk25_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_778, plain, (c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3))=c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 1.16/1.45 cnf(i_0_1165, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))). 1.16/1.45 cnf(i_0_392, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1281, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_374, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_85, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1442, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1586, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1278, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1453, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_66, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_784, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)))). 1.16/1.45 cnf(i_0_626, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,X2))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1071, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_470, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1396, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_494, plain, (c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1550, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))). 1.16/1.45 cnf(i_0_262, plain, (c_SEQ_Odecseq(X1,X2)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk19_2(X2,X1)),hAPP(X2,esk18_2(X2,X1))))). 1.16/1.45 cnf(i_0_761, plain, (c_SEQ_Oincseq(X1,X2)|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk40_2(X2,X1)),hAPP(X2,esk41_2(X2,X1))))). 1.16/1.45 cnf(i_0_894, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1))))). 1.16/1.45 cnf(i_0_404, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))). 1.16/1.45 cnf(i_0_142, plain, (X1=esk9_2(X2,X3)|X2!=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))). 1.16/1.45 cnf(i_0_522, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_87, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_239, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_224, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~class_Groups_Oordered__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_1136, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_713, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Groups_Oordered__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_701, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_1106, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1413, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_484, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1006, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1537, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_798, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1731, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_525, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1536, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1730, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_999, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_593, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_922, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2))). 1.16/1.45 cnf(i_0_687, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3))). 1.16/1.45 cnf(i_0_1573, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_686, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3))). 1.16/1.45 cnf(i_0_530, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1410, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1227, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3))). 1.16/1.45 cnf(i_0_1411, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Oordered__cancel__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3))). 1.16/1.45 cnf(i_0_42, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_412, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1739, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3))). 1.16/1.45 cnf(i_0_281, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 1.16/1.45 cnf(i_0_411, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)))). 1.16/1.45 cnf(i_0_1713, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)))). 1.16/1.45 cnf(i_0_354, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 1.16/1.45 cnf(i_0_1031, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))). 1.16/1.45 cnf(i_0_343, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1598, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_716, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3))). 1.16/1.45 cnf(i_0_280, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_378, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_969, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1212, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1272, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__comm__monoid__add(X1)|~c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1140, plain, (X1=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1669, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1434, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1678, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1436, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1017, plain, (X1=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_1016, plain, (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). 1.16/1.45 cnf(i_0_983, plain, (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_810, plain, (c_Groups_Oplus__class_Oplus(X1,X2,X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X2)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_984, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))). 1.16/1.45 cnf(i_0_923, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)))). 1.16/1.45 cnf(i_0_5, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)))). 1.16/1.45 cnf(i_0_1749, plain, (c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)))). 1.16/1.45 cnf(i_0_423, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)))). 1.16/1.45 cnf(i_0_685, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1539, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))). 1.16/1.45 cnf(i_0_1540, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))). 1.16/1.45 cnf(i_0_1541, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))). 1.16/1.45 cnf(i_0_1538, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))). 1.16/1.45 cnf(i_0_684, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_683, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_682, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_627, plain, (c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_397, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))). 1.16/1.45 cnf(i_0_600, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))). 1.16/1.45 cnf(i_0_1288, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))). 1.16/1.45 cnf(i_0_1363, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_184, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_133, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))). 1.16/1.45 cnf(i_0_599, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))). 