%------------------------------------------------------------------------------ % File : SPASS-SCL---0.1.1 % Problem : LCL809-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp % Command : /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % Computer : n028.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:10:29 PM UTC 2026 % Result : Unknown 0.12s 0.42s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL809-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.12/0.38 % Computer : n028.cluster.edu % 0.12/0.38 % Model : x86_64 x86_64 % 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.38 % Memory : 8046.5625MB % 0.12/0.38 % OS : Linux 6.8.0-71-generic % 0.12/0.38 % CPULimit : 300 % 0.12/0.38 % WCLimit : 300 % 0.12/0.38 % DateTime : Fri Sep 4 21:47:43 UTC 2026 % 0.12/0.38 % CPUTime : % 0.12/0.38 Running /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.12/0.41 % 0.12/0.41 % Input Clauses: % 0.12/0.41 % 1:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x3,x0),c_lessequals(x2,x1,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x3,x1,x0),c_HOL_Oinverse__class_Odivide(x3,x2,x0),x0) % 0.12/0.41 % 2:3:4:INP:TopTopTopTop: class_Ring__and__Field_Oidom(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x2,x3,x0),x0) % 0.12/0.41 % 3:3:4:INP:TopTopTopTop: class_Ring__and__Field_Oidom(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(x3,x1,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) % 0.12/0.41 % 4:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(x1,x2,x0),x3,x0),x2,x0),c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x1,x3,x0),x2,x0)) % 0.12/0.41 % 5:2:2:INP:TopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0)) % 0.12/0.41 % 6:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0),class_Int_Onumber__ring(x0) -> =(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0)) % 0.12/0.41 % 7:6:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_HOL_Oord__class_Oless(x1,x3,x0),c_HOL_Oord__class_Oless(x4,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x4,x1,x0),c_HOL_Otimes__class_Otimes(x2,x3,x0),x0) % 0.12/0.41 % 8:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_lessequals(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0) -> c_lessequals(x1,x2,x0) % 0.12/0.41 % 9:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_lessequals(c_HOL_Oone__class_Oone(x0),c_Power_Opower__class_Opower(x1,x2,x0),x0) % 0.12/0.41 % 10:3:2:INP:TopTop: class_Ring__and__Field_Osemiring__0(x0),class_Power_Opower(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(x0),c_Suc(x1),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 11:2:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(x1,x0),x0),c_HOL_Oabs__class_Oabs(x1,x0)) % 0.12/0.41 % 12:1:2:INP:TopTop: -> =(c_HOL_Oplus__class_Oplus(x0,c_Suc(x1),tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat))) % 0.12/0.41 % 13:1:2:INP:TopTop: -> =(c_HOL_Oplus__class_Oplus(c_Suc(x0),x1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat))) % 0.12/0.41 % 14:2:3:INP:TopTopTop: class_Ring__and__Field_Olordered__ring(x0) -> c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0),x0) % 0.12/0.41 % 15:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ouminus__class_Ouminus(x2,x0),x0) -> c_lessequals(x2,x1,x0) % 0.12/0.41 % 16:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x2,x0),c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.41 % 17:2:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oring(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x3,x1,x0),x2,x0),x4,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x2,x0),x4,x0)) % 0.12/0.41 % 18:3:5:INP:TopTopTopTopTop: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),x2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x1,tc_nat),x4,tc_nat),tc_nat),c_lessequals(x3,x0,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x0,x3,tc_nat),x1,tc_nat),x2,tc_nat),x4,tc_nat) % 0.12/0.41 % 19:3:5:INP:TopTopTopTopTop: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x2,tc_nat),x3,tc_nat),x4,tc_nat),c_lessequals(x1,x0,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),x3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),x4,tc_nat),tc_nat) % 0.12/0.41 % 20:3:5:INP:TopTopTopTopTop: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),x2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x1,tc_nat),x4,tc_nat),tc_nat),c_lessequals(x0,x3,tc_nat) -> c_HOL_Oord__class_Oless(x2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x3,x0,tc_nat),x1,tc_nat),x4,tc_nat),tc_nat) % 0.12/0.41 % 21:3:5:INP:TopTopTopTopTop: c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x2,tc_nat),x3,tc_nat),x4,tc_nat),tc_nat),c_lessequals(x2,x1,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x2,x3,tc_nat),x0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x3,tc_nat),x4,tc_nat),tc_nat) % 0.12/0.41 % 22:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Oring(x0),=(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x4,x2,x0),x5,x0)) -> =(x3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x4,x1,x0),x2,x0),x5,x0)) % 0.12/0.41 % 23:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Oring(x0),=(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x4,x2,x0),x5,x0)) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x4,x0),x2,x0),x3,x0),x5) % 0.12/0.41 % 24:1:2:INP:TopTop: -> c_HOL_Oord__class_Oless(x0,c_Suc(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat)),tc_nat) % 0.12/0.41 % 25:1:2:INP:TopTop: -> c_HOL_Oord__class_Oless(x0,c_Suc(c_HOL_Oplus__class_Oplus(x1,x0,tc_nat)),tc_nat) % 0.12/0.41 % 26:1:2:INP:TopTop: -> c_HOL_Oord__class_Oless(x0,c_Suc(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat)),tc_nat) % 0.12/0.41 % 27:3:3:INP:TopTopTop: c_lessequals(x0,c_HOL_Ominus__class_Ominus(x1,x2,tc_nat),tc_nat),c_lessequals(x2,x1,tc_nat) -> c_lessequals(c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),x1,tc_nat) % 0.12/0.41 % 28:3:3:INP:TopTopTop: c_lessequals(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x2,tc_nat),c_lessequals(x1,x2,tc_nat) -> c_lessequals(x0,c_HOL_Ominus__class_Ominus(x2,x1,tc_nat),tc_nat) % 0.12/0.41 % 29:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x3,x2,x0) -> c_lessequals(c_Orderings_Oord__class_Omax(x3,x1,x0),x2,x0) % 0.12/0.41 % 30:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x3,x2,x0) -> c_lessequals(c_Orderings_Oord__class_Omax(x3,x1,x0),x2,x0) % 0.12/0.41 % 31:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x3,x2,x0) -> c_lessequals(c_Orderings_Oord__class_Omax(x3,x1,x0),x2,x0) % 0.12/0.41 % 32:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_lessequals(x1,c_Orderings_Oord__class_Omax(x1,x2,x0),x0) % 0.12/0.41 % 33:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_lessequals(x1,c_Orderings_Oord__class_Omax(x2,x1,x0),x0) % 0.12/0.41 % 34:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oabs__class_Oabs(x1,x0),x0),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 35:2:2:INP:TopTop: class_Orderings_Obot(x0) -> c_lessequals(c_Orderings_Obot__class_Obot(x0),x1,x0) % 0.12/0.41 % 36:2:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(x1,x0),x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 37:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0),c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(x1,x3,x0),c_Orderings_Oord__class_Omin(x2,x3,x0),x0)) % 0.12/0.41 % 38:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omin(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0),c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(x1,x2,x0),c_Orderings_Oord__class_Omin(x1,x3,x0),x0)) % 0.12/0.41 % 39:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Oone__class_Oone(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,x3,tc_nat) -> c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(x1,x3,x0),c_Power_Opower__class_Opower(x1,x2,x0),x0) % 0.12/0.41 % 40:5:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),class_OrderedGroup_Ocomm__monoid__add(x0),c_lessequals(x1,x2,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_lessequals(x1,c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) % 0.12/0.41 % 41:5:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),class_OrderedGroup_Ocomm__monoid__add(x0),c_lessequals(x1,x2,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_lessequals(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0) % 0.12/0.41 % 42:3:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_lessequals(x1,x2,tc_nat) -> c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(x3,x1,x0),c_Power_Opower__class_Opower(x3,x2,x0),x0) % 0.12/0.41 % 43:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_lessequals(c_Suc(x0),x1,tc_nat) % 0.12/0.41 % 44:2:2:INP:TopTop: c_lessequals(c_Suc(x0),x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,x1,tc_nat) % 0.12/0.41 % 45:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_lessequals(c_Suc(x0),x1,tc_nat) % 0.12/0.41 % 46:2:2:INP:TopTop: c_lessequals(c_Suc(x0),x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,x1,tc_nat) % 0.12/0.41 % 47:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),=(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(x1,x0),c_HOL_Ozero__class_Ozero(x0)) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 48:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> =(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 49:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat) % 0.12/0.41 % 50:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),tc_nat) % 0.12/0.41 % 51:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x2,tc_nat) -> c_HOL_Oord__class_Oless(x0,x2,tc_nat) % 0.12/0.41 % 52:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat) % 0.12/0.41 % 53:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),tc_nat) % 0.12/0.41 % 54:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(x1,c_HOL_Oone__class_Oone(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,x3,tc_nat) -> c_lessequals(c_Power_Opower__class_Opower(x1,x3,x0),c_Power_Opower__class_Opower(x1,x2,x0),x0) % 0.12/0.41 % 55:1:1:INP:Top: -> =(c_HOL_Ominus__class_Ominus(c_Suc(x0),c_HOL_Oone__class_Oone(tc_nat),tc_nat),x0) % 0.12/0.41 % 56:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 57:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 58:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_lessequals(x1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x2,x3,x0),x4,x0),x5,x0),x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x4,x0),x1,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x2,x4,x0),x5,x0),x0) % 0.12/0.41 % 59:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x4,x2,x0),x5,x0),x0) -> c_lessequals(x3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x4,x1,x0),x2,x0),x5,x0),x0) % 0.12/0.41 % 60:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x2,x0),x3,x0),x4,x0),x5,x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x3,x0),x4,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x2,x3,x0),x5,x0),x0) % 0.12/0.41 % 61:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x4,x2,x0),x5,x0),x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x4,x0),x2,x0),x3,x0),x5,x0) % 0.12/0.41 % 62:4:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0),c_Ring__and__Field_Odvd__class_Odvd(x1,c_Divides_Odiv__class_Omod(x3,x2,x0),x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x3,x0) % 0.12/0.41 % 63:4:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x3,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_Divides_Odiv__class_Omod(x2,x3,x0),x0) % 0.12/0.41 % 64:4:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,c_Divides_Odiv__class_Omod(x2,x3,x0),x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x3,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) % 0.12/0.41 % 65:4:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x3,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_Divides_Odiv__class_Omod(x3,x2,x0),x0) % 0.12/0.41 % 66:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(c_Suc(x1),x0,tc_nat),c_Suc(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat))) % 0.12/0.41 % 67:1:0:INP:: -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat)) % 0.12/0.41 % 68:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0),x0) % 0.12/0.41 % 69:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 70:1:3:INP:TopTopTop: -> =(c_Lambda_Osubstn(c_Lambda_OdB_OAbs(x0),x1,x2),c_Lambda_OdB_OAbs(c_Lambda_Osubstn(x0,x1,c_HOL_Oplus__class_Oplus(x2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) % 0.12/0.41 % 71:2:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Otimes__class_Otimes(x2,x2,x0),x0),x0) % 0.12/0.41 % 72:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oone__class_Oone(x0),x0) % 0.12/0.41 % 73:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x2,x1,x0)) % 0.12/0.41 % 74:2:3:INP:TopTopTop: class_OrderedGroup_Ocomm__monoid__add(x0) -> =(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x2,x1,x0)) % 0.12/0.41 % 75:1:2:INP:TopTop: -> =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x1,x0,tc_nat)) % 0.12/0.41 % 76:3:4:INP:TopTopTopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x2,x3,tc_nat)),c_HOL_Oord__class_Oless(x2,x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,x3,tc_nat) % 0.12/0.41 % 77:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x2,x1,x0)) % 0.12/0.41 % 78:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 79:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 80:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 81:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 82:2:2:INP:TopTop: =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) -> =(x0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 83:2:2:INP:TopTop: =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) -> =(x1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 84:2:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Oabs__class_Oabs(x1,x0),x0),x1) % 0.12/0.41 % 85:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_HOL_Oord__class_Oless(x0,x2,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x1,x2,tc_nat),c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),tc_nat) % 0.12/0.41 % 86:2:3:INP:TopTopTop: class_Ring__and__Field_Oring__1(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(x0),x0),x2,x0),c_Power_Opower__class_Opower(x1,x2,x0),x0)) % 0.12/0.41 % 87:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(x0),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(x0),x1,x0),x0) % 0.12/0.41 % 88:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,x1,x0) -> c_lessequals(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0) % 0.12/0.41 % 89:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Oinverse__class_Oinverse(x2,x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) -> c_lessequals(x1,x2,x0) % 0.12/0.41 % 90:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0) -> c_lessequals(x2,x1,x0) % 0.12/0.41 % 91:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Oinverse__class_Oinverse(x2,x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) % 0.12/0.41 % 92:3:3:INP:TopTopTop: class_Nat_Osemiring__char__0(x0),=(c_Nat_Osemiring__1__class_Oof__nat(x1,x0),c_Nat_Osemiring__1__class_Oof__nat(x2,x0)) -> =(x1,x2) % 0.12/0.41 % 93:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x1,x0),x3,x0) -> c_lessequals(x2,c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) % 0.12/0.41 % 94:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x1,x0),x3,x0) % 0.12/0.41 % 95:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,c_HOL_Oinverse__class_Odivide(x3,x1,x0),x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),x3,x0) % 0.12/0.41 % 96:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),x3,x0) -> c_lessequals(x2,c_HOL_Oinverse__class_Odivide(x3,x1,x0),x0) % 0.12/0.41 % 97:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_lessequals(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x1,x3,x0),x2,x0) % 0.12/0.41 % 98:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(x1,c_HOL_Oinverse__class_Odivide(x3,x2,x0),x0) % 0.12/0.41 % 99:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) -> c_HOL_Oord__class_Oless(x2,x3,x0) % 0.12/0.41 % 100:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(x2,x3,x0) % 0.12/0.41 % 101:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semiring(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) -> c_HOL_Oord__class_Oless(x2,x3,x0) % 0.12/0.41 % 102:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_lessequals(x3,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x3,x1,x0),c_HOL_Oinverse__class_Odivide(x3,x2,x0),x0) % 0.12/0.41 % 103:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_lessequals(c_Orderings_Oord__class_Omin(x1,x2,x0),x1,x0) % 0.12/0.41 % 104:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_lessequals(c_Orderings_Oord__class_Omin(x1,x2,x0),x2,x0) % 0.12/0.41 % 105:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x1,x3,x0) -> c_lessequals(x1,c_Orderings_Oord__class_Omin(x3,x2,x0),x0) % 0.12/0.41 % 106:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x1,x3,x0) -> c_lessequals(x1,c_Orderings_Oord__class_Omin(x3,x2,x0),x0) % 0.12/0.41 % 107:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x1,x3,x0) -> c_lessequals(x1,c_Orderings_Oord__class_Omin(x3,x2,x0),x0) % 0.12/0.41 % 108:2:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oring(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x4,x2,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x4,x0),x2,x0),x3,x0),x0)) % 0.12/0.41 % 109:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 110:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.41 % 111:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),x1,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 112:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),x1,x0) % 0.12/0.41 % 113:3:2:INP:TopTop: class_OrderedGroup_Oordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 114:3:2:INP:TopTop: class_OrderedGroup_Oordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.41 % 115:3:2:INP:TopTop: class_OrderedGroup_Oordered__ab__group__add(x0),c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),x1,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 116:3:2:INP:TopTop: class_OrderedGroup_Oordered__ab__group__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),x1,x0) % 0.12/0.41 % 117:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_Power_Opower__class_Opower(x1,x2,x0),x0) % 0.12/0.41 % 118:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.41 % 119:2:2:INP:TopTop: =(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) -> c_lessequals(x0,x1,tc_nat) % 0.12/0.41 % 120:2:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0) -> =(c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(x1,x2,x0),x3,x0),c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(x1,x3,x0),c_HOL_Ominus__class_Ominus(x2,x3,x0),x0)) % 0.12/0.41 % 121:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x3,x2,x0) -> c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(x3,x1,x0),x2,x0) % 0.12/0.41 % 122:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat)),x2,tc_nat),c_HOL_Ominus__class_Ominus(c_Suc(x1),c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),tc_nat)) % 0.12/0.41 % 123:2:5:INP:TopTopTopTopTop: =(c_List_Oreplicate(x0,x1,x2),c_List_Oreplicate(x3,x4,x2)) -> =(x0,x3) % 0.12/0.41 % 124:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(x0),x1,x0),x1) % 0.12/0.41 % 125:1:1:INP:Top: -> =(c_HOL_Otimes__class_Otimes(x0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),x0) % 0.12/0.41 % 126:1:1:INP:Top: -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),x0,tc_nat),x0) % 0.12/0.41 % 127:2:2:INP:TopTop: class_OrderedGroup_Ocomm__monoid__mult(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(x0),x1,x0),x1) % 0.12/0.41 % 128:2:2:INP:TopTop: class_OrderedGroup_Omonoid__mult(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(x0),x1,x0),x1) % 0.12/0.41 % 129:2:2:INP:TopTop: class_OrderedGroup_Omonoid__mult(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Oone__class_Oone(x0),x0),x1) % 0.12/0.41 % 130:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Oone__class_Oone(x0),x0),x1) % 0.12/0.41 % 131:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(x0),x1,x0),x1) % 0.12/0.41 % 132:5:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),class_OrderedGroup_Ocomm__monoid__add(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) % 0.12/0.41 % 133:3:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x2,tc_nat) -> c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat) % 0.12/0.41 % 134:2:3:INP:TopTopTop: class_Ring__and__Field_Odvd(x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) % 0.12/0.41 % 135:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) % 0.12/0.41 % 136:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.41 % 