1.16/1.45 cnf(i_0_329, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1380, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_537, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_469, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_579, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1369, plain, (c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3),X4)|~class_Fields_Ofield(X1))). 1.16/1.45 cnf(i_0_1553, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1466, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk67_3(X1,X2,X3),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1))))). 1.16/1.45 cnf(i_0_789, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3))). 1.16/1.45 cnf(i_0_674, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3))). 1.16/1.45 cnf(i_0_788, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)))). 1.16/1.45 cnf(i_0_675, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))). 1.16/1.45 cnf(i_0_1615, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))). 1.16/1.45 cnf(i_0_512, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3))). 1.16/1.45 cnf(i_0_257, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3))). 1.16/1.45 cnf(i_0_958, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))). 1.16/1.45 cnf(i_0_225, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3))). 1.16/1.45 cnf(i_0_568, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_415, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))). 1.16/1.45 cnf(i_0_1640, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))). 1.16/1.45 cnf(i_0_1024, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_451, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))). 1.16/1.45 cnf(i_0_910, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_1555, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3))). 1.16/1.45 cnf(i_0_159, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1558, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))|~class_Groups_Omonoid__mult(X1))). 1.16/1.45 cnf(i_0_1458, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_893, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_1560, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 1.16/1.45 cnf(i_0_711, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk36_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1337, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk64_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_1469, plain, (hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1))))). 1.16/1.45 cnf(i_0_895, plain, (hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1))))). 1.16/1.45 cnf(i_0_194, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))). 1.16/1.45 cnf(i_0_287, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2)))). 1.16/1.45 cnf(i_0_490, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Groups_Oab__semigroup__mult(X1))). 1.16/1.45 cnf(i_0_369, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1050, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_335, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Groups_Omonoid__mult(X1))). 1.16/1.45 cnf(i_0_911, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))). 1.16/1.45 cnf(i_0_1022, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 1.16/1.45 cnf(i_0_127, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))). 1.16/1.45 cnf(i_0_375, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))). 1.16/1.45 cnf(i_0_601, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_1023, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))). 1.16/1.45 cnf(i_0_912, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))). 1.16/1.45 cnf(i_0_92, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_277, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1311, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_498, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1128, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_136, plain, (X2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))))). 1.16/1.45 cnf(i_0_1352, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_913, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Groups_Omonoid__mult(X1))). 1.16/1.45 cnf(i_0_322, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1))). 1.16/1.45 cnf(i_0_323, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1))). 1.16/1.45 cnf(i_0_419, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_724, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1664, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1098, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_148, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X4))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2))). 1.16/1.45 cnf(i_0_1582, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_563, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_372, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3))). 1.16/1.45 cnf(i_0_219, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1260, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)|~class_Power_Opower(X2))). 1.16/1.45 cnf(i_0_1034, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk49_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~hBOOL(hAPP(X1,X2)))). 1.16/1.45 cnf(i_0_165, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))=c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~class_Rings_Oordered__ring__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_164, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))=c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~class_Rings_Oordered__ring__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_167, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))=c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~class_Rings_Oordered__ring__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3))). 1.16/1.45 cnf(i_0_166, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))=c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~class_Rings_Oordered__ring__abs(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_370, plain, (c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))|~class_Rings_Olinordered__semidom(X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4))). 1.16/1.45 cnf(i_0_1714, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X4))). 1.16/1.45 cnf(i_0_15, plain, (c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))|~class_Rings_Olinordered__semidom(X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4))). 1.16/1.45 cnf(i_0_163, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X4))). 1.16/1.45 cnf(i_0_138, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oordered__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3))). 1.16/1.45 cnf(i_0_464, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_1696, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X5))). 1.16/1.45 cnf(i_0_299, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~c_Orderings_Oord__class_Oless(X1,X4,X5)|~c_Orderings_Oord__class_Oless(X1,X2,X3))). 