137:2:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x3,x4,x0),x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(x1,x3,x0),x0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(x2,x4,x0),x0),x0),x0) % 0.12/0.41 % 138:6:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x3,x4,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x3,x2,x0),c_HOL_Oinverse__class_Odivide(x4,x1,x0),x0) % 0.12/0.41 % 139:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),c_Power_Opower__class_Opower(x1,x2,x0),x0),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0),x2,x0)) % 0.12/0.41 % 140:1:0:INP:: -> =(c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 141:2:3:INP:TopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(x1,x2,x0),x2,x0),c_Divides_Odiv__class_Omod(x1,x2,x0)) % 0.12/0.41 % 142:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(x1,x0),c_Nat_Osemiring__1__class_Oof__nat(x2,x0),x0) -> c_lessequals(x1,x2,tc_nat) % 0.12/0.41 % 143:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(x1,x2,tc_nat) -> c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(x1,x0),c_Nat_Osemiring__1__class_Oof__nat(x2,x0),x0) % 0.12/0.41 % 144:1:1:INP:Top: -> =(c_Suc(x0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),x0,tc_nat)) % 0.12/0.41 % 145:1:1:INP:Top: -> =(c_Suc(x0),c_HOL_Oplus__class_Oplus(x0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) % 0.12/0.41 % 146:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0),c_HOL_Oinverse__class_Odivide(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 147:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 148:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 149:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 150:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 151:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x1,x3,x0) -> c_HOL_Oord__class_Oless(x1,c_Orderings_Oord__class_Omin(x3,x2,x0),x0) % 0.12/0.41 % 152:1:3:INP:TopTopTop: -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat)) % 0.12/0.41 % 153:1:3:INP:TopTopTop: -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat)) % 0.12/0.41 % 154:3:4:INP:TopTopTopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0)) % 0.12/0.41 % 155:3:4:INP:TopTopTopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0)) % 0.12/0.41 % 156:1:2:INP:TopTop: -> =(c_Orderings_Oord__class_Omax(c_Suc(x0),c_Suc(x1),tc_nat),c_Suc(c_Orderings_Oord__class_Omax(x0,x1,tc_nat))) % 0.12/0.41 % 157:2:1:INP:Top: c_HOL_Oord__class_Oless(x0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) -> =(x0,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.41 % 158:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(x1,x1,x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 159:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(x1,x1,x0),x0) % 0.12/0.41 % 160:2:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0),x0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(x1,x2,x0),x0),x0) % 0.12/0.41 % 161:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omin(x1,c_Orderings_Oord__class_Omin(x1,x2,x0),x0),c_Orderings_Oord__class_Omin(x1,x2,x0)) % 0.12/0.41 % 162:3:3:INP:TopTopTop: -> =(c_Lambda_Osubst(c_Lambda_OdB_OVar(x0),x1,x2),c_Lambda_OdB_OVar(x0)),=(x0,x2),c_HOL_Oord__class_Oless(x2,x0,tc_nat) % 0.12/0.41 % 163:4:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0),c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(x3,x0),x4,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(x3,x0),c_HOL_Oabs__class_Oabs(x1,x0),x0),c_HOL_Otimes__class_Otimes(x4,x2,x0),x0) % 0.12/0.41 % 164:2:5:INP:TopTopTopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),x3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),x4,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(x3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),x2,tc_nat),x4,tc_nat),tc_nat)) % 0.12/0.41 % 165:2:5:INP:TopTopTopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),x3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),x4,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),x2,tc_nat),x3,tc_nat),x4,tc_nat)) % 0.12/0.41 % 166:2:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(x1,x2,x0),x2,x0),x1) % 0.12/0.41 % 167:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 168:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) % 0.12/0.41 % 169:3:2:INP:TopTop: class_Ring__and__Field_Odivision__ring(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(x1,x0),x0),x1) % 0.12/0.41 % 170:2:3:INP:TopTopTop: -> c_lessequals(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat) % 0.12/0.41 % 171:2:3:INP:TopTopTop: -> c_lessequals(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) % 0.12/0.41 % 172:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(x1,x2,x0),x3,x0),c_Power_Opower__class_Opower(x1,c_HOL_Otimes__class_Otimes(x2,x3,tc_nat),x0)) % 0.12/0.41 % 173:2:3:INP:TopTopTop: class_OrderedGroup_Omonoid__mult(x0) -> =(c_Power_Opower__class_Opower(x1,c_Suc(x2),x0),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(x1,x2,x0),x1,x0)) % 0.12/0.41 % 174:2:3:INP:TopTopTop: class_Power_Opower(x0) -> =(c_Power_Opower__class_Opower(x1,c_Suc(x2),x0),c_HOL_Otimes__class_Otimes(x1,c_Power_Opower__class_Opower(x1,x2,x0),x0)) % 0.12/0.41 % 175:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_Power_Opower__class_Opower(x1,c_Suc(x2),x0),c_HOL_Otimes__class_Otimes(x1,c_Power_Opower__class_Opower(x1,x2,x0),x0)) % 0.12/0.41 % 176:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_Power_Opower__class_Opower(x1,c_Suc(x2),x0),c_HOL_Otimes__class_Otimes(x1,c_Power_Opower__class_Opower(x1,x2,x0),x0)) % 0.12/0.41 % 177:3:4:INP:TopTopTopTop: c_lessequals(x0,x1,tc_nat),c_lessequals(x2,x3,tc_nat) -> c_lessequals(c_HOL_Oplus__class_Oplus(x2,x0,tc_nat),c_HOL_Oplus__class_Oplus(x3,x1,tc_nat),tc_nat) % 0.12/0.41 % 178:4:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add(x0),c_lessequals(x1,x2,x0),c_lessequals(x3,x4,x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(x3,x1,x0),c_HOL_Oplus__class_Oplus(x4,x2,x0),x0) % 0.12/0.41 % 179:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,c_Suc(x1),tc_nat) % 0.12/0.41 % 180:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,c_Suc(x1),tc_nat) -> c_lessequals(x0,x1,tc_nat) % 0.12/0.41 % 181:2:1:INP:Top: c_lessequals(x0,x0,tc_nat) -> c_HOL_Oord__class_Oless(x0,c_Suc(x0),tc_nat) % 0.12/0.41 % 182:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x2,x1,x0)) % 0.12/0.41 % 183:1:2:INP:TopTop: -> =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x1,x0,tc_nat)) % 0.12/0.41 % 184:4:1:INP:Top: class_OrderedGroup_Opordered__comm__monoid__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 185:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x2,x1,x0)) % 0.12/0.41 % 186:1:2:INP:TopTop: -> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),c_Suc(x0),tc_nat) % 0.12/0.41 % 187:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(x1,x3,x0),c_Divides_Odiv__class_Omod(x2,x3,x0),x0),x3,x0)) % 0.12/0.41 % 188:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(x2,x1,x0),x0) % 0.12/0.41 % 189:2:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0),x0) % 0.12/0.41 % 190:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0) -> c_HOL_Oord__class_Oless(x2,x1,x0) % 0.12/0.41 % 191:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x2,x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) % 0.12/0.41 % 192:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x2,x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) -> c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.41 % 193:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0) % 0.12/0.41 % 194:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(x1,x0),x1) % 0.12/0.41 % 195:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),=(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(x1,x0),x1) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 196:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Oone__class_Oone(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(x1,c_Suc(x2),x0),c_HOL_Oone__class_Oone(x0),x0) % 0.12/0.41 % 197:2:2:INP:TopTop: -> =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x1,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),x1,tc_nat),tc_nat)),=(x0,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.41 % 198:4:4:INP:TopTopTopTop: class_Orderings_Opreorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x3,x1,x0) -> c_HOL_Oord__class_Oless(x3,x2,x0) % 0.12/0.41 % 199:4:4:INP:TopTopTopTop: class_Orderings_Oorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(x1,x3,x0) % 0.12/0.41 % 200:4:2:INP:TopTop: class_Ring__and__Field_Osgn__if(x0) -> =(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(x0),x0)),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 201:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> =(c_Orderings_Oord__class_Omax(x1,x2,x0),x2) % 0.12/0.41 % 202:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semiring(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(x2,x3,x0) % 0.12/0.41 % 203:4:3:INP:TopTopTop: class_Ring__and__Field_Oidom(x0),=(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Otimes__class_Otimes(x2,x2,x0)) -> =(x1,c_HOL_Ouminus__class_Ouminus(x2,x0)),=(x1,x2) % 0.12/0.41 % 204:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> =(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Ouminus__class_Ouminus(x1,x0)) % 0.12/0.41 % 205:4:2:INP:TopTop: class_Orderings_Olinorder(x0),class_OrderedGroup_Olordered__ab__group__add__abs(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> =(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Ouminus__class_Ouminus(x1,x0)) % 0.12/0.41 % 206:3:2:INP:TopTop: class_Ring__and__Field_Oabs__if(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> =(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Ouminus__class_Ouminus(x1,x0)) % 0.12/0.41 % 207:3:4:INP:TopTopTopTop: class_Divides_Oring__div(x0),=(c_Divides_Odiv__class_Omod(x1,x2,x0),c_Divides_Odiv__class_Omod(x3,x2,x0)) -> =(c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0),c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(x3,x0),x2,x0)) % 0.12/0.41 % 208:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(x1,x3,x0),c_Divides_Odiv__class_Omod(x2,x3,x0),x0),x3,x0)) % 0.12/0.41 % 209:4:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__ring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x3,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Ominus__class_Ominus(x3,x2,x0),x0) % 0.12/0.41 % 210:2:3:INP:TopTopTop: class_OrderedGroup_Omonoid__mult(x0) -> =(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(x1,x2,x0),x1,x0),c_HOL_Otimes__class_Otimes(x1,c_Power_Opower__class_Opower(x1,x2,x0),x0)) % 0.12/0.41 % 211:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0) -> c_lessequals(x1,x3,x0),c_lessequals(x1,x2,x0) % 0.12/0.41 % 212:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x1,x3,x0),x0),c_Power_Opower__class_Opower(x1,c_HOL_Oplus__class_Oplus(x2,x3,tc_nat),x0)) % 0.12/0.41 % 213:1:3:INP:TopTopTop: -> =(c_Lambda_Oliftn(c_Suc(x0),x1,x2),c_Lambda_Olift(c_Lambda_Oliftn(x0,x1,x2),x2)) % 0.12/0.41 % 214:2:4:INP:TopTopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),x3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),x2,tc_nat),x3,tc_nat),tc_nat)) % 0.12/0.41 % 215:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0) -> c_lessequals(x1,x3,x0) % 0.12/0.41 % 216:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0) -> c_lessequals(x1,x2,x0) % 0.12/0.41 % 217:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_Orderings_Oord__class_Omin(x3,x1,x0),x2,x0) % 0.12/0.41 % 218:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_Orderings_Oord__class_Omin(x1,x3,x0),x2,x0) % 0.12/0.41 % 219:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_Orderings_Oord__class_Omin(x3,x1,x0),x2,x0) % 0.12/0.41 % 220:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_Orderings_Oord__class_Omin(x1,x3,x0),x2,x0) % 0.12/0.41 % 221:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0) -> c_lessequals(x1,x3,x0) % 0.12/0.41 % 222:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0) -> c_lessequals(x1,x2,x0) % 0.12/0.41 % 223:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Osgn__class_Osgn(x1,x0),x0) % 0.12/0.41 % 224:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Osgn__class_Osgn(x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 225:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x1,x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x3,x1,x0),x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 226:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x3,x1,x0),x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 227:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x3,x2,x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.41 % 228:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x3,x0),x1,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 229:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Oinverse__class_Odivide(x3,x1,x0),x0) -> c_HOL_Oord__class_Oless(x3,c_HOL_Otimes__class_Otimes(x2,x1,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 230:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) -> c_HOL_Oord__class_Oless(x3,c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 231:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) % 0.12/0.41 % 232:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oinverse__class_Odivide(x3,x2,x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 233:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_lessequals(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oone__class_Oone(x0),x0) % 0.12/0.41 % 234:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(x1,x1,x0),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(x0),c_HOL_Oone__class_Oone(x0),x0),x1,x0)) % 0.12/0.41 % 235:5:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),=(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 236:5:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),=(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 237:2:2:INP:TopTop: =(c_Suc(x0),c_Suc(x1)) -> =(x0,x1) % 0.12/0.41 % 238:2:2:INP:TopTop: =(c_Suc(x0),c_Suc(x1)) -> =(x0,x1) % 0.12/0.41 % 239:2:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Oabs__class_Oabs(x1,x0),x0) % 0.12/0.41 % 240:1:0:INP:: -> =(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) % 0.12/0.41 % 241:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(x1,x2,x0),x3,x0),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(x1,x3,x0),c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0)) % 0.12/0.41 % 242:2:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(x1,c_HOL_Oabs__class_Oabs(x1,x0),x0) % 0.12/0.41 % 243:1:2:INP:TopTop: =(c_Lambda_OdB_OVar(x0),c_Lambda_OdB_OAbs(x1)) -> % 0.12/0.41 % 244:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x2,x3,x0),x4,x0),x5,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x4,x0),x1,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x2,x4,x0),x5,x0),x0) % 0.12/0.41 % 245:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x4,x2,x0),x5,x0),x0) -> c_HOL_Oord__class_Oless(x3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x4,x1,x0),x2,x0),x5,x0),x0) % 0.12/0.41 % 246:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x2,x0),x3,x0),x4,x0),x5,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x3,x0),x4,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x2,x3,x0),x5,x0),x0) % 0.12/0.41 % 247:3:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x4,x2,x0),x5,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x4,x0),x2,x0),x3,x0),x5,x0) % 0.12/0.41 % 248:3:5:INP:TopTopTopTopTop: =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),x2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x1,tc_nat),x4,tc_nat)),c_lessequals(x3,x0,tc_nat) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x0,x3,tc_nat),x1,tc_nat),x2,tc_nat),x4) % 0.12/0.41 % 249:3:5:INP:TopTopTopTopTop: =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),x2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x1,tc_nat),x4,tc_nat)),c_lessequals(x0,x3,tc_nat) -> =(x2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x3,x0,tc_nat),x1,tc_nat),x4,tc_nat)) % 0.12/0.41 % 250:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_Power_Opower__class_Opower(x1,c_HOL_Oone__class_Oone(tc_nat),x0),x1) % 0.12/0.41 % 251:2:2:INP:TopTop: class_OrderedGroup_Omonoid__mult(x0) -> =(c_Power_Opower__class_Opower(x1,c_HOL_Oone__class_Oone(tc_nat),x0),x1) % 0.12/0.41 % 252:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(c_Orderings_Oord__class_Omin(x1,x2,x0),x3,x0) -> c_lessequals(x2,x3,x0),c_lessequals(x1,x3,x0) % 0.12/0.41 % 253:2:4:INP:TopTopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),x2,tc_nat),x3,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),x3,tc_nat)) % 0.12/0.41 % 254:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),x1,x0),x1,x0)) % 0.12/0.41 % 255:4:6:INP:TopTopTopTopTopTop: class_Divides_Osemiring__div(x0),=(c_Divides_Odiv__class_Omod(x1,x2,x0),c_Divides_Odiv__class_Omod(x3,x2,x0)),=(c_Divides_Odiv__class_Omod(x4,x2,x0),c_Divides_Odiv__class_Omod(x5,x2,x0)) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x4,x1,x0),x2,x0),c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x5,x3,x0),x2,x0)) % 0.12/0.41 % 256:1:0:INP:: -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) % 0.12/0.41 % 257:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 258:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 259:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 260:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 261:3:2:INP:TopTop: =(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(x0,x1,tc_nat)) -> =(x1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),=(x0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 262:3:2:INP:TopTop: =(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(x0,x1,tc_nat)) -> =(x0,c_HOL_Ozero__class_Ozero(tc_nat)),=(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.41 % 263:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.41 % 264:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.41 % 265:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.41 % 266:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.41 % 267:3:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(x1,x0,tc_nat),tc_nat) % 0.12/0.41 % 268:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(x2,x3,x0),c_Power_Opower__class_Opower(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(x2,x1,x0) % 0.12/0.41 % 269:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0) -> c_lessequals(x2,x3,x0) % 0.12/0.41 % 270:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0) -> c_lessequals(x1,x3,x0) % 0.12/0.41 % 271:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> c_lessequals(x1,c_Orderings_Oord__class_Omax(x3,x2,x0),x0) % 0.12/0.41 % 272:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> c_lessequals(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0) % 0.12/0.41 % 273:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> c_lessequals(x1,c_Orderings_Oord__class_Omax(x3,x2,x0),x0) % 0.12/0.41 % 274:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> c_lessequals(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0) % 0.12/0.41 % 275:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0) -> c_lessequals(x2,x3,x0) % 0.12/0.41 % 276:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_lessequals(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0) -> c_lessequals(x1,x3,x0) % 0.12/0.41 % 277:2:3:INP:TopTopTop: c_lessequals(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x2,tc_nat) -> c_lessequals(x0,c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),tc_nat) % 0.12/0.41 % 278:2:3:INP:TopTopTop: c_lessequals(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat) -> c_lessequals(c_HOL_Ominus__class_Ominus(x0,x2,tc_nat),x1,tc_nat) % 0.12/0.41 % 279:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_Power_Opower__class_Opower(x1,x2,x0),x0) % 0.12/0.41 % 280:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0) -> c_HOL_Oord__class_Oless(x1,x3,x0),c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.41 % 281:1:2:INP:TopTop: -> =(c_HOL_Otimes__class_Otimes(x0,c_Suc(x1),tc_nat),c_HOL_Oplus__class_Oplus(x0,c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat)) % 0.12/0.41 % 282:1:2:INP:TopTop: -> =(c_HOL_Otimes__class_Otimes(c_Suc(x0),x1,tc_nat),c_HOL_Oplus__class_Oplus(x1,c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat)) % 0.12/0.41 % 283:3:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0),=(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ouminus__class_Ouminus(x2,x0)) % 0.12/0.41 % 284:3:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0),=(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(c_HOL_Ouminus__class_Ouminus(x1,x0),x2) % 0.12/0.41 % 285:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0) % 0.12/0.41 % 286:3:3:INP:TopTopTop: -> =(c_Lambda_Osubstn(c_Lambda_OdB_OVar(x0),x1,x2),c_Lambda_OdB_OVar(x0)),=(x0,x2),c_HOL_Oord__class_Oless(x2,x0,tc_nat) % 0.12/0.41 % 287:2:1:INP:Top: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),c_HOL_Ozero__class_Ozero(x0),x0) -> % 0.12/0.41 % 288:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0) -> c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.41 % 289:4:2:INP:TopTop: class_Ring__and__Field_Osgn__if(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Oone__class_Oone(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 290:2:2:INP:TopTop: =(c_Lambda_OdB_OAbs(x0),c_Lambda_OdB_OAbs(x1)) -> =(x0,x1) % 0.12/0.41 % 291:2:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Otimes__class_Otimes(x2,x2,x0),x0),c_HOL_Ozero__class_Ozero(x0),x0) -> % 0.12/0.41 % 292:3:5:INP:TopTopTopTopTop: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),x2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x1,tc_nat),x4,tc_nat),tc_nat),c_lessequals(x3,x0,tc_nat) -> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x0,x3,tc_nat),x1,tc_nat),x2,tc_nat),x4,tc_nat) % 0.12/0.41 % 293:3:5:INP:TopTopTopTopTop: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x2,tc_nat),x3,tc_nat),x4,tc_nat),c_lessequals(x1,x0,tc_nat) -> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),x3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),x4,tc_nat),tc_nat) % 0.12/0.41 % 294:3:5:INP:TopTopTopTopTop: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),x2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x1,tc_nat),x4,tc_nat),tc_nat),c_lessequals(x0,x3,tc_nat) -> c_lessequals(x2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x3,x0,tc_nat),x1,tc_nat),x4,tc_nat),tc_nat) % 0.12/0.41 % 295:3:5:INP:TopTopTopTopTop: c_lessequals(x0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x1,x2,tc_nat),x3,tc_nat),x4,tc_nat),tc_nat),c_lessequals(x2,x1,tc_nat) -> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x2,x3,tc_nat),x0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x3,tc_nat),x4,tc_nat),tc_nat) % 0.12/0.41 % 296:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),x3,x0),c_lessequals(x3,c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x3,x1,x0),x2,x0) % 0.12/0.41 % 297:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Otimes__class_Otimes(x3,x1,x0),x0),c_lessequals(c_HOL_Otimes__class_Otimes(x3,x1,x0),x2,x0) -> c_lessequals(x3,c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.41 % 298:2:3:INP:TopTopTop: class_Ring__and__Field_Osemiring__1(x0) -> =(c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),x0),c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(x1,x0),c_Nat_Osemiring__1__class_Oof__nat(x2,x0),x0)) % 0.12/0.41 % 299:4:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(x1,x2,x0),x3,x0) -> c_HOL_Oord__class_Oless(x2,x3,x0),c_HOL_Oord__class_Oless(x1,x3,x0) % 0.12/0.41 % 300:5:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0),=(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x4,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x4,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0)) -> =(x2,x4),=(x1,x3) % 0.12/0.41 % 301:5:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0),=(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x4,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x4,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0)) -> =(x2,x4),=(x1,x3) % 0.12/0.41 % 302:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0),=(c_Orderings_Oord__class_Omax(x1,x2,x0),x2) -> c_lessequals(x1,x2,x0) % 0.12/0.41 % 303:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> =(c_Orderings_Oord__class_Omax(x2,x1,x0),x2) % 0.12/0.41 % 304:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0)) % 0.12/0.41 % 305:2:4:INP:TopTopTopTop: class_OrderedGroup_Oab__group__add(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0),c_HOL_Oplus__class_Oplus(x2,c_HOL_Oplus__class_Oplus(x1,x3,x0),x0)) % 0.12/0.41 % 306:1:3:INP:TopTopTop: -> =(c_HOL_Oplus__class_Oplus(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),tc_nat)) % 0.12/0.41 % 307:1:3:INP:TopTopTop: -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x2,tc_nat),c_HOL_Oplus__class_Oplus(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat)) % 0.12/0.41 % 308:2:4:INP:TopTopTopTop: class_OrderedGroup_Ocomm__monoid__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0)) % 0.12/0.41 % 309:2:4:INP:TopTopTopTop: class_OrderedGroup_Ocomm__monoid__add(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0),c_HOL_Oplus__class_Oplus(x2,c_HOL_Oplus__class_Oplus(x1,x3,x0),x0)) % 0.12/0.41 % 310:2:4:INP:TopTopTopTop: class_OrderedGroup_Oab__semigroup__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0)) % 0.12/0.41 % 311:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0)) % 0.12/0.41 % 312:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x1,x3,x0),x2,x0)) % 0.12/0.41 % 313:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0),c_HOL_Oplus__class_Oplus(x2,c_HOL_Oplus__class_Oplus(x1,x3,x0),x0)) % 0.12/0.41 % 314:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0)) % 0.12/0.41 % 315:3:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) % 0.12/0.41 % 316:2:4:INP:TopTopTopTop: class_OrderedGroup_Omonoid__mult(x0) -> =(c_Power_Opower__class_Opower(x1,c_HOL_Oplus__class_Oplus(x2,x3,tc_nat),x0),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x1,x3,x0),x0)) % 0.12/0.41 % 317:2:2:INP:TopTop: c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat) -> c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x1,tc_nat) % 0.12/0.41 % 318:2:2:INP:TopTop: c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat) -> c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x0,tc_nat) % 0.12/0.41 % 319:3:5:INP:TopTopTopTopTop: class_OrderedGroup_Oab__group__add(x0),=(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0),c_HOL_Oplus__class_Oplus(x2,x4,x0)) -> =(c_HOL_Oplus__class_Oplus(x1,x3,x0),x4) % 0.12/0.41 % 320:2:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(x1,x2,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0),x0) % 0.12/0.41 % 321:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(x0,c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),tc_nat) % 0.12/0.41 % 322:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat) % 0.12/0.41 % 323:2:3:INP:TopTopTop: c_lessequals(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x2,tc_nat) -> c_lessequals(x1,x2,tc_nat) % 0.12/0.41 % 324:2:3:INP:TopTopTop: c_lessequals(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x2,tc_nat) -> c_lessequals(x0,x2,tc_nat) % 0.12/0.41 % 325:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(x0,c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),tc_nat) % 0.12/0.41 % 326:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat) % 0.12/0.41 % 327:2:4:INP:TopTopTopTop: class_Divides_Oring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(x1,x2,x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(x1,x3,x0),x2,x0),x3,x0)) % 0.12/0.41 % 328:2:4:INP:TopTopTopTop: class_Divides_Oring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(x1,x2,x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(x1,c_Divides_Odiv__class_Omod(x2,x3,x0),x0),x3,x0)) % 0.12/0.41 % 329:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 330:2:2:INP:TopTop: -> =(c_Lambda_Olift(c_Lambda_OdB_OVar(x0),x1),c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(x0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),c_HOL_Oord__class_Oless(x0,x1,tc_nat) % 0.12/0.41 % 331:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 332:2:2:INP:TopTop: class_OrderedGroup_Omonoid__mult(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(x0),x1,x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.41 % 333:3:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(x1,x0),x0),c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(x1,x0),x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 334:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> =(c_Orderings_Oord__class_Omin(x1,x2,x0),x1) % 0.12/0.41 % 335:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0),=(c_Orderings_Oord__class_Omin(x1,x2,x0),x1) -> c_lessequals(x1,x2,x0) % 0.12/0.41 % 336:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> =(c_Orderings_Oord__class_Omin(x2,x1,x0),x1) % 0.12/0.41 % 337:2:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0) -> =(c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0),c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(x1,x3,x0),c_HOL_Ominus__class_Ominus(x2,x3,x0),x0)) % 0.12/0.41 % 338:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),c_lessequals(x2,x1,x0) % 0.12/0.41 % 339:3:2:INP:TopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x1,x0),c_HOL_Oord__class_Oless(x1,x1,x0) -> % 0.12/0.41 % 340:3:2:INP:TopTop: class_Orderings_Olinorder(x0) -> c_HOL_Oord__class_Oless(x1,x1,x0),c_lessequals(x1,x1,x0) % 0.12/0.41 % 341:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_lessequals(x2,x1,x0) -> % 0.12/0.41 % 342:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0) % 0.12/0.41 % 343:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0) -> % 0.12/0.41 % 344:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),c_lessequals(x2,x1,x0) % 0.12/0.41 % 345:3:3:INP:TopTopTop: class_Orderings_Opreorder(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0) -> % 0.12/0.41 % 346:2:2:INP:TopTop: -> c_HOL_Oord__class_Oless(x0,x0,tc_nat),=(c_Lambda_Osubst(c_Lambda_OdB_OVar(x0),x1,x0),x1) % 0.12/0.41 % 347:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ouminus__class_Ouminus(x1,x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 348:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.41 % 349:4:2:INP:TopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(x1,x1,x0),c_HOL_Oone__class_Oone(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 350:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oinverse__class_Odivide(x1,x1,x0),c_HOL_Oone__class_Oone(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 351:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0) -> =(x1,c_HOL_Ozero__class_Ozero(x0)),=(c_HOL_Oinverse__class_Odivide(x1,x1,x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.41 % 352:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(x1,x3,x0),x2,x0),x3,x0)) % 0.12/0.41 % 353:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,c_Divides_Odiv__class_Omod(x2,x3,x0),x0),x3,x0)) % 0.12/0.41 % 354:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0) -> c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.41 % 355:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.41 % 356:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0) -> c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 357:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 358:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(x1,x2,x0),x3,x0),c_Orderings_Oord__class_Omin(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0)) % 0.12/0.41 % 359:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omin(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0),c_Orderings_Oord__class_Omin(x2,c_Orderings_Oord__class_Omin(x1,x3,x0),x0)) % 0.12/0.41 % 360:2:2:INP:TopTop: =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Oone__class_Oone(tc_nat)) -> =(x1,c_HOL_Oone__class_Oone(tc_nat)) % 0.12/0.41 % 361:2:2:INP:TopTop: =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Oone__class_Oone(tc_nat)) -> =(x0,c_HOL_Oone__class_Oone(tc_nat)) % 0.12/0.41 % 362:1:0:INP:: -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 363:5:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),class_OrderedGroup_Ocomm__monoid__add(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) % 0.12/0.41 % 364:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_HOL_Oone__class_Oone(x0),x1,x0),c_lessequals(x2,x3,tc_nat) -> c_lessequals(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x1,x3,x0),x0) % 0.12/0.41 % 365:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_HOL_Ominus__class_Ominus(x2,x1,tc_nat),c_HOL_Ominus__class_Ominus(x2,x0,tc_nat),tc_nat) % 0.12/0.41 % 366:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_HOL_Ominus__class_Ominus(x0,x2,tc_nat),c_HOL_Ominus__class_Ominus(x1,x2,tc_nat),tc_nat) % 0.12/0.41 % 367:4:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat),c_lessequals(x2,x1,tc_nat),c_lessequals(x2,x0,tc_nat) -> c_lessequals(c_HOL_Ominus__class_Ominus(x0,x2,tc_nat),c_HOL_Ominus__class_Ominus(x1,x2,tc_nat),tc_nat) % 0.12/0.41 % 368:4:3:INP:TopTopTop: c_lessequals(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),c_HOL_Ominus__class_Ominus(x2,x1,tc_nat),tc_nat),c_lessequals(x1,x2,tc_nat),c_lessequals(x1,x0,tc_nat) -> c_lessequals(x0,x2,tc_nat) % 0.12/0.41 % 369:1:2:INP:TopTop: -> =(c_HOL_Ominus__class_Ominus(x0,c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.41 % 370:1:3:INP:TopTopTop: -> =(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x2,tc_nat),c_HOL_Ominus__class_Ominus(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat)) % 0.12/0.41 % 371:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_Power_Opower__class_Opower(x1,x3,x0),c_Power_Opower__class_Opower(x2,x3,x0),x0) % 0.12/0.41 % 372:2:1:INP:Top: class_Ring__and__Field_Osemiring__1(x0) -> =(c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.41 % 373:3:4:INP:TopTopTopTop: class_OrderedGroup_Oab__group__add(x0),=(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ominus__class_Ominus(x3,x3,x0)) -> =(x1,x2) % 0.12/0.41 % 374:3:4:INP:TopTopTopTop: class_OrderedGroup_Oab__group__add(x0),=(c_HOL_Ominus__class_Ominus(x1,x1,x0),c_HOL_Ominus__class_Ominus(x2,x3,x0)) -> =(x2,x3) % 0.12/0.41 % 375:4:3:INP:TopTopTop: =(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),c_HOL_Ominus__class_Ominus(x2,x1,tc_nat)),c_lessequals(x1,x2,tc_nat),c_lessequals(x1,x0,tc_nat) -> =(x0,x2) % 0.12/0.41 % 376:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omin(x1,c_Orderings_Oord__class_Omax(x1,x2,x0),x0),x1) % 0.12/0.41 % 377:3:3:INP:TopTopTop: =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat)),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) -> =(x1,x2) % 0.12/0.41 % 378:3:2:INP:TopTop: =(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(x0,x1,tc_nat)) -> =(x1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),=(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.41 % 379:3:2:INP:TopTop: =(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(x0,x1,tc_nat)) -> =(x0,c_HOL_Ozero__class_Ozero(tc_nat)),=(x0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 380:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat) % 0.12/0.41 % 381:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) % 0.12/0.41 % 382:2:2:INP:TopTop: class_Ring__and__Field_Osemiring__1(x0) -> =(c_Nat_Osemiring__1__class_Oof__nat(c_Suc(x1),x0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(x0),c_Nat_Osemiring__1__class_Oof__nat(x1,x0),x0)) % 0.12/0.41 % 383:5:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oone__class_Oone(x0),x0) -> c_lessequals(c_HOL_Oone__class_Oone(x0),x1,x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 384:1:2:INP:TopTop: -> =(c_HOL_Oplus__class_Oplus(c_Suc(x0),x1,tc_nat),c_HOL_Oplus__class_Oplus(x0,c_Suc(x1),tc_nat)) % 0.12/0.41 % 385:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x0,tc_nat),c_HOL_Otimes__class_Otimes(x2,x0,tc_nat),tc_nat) -> c_lessequals(x1,x2,tc_nat) % 0.12/0.41 % 386:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_lessequals(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat) -> c_lessequals(x1,x2,tc_nat) % 0.12/0.41 % 387:3:3:INP:TopTopTop: c_lessequals(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) -> c_lessequals(x1,x2,tc_nat) % 0.12/0.41 % 388:3:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x2,tc_nat) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x0,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat) % 0.12/0.41 % 389:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x3,x2,x0) % 0.12/0.41 % 390:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x3,x2,x0),c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) % 0.12/0.41 % 391:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(x2,x3,x0) % 0.12/0.41 % 392:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x3,x1,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) % 0.12/0.41 % 393:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_lessequals(x2,x3,x0) % 0.12/0.41 % 394:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) -> c_lessequals(x2,x3,x0) % 0.12/0.41 % 395:3:2:INP:TopTop: c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x0,tc_nat),c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x1,tc_nat) -> c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat) % 0.12/0.41 % 396:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0) -> c_lessequals(x1,c_HOL_Oinverse__class_Odivide(x3,x2,x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 397:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_lessequals(x1,c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) % 0.12/0.41 % 398:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x3,x0),x1,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 399:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x3,x2,x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.41 % 400:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ouminus__class_Ouminus(x2,x0),x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0)) % 0.12/0.41 % 401:1:3:INP:TopTopTop: -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(x0,x2,tc_nat)) % 0.12/0.41 % 402:3:4:INP:TopTopTopTop: =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x2,x3,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x3,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat)) -> =(x1,x3),=(x0,x2) % 0.12/0.41 % 403:3:4:INP:TopTopTopTop: =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x2,x3,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x3,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat)) -> =(x1,x3),=(x0,x2) % 0.12/0.41 % 404:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(x2,x0),x1,x0),c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0)) % 0.12/0.41 % 405:2:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x1,x0),x0),c_HOL_Otimes__class_Otimes(x1,x1,x0)) % 0.12/0.41 % 406:1:1:INP:Top: -> =(c_Nat_Osize__class_Osize(x0,tc_nat),x0) % 0.12/0.41 % 407:3:2:INP:TopTop: class_Ring__and__Field_Odivision__ring(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(x1,x0),x0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(x1,x0),x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 408:3:3:INP:TopTopTop: class_Ring__and__Field_Odivision__ring(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(x1,x2,x0),x0),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(x1,x0),x2,x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 409:1:2:INP:TopTop: -> =(c_HOL_Ominus__class_Ominus(c_Suc(x0),c_Suc(x1),tc_nat),c_HOL_Ominus__class_Ominus(x0,x1,tc_nat)) % 0.12/0.41 % 410:1:3:INP:TopTopTop: =(c_Lambda_OdB_OVar(x0),c_Lambda_OdB_OApp(x1,x2)) -> % 0.12/0.41 % 411:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x2,x0),c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.41 % 412:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ouminus__class_Ouminus(x2,x0),x0) -> c_HOL_Oord__class_Oless(x2,x1,x0) % 0.12/0.41 % 413:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 414:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 415:3:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,c_Suc(x1),tc_nat) -> =(x0,x1),c_HOL_Oord__class_Oless(x0,x1,tc_nat) % 0.12/0.41 % 416:3:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,c_Suc(x1),tc_nat) -> =(x1,x0),c_HOL_Oord__class_Oless(x0,x1,tc_nat) % 0.12/0.41 % 417:3:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,c_Suc(x1),tc_nat) -> =(x0,x1),c_HOL_Oord__class_Oless(x0,x1,tc_nat) % 0.12/0.41 % 418:3:2:INP:TopTop: =(x0,c_HOL_Otimes__class_Otimes(x0,x1,tc_nat)) -> =(x0,c_HOL_Ozero__class_Ozero(tc_nat)),=(x1,c_HOL_Oone__class_Oone(tc_nat)) % 0.12/0.41 % 419:2:1:INP:Top: class_Ring__and__Field_Oordered__ring__strict(x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 420:4:6:INP:TopTopTopTopTopTop: class_Divides_Osemiring__div(x0),=(c_Divides_Odiv__class_Omod(x1,x2,x0),c_Divides_Odiv__class_Omod(x3,x2,x0)),=(c_Divides_Odiv__class_Omod(x4,x2,x0),c_Divides_Odiv__class_Omod(x5,x2,x0)) -> =(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x4,x1,x0),x2,x0),c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x5,x3,x0),x2,x0)) % 0.12/0.41 % 421:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),x0,tc_nat),c_HOL_Oplus__class_Oplus(x2,c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),tc_nat)) % 0.12/0.41 % 422:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),x0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),x2,tc_nat)) % 0.12/0.41 % 