1.16/1.45 cnf(i_0_344, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_206, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1496, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1247, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_833, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1604, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_570, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_608, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1043, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_840, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Oordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_1335, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_1262, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Oordered__comm__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_1225, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Oordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_274, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_359, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_1054, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Olinordered__comm__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_558, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_1075, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_571, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_1044, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X3,X4)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_33, plain, (c_Groups_Ozero__class_Ozero(X1)=X3|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_RealVector_Onorm__class_Onorm(X1,X4))))). 1.16/1.45 cnf(i_0_504, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_828, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1514, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk68_3(X2,X1,X3))=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))))). 1.16/1.45 cnf(i_0_319, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk23_3(X1,X2,X3))=X2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))))). 1.16/1.45 cnf(i_0_760, plain, (c_RComplete_Onatfloor(X2)=X1|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))). 1.16/1.45 cnf(i_0_493, plain, (c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1117, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),X3)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1264, plain, (X2=X4|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))). 1.16/1.45 cnf(i_0_438, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))!=X1|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_1465, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk67_3(X2,X3,X1),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1513, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk68_3(X3,X2,X1))=X2|hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_317, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk23_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_890, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))))). 1.16/1.45 cnf(i_0_864, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))))). 1.16/1.45 cnf(i_0_1192, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))!=X1|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_892, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3)))). 1.16/1.45 cnf(i_0_874, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_391, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))). 1.16/1.45 cnf(i_0_1277, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))). 1.16/1.45 cnf(i_0_24, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_819, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)))). 1.16/1.45 cnf(i_0_1013, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_1157, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2))). 1.16/1.45 cnf(i_0_1003, plain, (X2=X3|hAPP(c_Polynomial_Ocoeff(X1,X2),esk48_3(X2,X3,X1))!=hAPP(c_Polynomial_Ocoeff(X1,X3),esk48_3(X2,X3,X1))|~class_Groups_Ozero(X1))). 1.16/1.45 cnf(i_0_920, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1499, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_521, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_88, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1681, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_1137, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)))). 1.16/1.45 cnf(i_0_1744, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)))). 1.16/1.45 cnf(i_0_700, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)))). 1.16/1.45 cnf(i_0_1068, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)))). 1.16/1.45 cnf(i_0_334, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)))). 1.16/1.45 cnf(i_0_1105, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)))). 1.16/1.45 cnf(i_0_483, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)))). 1.16/1.45 cnf(i_0_837, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)))). 1.16/1.45 cnf(i_0_1398, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3))|~class_RealVector_Oreal__normed__algebra__1(X1))). 1.16/1.45 cnf(i_0_123, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2))). 1.16/1.45 cnf(i_0_1228, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3))). 1.16/1.45 cnf(i_0_621, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3))). 1.16/1.45 cnf(i_0_836, plain, (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)),X2))). 1.16/1.45 cnf(i_0_245, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),X2))). 1.16/1.45 cnf(i_0_1561, plain, (c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3)),X2))). 1.16/1.45 cnf(i_0_1680, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3))). 1.16/1.45 cnf(i_0_1679, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))). 1.16/1.45 cnf(i_0_1510, plain, (hBOOL(hAPP(X4,X3))|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)|~hBOOL(hAPP(X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))))). 1.16/1.45 cnf(i_0_315, plain, (hBOOL(hAPP(X1,X2))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)!=X4|~hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X3))))). 1.16/1.45 cnf(i_0_316, plain, (hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))))). 1.16/1.45 cnf(i_0_1509, plain, (hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))))). 1.16/1.45 cnf(i_0_1027, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))=hAPP(c_Polynomial_Opoly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4)|~class_Rings_Ocomm__ring(X1))). 1.16/1.45 cnf(i_0_844, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Ocoeff(X1,X2),X4),hAPP(c_Polynomial_Ocoeff(X1,X3),X4))=hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4)|~class_Groups_Ocomm__monoid__add(X1))). 1.16/1.45 cnf(i_0_663, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(c_Polynomial_Ocoeff(X1,X2),X4),hAPP(c_Polynomial_Ocoeff(X1,X3),X4))=hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4)|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_20, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3),hAPP(c_Polynomial_Opoly(X1,X4),X3))=hAPP(c_Polynomial_Opoly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X4)),X3)|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_614, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk34_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_RealVector_Oreal__normed__vector(X1)|~c_SEQ_OBseq(X1,X2))). 1.16/1.45 cnf(i_0_1617, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk72_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_RealVector_Oreal__normed__vector(X1)|~c_SEQ_OBseq(X1,X2))). 