423:4:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Oinverse__class_Odivide(x3,x4,x0),x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x4,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0),c_HOL_Otimes__class_Otimes(x2,x4,x0),x0)),=(x4,c_HOL_Ozero__class_Ozero(x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 424:1:0:INP:: -> =(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 425:2:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x4,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x2,x4,x0),x0)) % 0.12/0.41 % 426:2:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x4,x0),x0),c_HOL_Otimes__class_Otimes(x1,c_HOL_Otimes__class_Otimes(x2,c_HOL_Otimes__class_Otimes(x3,x4,x0),x0),x0)) % 0.12/0.41 % 427:2:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x4,x0),x0),c_HOL_Otimes__class_Otimes(x3,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x2,x0),x4,x0),x0)) % 0.12/0.41 % 428:4:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(x1,c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x2,x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 429:4:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x2,x0),x1),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 430:2:1:INP:Top: class_Ring__and__Field_Oordered__semidom(x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oone__class_Oone(x0),x0) % 0.12/0.41 % 431:2:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0),x0),c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(x1,x2,x0),x0)) % 0.12/0.41 % 432:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x2,x0),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oone__class_Oone(x0),x0),x2,x0)) % 0.12/0.41 % 433:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Otimes__class_Otimes(x2,x1,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(x2,c_HOL_Oone__class_Oone(x0),x0),x1,x0)) % 0.12/0.41 % 434:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(x2,c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x2,x0,tc_nat),x1,tc_nat)) % 0.12/0.41 % 435:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oone__class_Oone(x0),x0) % 0.12/0.41 % 436:2:2:INP:TopTop: -> =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(x0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),x1,tc_nat))),=(x0,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.41 % 437:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x0,x2,tc_nat),x1,tc_nat) % 0.12/0.41 % 438:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_lessequals(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 439:1:1:INP:Top: -> =(c_Nat_Osize__class_Osize(c_Suc(x0),tc_nat),c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(x0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) % 0.12/0.41 % 440:2:2:INP:TopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(x1,c_HOL_Oone__class_Oone(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 441:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(x2,x0),x1,x0),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(x2,x1,x0),x0)) % 0.12/0.41 % 442:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 443:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 444:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oone__class_Oone(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) -> c_lessequals(x1,c_HOL_Oone__class_Oone(x0),x0) % 0.12/0.41 % 445:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Oabs__class_Oabs(x2,x0),x0) % 0.12/0.41 % 446:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Oabs__class_Oabs(x2,x0),x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) % 0.12/0.41 % 447:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0) % 0.12/0.41 % 448:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) % 0.12/0.41 % 449:1:0:INP:: -> =(c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 450:4:3:INP:TopTopTop: class_Orderings_Opreorder(x0),c_lessequals(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),c_lessequals(x2,x1,x0) % 0.12/0.41 % 451:1:1:INP:Top: c_HOL_Oord__class_Oless(x0,x0,tc_nat) -> % 0.12/0.41 % 452:1:1:INP:Top: c_HOL_Oord__class_Oless(x0,x0,tc_nat) -> % 0.12/0.41 % 453:2:2:INP:TopTop: class_Orderings_Oorder(x0),c_HOL_Oord__class_Oless(x1,x1,x0) -> % 0.12/0.41 % 454:2:2:INP:TopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x1,x0) -> % 0.12/0.41 % 455:2:2:INP:TopTop: class_Orderings_Opreorder(x0),c_HOL_Oord__class_Oless(x1,x1,x0) -> % 0.12/0.41 % 456:2:2:INP:TopTop: c_lessequals(x0,c_HOL_Oplus__class_Oplus(x1,x0,tc_nat),tc_nat) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x1,x0,tc_nat),x0,tc_nat),x1) % 0.12/0.41 % 457:2:2:INP:TopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omin(x1,x1,x0),x1) % 0.12/0.41 % 458:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0) -> =(x1,c_HOL_Ozero__class_Ozero(x0)),=(x2,c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(x2,x1,x0),x1,x0)) % 0.12/0.41 % 459:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0) -> =(x1,c_HOL_Ozero__class_Ozero(x0)),=(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(x2,x1,x0),x1,x0),x2) % 0.12/0.41 % 460:4:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(x1,x2,x0),x2,x0),x1),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 461:4:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(x1,c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(x1,x2,x0),x2,x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 462:3:4:INP:TopTopTopTop: class_OrderedGroup_Olordered__ab__group__add__abs(x0),c_lessequals(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0) -> c_lessequals(x1,c_HOL_Oplus__class_Oplus(x3,c_HOL_Oabs__class_Oabs(x2,x0),x0),x0) % 0.12/0.41 % 463:2:3:INP:TopTopTop: -> =(c_Lambda_Oliftn(x0,c_Lambda_OdB_OVar(x1),x2),c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(x1,x0,tc_nat))),c_HOL_Oord__class_Oless(x1,x2,tc_nat) % 0.12/0.41 % 464:1:2:INP:TopTop: -> c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(x0),x1),c_Lambda_Osubst(x0,x1,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 465:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(x2,x1,x0),x0) % 0.12/0.41 % 466:1:2:INP:TopTop: -> c_lessequals(x0,c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),tc_nat) % 0.12/0.41 % 467:1:2:INP:TopTop: -> c_lessequals(x0,c_HOL_Oplus__class_Oplus(x1,x0,tc_nat),tc_nat) % 0.12/0.41 % 468:1:2:INP:TopTop: -> c_lessequals(x0,c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),tc_nat) % 0.12/0.41 % 469:1:2:INP:TopTop: -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x1,tc_nat),c_Orderings_Oord__class_Omax(x0,x1,tc_nat)) % 0.12/0.41 % 470:3:3:INP:TopTopTop: class_Lattices_Oboolean__algebra(x0),=(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ouminus__class_Ouminus(x2,x0)) -> =(x1,x2) % 0.12/0.41 % 471:3:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0),=(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ouminus__class_Ouminus(x2,x0)) -> =(x1,x2) % 0.12/0.41 % 472:3:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x3,x0),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(x1,x3,x0),c_Power_Opower__class_Opower(x2,x3,x0),x0)) % 0.12/0.41 % 473:2:1:INP:Top: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_HOL_Oone__class_Oone(x0),c_HOL_Ozero__class_Ozero(x0),x0) -> % 0.12/0.41 % 474:3:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 475:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 476:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 477:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),c_HOL_Otimes__class_Otimes(x1,c_Power_Opower__class_Opower(x1,x2,x0),x0),x0) % 0.12/0.41 % 478:1:3:INP:TopTopTop: -> =(c_Lambda_Oliftn(x0,c_Lambda_OdB_OAbs(x1),x2),c_Lambda_OdB_OAbs(c_Lambda_Oliftn(x0,x1,c_HOL_Oplus__class_Oplus(x2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) % 0.12/0.41 % 479:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0),=(x2,x1) % 0.12/0.41 % 480:4:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> =(x1,x2),c_HOL_Oord__class_Oless(x2,x1,x0),c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.41 % 481:3:2:INP:TopTop: c_lessequals(x0,x1,tc_nat),c_lessequals(x1,x0,tc_nat) -> =(x1,x0) % 0.12/0.41 % 482:3:2:INP:TopTop: -> c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_HOL_Oord__class_Oless(x1,x0,tc_nat),=(x1,x0) % 0.12/0.41 % 483:3:2:INP:TopTop: -> c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_HOL_Oord__class_Oless(x1,x0,tc_nat),=(x1,x0) % 0.12/0.41 % 484:4:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x2,x1,x0) -> =(x2,x1) % 0.12/0.41 % 485:4:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0),=(x2,x1) % 0.12/0.41 % 486:4:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x2,x1,x0) -> =(x2,x1) % 0.12/0.41 % 487:4:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x2,x1,x0) -> =(x1,x2) % 0.12/0.41 % 488:4:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),=(x2,x1),c_HOL_Oord__class_Oless(x2,x1,x0) % 0.12/0.41 % 489:4:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> =(x1,x2),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0) % 0.12/0.41 % 490:4:6:INP:TopTopTopTopTopTop: class_Divides_Oring__div(x0),=(c_Divides_Odiv__class_Omod(x1,x2,x0),c_Divides_Odiv__class_Omod(x3,x2,x0)),=(c_Divides_Odiv__class_Omod(x4,x2,x0),c_Divides_Odiv__class_Omod(x5,x2,x0)) -> =(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(x4,x1,x0),x2,x0),c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(x5,x3,x0),x2,x0)) % 0.12/0.41 % 491:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,x2,x0) % 0.12/0.41 % 492:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 493:2:1:INP:Top: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) -> =(c_Suc(c_HOL_Ominus__class_Ominus(x0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),x0) % 0.12/0.41 % 494:2:1:INP:Top: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) -> =(x0,c_Suc(c_HOL_Ominus__class_Ominus(x0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) % 0.12/0.41 % 495:2:2:INP:TopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omax(x1,x1,x0),x1) % 0.12/0.41 % 496:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(c_HOL_Oabs__class_Oabs(x1,x0),x1) % 0.12/0.41 % 497:2:4:INP:TopTopTopTop: =(c_Lambda_OdB_OApp(x0,x1),c_Lambda_OdB_OApp(x2,x3)) -> =(x1,x3) % 0.12/0.41 % 498:2:4:INP:TopTopTopTop: =(c_Lambda_OdB_OApp(x0,x1),c_Lambda_OdB_OApp(x2,x3)) -> =(x0,x2) % 0.12/0.41 % 499:4:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x3,x4,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x3,x1,x0),c_HOL_Oplus__class_Oplus(x4,x2,x0),x0) % 0.12/0.41 % 500:3:4:INP:TopTopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_HOL_Oord__class_Oless(x2,x3,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x2,x0,tc_nat),c_HOL_Oplus__class_Oplus(x3,x1,tc_nat),tc_nat) % 0.12/0.41 % 501:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_lessequals(x0,x1,tc_nat) % 0.12/0.41 % 502:1:3:INP:TopTopTop: -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(x1,x2,tc_nat)) % 0.12/0.41 % 503:1:1:INP:Top: -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(x0),tc_nat) % 0.12/0.41 % 504:1:1:INP:Top: -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(x0),tc_nat) % 0.12/0.41 % 505:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oone__class_Oone(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 506:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0) % 0.12/0.41 % 507:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,c_Orderings_Oord__class_Omax(x3,x2,x0),x0) % 0.12/0.41 % 508:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0) % 0.12/0.41 % 509:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,c_Orderings_Oord__class_Omax(x3,x2,x0),x0) % 0.12/0.41 % 510:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0) -> c_HOL_Oord__class_Oless(x1,x3,x0) % 0.12/0.41 % 511:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0) -> c_HOL_Oord__class_Oless(x2,x3,x0) % 0.12/0.41 % 512:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omin(x1,x2,x0),c_Orderings_Oord__class_Omin(x2,x1,x0)) % 0.12/0.41 % 513:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),c_Power_Opower__class_Opower(x2,x1,x0),x0) % 0.12/0.41 % 514:1:4:INP:TopTopTopTop: -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),x3,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),x1,tc_nat),x3,tc_nat)) % 0.12/0.41 % 515:2:5:INP:TopTopTopTopTop: class_Ring__and__Field_Osemiring(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x3,x2,x0),x4,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(x1,x3,x0),x2,x0),x4,x0)) % 0.12/0.41 % 516:1:2:INP:TopTop: -> c_lessequals(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x0,tc_nat) % 0.12/0.41 % 517:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(x1,x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 518:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Ouminus__class_Ouminus(x1,x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 519:2:2:INP:TopTop: class_OrderedGroup_Oab__group__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(x1,x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 520:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(x1,x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 521:2:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat) % 0.12/0.41 % 522:2:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) % 0.12/0.41 % 523:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 524:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(x2,x1,x0),c_Power_Opower__class_Opower(x3,x1,x0),x0) % 0.12/0.41 % 525:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Otimes__class_Otimes(x2,x2,x0),x0),c_HOL_Ozero__class_Ozero(x0),x0) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 526:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Otimes__class_Otimes(x2,x2,x0),x0),c_HOL_Ozero__class_Ozero(x0),x0) -> =(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 527:1:3:INP:TopTopTop: -> =(c_HOL_Otimes__class_Otimes(x0,c_HOL_Ominus__class_Ominus(x1,x2,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat)) % 0.12/0.41 % 528:1:3:INP:TopTopTop: -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x2,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),tc_nat)) % 0.12/0.41 % 529:4:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0),c_lessequals(x1,x2,tc_nat) -> =(c_Power_Opower__class_Opower(x3,c_HOL_Ominus__class_Ominus(x2,x1,tc_nat),x0),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(x3,x2,x0),c_Power_Opower__class_Opower(x3,x1,x0),x0)),=(x3,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 530:3:3:INP:TopTopTop: class_Divides_Osemiring__div(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> =(c_Divides_Odiv__class_Omod(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 531:3:3:INP:TopTopTop: class_Divides_Osemiring__div(x0),=(c_Divides_Odiv__class_Omod(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> c_Ring__and__Field_Odvd__class_Odvd(x2,x1,x0) % 0.12/0.41 % 532:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(x1,x3,x0),x2,x0) % 0.12/0.41 % 533:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(x3,x1,x0),x2,x0) % 0.12/0.41 % 534:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0) -> c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.41 % 535:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0) -> c_HOL_Oord__class_Oless(x1,x3,x0) % 0.12/0.41 % 536:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(x1,x3,x0),x2,x0) % 0.12/0.41 % 537:3:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(x3,x1,x0),x2,x0) % 0.12/0.41 % 538:3:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat),c_lessequals(x0,x2,tc_nat) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(x2,x0,tc_nat),c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(x2,x1,tc_nat)) % 0.12/0.41 % 539:1:3:INP:TopTopTop: -> =(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x2,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(x0,x2,tc_nat),x1,tc_nat)) % 0.12/0.41 % 540:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 541:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 542:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(x2,x1,x0),x0) % 0.12/0.41 % 543:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(x2,x1,x0),x0) % 0.12/0.41 % 544:2:1:INP:Top: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 545:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0)) % 0.12/0.41 % 546:4:3:INP:TopTopTop: class_Ring__and__Field_Odivision__ring(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(x2,x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 547:3:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat),c_HOL_Oord__class_Oless(x1,x2,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),c_HOL_Ominus__class_Ominus(x2,x0,tc_nat),tc_nat) % 0.12/0.41 % 548:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 549:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 550:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__cancel__semiring(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 551:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__cancel__semiring(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 552:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__cancel__semiring(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 553:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__cancel__semiring(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 554:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__cancel__semiring(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 555:2:2:INP:TopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> % 0.12/0.41 % 556:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(x2),x0,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(x2),x1,tc_nat),tc_nat) % 0.12/0.41 % 557:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(x0),x1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(x0),x2,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(x1,x2,tc_nat) % 0.12/0.41 % 558:3:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(c_Suc(x0),x1,tc_nat),=(c_Suc(x0),x1) % 0.12/0.41 % 559:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat),c_lessequals(c_Suc(x1),x0,tc_nat) -> % 0.12/0.41 % 560:2:2:INP:TopTop: -> c_lessequals(c_Suc(x0),x1,tc_nat),c_lessequals(x1,x0,tc_nat) % 0.12/0.41 % 561:2:3:INP:TopTopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x0,x2,tc_nat)) -> =(x1,x2) % 0.12/0.41 % 562:2:3:INP:TopTopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x2,x1,tc_nat)) -> =(x0,x2) % 0.12/0.41 % 563:2:3:INP:TopTopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x0,x2,tc_nat)) -> =(x1,x2) % 0.12/0.41 % 564:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0),=(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x1,x3,x0)) -> =(x2,x3) % 0.12/0.41 % 565:3:4:INP:TopTopTopTop: class_OrderedGroup_Ocancel__ab__semigroup__add(x0),=(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x1,x3,x0)) -> =(x2,x3) % 0.12/0.41 % 566:3:4:INP:TopTopTopTop: class_OrderedGroup_Ocancel__semigroup__add(x0),=(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x1,x3,x0)) -> =(x2,x3) % 0.12/0.41 % 567:3:4:INP:TopTopTopTop: class_OrderedGroup_Ocancel__semigroup__add(x0),=(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x3,x2,x0)) -> =(x1,x3) % 0.12/0.41 % 568:2:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(x1,x0),x0),c_HOL_Oabs__class_Oabs(x1,x0)) % 0.12/0.41 % 569:4:2:INP:TopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0),=(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oone__class_Oone(x0)) -> =(x1,c_HOL_Oone__class_Oone(x0)) % 0.12/0.41 % 570:5:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oone__class_Oone(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 571:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0) % 0.12/0.41 % 572:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0) % 0.12/0.41 % 573:2:2:INP:TopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oinverse__class_Odivide(x1,c_HOL_Oone__class_Oone(x0),x0),x1) % 0.12/0.41 % 574:2:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0) -> =(c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(x1,x2,x0),x3,x0),c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(x1,x3,x0),c_HOL_Oplus__class_Oplus(x2,x3,x0),x0)) % 0.12/0.41 % 575:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(x2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),x0,tc_nat),tc_nat) % 0.12/0.41 % 576:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_lessequals(x1,c_HOL_Oone__class_Oone(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),x2,x0) % 0.12/0.41 % 577:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.41 % 578:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.41 % 579:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_lessequals(x1,c_HOL_Oone__class_Oone(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),x2,x0) % 0.12/0.41 % 580:2:4:INP:TopTopTopTop: class_Divides_Oring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(x1,x2,x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(x1,x3,x0),c_Divides_Odiv__class_Omod(x2,x3,x0),x0),x3,x0)) % 0.12/0.41 % 