1.16/1.45 cnf(i_0_235, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1531, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_450, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_899, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_32, plain, (c_RComplete_Onatceiling(X2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))). 1.16/1.45 cnf(i_0_513, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)|~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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)))). 1.16/1.45 cnf(i_0_258, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2)))). 1.16/1.45 cnf(i_0_957, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))). 1.16/1.45 cnf(i_0_1445, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))). 1.16/1.45 cnf(i_0_1535, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))). 1.16/1.45 cnf(i_0_226, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2)))). 1.16/1.45 cnf(i_0_416, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))). 1.16/1.45 cnf(i_0_1627, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3)))). 1.16/1.45 cnf(i_0_479, plain, (X5=X6|c_Groups_Ozero__class_Ozero(X1)=X2|X3!=X4|c_Groups_Oplus__class_Oplus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5))!=c_Groups_Oplus__class_Oplus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X6))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 1.16/1.45 cnf(i_0_114, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_1199, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_1222, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_465, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_889, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_863, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_228, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_842, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_930, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)=X4|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2)!=X3|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_891, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_873, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_79, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_636, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))|~class_Groups_Omonoid__mult(X1))). 1.16/1.45 cnf(i_0_1251, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_489, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_1224, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_1045, plain, (c_Orderings_Oord__class_Oless(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))). 1.16/1.45 cnf(i_0_574, plain, (c_Orderings_Oord__class_Oless(X1,X3,X2)|c_Orderings_Oord__class_Oless(X1,X2,X3)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_1517, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_706, plain, (c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5))=c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4))|X1!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3))). 1.16/1.45 cnf(i_0_1592, plain, (c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5))=c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4))|X1!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3))). 1.16/1.45 cnf(i_0_575, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))). 1.16/1.45 cnf(i_0_1046, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_1047, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))). 1.16/1.45 cnf(i_0_572, plain, (c_Orderings_Oord__class_Oless(X1,X2,X3)|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_291, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk21_2(X1,X2))),X1))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_994, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_786, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1637, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)|~class_Rings_Ocomm__semiring(X1))). 1.16/1.45 cnf(i_0_725, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1594, plain, (c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_970, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3)|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1529, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_328, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk24_2(X2,X1)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1067, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk52_2(X2,X1)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1187, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk55_2(X2,X1)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1549, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_259, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk17_2(X3,X1)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_905, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk46_2(X3,X1)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1229, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk61_2(X3,X1)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_573, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))). 1.16/1.45 cnf(i_0_1048, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_1421, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4))). 1.16/1.45 cnf(i_0_717, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2)=c_Groups_Oplus__class_Oplus(X1,X3,c_Divides_Odiv__class_Odiv(X1,X4,X2))|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_748, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2)=c_Groups_Oplus__class_Oplus(X1,X3,c_Divides_Odiv__class_Odiv(X1,X4,X2))|~class_Divides_Osemiring__div(X1))). 1.16/1.45 cnf(i_0_59, plain, (hAPP(X2,esk6_3(X1,X2,X3))=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk5_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_744, plain, (hAPP(X2,esk39_3(X1,X2,X3))=X1|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk38_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_781, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_1309, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_939, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))=c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_634, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ominus__class_Ominus(X1,X4,X5))=c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))|~class_Groups_Oab__group__add(X1))). 1.16/1.45 cnf(i_0_1374, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_929, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)=X4|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2)!=X3|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_514, plain, (hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),X2),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_860, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X2,X3))|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))))). 1.16/1.45 cnf(i_0_720, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))). 1.16/1.45 cnf(i_0_751, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 1.16/1.45 cnf(i_0_371, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))). 1.16/1.45 cnf(i_0_1083, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))). 1.16/1.45 cnf(i_0_16, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))). 1.16/1.45 cnf(i_0_604, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))). 