581:2:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(x1,x2,x0),x0),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0)) % 0.12/0.41 % 582:2:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(x1,x0),x0),c_Nat_Osemiring__1__class_Oof__nat(x1,x0)) % 0.12/0.41 % 583:3:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(x1,x3,x0),c_Power_Opower__class_Opower(x2,x3,x0),x0) % 0.12/0.41 % 584:3:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(x1,x0),x0),c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(x1,x0),x0)) % 0.12/0.41 % 585:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Oinverse__class_Odivide(x3,x1,x0),x0) % 0.12/0.41 % 586:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x3,x1,x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.41 % 587:2:5:INP:TopTopTopTopTop: c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) -> =(c_Lambda_Osubst(c_Lambda_Osubst(x2,c_Lambda_Olift(x3,x0),c_Suc(x1)),c_Lambda_Osubst(x4,x3,x1),x0),c_Lambda_Osubst(c_Lambda_Osubst(x2,x4,x0),x3,x1)) % 0.12/0.41 % 588:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0)) % 0.12/0.41 % 589:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(c_HOL_Oabs__class_Oabs(x1,x0),x1) % 0.12/0.41 % 590:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 591:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) % 0.12/0.41 % 592:3:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) % 0.12/0.41 % 593:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(x1,x3,x0),x2,x0),x3,x0)) % 0.12/0.41 % 594:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x1,c_Divides_Odiv__class_Omod(x2,x3,x0),x0),x3,x0)) % 0.12/0.41 % 595:3:2:INP:TopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) -> =(x1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),=(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.41 % 596:3:2:INP:TopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) -> =(x0,c_HOL_Ozero__class_Ozero(tc_nat)),=(x0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.41 % 597:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 598:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 599:1:3:INP:TopTopTop: -> =(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(x0),x1,tc_nat),c_Suc(x2),tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x2,tc_nat)) % 0.12/0.41 % 600:3:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__ring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) % 0.12/0.41 % 601:3:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__ring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0) % 0.12/0.41 % 602:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_lessequals(x0,x1,tc_nat) % 0.12/0.41 % 603:3:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_lessequals(x1,x2,x0) % 0.12/0.41 % 604:3:3:INP:TopTopTop: class_Orderings_Opreorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_lessequals(x1,x2,x0) % 0.12/0.41 % 605:2:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Oplus__class_Oplus(x1,x2,x0),x0),x2) % 0.12/0.41 % 606:2:3:INP:TopTopTop: class_OrderedGroup_Oab__group__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Oplus__class_Oplus(x2,x1,x0),x0),x2) % 0.12/0.41 % 607:2:1:INP:Top: class_Ring__and__Field_Odivision__ring(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(x0),x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.41 % 608:5:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Oone__class_Oone(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) % 0.12/0.41 % 609:3:1:INP:Top: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(x0),x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.41 % 610:4:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0),c_Ring__and__Field_Odvd__class_Odvd(x3,x1,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x3,x2,x0) % 0.12/0.41 % 611:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x1,x0) % 0.12/0.41 % 612:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.41 % 613:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.41 % 614:6:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x3,x4,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x3,x2,x0),c_HOL_Oinverse__class_Odivide(x4,x1,x0),x0) % 0.12/0.41 % 615:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),c_Power_Opower__class_Opower(x1,c_Suc(x2),x0),x0) % 0.12/0.41 % 616:1:2:INP:TopTop: c_Lambda_Obeta(c_Lambda_OdB_OVar(x0),x1) -> % 0.12/0.41 % 617:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(x2,c_Suc(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat)),tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x2,x0,tc_nat),c_Suc(x1),tc_nat)) % 0.12/0.41 % 618:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.41 % 619:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 620:2:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> % 0.12/0.41 % 621:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(x1,x2,tc_nat) -> c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(x1,x0),c_Nat_Osemiring__1__class_Oof__nat(x2,x0),x0) % 0.12/0.41 % 622:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(x1,x0),c_Nat_Osemiring__1__class_Oof__nat(x2,x0),x0) -> c_HOL_Oord__class_Oless(x1,x2,tc_nat) % 0.12/0.41 % 623:2:3:INP:TopTopTop: class_Ring__and__Field_Oidom(x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Otimes__class_Otimes(x2,c_HOL_Ozero__class_Ozero(x0),x0),x0) % 0.12/0.41 % 624:2:3:INP:TopTopTop: class_Ring__and__Field_Oidom(x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),x2,x0),x0) % 0.12/0.41 % 625:1:1:INP:Top: -> c_HOL_Oord__class_Oless(x0,c_Suc(x0),tc_nat) % 0.12/0.41 % 626:1:1:INP:Top: -> c_HOL_Oord__class_Oless(x0,c_Suc(x0),tc_nat) % 0.12/0.41 % 627:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_HOL_Oord__class_Oless(x2,x0,tc_nat) -> c_HOL_Oord__class_Oless(c_Suc(x2),x1,tc_nat) % 0.12/0.41 % 628:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(x1,x3,x0),c_HOL_Oplus__class_Oplus(x2,x3,x0),x0) % 0.12/0.41 % 629:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),c_lessequals(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) -> c_lessequals(x1,x3,x0) % 0.12/0.41 % 630:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(x3,x1,x0),c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) % 0.12/0.41 % 631:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),c_lessequals(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x1,x3,x0),x0) -> c_lessequals(x2,x3,x0) % 0.12/0.41 % 632:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(x1,x3,x0),c_HOL_Oplus__class_Oplus(x2,x3,x0),x0) % 0.12/0.41 % 633:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add(x0),c_lessequals(x1,x2,x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(x3,x1,x0),c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) % 0.12/0.41 % 634:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat) % 0.12/0.41 % 635:2:3:INP:TopTopTop: c_lessequals(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),tc_nat) -> c_lessequals(x1,x2,tc_nat) % 0.12/0.41 % 636:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_HOL_Oplus__class_Oplus(x2,x0,tc_nat),c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),tc_nat) % 0.12/0.41 % 637:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__ring__abs(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(x2,x1,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(x2,x0),c_HOL_Oabs__class_Oabs(x1,x0),x0)) % 0.12/0.41 % 638:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__ring__abs(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(x2,x1,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(x2,x0),c_HOL_Oabs__class_Oabs(x1,x0),x0)) % 0.12/0.41 % 639:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__ring__abs(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(x2,x1,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(x2,x0),c_HOL_Oabs__class_Oabs(x1,x0),x0)) % 0.12/0.41 % 640:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__ring__abs(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(x2,x1,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(x2,x0),c_HOL_Oabs__class_Oabs(x1,x0),x0)) % 0.12/0.41 % 641:2:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0)) % 0.12/0.41 % 642:2:1:INP:Top: class_Ring__and__Field_Oordered__semidom(x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oone__class_Oone(x0),x0) % 0.12/0.41 % 643:3:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Oinverse__class_Odivide(x3,x4,x0),x0),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x2,x4,x0),x0)) % 0.12/0.41 % 644:2:3:INP:TopTopTop: class_Ring__and__Field_Oring(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Otimes__class_Otimes(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0)) % 0.12/0.41 % 645:2:3:INP:TopTopTop: class_Ring__and__Field_Oring(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0)) % 0.12/0.41 % 646:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> =(x1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),x0,tc_nat)) % 0.12/0.41 % 647:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Oplus__class_Oplus(x0,c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),tc_nat),x1) % 0.12/0.41 % 648:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),x0,tc_nat),x1) % 0.12/0.41 % 649:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(x1,x2,tc_nat) % 0.12/0.41 % 650:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(x0,x2,tc_nat) % 0.12/0.41 % 651:3:3:INP:TopTopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0) % 0.12/0.41 % 652:3:3:INP:TopTopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 653:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x3,x1,x0),c_HOL_Oinverse__class_Odivide(x3,x2,x0),x0) % 0.12/0.41 % 654:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0),c_HOL_Oord__class_Oless(x2,x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x3,x1,x0),c_HOL_Oinverse__class_Odivide(x3,x2,x0),x0) % 0.12/0.41 % 655:2:2:INP:TopTop: class_Ring__and__Field_Oordered__semidom(x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oplus__class_Oplus(x1,c_HOL_Oone__class_Oone(x0),x0),x0) % 0.12/0.41 % 656:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Oplus__class_Oplus(x2,c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),x0,tc_nat)) % 0.12/0.41 % 657:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),x2,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),x0,tc_nat)) % 0.12/0.41 % 658:1:4:INP:TopTopTopTop: -> =(c_List_Odrop(x0,c_List_Odrop(x1,x2,x3),x3),c_List_Odrop(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x2,x3)) % 0.12/0.41 % 659:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_Power_Opower__class_Opower(x2,c_Suc(x3),x0),c_Power_Opower__class_Opower(x1,c_Suc(x3),x0),x0) -> c_lessequals(x2,x1,x0) % 0.12/0.41 % 660:2:3:INP:TopTopTop: class_OrderedGroup_Oab__semigroup__idem__mult(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Otimes__class_Otimes(x1,x2,x0)) % 0.12/0.41 % 661:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 662:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 663:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 664:3:2:INP:TopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_Nat_Osemiring__1__class_Oof__nat(x1,x0),x0) % 0.12/0.41 % 665:3:2:INP:TopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_Nat_Osemiring__1__class_Oof__nat(x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat) % 0.12/0.41 % 666:6:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_lessequals(x1,x3,x0),c_HOL_Oord__class_Oless(x2,x4,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Otimes__class_Otimes(x4,x3,x0),x0) % 0.12/0.41 % 667:6:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_HOL_Oord__class_Oless(x1,x3,x0),c_lessequals(x2,x4,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Otimes__class_Otimes(x4,x3,x0),x0) % 0.12/0.41 % 668:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(x0),x1,x0) % 0.12/0.41 % 669:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),=(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x1,x3,x0)),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0) -> =(x2,x3) % 0.12/0.41 % 670:2:2:INP:TopTop: class_Power_Opower(x0) -> =(c_Power_Opower__class_Opower(x1,c_HOL_Ozero__class_Ozero(tc_nat),x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.41 % 671:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_Power_Opower__class_Opower(x1,c_HOL_Ozero__class_Ozero(tc_nat),x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.41 % 672:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> =(c_Lambda_Osubst(c_Lambda_OdB_OVar(x1),x2,x0),c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) % 0.12/0.41 % 673:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> =(c_Lambda_Osubst(c_Lambda_OdB_OVar(x1),x2,x0),c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) % 0.12/0.41 % 674:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),=(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(x0),x0)) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 675:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> =(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(x0),x0)) % 0.12/0.41 % 676:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_Power_Opower__class_Opower(x1,x2,x0),x0),c_Power_Opower__class_Opower(x1,c_Suc(x2),x0)) % 0.12/0.41 % 677:2:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(x1,x2,x0),x1,x0),c_Power_Opower__class_Opower(x1,c_Suc(x2),x0)) % 0.12/0.41 % 678:2:3:INP:TopTopTop: class_Ring__and__Field_Oring(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0),c_HOL_Otimes__class_Otimes(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0)) % 0.12/0.41 % 679:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0) % 0.12/0.41 % 680:2:3:INP:TopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,x2,x0),x2,x0),c_Divides_Odiv__class_Omod(x1,x2,x0)) % 0.12/0.41 % 681:2:3:INP:TopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,x2,x0),x1,x0),c_Divides_Odiv__class_Omod(x2,x1,x0)) % 0.12/0.41 % 682:2:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(x1,x2,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0),x0) % 0.12/0.41 % 683:4:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_lessequals(x1,x2,tc_nat),c_Ring__and__Field_Odvd__class_Odvd(x3,x4,x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(x3,x1,x0),c_Power_Opower__class_Opower(x4,x2,x0),x0) % 0.12/0.41 % 684:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 685:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 686:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 687:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 688:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 689:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 690:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 691:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_lessequals(c_HOL_Oabs__class_Oabs(x1,x0),x2,x0) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0) % 0.12/0.41 % 692:2:2:INP:TopTop: c_lessequals(c_Suc(x0),x1,tc_nat) -> c_lessequals(x0,x1,tc_nat) % 0.12/0.41 % 693:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(x0,c_Suc(x1),tc_nat) % 0.12/0.41 % 694:3:2:INP:TopTop: c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x0,tc_nat),c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x1,tc_nat) -> c_HOL_Oord__class_Oless(x1,c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),tc_nat) % 0.12/0.41 % 695:3:2:INP:TopTop: c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x0,tc_nat),c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x1,tc_nat) -> c_HOL_Oord__class_Oless(x1,c_HOL_Otimes__class_Otimes(x1,x0,tc_nat),tc_nat) % 0.12/0.41 % 696:2:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0),x0),x2) % 0.12/0.41 % 697:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Int_Onumber__ring(x0) -> =(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,c_HOL_Oinverse__class_Oinverse(x2,x0),x0)) % 0.12/0.41 % 698:2:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,c_HOL_Oinverse__class_Oinverse(x2,x0),x0)) % 0.12/0.41 % 699:1:1:INP:Top: c_lessequals(c_Suc(x0),x0,tc_nat) -> % 0.12/0.41 % 700:3:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x2,x3,x0) % 0.12/0.41 % 701:3:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x3,x0) % 0.12/0.41 % 702:3:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__ring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) % 0.12/0.41 % 703:3:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__ring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0) % 0.12/0.41 % 704:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ouminus__class_Ouminus(x2,x0),x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 705:2:3:INP:TopTopTop: class_Int_Onumber__ring(x0) -> =(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0)) % 0.12/0.41 % 706:2:3:INP:TopTopTop: class_OrderedGroup_Oab__group__add(x0) -> =(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0)) % 0.12/0.41 % 707:2:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0)) % 0.12/0.41 % 708:2:3:INP:TopTopTop: class_OrderedGroup_Oab__group__add(x0) -> =(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0)) % 0.12/0.41 % 709:1:2:INP:TopTop: -> =(c_HOL_Ominus__class_Ominus(x0,c_Suc(x1),tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(x0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),x1,tc_nat)) % 0.12/0.41 % 710:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(x2),x0,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(x2),x1,tc_nat),tc_nat) % 0.12/0.41 % 711:2:3:INP:TopTopTop: c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(x0),x1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(x0),x2,tc_nat),tc_nat) -> c_lessequals(x1,x2,tc_nat) % 0.12/0.41 % 712:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Otimes__class_Otimes(x2,x2,x0),x0),x0),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 713:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Otimes__class_Otimes(x2,x2,x0),x0),x0),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 714:2:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x3,x4,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(x1,x3,x0),c_HOL_Oplus__class_Oplus(x2,x4,x0),x0)) % 0.12/0.41 % 715:4:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(x2,c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),x3,x0)),=(x3,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 716:4:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x3,x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(x1,c_HOL_Otimes__class_Otimes(x3,x2,x0),x0),x2,x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 717:2:3:INP:TopTopTop: c_Lambda_Obeta(x0,x1) -> c_Lambda_Obeta(c_Lambda_OdB_OApp(x2,x0),c_Lambda_OdB_OApp(x2,x1)) % 0.12/0.41 % 718:2:3:INP:TopTopTop: c_Lambda_Obeta(x0,x1) -> c_Lambda_Obeta(c_Lambda_OdB_OApp(x0,x2),c_Lambda_OdB_OApp(x1,x2)) % 0.12/0.41 % 719:2:2:INP:TopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> % 0.12/0.41 % 720:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 721:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.41 % 722:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 723:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.41 % 724:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(x0),c_HOL_Oone__class_Oone(x0),x0),x0),x0) % 0.12/0.41 % 725:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(x0),c_HOL_Oone__class_Oone(x0),x0),x0),x2,x0) % 0.12/0.41 % 726:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Ouminus__class_Ouminus(x1,x0)) % 0.12/0.41 % 727:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> =(c_Lambda_Osubstn(c_Lambda_OdB_OVar(x1),x2,x0),c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) % 0.12/0.41 % 728:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omax(x1,x2,x0),c_Orderings_Oord__class_Omax(x2,x1,x0)) % 0.12/0.41 % 729:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),=(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x3,x2,x0)),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x2,tc_nat),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x3,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(x1,x3) % 0.12/0.41 % 730:3:4:INP:TopTopTopTop: class_OrderedGroup_Oab__group__add(x0),=(c_HOL_Oplus__class_Oplus(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0),x2) -> =(x1,c_HOL_Ouminus__class_Ouminus(x3,x0)) % 0.12/0.41 % 731:2:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Otimes__class_Otimes(x1,c_HOL_Osgn__class_Osgn(x1,x0),x0)) % 0.12/0.41 % 732:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> =(c_Lambda_Oliftn(x2,c_Lambda_OdB_OVar(x0),x1),c_Lambda_OdB_OVar(x0)) % 0.12/0.41 % 733:4:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_HOL_Oinverse__class_Odivide(x2,x3,x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 734:4:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0),c_HOL_Oinverse__class_Odivide(x1,x3,x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 735:4:3:INP:TopTopTop: class_Ring__and__Field_Odivision__ring(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oplus__class_Oplus(x1,x2,x0),x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 736:4:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.41 % 737:4:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x3,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) % 0.12/0.41 % 738:1:1:INP:Top: -> c_lessequals(c_Suc(x0),c_Suc(x0),tc_nat) % 0.12/0.41 % 739:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oone__class_Oone(x0),x0) % 0.12/0.41 % 740:1:4:INP:TopTopTopTop: -> =(c_List_Odrop(x0,c_List_Oreplicate(x1,x2,x3),x3),c_List_Oreplicate(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),x2,x3)) % 0.12/0.41 % 741:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(x1,x2,x0),c_Orderings_Oord__class_Omin(x1,x3,x0),x0),c_Orderings_Oord__class_Omin(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0),x0) % 0.12/0.41 % 742:1:4:INP:TopTopTopTop: -> =(c_Lambda_Oliftn(x0,c_Lambda_OdB_OApp(x1,x2),x3),c_Lambda_OdB_OApp(c_Lambda_Oliftn(x0,x1,x3),c_Lambda_Oliftn(x0,x2,x3))) % 0.12/0.41 % 743:2:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(x1,x0),x0) % 0.12/0.42 % 744:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.42 % 745:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.42 % 746:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.42 % 747:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.42 % 748:1:1:INP:Top: -> =(c_nat_Onat__size(c_Suc(x0)),c_HOL_Oplus__class_Oplus(c_nat_Onat__size(x0),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) % 0.12/0.42 % 749:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omax(x1,c_Orderings_Oord__class_Omin(x1,x2,x0),x0),x1) % 0.12/0.42 % 750:2:3:INP:TopTopTop: class_Divides_Oring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0),c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(x1,x2,x0),x0),x2,x0)) % 0.12/0.42 % 751:1:1:INP:Top: -> c_lessequals(x0,c_HOL_Otimes__class_Otimes(x0,x0,tc_nat),tc_nat) % 0.12/0.42 % 752:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 753:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(x3,x2,x0),c_HOL_Oord__class_Oless(x2,x3,x0) % 0.12/0.42 % 754:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) -> c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.42 % 755:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) -> c_HOL_Oord__class_Oless(x3,x1,x0),c_HOL_Oord__class_Oless(x1,x3,x0) % 0.12/0.42 % 756:3:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x3,x0),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(x1,x3,x0),x2,x0)) % 0.12/0.42 % 757:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> =(c_HOL_Ominus__class_Ominus(x1,c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),tc_nat),x0) % 0.12/0.42 % 758:1:0:INP:: -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat)) % 0.12/0.42 % 759:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> =(c_Lambda_Olift(c_Lambda_OdB_OVar(x0),x1),c_Lambda_OdB_OVar(x0)) % 0.12/0.42 % 760:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Oone__class_Oone(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,c_Power_Opower__class_Opower(x1,x2,x0),x0),c_Power_Opower__class_Opower(x1,x2,x0),x0) % 0.12/0.42 % 761:1:2:INP:TopTop: -> =(c_Orderings_Oord__class_Omin(c_Suc(x0),c_Suc(x1),tc_nat),c_Suc(c_Orderings_Oord__class_Omin(x0,x1,tc_nat))) % 0.12/0.42 % 762:2:2:INP:TopTop: -> c_HOL_Oord__class_Oless(x0,x0,tc_nat),=(c_Lambda_Osubstn(c_Lambda_OdB_OVar(x0),x1,x0),c_Lambda_Oliftn(x0,x1,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.42 % 763:3:2:INP:TopTop: c_lessequals(x0,c_Suc(x1),tc_nat) -> =(x0,c_Suc(x1)),c_lessequals(x0,x1,tc_nat) % 0.12/0.42 % 764:2:1:INP:Top: -> c_HOL_Oord__class_Oless(x0,x0,tc_nat),c_HOL_Oord__class_Oless(x0,c_Suc(x0),tc_nat) % 0.12/0.42 % 765:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_HOL_Oord__class_Oless(x1,c_Suc(x0),tc_nat) -> % 0.12/0.42 % 766:2:2:INP:TopTop: -> c_HOL_Oord__class_Oless(x0,c_Suc(x1),tc_nat),c_HOL_Oord__class_Oless(x1,x0,tc_nat) % 0.12/0.42 % 767:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) -> =(c_Lambda_Olift(c_Lambda_Olift(x2,x0),c_Suc(x1)),c_Lambda_Olift(c_Lambda_Olift(x2,x1),x0)) % 0.12/0.42 % 768:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> =(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Ouminus__class_Ouminus(x1,x0)) % 0.12/0.42 % 769:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x2,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),tc_nat) % 0.12/0.42 % 770:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x2,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x0,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat) % 0.12/0.42 % 771:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_HOL_Oord__class_Oless(x1,x2,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat) % 0.12/0.42 % 772:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_HOL_Oord__class_Oless(x1,x2,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x0,tc_nat),c_HOL_Otimes__class_Otimes(x2,x0,tc_nat),tc_nat) % 0.12/0.42 % 773:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) -> c_HOL_Oord__class_Oless(x1,x2,tc_nat) % 0.12/0.42 % 774:3:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x2,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x0,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat) % 0.12/0.42 % 775:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x3,x2,x0) % 0.12/0.42 % 776:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x3,x2,x0),c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) % 0.12/0.42 % 777:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(x2,x3,x0) % 0.12/0.42 % 778:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x3,x1,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) % 0.12/0.42 % 779:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) % 0.12/0.42 % 780:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) % 0.12/0.42 % 781:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x3,x1,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) % 0.12/0.42 % 782:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x3,x2,x0),c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) % 0.12/0.42 % 783:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x3,x1,x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.42 % 784:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) % 0.12/0.42 % 785:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x2,x3,x0),x0) % 0.12/0.42 % 786:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x3,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) % 0.12/0.42 % 787:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__comm__semiring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) % 0.12/0.42 % 788:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x3,x0),x2,x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0) % 0.12/0.42 % 789:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,c_HOL_Otimes__class_Otimes(x3,x1,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x3,x1,x0),x2,x0) -> c_HOL_Oord__class_Oless(x3,c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.42 % 790:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) % 0.12/0.42 % 791:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) % 0.12/0.42 % 792:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x3,x2,x0),x1,x0) % 0.12/0.42 % 793:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),x3,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x3,x1,x0),x2,x0) % 0.12/0.42 % 794:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x3,x0),x1,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) % 0.12/0.42 % 795:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.42 % 796:2:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0) -> =(c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0),c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(x1,x3,x0),c_HOL_Oplus__class_Oplus(x2,x3,x0),x0)) % 0.12/0.42 % 797:2:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(x1,x0),x0),c_HOL_Osgn__class_Osgn(x1,x0)) % 0.12/0.42 % 798:2:2:INP:TopTop: c_InductTermi_OIT(x0) -> c_InductTermi_OIT(c_Lambda_OdB_OApp(x0,c_Lambda_OdB_OVar(x1))) % 0.12/0.42 % 799:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),=(c_Power_Opower__class_Opower(x1,c_Suc(x2),x0),c_Power_Opower__class_Opower(x3,c_Suc(x2),x0)),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x3,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(x1,x3) % 0.12/0.42 % 800:3:4:INP:TopTopTopTop: c_lessequals(x0,x1,tc_nat),c_lessequals(x2,x3,tc_nat) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x0,tc_nat),c_HOL_Otimes__class_Otimes(x3,x1,tc_nat),tc_nat) % 0.12/0.42 % 801:1:1:INP:Top: -> c_lessequals(x0,c_HOL_Otimes__class_Otimes(x0,c_HOL_Otimes__class_Otimes(x0,x0,tc_nat),tc_nat),tc_nat) % 0.12/0.42 % 802:3:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0) % 0.12/0.42 % 803:3:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) % 0.12/0.42 % 804:4:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),c_HOL_Ominus__class_Ominus(x2,x1,tc_nat),tc_nat),c_lessequals(x1,x2,tc_nat),c_lessequals(x1,x0,tc_nat) -> c_HOL_Oord__class_Oless(x0,x2,tc_nat) % 0.12/0.42 % 805:4:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat),c_lessequals(x2,x1,tc_nat),c_lessequals(x2,x0,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x0,x2,tc_nat),c_HOL_Ominus__class_Ominus(x1,x2,tc_nat),tc_nat) % 0.12/0.42 % 806:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) % 0.12/0.42 % 807:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> =(c_Lambda_Osubst(c_Lambda_OdB_OVar(x0),x2,x1),c_Lambda_OdB_OVar(x0)) % 0.12/0.42 % 808:3:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) -> =(c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(x3,x2,x0),x1,x0),c_Divides_Odiv__class_Omod(x3,x1,x0)) % 0.12/0.42 % 809:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0),x0) % 0.12/0.42 % 810:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 811:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 812:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_lessequals(c_HOL_Oplus__class_Oplus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 813:4:2:INP:TopTop: class_Orderings_Olinorder(x0),class_OrderedGroup_Olordered__ab__group__add__abs(x0) -> =(c_HOL_Oabs__class_Oabs(x1,x0),x1),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 814:3:2:INP:TopTop: class_Ring__and__Field_Oabs__if(x0) -> =(c_HOL_Oabs__class_Oabs(x1,x0),x1),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 815:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(x1,x2,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x3,x0) -> c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(x3,x1,x0),c_Power_Opower__class_Opower(x3,x2,x0),x0) % 0.12/0.42 % 816:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x1,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_HOL_Oord__class_Oless(x2,x3,tc_nat) % 0.12/0.42 % 817:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0),c_HOL_Oord__class_Oless(x2,x3,tc_nat) -> c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x1,x3,x0),x0) % 0.12/0.42 % 818:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x1,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_HOL_Oord__class_Oless(x2,x3,tc_nat) % 0.12/0.42 % 819:1:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x0,tc_nat) -> % 0.12/0.42 % 820:1:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x1,tc_nat) -> % 0.12/0.42 % 821:3:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x3,x0),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(x1,x3,x0),c_Power_Opower__class_Opower(x2,x3,x0),x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 822:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 823:3:3:INP:TopTopTop: class_Ring__and__Field_Oring__1(x0),c_lessequals(x1,x2,tc_nat) -> =(c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(x2,x1,tc_nat),x0),c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(x2,x0),c_Nat_Osemiring__1__class_Oof__nat(x1,x0),x0)) % 0.12/0.42 % 824:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,c_Power_Opower__class_Opower(x1,x2,x0),x0),x0) % 0.12/0.42 % 825:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0)) % 0.12/0.42 % 826:4:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0),c_Ring__and__Field_Odvd__class_Odvd(x3,x4,x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(x3,x1,x0),c_HOL_Otimes__class_Otimes(x4,x2,x0),x0) % 0.12/0.42 % 827:4:4:INP:TopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,x3,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x3,x1,x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.42 % 828:4:4:INP:TopTopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,x3,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) % 0.12/0.42 % 829:4:4:INP:TopTopTopTop: class_Ring__and__Field_Omult__mono(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,x3,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) % 0.12/0.42 % 830:4:4:INP:TopTopTopTop: class_Ring__and__Field_Omult__mono(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,x3,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) % 0.12/0.42 % 831:4:4:INP:TopTopTopTop: class_Ring__and__Field_Omult__mono1(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,x3,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) % 0.12/0.42 % 832:5:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0),=(c_HOL_Oplus__class_Oplus(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0),c_HOL_Oplus__class_Oplus(x1,c_HOL_Otimes__class_Otimes(x2,x4,x0),x0)) -> =(x3,x4),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 833:3:4:INP:TopTopTopTop: =(c_HOL_Oplus__class_Oplus(x0,c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(x0,c_HOL_Otimes__class_Otimes(x1,x3,tc_nat),tc_nat)) -> =(x2,x3),=(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 834:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),=(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Otimes__class_Otimes(x2,x2,x0),x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 835:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),=(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x1,x0),c_HOL_Otimes__class_Otimes(x2,x2,x0),x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 836:2:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0)) % 0.12/0.42 % 837:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,c_HOL_Ominus__class_Ominus(x1,x2,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),x1,tc_nat) % 0.12/0.42 % 838:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x2,tc_nat) -> c_HOL_Oord__class_Oless(x0,c_HOL_Ominus__class_Ominus(x2,x1,tc_nat),tc_nat) % 0.12/0.42 % 839:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x1,x0),x3,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x3,x1,x0),x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 840:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),x3,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x3,x1,x0),x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 841:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Oinverse__class_Odivide(x3,x1,x0),x0) -> c_lessequals(x3,c_HOL_Otimes__class_Otimes(x2,x1,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 842:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) -> c_lessequals(x3,c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 843:1:1:INP:Top: =(c_Suc(x0),x0) -> % 0.12/0.42 % 844:1:1:INP:Top: =(x0,c_Suc(x0)) -> % 0.12/0.42 % 845:3:3:INP:TopTopTop: class_Ring__and__Field_Odivision__ring(x0),=(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Oone__class_Oone(x0)) -> =(c_HOL_Oinverse__class_Oinverse(x1,x0),x2) % 0.12/0.42 % 846:2:1:INP:Top: class_OrderedGroup_Opordered__ab__group__add__abs(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(x0),x0),x0) -> % 0.12/0.42 % 847:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Oinverse__class_Odivide(x3,x2,x0),x0) % 0.12/0.42 % 848:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x1,x3,x0),x2,x0) % 0.12/0.42 % 849:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x1,x0),x3,x0) -> c_HOL_Oord__class_Oless(x2,c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) % 0.12/0.42 % 850:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,c_HOL_Otimes__class_Otimes(x3,x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x1,x0),x3,x0) % 0.12/0.42 % 851:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,c_HOL_Oinverse__class_Odivide(x3,x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),x3,x0) % 0.12/0.42 % 852:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),x3,x0) -> c_HOL_Oord__class_Oless(x2,c_HOL_Oinverse__class_Odivide(x3,x1,x0),x0) % 0.12/0.42 % 853:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 854:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 855:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 856:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 857:3:3:INP:TopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat) -> c_Ring__and__Field_Odvd__class_Odvd(x2,c_Power_Opower__class_Opower(x2,x1,x0),x0) % 0.12/0.42 % 858:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x1,x3,x0),c_HOL_Oplus__class_Oplus(x2,x3,x0),x0) % 0.12/0.42 % 859:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x1,x3,x0),c_HOL_Oplus__class_Oplus(x2,x3,x0),x0) % 0.12/0.42 % 860:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) -> c_HOL_Oord__class_Oless(x1,x3,x0) % 0.12/0.42 % 861:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x3,x1,x0),c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) % 0.12/0.42 % 862:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x3,x1,x0),c_HOL_Oplus__class_Oplus(x3,x2,x0),x0) % 0.12/0.42 % 863:3:4:INP:TopTopTopTop: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(x0),c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x1,x2,x0),c_HOL_Oplus__class_Oplus(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(x2,x3,x0) % 0.12/0.42 % 864:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat) % 0.12/0.42 % 865:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Oplus__class_Oplus(x0,x2,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(x1,x2,tc_nat) % 0.12/0.42 % 866:2:3:INP:TopTopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x2,x0,tc_nat),c_HOL_Oplus__class_Oplus(x2,x1,tc_nat),tc_nat) % 0.12/0.42 % 867:3:2:INP:TopTop: c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x0,tc_nat),c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),x1,tc_nat) -> c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(x1,x0,tc_nat),tc_nat) % 0.12/0.42 % 868:4:4:INP:TopTopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x2,x3,x0) -> c_lessequals(x1,x3,x0) % 0.12/0.42 % 869:4:4:INP:TopTopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x3,x0) -> c_HOL_Oord__class_Oless(x1,x3,x0) % 0.12/0.42 % 870:4:4:INP:TopTopTopTop: class_Orderings_Oorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_lessequals(x2,x3,x0) -> c_HOL_Oord__class_Oless(x1,x3,x0) % 0.12/0.42 % 871:4:3:INP:TopTopTop: class_OrderedGroup_Opordered__comm__monoid__add(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Oplus__class_Oplus(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 872:4:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_lessequals(x1,x2,tc_nat),c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(x3,x2,x0),x4,x0) -> c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(x3,x1,x0),x4,x0) % 0.12/0.42 % 873:4:4:INP:TopTopTopTop: class_Orderings_Opreorder(x0),c_lessequals(x1,x2,x0),c_lessequals(x3,x1,x0) -> c_lessequals(x3,x2,x0) % 0.12/0.42 % 874:1:1:INP:Top: -> c_lessequals(x0,x0,tc_nat) % 0.12/0.42 % 875:3:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat),c_lessequals(x2,x0,tc_nat) -> c_lessequals(x2,x1,tc_nat) % 0.12/0.42 % 876:1:1:INP:Top: -> c_lessequals(x0,x0,tc_nat) % 0.12/0.42 % 877:2:2:INP:TopTop: class_Orderings_Oorder(x0) -> c_lessequals(x1,x1,x0) % 0.12/0.42 % 878:2:2:INP:TopTop: class_Orderings_Opreorder(x0) -> c_lessequals(x1,x1,x0) % 0.12/0.42 % 879:4:4:INP:TopTopTopTop: class_Orderings_Opreorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_lessequals(x3,x1,x0) -> c_HOL_Oord__class_Oless(x3,x2,x0) % 0.12/0.42 % 880:4:4:INP:TopTopTopTop: class_Orderings_Opreorder(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(x3,x1,x0) -> c_HOL_Oord__class_Oless(x3,x2,x0) % 0.12/0.42 % 881:4:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(x1,x2,x0),c_lessequals(x3,c_HOL_Oplus__class_Oplus(x4,x1,x0),x0) -> c_lessequals(x3,c_HOL_Oplus__class_Oplus(x4,x2,x0),x0) % 0.12/0.42 % 882:1:3:INP:TopTopTop: =(c_Lambda_OdB_OAbs(x0),c_Lambda_OdB_OApp(x1,x2)) -> % 0.12/0.42 % 883:4:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oone__class_Oone(x0),x0) % 0.12/0.42 % 884:1:3:INP:TopTopTop: -> =(c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),c_HOL_Ominus__class_Ominus(x2,x1,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(x0,x2,tc_nat),x1,tc_nat)) % 0.12/0.42 % 