1.16/1.45 cnf(i_0_862, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3)))). 1.16/1.45 cnf(i_0_870, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_1497, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,X3)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_1603, plain, (c_Orderings_Oord__class_Oless(X1,X4,X3)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_1431, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_1334, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X4)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_351, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))). 1.16/1.45 cnf(i_0_598, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_557, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_1263, plain, (c_Orderings_Oord__class_Oless(X1,X3,X4)|~class_Rings_Olinordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))). 1.16/1.45 cnf(i_0_981, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))). 1.16/1.45 cnf(i_0_480, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))). 1.16/1.45 cnf(i_0_1182, plain, (c_Orderings_Oord__class_Oless(X1,X2,X4)|~class_Rings_Olinordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)|~c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))). 1.16/1.45 cnf(i_0_901, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2))). 1.16/1.45 cnf(i_0_1092, plain, (c_SEQ_OBseq(X4,X3)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk54_4(X2,X3,X1,X4))|~class_RealVector_Oreal__normed__vector(X4))). 1.16/1.45 cnf(i_0_872, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_564, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1735, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))). 1.16/1.45 cnf(i_0_1734, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 1.16/1.45 cnf(i_0_353, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1)))=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Oone__class_Oone(X1))|~class_Rings_Oring__1(X1))). 1.16/1.45 cnf(i_0_60, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk6_3(X1,X2,X3),X3)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk5_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_745, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk39_3(X1,X2,X3),X3)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk38_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_283, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1370, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))|~class_Rings_Olinordered__ring(X1))). 1.16/1.45 cnf(i_0_454, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)))|~class_Rings_Olinordered__ring__strict(X2))). 1.16/1.45 cnf(i_0_453, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)))|~class_Rings_Olinordered__ring__strict(X2))). 1.16/1.45 cnf(i_0_1127, plain, (c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),c_Groups_Ozero__class_Ozero(X2))|X3!=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2))). 1.16/1.45 cnf(i_0_859, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_861, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_869, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_35, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk1_2(X1,X2))),X2),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2))). 1.16/1.45 cnf(i_0_871, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_1684, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)|~class_Groups_Ocomm__monoid__mult(X1))). 1.16/1.45 cnf(i_0_1414, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1462, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)))|~hBOOL(hAPP(X2,esk66_3(X1,X3,X2))))). 1.16/1.45 cnf(i_0_928, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)=X4|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2)!=X3|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_907, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X5))|~class_RealVector_Oreal__normed__algebra(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3))). 1.16/1.45 cnf(i_0_1742, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Oordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3))). 1.16/1.45 cnf(i_0_1673, plain, (c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Oordered__semiring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_617, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X5)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4))). 1.16/1.45 cnf(i_0_1659, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless(X1,X4,X5)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_618, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X4,X5)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_267, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__semiring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X4,X5)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3))). 1.16/1.45 cnf(i_0_229, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))). 1.16/1.45 cnf(i_0_841, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))). 1.16/1.45 cnf(i_0_949, plain, (c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4))). 1.16/1.45 cnf(i_0_950, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3))). 1.16/1.45 cnf(i_0_1613, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))). 1.16/1.45 cnf(i_0_426, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4))=hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4)|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_532, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3))). 1.16/1.45 cnf(i_0_201, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~class_Fields_Olinordered__field(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,esk14_3(X3,X2,X1))))). 1.16/1.45 cnf(i_0_305, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X5))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3))). 1.16/1.45 cnf(i_0_1014, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_1643, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_320, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)|hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,esk23_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_1512, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)|hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))|~hBOOL(hAPP(X3,esk68_3(X2,X1,X3))))). 1.16/1.45 cnf(i_0_505, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_603, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_1433, plain, (c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X4),X5)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3))). 1.16/1.45 cnf(i_0_318, plain, (hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk23_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_1511, plain, (hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk68_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_1461, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk66_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_886, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2))))). 1.16/1.45 cnf(i_0_854, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk42_3(X1,X3,X2))))). 1.16/1.45 cnf(i_0_1107, plain, (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X4)),X3)|~class_Rings_Ocomm__semiring__0(X1))). 1.16/1.45 cnf(i_0_1323, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_241, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))))). 1.16/1.45 cnf(i_0_303, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)))). 1.16/1.45 cnf(i_0_1059, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 1.16/1.45 cnf(i_0_1464, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk66_3(X1,X2,X3)),esk67_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1))))). 1.16/1.45 cnf(i_0_780, plain, (X2=X4|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2))). 1.16/1.45 cnf(i_0_1470, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X5,X3))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X2)!=X4|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4,X1))))). 1.16/1.45 cnf(i_0_430, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_529, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1063, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_1599, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_885, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_853, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_538, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1028, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_1463, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk66_3(X2,X3,X1)),esk67_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 1.16/1.45 cnf(i_0_888, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))))). 1.16/1.45 cnf(i_0_884, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X2,X3)),esk43_3(X1,X2,X3))=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))))). 1.16/1.45 cnf(i_0_723, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3)))). 1.16/1.45 cnf(i_0_40, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,X3),c_Groups_Ouminus__class_Ouminus(X1,esk4_2(X2,X1)))),esk3_2(X2,X1))|~class_RealVector_Oreal__normed__vector(X1)|~c_SEQ_OBseq(X1,X2))). 1.16/1.45 cnf(i_0_1390, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_377, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)|~class_Rings_Oring__1(X1))). 1.16/1.45 cnf(i_0_856, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X3,X2))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2))))). 1.16/1.45 cnf(i_0_850, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk42_3(X1,X2,X3))))). 1.16/1.45 cnf(i_0_852, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3))|~hBOOL(hAPP(X3,esk42_3(X1,X2,X3))))). 1.16/1.45 cnf(i_0_866, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X3,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2))))). 1.16/1.45 cnf(i_0_1736, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_338, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))). 1.16/1.45 cnf(i_0_951, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3)|~class_Rings_Olinordered__idom(X1)|~c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,X2,X3))|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4))). 1.16/1.45 cnf(i_0_887, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_883, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_1486, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Groups_Ouminus__class_Ouminus(X1,X2)!=X3|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_1591, plain, (X3=X5|X2=X4|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))!=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 1.16/1.45 cnf(i_0_704, plain, (X3=X4|X1=X2|c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4))!=c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5))). 1.16/1.45 cnf(i_0_243, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X1)),esk15_3(X2,X3,X4)))). 1.16/1.45 cnf(i_0_242, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X4)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2)),esk15_3(X4,X3,X1)))). 1.16/1.45 cnf(i_0_140, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X1)),esk8_3(X2,X3,X4)))). 1.16/1.45 cnf(i_0_139, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X4)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2)),esk8_3(X4,X3,X1)))). 1.16/1.45 cnf(i_0_1519, plain, (X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))). 1.16/1.45 cnf(i_0_855, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_849, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_851, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_865, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_1291, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2)|~class_Groups_Omonoid__mult(X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))). 1.16/1.45 cnf(i_0_858, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk43_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))))). 1.16/1.45 cnf(i_0_880, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X2,X3)),esk43_3(X1,X2,X3))=X2|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X1,X2,X3),X1)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))))). 1.16/1.45 cnf(i_0_882, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X2,X3)),esk43_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X1,X2,X3)))). 1.16/1.45 cnf(i_0_868, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_897, plain, (hBOOL(hAPP(X5,X2))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3)!=X4|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X1))))). 1.16/1.45 cnf(i_0_896, plain, (hBOOL(hAPP(X5,X3))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),X2)!=X4|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X1))))). 1.16/1.45 cnf(i_0_980, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)))). 1.16/1.45 cnf(i_0_801, plain, (~class_Rings_Olinordered__ring(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),c_Groups_Ozero__class_Ozero(X1)))). 1.16/1.45 cnf(i_0_1126, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),c_Groups_Ozero__class_Ozero(X2)))). 1.16/1.45 cnf(i_0_1125, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2)|~c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),c_Groups_Ozero__class_Ozero(X2)))). 1.16/1.45 cnf(i_0_857, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,esk43_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_879, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|c_Orderings_Oord__class_Oless(tc_Int_Oint,esk45_3(X2,X3,X1),X2)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_881, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk45_3(X2,X3,X1))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_867, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk43_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_992, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5))|~class_Rings_Ocomm__semiring__1(X1))). 1.16/1.45 cnf(i_0_452, plain, (X3!=c_Groups_Ozero__class_Ozero(X1)|X2!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))). 1.16/1.45 cnf(i_0_610, plain, (c_Orderings_Oord__class_Oless__eq(X1,X3,X2)|~class_Fields_Olinordered__field__inverse__zero(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk33_3(X2,X3,X1)),X3),X2))). 1.16/1.45 cnf(i_0_576, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X4))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2),X4))). 1.16/1.45 cnf(i_0_1040, plain, (c_SEQ_OBseq(X2,X3)|~class_RealVector_Oreal__normed__vector(X2)|~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,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk51_3(X3,X2,X1))),X1))). 