885:1:0:INP:: -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.42 % 886:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0) -> c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.42 % 887:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.42 % 888:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0) -> c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 889:5:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 890:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 891:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__field(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 892:2:2:INP:TopTop: class_OrderedGroup_Oab__semigroup__idem__mult(x0) -> =(c_HOL_Otimes__class_Otimes(x1,x1,x0),x1) % 0.12/0.42 % 893:2:3:INP:TopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x1,x2,x0),x2,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 894:2:3:INP:TopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x1,x2,x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 895:2:2:INP:TopTop: =(c_Lambda_OdB_OVar(x0),c_Lambda_OdB_OVar(x1)) -> =(x0,x1) % 0.12/0.42 % 896:6:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oordered__semiring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_HOL_Oord__class_Oless(x1,x3,x0),c_HOL_Oord__class_Oless(x2,x4,x0) -> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Otimes__class_Otimes(x4,x3,x0),x0) % 0.12/0.42 % 897:3:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,c_Suc(x1),tc_nat),c_lessequals(x1,x0,tc_nat) -> =(x0,x1) % 0.12/0.42 % 898:4:3:INP:TopTopTop: class_Ring__and__Field_Odivision__ring(x0) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Ominus__class_Ominus(x2,x1,x0),x0),c_HOL_Oinverse__class_Oinverse(x2,x0),x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 899:1:3:INP:TopTopTop: =(c_Lambda_OdB_OApp(x0,x1),c_Lambda_OdB_OAbs(x2)) -> % 0.12/0.42 % 900:1:2:INP:TopTop: =(c_Lambda_OdB_OAbs(x0),c_Lambda_OdB_OVar(x1)) -> % 0.12/0.42 % 901:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),tc_nat) % 0.12/0.42 % 902:6:5:INP:TopTopTopTopTop: class_Ring__and__Field_Opordered__semiring(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_lessequals(x1,x3,x0),c_lessequals(x4,x2,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x4,x1,x0),c_HOL_Otimes__class_Otimes(x2,x3,x0),x0) % 0.12/0.42 % 903:6:5:INP:TopTopTopTopTop: class_Ring__and__Field_Opordered__semiring(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0),c_lessequals(x1,x3,x0),c_lessequals(x2,x4,x0) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x1,x0),c_HOL_Otimes__class_Otimes(x4,x3,x0),x0) % 0.12/0.42 % 904:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(x1,x0),x1,x0),c_HOL_Oone__class_Oone(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 905:3:2:INP:TopTop: class_Ring__and__Field_Odivision__ring(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(x1,x0),x1,x0),c_HOL_Oone__class_Oone(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 906:3:2:INP:TopTop: class_Ring__and__Field_Odivision__ring(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Oinverse__class_Oinverse(x1,x0),x0),c_HOL_Oone__class_Oone(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 907:2:2:INP:TopTop: class_Ring__and__Field_Oidom(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ouminus__class_Ouminus(x1,x0),x0),c_HOL_Otimes__class_Otimes(x1,x1,x0)) % 0.12/0.42 % 908:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(x1,x2,x0),x3,x0),c_Orderings_Oord__class_Omax(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0)) % 0.12/0.42 % 909:2:3:INP:TopTopTop: class_Ring__and__Field_Oring(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ouminus__class_Ouminus(x2,x0),x0),c_HOL_Otimes__class_Otimes(x1,x2,x0)) % 0.12/0.42 % 910:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omax(x1,c_Orderings_Oord__class_Omax(x2,x3,x0),x0),c_Orderings_Oord__class_Omax(x2,c_Orderings_Oord__class_Omax(x1,x3,x0),x0)) % 0.12/0.42 % 911:2:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ominus__class_Ominus(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0),c_HOL_Oplus__class_Oplus(x1,x2,x0)) % 0.12/0.42 % 912:2:1:INP:Top: class_Ring__and__Field_Oordered__semidom(x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(x0),c_HOL_Oone__class_Oone(x0),x0),x0) % 0.12/0.42 % 913:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0),x3,x0),c_Divides_Odiv__class_Omod(x1,x3,x0)) % 0.12/0.42 % 914:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0),x2,x0),c_Divides_Odiv__class_Omod(x1,x2,x0)) % 0.12/0.42 % 915:4:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Oinverse__class_Odivide(x3,x4,x0),x0),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(x1,x4,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0),c_HOL_Otimes__class_Otimes(x2,x4,x0),x0)),=(x4,c_HOL_Ozero__class_Ozero(x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 916:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(x1,x3,x0),x2,x0)) % 0.12/0.42 % 917:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oidom(x0),c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_Ring__and__Field_Odvd__class_Odvd(x2,x3,x0),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 918:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oidom(x0),c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x3,x0),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 919:2:1:INP:Top: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(x0),x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.42 % 920:2:2:INP:TopTop: class_Ring__and__Field_Oordered__semidom(x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_Nat_Osemiring__1__class_Oof__nat(x1,x0),x0) % 0.12/0.42 % 921:2:2:INP:TopTop: class_Ring__and__Field_Oordered__semidom(x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_Nat_Osemiring__1__class_Oof__nat(x1,x0),x0) % 0.12/0.42 % 922:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(x0),x1,x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 923:2:1:INP:Top: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),x0),x0) -> % 0.12/0.42 % 924:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x3,x0),x2,x0) -> c_lessequals(x1,c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0) % 0.12/0.42 % 925:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(x1,c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) % 0.12/0.42 % 926:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) % 0.12/0.42 % 927:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_lessequals(x3,c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x3,x2,x0),x1,x0) % 0.12/0.42 % 928:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x3,x0),x1,x0),c_HOL_Oord__class_Oless(x3,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x3,x0) % 0.12/0.42 % 929:6:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x3,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),x3,x0),c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.42 % 930:2:2:INP:TopTop: c_Lambda_Obeta(x0,x1) -> c_Lambda_Obeta(c_Lambda_OdB_OAbs(x0),c_Lambda_OdB_OAbs(x1)) % 0.12/0.42 % 931:2:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omax(x1,c_Orderings_Oord__class_Omax(x1,x2,x0),x0),c_Orderings_Oord__class_Omax(x1,x2,x0)) % 0.12/0.42 % 932:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 933:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) -> c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 934:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) -> c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.42 % 935:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x2,x0),x0) -> c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.42 % 936:1:4:INP:TopTopTopTop: -> =(c_Lambda_Osubstn(c_Lambda_OdB_OApp(x0,x1),x2,x3),c_Lambda_OdB_OApp(c_Lambda_Osubstn(x0,x2,x3),c_Lambda_Osubstn(x1,x2,x3))) % 0.12/0.42 % 937:1:2:INP:TopTop: -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x1,tc_nat),x0) % 0.12/0.42 % 938:1:2:INP:TopTop: -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x0,tc_nat),x1) % 0.12/0.42 % 939:2:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(x1,x2,x0),x2,x0),x1) % 0.12/0.42 % 940:5:2:INP:TopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Oone__class_Oone(x0),x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_lessequals(c_HOL_Oone__class_Oone(x0),c_HOL_Oinverse__class_Oinverse(x1,x0),x0) % 0.12/0.42 % 941:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x1,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_lessequals(x2,x3,tc_nat) % 0.12/0.42 % 942:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(c_Power_Opower__class_Opower(x1,x2,x0),c_Power_Opower__class_Opower(x1,x3,x0),x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0) -> c_lessequals(x2,x3,tc_nat) % 0.12/0.42 % 943:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_lessequals(x1,x2,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x3,x0) -> c_lessequals(c_Power_Opower__class_Opower(x3,x1,x0),c_Power_Opower__class_Opower(x3,x2,x0),x0) % 0.12/0.42 % 944:3:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0),c_HOL_Oinverse__class_Odivide(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0)) % 0.12/0.42 % 945:2:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(x1,x2,x0),x0),c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0)) % 0.12/0.42 % 946:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(x1,x3,x0),c_HOL_Oinverse__class_Odivide(x2,x3,x0),x0)) % 0.12/0.42 % 947:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__semidom(x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x1,x0),c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.42 % 948:2:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(x1,x2,x0),x0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(x2,x1,x0),x0)) % 0.12/0.42 % 949:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(x1,x0),x0),x1) % 0.12/0.42 % 950:2:2:INP:TopTop: class_Lattices_Oboolean__algebra(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(x1,x0),x0),x1) % 0.12/0.42 % 951:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(x1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(x1,x0),x0)) % 0.12/0.42 % 952:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(x1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(x1,x0),x0)) % 0.12/0.42 % 953:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(x1,x0),x0),x1) % 0.12/0.42 % 954:2:3:INP:TopTopTop: class_OrderedGroup_Oab__group__add(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x1,x2,x0),x0),c_HOL_Ominus__class_Ominus(x2,x1,x0)) % 0.12/0.42 % 955:4:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_lessequals(x3,x4,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x3,x1,x0),c_HOL_Oplus__class_Oplus(x4,x2,x0),x0) % 0.12/0.42 % 956:4:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(x3,x4,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(x3,x1,x0),c_HOL_Oplus__class_Oplus(x4,x2,x0),x0) % 0.12/0.42 % 957:1:3:INP:TopTopTop: =(c_Lambda_OdB_OApp(x0,x1),c_Lambda_OdB_OVar(x2)) -> % 0.12/0.42 % 958:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(c_Suc(x0),c_Suc(x1),tc_nat) % 0.12/0.42 % 959:2:2:INP:TopTop: c_HOL_Oord__class_Oless(c_Suc(x0),c_Suc(x1),tc_nat) -> c_HOL_Oord__class_Oless(x0,x1,tc_nat) % 0.12/0.42 % 960:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(c_Suc(x0),c_Suc(x1),tc_nat) % 0.12/0.42 % 961:2:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(x1,x0,tc_nat),tc_nat) % 0.12/0.42 % 962:2:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),tc_nat) % 0.12/0.42 % 963:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(x1,x1,x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 964:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oplus__class_Oplus(x1,x1,x0),x0) % 0.12/0.42 % 965:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0) -> c_lessequals(x2,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.42 % 966:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0) -> c_lessequals(x2,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.42 % 967:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x2,x0),x1,x0) % 0.12/0.42 % 968:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_lessequals(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x2,x0),x1,x0) % 0.12/0.42 % 969:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0) -> c_HOL_Oord__class_Oless(x2,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.42 % 970:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ouminus__class_Ouminus(x2,x0),x0) -> c_HOL_Oord__class_Oless(x2,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.42 % 971:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x2,x0),x1,x0) % 0.12/0.42 % 972:3:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x1,x0),x2,x0) -> c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(x2,x0),x1,x0) % 0.12/0.42 % 973:2:4:INP:TopTopTopTop: c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) -> =(c_Lambda_Olift(c_Lambda_Osubst(x2,x3,x1),x0),c_Lambda_Osubst(c_Lambda_Olift(x2,x0),c_Lambda_Olift(x3,x0),c_HOL_Oplus__class_Oplus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) % 0.12/0.42 % 974:2:4:INP:TopTopTopTop: c_HOL_Oord__class_Oless(x0,c_HOL_Oplus__class_Oplus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) -> =(c_Lambda_Olift(c_Lambda_Osubst(x2,x3,x0),x1),c_Lambda_Osubst(c_Lambda_Olift(x2,c_HOL_Oplus__class_Oplus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(x3,x1),x0)) % 0.12/0.42 % 975:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oinverse__class_Odivide(x1,c_HOL_Ozero__class_Ozero(x0),x0)) % 0.12/0.42 % 976:3:1:INP:Top: class_Ring__and__Field_Odivision__ring(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 977:2:1:INP:Top: class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 978:5:3:INP:TopTopTop: class_Ring__and__Field_Odivision__ring(x0),=(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0)) -> =(x1,x2),=(x2,c_HOL_Ozero__class_Ozero(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 979:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0),=(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 980:2:1:INP:Top: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 981:2:1:INP:Top: class_OrderedGroup_Oordered__ab__group__add(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 982:4:2:INP:TopTop: class_Ring__and__Field_Odivision__ring(x0),class_Ring__and__Field_Odivision__by__zero(x0),=(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 983:3:2:INP:TopTop: class_Ring__and__Field_Odivision__ring(x0),=(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 984:6:3:INP:TopTopTop: class_Ring__and__Field_Ozero__neq__one(x0),class_Ring__and__Field_Ono__zero__divisors(x0),class_Ring__and__Field_Omult__zero(x0),class_Power_Opower(x0),=(c_Power_Opower__class_Opower(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 985:3:3:INP:TopTopTop: class_Ring__and__Field_Oring__1__no__zero__divisors(x0),=(c_Power_Opower__class_Opower(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 986:2:1:INP:Top: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(x0),x0)) % 0.12/0.42 % 987:2:1:INP:Top: class_Ring__and__Field_Osgn__if(x0) -> =(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 988:2:1:INP:Top: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 989:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 990:2:2:INP:TopTop: class_Ring__and__Field_Omult__zero(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 991:2:2:INP:TopTop: class_Ring__and__Field_Omult__zero(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 992:2:2:INP:TopTop: class_Ring__and__Field_Oring__no__zero__divisors(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 993:2:2:INP:TopTop: class_Ring__and__Field_Oring__no__zero__divisors(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 994:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 995:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 996:3:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0),=(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 997:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 998:2:1:INP:Top: class_Ring__and__Field_Ozero__neq__one(x0),=(c_HOL_Oone__class_Oone(x0),c_HOL_Ozero__class_Ozero(x0)) -> % 0.12/0.42 % 999:4:3:INP:TopTopTop: class_Ring__and__Field_Ono__zero__divisors(x0),=(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1000:4:3:INP:TopTopTop: class_Ring__and__Field_Ono__zero__divisors(x0),=(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x2,c_HOL_Ozero__class_Ozero(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1001:4:3:INP:TopTopTop: class_Ring__and__Field_Oring__no__zero__divisors(x0),=(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x2,c_HOL_Ozero__class_Ozero(x0)),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1002:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x0,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat) % 0.12/0.42 % 1003:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_HOL_Otimes__class_Otimes(x2,x0,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat),tc_nat) % 0.12/0.42 % 1004:2:3:INP:TopTopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),tc_nat) % 0.12/0.42 % 1005:2:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),tc_nat) -> c_HOL_Oord__class_Oless(x1,x0,tc_nat) % 0.12/0.42 % 1006:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),tc_nat) % 0.12/0.42 % 1007:2:2:INP:TopTop: c_HOL_Oord__class_Oless(c_Suc(x0),x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,x1,tc_nat) % 0.12/0.42 % 1008:2:2:INP:TopTop: c_HOL_Oord__class_Oless(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,c_Suc(x1),tc_nat) % 0.12/0.42 % 1009:4:3:INP:TopTopTop: class_Ring__and__Field_Odivision__ring(x0),class_Ring__and__Field_Odivision__by__zero(x0),=(c_HOL_Oinverse__class_Oinverse(x1,x0),c_HOL_Oinverse__class_Oinverse(x2,x0)) -> =(x1,x2) % 0.12/0.42 % 1010:2:1:INP:Top: class_Ring__and__Field_Oordered__ring__strict(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1011:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) -> c_HOL_Oord__class_Oless(x2,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x1,x3,x0) % 0.12/0.42 % 1012:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0) -> c_HOL_Oord__class_Oless(x3,x1,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x2,x0) % 0.12/0.42 % 1013:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Oord__class_Oless(x2,x3,x0) % 0.12/0.42 % 1014:4:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0) -> c_HOL_Oord__class_Oless(x3,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 1015:2:3:INP:TopTopTop: =(c_HOL_Otimes__class_Otimes(c_Suc(x0),x1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(x0),x2,tc_nat)) -> =(x1,x2) % 0.12/0.42 % 1016:2:1:INP:Top: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) -> =(c_Suc(c_HOL_Ominus__class_Ominus(x0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)),x0) % 0.12/0.42 % 1017:2:3:INP:TopTopTop: class_Ring__and__Field_Osemiring__1(x0) -> =(c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),x0),c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(x1,x0),c_Nat_Osemiring__1__class_Oof__nat(x2,x0),x0)) % 0.12/0.42 % 1018:3:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),x0,tc_nat) % 0.12/0.42 % 1019:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> c_lessequals(c_Orderings_Oord__class_Omax(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(x1,x2,x0),c_Orderings_Oord__class_Omax(x1,x3,x0),x0),x0) % 0.12/0.42 % 1020:4:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),=(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ominus__class_Ominus(x3,x4,x0)),c_lessequals(x2,x1,x0) -> c_lessequals(x4,x3,x0) % 0.12/0.42 % 1021:4:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),=(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ominus__class_Ominus(x3,x4,x0)),c_lessequals(x4,x3,x0) -> c_lessequals(x2,x1,x0) % 0.12/0.42 % 1022:4:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),=(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ominus__class_Ominus(x3,x4,x0)),c_HOL_Oord__class_Oless(x1,x2,x0) -> c_HOL_Oord__class_Oless(x3,x4,x0) % 0.12/0.42 % 1023:4:5:INP:TopTopTopTopTop: class_OrderedGroup_Opordered__ab__group__add(x0),=(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ominus__class_Ominus(x3,x4,x0)),c_HOL_Oord__class_Oless(x3,x4,x0) -> c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.42 % 1024:2:4:INP:TopTopTopTop: class_OrderedGroup_Ocomm__monoid__mult(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(x1,x3,x0),c_Power_Opower__class_Opower(x2,x3,x0),x0)) % 0.12/0.42 % 1025:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(x1,x3,x0),c_Power_Opower__class_Opower(x2,x3,x0),x0)) % 0.12/0.42 % 1026:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(x1,x2,x0),x3,x0),x2,x0),c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,x3,x0),x2,x0)) % 0.12/0.42 % 1027:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,c_Divides_Odiv__class_Omod(x2,x3,x0),x0),x3,x0),c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0)) % 