1.16/1.45 cnf(i_0_1298, plain, (c_SEQ_OBseq(X1,X3)|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X3,esk63_3(X3,X2,X1))),X2))). 1.16/1.45 cnf(i_0_846, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk42_3(X1,X3,X2)))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2))))). 1.16/1.45 cnf(i_0_569, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4)),X3)|c_Groups_Oplus__class_Oplus(X1,X5,X6)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__semiring__1(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X5))). 1.16/1.45 cnf(i_0_1471, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4)),X3)|c_Groups_Oplus__class_Oplus(X1,X5,X6)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__semiring__1__strict(X1)|~c_Orderings_Oord__class_Oless(X1,X4,X3)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X5))). 1.16/1.45 cnf(i_0_1543, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,esk70_4(X3,X2,X1,X4))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(X3,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,hAPP(X3,X2))))|~class_RealVector_Oreal__normed__vector(X4)|~class_Orderings_Oord(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X5))). 1.16/1.45 cnf(i_0_1478, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5))=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3),X5)|~class_Rings_Osemiring(X1))). 1.16/1.45 cnf(i_0_845, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_273, plain, (hBOOL(hAPP(X1,esk20_3(X2,X1,X3)))|hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(X1,X4))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3))). 1.16/1.45 cnf(i_0_1416, plain, (hBOOL(hAPP(X1,esk65_3(X2,X1,X3)))|hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(X1,X4))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3))). 1.16/1.45 cnf(i_0_562, plain, (X4=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)!=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)|~class_Rings_Oring(X1))). 1.16/1.45 cnf(i_0_200, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4)=X6|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)!=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)|~class_Rings_Oring(X1))). 1.16/1.45 cnf(i_0_876, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X3,X2)),esk43_3(X1,X3,X2))=X3|hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk44_3(X1,X3,X2))))). 1.16/1.45 cnf(i_0_848, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk42_3(X1,X2,X3))))). 1.16/1.45 cnf(i_0_1548, plain, (X3=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4))). 1.16/1.45 cnf(i_0_1152, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3)=X5|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1))). 1.16/1.45 cnf(i_0_368, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))|~class_Groups_Omonoid__mult(X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3))). 1.16/1.45 cnf(i_0_875, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk44_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_847, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk42_3(X2,X3,X1))))). 1.16/1.45 cnf(i_0_714, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))). 1.16/1.45 cnf(i_0_170, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X4))=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X4))|~class_Rings_Oring(X1))). 1.16/1.45 cnf(i_0_878, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk42_3(X1,X2,X3)),esk43_3(X1,X2,X3))=X2|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk44_3(X1,X2,X3)),esk45_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))))). 1.16/1.45 cnf(i_0_192, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,X3),c_Groups_Ouminus__class_Ouminus(X1,hAPP(X2,esk11_2(X2,X1))))),esk10_2(X2,X1))|~class_RealVector_Oreal__normed__vector(X1)|~c_SEQ_OBseq(X1,X2))). 1.16/1.45 cnf(i_0_124, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1631, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_877, plain, (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk42_3(X2,X3,X1)),esk43_3(X2,X3,X1))=X3|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk44_3(X2,X3,X1)),esk45_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 1.16/1.45 cnf(i_0_561, plain, (c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5),X6)=c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5),X1)|X1!=c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X3,X4)),X5),X6)|~class_Rings_Oring(X2))). 1.16/1.45 cnf(i_0_199, plain, (c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5)=c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)|c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5)!=X6|~class_Rings_Oring(X1))). 1.16/1.45 cnf(i_0_1547, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1)|X1!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2))). 1.16/1.45 cnf(i_0_1153, plain, (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4)!=X5|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1))). 1.16/1.45 cnf(i_0_275, plain, (c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Rings_Olinordered__semidom(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 1.16/1.45 cnf(i_0_1485, plain, (X2=X3|c_Groups_Ouminus__class_Ouminus(X1,X3)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Oidom(X1))). 1.16/1.45 cnf(i_0_613, plain, (c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk35_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 1.16/1.45 cnf(i_0_1618, plain, (c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk71_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 1.16/1.45 cnf(i_0_1740, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X5)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X5)))). 1.16/1.45 cnf(i_0_1284, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X5)))). 1.16/1.45 cnf(i_0_721, negated_conjecture, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))). 1.16/1.45 cnf(i_0_500, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk28_2(X1,X2))|~class_RealVector_Oreal__normed__vector(X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk27_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 1.16/1.45 cnf(i_0_1206, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk58_2(X1,X2))|~class_RealVector_Oreal__normed__vector(X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk57_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 1.16/1.45 cnf(i_0_102, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk7_1(X1)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_581, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk32_1(X1)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_996, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk47_1(X1)))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1324, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6)))). 1.16/1.45 cnf(i_0_1614, plain, (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_501, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk28_2(X2,X1))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk27_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 1.16/1.45 cnf(i_0_1207, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk58_2(X2,X1))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk57_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 1.16/1.45 cnf(i_0_499, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk30_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk29_3(X2,X1,X3))),X3))). 1.16/1.45 cnf(i_0_1205, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk60_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk59_3(X2,X1,X3))),X3))). 1.16/1.45 cnf(i_0_496, plain, (c_Polynomial_Opoly__rec(X4,X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))=X2|hAPP(hAPP(hAPP(X3,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2)!=X2|~class_Groups_Ozero(X1))). 1.16/1.45 cnf(i_0_36, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk1_2(X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2))). 1.16/1.45 cnf(i_0_125, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))). 1.16/1.45 cnf(i_0_1632, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))). 1.16/1.45 cnf(i_0_1415, plain, (hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(X1,X4))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,esk65_3(X2,X1,X3),X3))))). 1.16/1.45 cnf(i_0_272, plain, (hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(X1,X4))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)|~hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,esk20_3(X2,X1,X3),X3))))). 1.16/1.45 cnf(i_0_944, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1387, plain, (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2))). 1.16/1.45 cnf(i_0_1250, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,X2,X3))=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Rings_Ocomm__ring__1(X1))). 1.16/1.45 cnf(i_0_1089, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))|~class_RealVector_Oreal__normed__vector(X1))). 1.16/1.45 cnf(i_0_1752, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 1.16/1.45 cnf(i_0_1610, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)))). 1.16/1.45 cnf(i_0_547, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)))). 1.16/1.45 cnf(i_0_1331, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)))). 1.16/1.45 cnf(i_0_1563, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)))). 1.16/1.45 cnf(i_0_1116, plain, (c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)))). 1.16/1.45 cnf(i_0_620, plain, (c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)))). 1.16/1.45 cnf(i_0_265, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)))). 1.16/1.45 cnf(i_0_462, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)))). 1.16/1.45 cnf(i_0_1611, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5)))). 1.16/1.45 cnf(i_0_546, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5)))). 1.16/1.45 cnf(i_0_1332, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4),X5))). 1.16/1.45 cnf(i_0_1564, plain, (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))|~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)|~c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4),X5))). 1.16/1.45 cnf(i_0_1115, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6)))). 1.16/1.45 cnf(i_0_619, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6)))). 1.16/1.45 cnf(i_0_264, plain, (c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6))). 1.16/1.45 cnf(i_0_463, plain, (c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))|~class_Rings_Oordered__ring(X1)|~c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6))). 1.16/1.45 cnf(i_0_1204, plain, (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4))))))). 1.16/1.45 cnf(i_0_448, plain, (c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)))=c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))|~class_RealVector_Oreal__normed__algebra(X1))). 1.16/1.45 cnf(i_0_1091, plain, (c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk54_4(X3,X2,X4,X1))),X3))). 1.16/1.45 cnf(i_0_1195, plain, (c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)|~class_Orderings_Oord(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk56_4(X3,X2,X4,X1)),hAPP(X3,esk56_4(X3,X2,X4,X1))))). 1.16/1.45 cnf(i_0_1252, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_502, plain, (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),X3)|~c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))). 1.16/1.45 cnf(i_0_57, plain, (hAPP(X2,esk6_3(X1,X2,X3))=X1|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_3(X1,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk5_3(X1,X2,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_742, plain, (hAPP(X2,esk39_3(X1,X2,X3))=X1|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk38_3(X1,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk38_3(X1,X2,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_58, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk6_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_3(X1,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk5_3(X1,X2,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_743, plain, (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk39_3(X1,X2,X3),X3)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,hAPP(X2,X3))|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk38_3(X1,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk38_3(X1,X2,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 1.16/1.45 cnf(i_0_41, plain, (c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,esk2_4(X2,X1,X3,X4)),c_Groups_Ouminus__class_Ouminus(X1,X4))),X3))). 1.16/1.45 cnf(i_0_190, plain, (c_SEQ_OBseq(X1,X2)|~class_RealVector_Oreal__normed__vector(X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,esk12_4(X2,X1,X3,X4)),c_Groups_Ouminus__class_Ouminus(X1,hAPP(X2,X4)))),X3))). 1.16/1.45 cnf(i_0_1542, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))))|~class_RealVector_Oreal__normed__vector(X1)|~class_Orderings_Oord(X4)|~c_Orderings_Oord__class_Oless__eq(X4,X3,X5)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(X2,X3),hAPP(X2,esk70_4(X2,X3,X4,X1)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). 1.16/1.45 # End listing active clauses. There is an equivalent clause to each of these in the clausification! 1.16/1.45 # Begin printing tableau 1.16/1.45 # 2,0,0,1 x c 1.16/1.45 cnf(i_0_2328, plain, (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))). 1.16/1.45 # 1,3,1268,0 1.16/1.45 cnf(i_0_1760, plain, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))). 1.16/1.45 # 0,1,721,0 1.16/1.45 cnf(i_0_721, watchlist, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))). 1.16/1.45 1.16/1.45 # 2,0,0,0 c s 1.16/1.45 cnf(i_0_2329, plain, (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). 1.16/1.45 # 1,3,1268,0 1.16/1.45 cnf(i_0_1760, plain, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))). 1.16/1.45 # 0,1,721,0 1.16/1.45 cnf(i_0_721, watchlist, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))). 1.16/1.45 1.16/1.45 # 2,0,0,0 c 1.16/1.45 cnf(i_0_2330, plain, (~class_Rings_Olinordered__idom(tc_RealDef_Oreal))). 1.16/1.45 # 1,3,1268,0 1.16/1.45 cnf(i_0_1760, plain, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))). 1.16/1.45 # 0,1,721,0 1.16/1.45 cnf(i_0_721, watchlist, (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))). 1.16/1.45 1.16/1.45 # End printing tableau 1.16/1.45 # SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 1.16/1.45 # Branches closed with saturation will be marked with an "s" 1.16/1.45 # Proof search success! 1.16/1.45 # Exiting... 1.16/1.45 EOF