0.12/0.42 % 1028:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.42 % 1029:3:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ouminus__class_Ouminus(x1,x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 1030:2:2:INP:TopTop: -> =(c_HOL_Oplus__class_Oplus(x0,c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),tc_nat),x1),c_HOL_Oord__class_Oless(x1,x0,tc_nat) % 0.12/0.42 % 1031:2:2:INP:TopTop: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) -> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(x0,c_Suc(x1),tc_nat),x0,tc_nat) % 0.12/0.42 % 1032:5:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Odvd(x0),class_Ring__and__Field_Ocomm__ring(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(x2,c_HOL_Otimes__class_Otimes(x3,x4,x0),x0),x5,x0),x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x4,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Oplus__class_Oplus(x2,x5,x0),x0) % 0.12/0.42 % 1033:5:6:INP:TopTopTopTopTopTop: class_Ring__and__Field_Odvd(x0),class_Ring__and__Field_Ocomm__ring(x0),c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0),c_Ring__and__Field_Odvd__class_Odvd(x1,x4,x0) -> c_Ring__and__Field_Odvd__class_Odvd(x1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(x2,c_HOL_Otimes__class_Otimes(x5,x4,x0),x0),x3,x0),x0) % 0.12/0.42 % 1034:5:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ofield(x0),=(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x4,x0)) -> =(x2,c_HOL_Ozero__class_Ozero(x0)),=(x4,c_HOL_Ozero__class_Ozero(x0)),=(c_HOL_Oinverse__class_Odivide(x1,x4,x0),c_HOL_Oinverse__class_Odivide(x3,x2,x0)) % 0.12/0.42 % 1035:5:5:INP:TopTopTopTopTop: class_Ring__and__Field_Ofield(x0),=(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Oinverse__class_Odivide(x3,x4,x0)) -> =(x4,c_HOL_Ozero__class_Ozero(x0)),=(x2,c_HOL_Ozero__class_Ozero(x0)),=(c_HOL_Otimes__class_Otimes(x1,x4,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0)) % 0.12/0.42 % 1036:3:2:INP:TopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) -> =(x1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),=(x0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.42 % 1037:3:2:INP:TopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) -> =(x0,c_HOL_Ozero__class_Ozero(tc_nat)),=(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1038:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(x1,x2,x0),x3,x0),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(x1,x3,x0),c_Orderings_Oord__class_Omax(x2,x3,x0),x0)) % 0.12/0.42 % 1039:2:4:INP:TopTopTopTop: class_Orderings_Olinorder(x0) -> =(c_Orderings_Oord__class_Omax(x1,c_Orderings_Oord__class_Omin(x2,x3,x0),x0),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(x1,x2,x0),c_Orderings_Oord__class_Omax(x1,x3,x0),x0)) % 0.12/0.42 % 1040:2:4:INP:TopTopTopTop: class_OrderedGroup_Omonoid__mult(x0) -> =(c_Power_Opower__class_Opower(x1,c_HOL_Otimes__class_Otimes(x2,x3,tc_nat),x0),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(x1,x2,x0),x3,x0)) % 0.12/0.42 % 1041:4:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),=(x2,x1) % 0.12/0.42 % 1042:4:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),=(x2,x1) % 0.12/0.42 % 1043:3:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,x1,tc_nat),=(x0,x1) % 0.12/0.42 % 1044:3:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> =(x0,x1),c_HOL_Oord__class_Oless(x0,x1,tc_nat) % 0.12/0.42 % 1045:3:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> c_HOL_Oord__class_Oless(x0,x1,tc_nat),=(x0,x1) % 0.12/0.42 % 1046:4:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0) -> =(x1,x2),c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.42 % 1047:4:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),=(x1,x2) % 0.12/0.42 % 1048:4:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),=(x1,x2) % 0.12/0.42 % 1049:4:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_lessequals(x1,x2,x0) -> c_HOL_Oord__class_Oless(x1,x2,x0),=(x1,x2) % 0.12/0.42 % 1050:4:3:INP:TopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> =(x1,x2),c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.42 % 1051:4:3:INP:TopTopTop: class_Orderings_Olinorder(x0),c_lessequals(x1,x2,x0) -> =(x1,x2),c_HOL_Oord__class_Oless(x1,x2,x0) % 0.12/0.42 % 1052:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,x3,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x3,x1,x0),c_HOL_Oinverse__class_Odivide(x2,x1,x0),x0) % 0.12/0.42 % 1053:5:4:INP:TopTopTopTop: class_Ring__and__Field_Oordered__field(x0),class_Ring__and__Field_Odivision__by__zero(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(x2,x3,x0) -> c_lessequals(c_HOL_Oinverse__class_Odivide(x2,x1,x0),c_HOL_Oinverse__class_Odivide(x3,x1,x0),x0) % 0.12/0.42 % 1054:3:3:INP:TopTopTop: class_Ring__and__Field_Odivision__ring(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(x1,x2,x0),x0),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(x1,x0),x2,x0)) % 0.12/0.42 % 1055:3:2:INP:TopTop: class_Ring__and__Field_Odivision__ring(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(x1,x0),x0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(x1,x0),x0)) % 0.12/0.42 % 1056:2:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0) -> =(c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(x1,x2,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Osgn__class_Osgn(x2,x0),x0)) % 0.12/0.42 % 1057:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__cancel__semiring(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.42 % 1058:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.42 % 1059:4:3:INP:TopTopTop: class_Ring__and__Field_Oordered__ring__strict(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.42 % 1060:2:2:INP:TopTop: class_Ring__and__Field_Oordered__ring__strict(x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x1,x1,x0),x0) % 0.12/0.42 % 1061:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.42 % 1062:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_lessequals(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_lessequals(x2,c_HOL_Ozero__class_Ozero(x0),x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.42 % 1063:4:3:INP:TopTopTop: class_Ring__and__Field_Opordered__ring(x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x2,x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Otimes__class_Otimes(x2,x1,x0),x0) % 0.12/0.42 % 1064:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x3,x2,x0),x0),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(x1,x3,x0),x2,x0)) % 0.12/0.42 % 1065:2:4:INP:TopTopTopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0),c_HOL_Otimes__class_Otimes(x1,c_Divides_Odiv__class_Omod(x2,x3,x0),x0)) % 0.12/0.42 % 1066:1:2:INP:TopTop: -> =(c_Lambda_Olift(c_Lambda_OdB_OAbs(x0),x1),c_Lambda_OdB_OAbs(c_Lambda_Olift(x0,c_HOL_Oplus__class_Oplus(x1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) % 0.12/0.42 % 1067:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) % 0.12/0.42 % 1068:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(x1,c_HOL_Ozero__class_Ozero(x0),x0) -> c_HOL_Oord__class_Oless(x1,c_HOL_Ouminus__class_Ouminus(x1,x0),x0) % 0.12/0.42 % 1069:4:3:INP:TopTopTop: class_Ring__and__Field_Ofield(x0),=(c_HOL_Oinverse__class_Odivide(x1,x2,x0),c_HOL_Oone__class_Oone(x0)) -> =(x2,c_HOL_Ozero__class_Ozero(x0)),=(x1,x2) % 0.12/0.42 % 1070:2:2:INP:TopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oabs__class_Oabs(x1,x0),x0) % 0.12/0.42 % 1071:2:2:INP:TopTop: class_Int_Onumber__ring(x0) -> =(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(x0),x0),x1,x0)) % 0.12/0.42 % 1072:2:2:INP:TopTop: c_lessequals(c_Suc(x0),c_Suc(x1),tc_nat) -> c_lessequals(x0,x1,tc_nat) % 0.12/0.42 % 1073:2:2:INP:TopTop: c_lessequals(x0,x1,tc_nat) -> c_lessequals(c_Suc(x0),c_Suc(x1),tc_nat) % 0.12/0.42 % 1074:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(x0),x1,x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1075:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),=(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Oone__class_Oone(x0)) -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) % 0.12/0.42 % 1076:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.42 % 1077:2:3:INP:TopTopTop: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0),x0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(x1,x2,x0),x0),x0) % 0.12/0.42 % 1078:2:2:INP:TopTop: =(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(x0,x1,tc_nat)) -> =(x0,c_HOL_Oone__class_Oone(tc_nat)) % 0.12/0.42 % 1079:2:2:INP:TopTop: =(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(x0,x1,tc_nat)) -> =(x1,c_HOL_Oone__class_Oone(tc_nat)) % 0.12/0.42 % 1080:2:4:INP:TopTopTopTop: class_OrderedGroup_Oab__semigroup__mult(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Otimes__class_Otimes(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0)) % 0.12/0.42 % 1081:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x3,x0),x2,x0)) % 0.12/0.42 % 1082:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0),c_HOL_Otimes__class_Otimes(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0)) % 0.12/0.42 % 1083:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0)) % 0.12/0.42 % 1084:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0),c_HOL_Otimes__class_Otimes(x2,c_HOL_Otimes__class_Otimes(x1,x3,x0),x0)) % 0.12/0.42 % 1085:1:3:INP:TopTopTop: -> =(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),x2,tc_nat),c_HOL_Otimes__class_Otimes(x0,c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),tc_nat)) % 0.12/0.42 % 1086:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Otimes__class_Otimes(x2,x3,x0),x0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(x1,x2,x0),x3,x0)) % 0.12/0.42 % 1087:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x2,x3,x0),x0)) % 0.12/0.42 % 1088:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring(x0) -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(x1,x2,x0),x3,x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x3,x0),c_HOL_Otimes__class_Otimes(x2,x3,x0),x0)) % 0.12/0.42 % 1089:1:3:INP:TopTopTop: -> =(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),c_HOL_Otimes__class_Otimes(x1,x2,tc_nat),tc_nat)) % 0.12/0.42 % 1090:1:3:INP:TopTopTop: -> =(c_HOL_Otimes__class_Otimes(x0,c_HOL_Oplus__class_Oplus(x1,x2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat),tc_nat)) % 0.12/0.42 % 1091:2:4:INP:TopTopTopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Otimes__class_Otimes(x1,c_HOL_Oplus__class_Oplus(x2,x3,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(x1,x2,x0),c_HOL_Otimes__class_Otimes(x1,x3,x0),x0)) % 0.12/0.42 % 1092:3:3:INP:TopTopTop: class_Ring__and__Field_Oordered__idom(x0),=(c_HOL_Oabs__class_Oabs(x1,x0),c_HOL_Oabs__class_Oabs(x2,x0)) -> c_Ring__and__Field_Odvd__class_Odvd(x1,x2,x0) % 0.12/0.42 % 1093:2:3:INP:TopTopTop: class_OrderedGroup_Oab__group__add(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(x1,x2,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(x1,x0),c_HOL_Ouminus__class_Ouminus(x2,x0),x0)) % 0.12/0.42 % 1094:2:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(x1,x2,x0),x0),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(x2,x0),c_HOL_Ouminus__class_Ouminus(x1,x0),x0)) % 0.12/0.42 % 1095:6:5:INP:TopTopTopTopTop: class_Ring__and__Field_Oordered__field(x0),c_lessequals(x1,x2,x0),c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Oord__class_Oless(x3,x4,x0),c_lessequals(c_HOL_Ozero__class_Ozero(x0),x3,x0) -> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x3,x2,x0),c_HOL_Oinverse__class_Odivide(x4,x1,x0),x0) % 0.12/0.42 % 1096:3:3:INP:TopTopTop: class_Orderings_Oorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0) -> % 0.12/0.42 % 1097:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0) -> % 0.12/0.42 % 1098:2:2:INP:TopTop: -> c_lessequals(x0,x1,tc_nat),c_lessequals(x1,x0,tc_nat) % 0.12/0.42 % 1099:3:3:INP:TopTopTop: class_Orderings_Olinorder(x0) -> c_lessequals(x1,x2,x0),c_lessequals(x2,x1,x0) % 0.12/0.42 % 1100:3:3:INP:TopTopTop: class_Orderings_Opreorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0) -> % 0.12/0.42 % 1101:3:3:INP:TopTopTop: class_Orderings_Opreorder(x0),c_HOL_Oord__class_Oless(x1,x2,x0),c_HOL_Oord__class_Oless(x2,x1,x0) -> % 0.12/0.42 % 1102:3:2:INP:TopTop: class_OrderedGroup_Olordered__ab__group__add(x0),=(c_HOL_Oplus__class_Oplus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1103:3:2:INP:TopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0) -> =(c_HOL_Ominus__class_Ominus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1104:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ominus__class_Ominus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1105:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ominus__class_Ominus(x1,c_HOL_Ozero__class_Ozero(x0),x0),x1) % 0.12/0.42 % 1106:2:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0) -> =(c_HOL_Ominus__class_Ominus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1107:2:2:INP:TopTop: class_OrderedGroup_Oab__group__add(x0) -> =(c_HOL_Ominus__class_Ominus(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1108:4:3:INP:TopTopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0),=(x1,c_HOL_Oplus__class_Oplus(x1,x2,x0)) -> =(x2,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1109:2:2:INP:TopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(x1,x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1110:2:2:INP:TopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(x1,c_HOL_Ozero__class_Ozero(x0),x0),x1) % 0.12/0.42 % 1111:2:1:INP:Top: class_OrderedGroup_Olordered__ab__group__add(x0) -> =(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1112:2:2:INP:TopTop: class_Divides_Osemiring__div(x0) -> =(c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1113:2:1:INP:Top: class_OrderedGroup_Olordered__ab__group__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1114:2:1:INP:Top: class_OrderedGroup_Opordered__ab__group__add__abs(x0) -> =(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1115:3:2:INP:TopTop: class_OrderedGroup_Ogroup__add(x0),=(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ouminus__class_Ouminus(x1,x0)) -> =(c_HOL_Ozero__class_Ozero(x0),x1) % 0.12/0.42 % 1116:2:1:INP:Top: class_Ring__and__Field_Ozero__neq__one(x0),=(c_HOL_Ozero__class_Ozero(x0),c_HOL_Oone__class_Oone(x0)) -> % 0.12/0.42 % 1117:3:2:INP:TopTop: class_Ring__and__Field_Odivision__ring(x0) -> =(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(x1,x0),x0),x1),=(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1118:3:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0),c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(x0),x1,x0) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1119:4:3:INP:TopTopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0),=(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,x2) % 0.12/0.42 % 1120:3:3:INP:TopTopTop: class_OrderedGroup_Ogroup__add(x0),=(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,x2) % 0.12/0.42 % 1121:3:3:INP:TopTopTop: class_OrderedGroup_Oab__group__add(x0),=(c_HOL_Ominus__class_Ominus(x1,x2,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,x2) % 0.12/0.42 % 1122:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1123:3:2:INP:TopTop: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(x1,c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1124:2:2:INP:TopTop: class_Ring__and__Field_Ofield(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1125:3:1:INP:Top: class_Ring__and__Field_Ofield(x0),class_Ring__and__Field_Odivision__by__zero(x0) -> =(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(x0),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1126:3:2:INP:TopTop: class_Ring__and__Field_Oordered__idom(x0),=(c_HOL_Osgn__class_Osgn(x1,x0),c_HOL_Ozero__class_Ozero(x0)) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1127:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(x0),x1,x0),x1) % 0.12/0.42 % 1128:2:2:INP:TopTop: class_OrderedGroup_Ocomm__monoid__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(x0),x1,x0),x1) % 0.12/0.42 % 1129:3:2:INP:TopTop: class_Ring__and__Field_Oidom(x0),class_Int_Onumber__ring(x0) -> =(x1,c_HOL_Oplus__class_Oplus(x1,c_HOL_Ozero__class_Ozero(x0),x0)) % 0.12/0.42 % 1130:2:2:INP:TopTop: class_OrderedGroup_Ocomm__monoid__add(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Ozero__class_Ozero(x0),x0),x1) % 0.12/0.42 % 1131:2:2:INP:TopTop: class_OrderedGroup_Omonoid__add(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(x0),x1,x0),x1) % 0.12/0.42 % 1132:2:2:INP:TopTop: class_OrderedGroup_Omonoid__add(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Ozero__class_Ozero(x0),x0),x1) % 0.12/0.42 % 1133:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(x1,c_HOL_Ozero__class_Ozero(x0),x0),x1) % 0.12/0.42 % 1134:2:2:INP:TopTop: class_Ring__and__Field_Ocomm__semiring__1(x0) -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(x0),x1,x0),x1) % 0.12/0.42 % 1135:3:2:INP:TopTop: class_OrderedGroup_Oordered__ab__group__add(x0),=(c_HOL_Ouminus__class_Ouminus(x1,x0),x1) -> =(x1,c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1136:3:1:INP:Top: class_Ring__and__Field_Osemiring__0(x0),class_Power_Opower(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(x0),c_HOL_Ozero__class_Ozero(tc_nat),x0),c_HOL_Oone__class_Oone(x0)) % 0.12/0.42 % 1137:1:0:INP:: -> =(c_Nat_Osize__class_Osize(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1138:1:0:INP:: -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) % 0.12/0.42 % 1139:1:2:INP:TopTop: -> =(c_HOL_Otimes__class_Otimes(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(x1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)) % 0.12/0.42 % 1140:1:2:INP:TopTop: -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),x1,tc_nat)) % 0.12/0.42 % 1141:1:0:INP:: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) -> % 0.12/0.42 % 1142:1:2:INP:TopTop: -> =(c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),x0,x1),x0) % 0.12/0.42 % 1143:2:1:INP:Top: -> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),=(x0,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1144:1:1:INP:Top: =(c_Suc(x0),c_HOL_Ozero__class_Ozero(tc_nat)) -> % 0.12/0.42 % 1145:1:1:INP:Top: =(c_Suc(x0),c_HOL_Ozero__class_Ozero(tc_nat)) -> % 0.12/0.42 % 1146:3:2:INP:TopTop: =(c_HOL_Ominus__class_Ominus(x0,x1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),=(c_HOL_Ominus__class_Ominus(x1,x0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) -> =(x1,x0) % 0.12/0.42 % 1147:2:1:INP:Top: c_lessequals(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) -> =(x0,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1148:1:1:INP:Top: -> =(c_HOL_Otimes__class_Otimes(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1149:1:1:INP:Top: -> =(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1150:3:2:INP:TopTop: =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) -> =(x1,c_HOL_Ozero__class_Ozero(tc_nat)),=(x0,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1151:2:2:INP:TopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) -> =(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1152:2:2:INP:TopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) -> =(x0,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1153:1:1:INP:Top: -> =(c_Orderings_Oord__class_Omin(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1154:1:1:INP:Top: -> =(c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1155:3:3:INP:TopTopTop: =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x2,x1,tc_nat)) -> =(x1,c_HOL_Ozero__class_Ozero(tc_nat)),=(x0,x2) % 0.12/0.42 % 1156:3:3:INP:TopTopTop: =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat)) -> =(x0,c_HOL_Ozero__class_Ozero(tc_nat)),=(x1,x2) % 0.12/0.42 % 1157:3:3:INP:TopTopTop: =(c_HOL_Otimes__class_Otimes(x0,x1,tc_nat),c_HOL_Otimes__class_Otimes(x0,x2,tc_nat)) -> =(x1,x2),=(x0,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1158:1:1:INP:Top: -> =(c_HOL_Ominus__class_Ominus(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),x0) % 0.12/0.42 % 1159:1:1:INP:Top: -> =(c_HOL_Ominus__class_Ominus(x0,x0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1160:2:2:INP:TopTop: =(x0,c_HOL_Oplus__class_Oplus(x0,x1,tc_nat)) -> =(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1161:2:2:INP:TopTop: =(c_HOL_Oplus__class_Oplus(x0,x1,tc_nat),x0) -> =(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1162:1:1:INP:Top: =(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(x0)) -> % 0.12/0.42 % 1163:1:1:INP:Top: =(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(x0)) -> % 0.12/0.42 % 1164:1:1:INP:Top: -> =(c_Nitpick_Onat__gcd(x0,c_HOL_Ozero__class_Ozero(tc_nat)),x0) % 0.12/0.42 % 1165:1:0:INP:: -> =(c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1166:1:1:INP:Top: -> =(c_String_Ochar_Ochar__size(x0),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1167:1:0:INP:: -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1168:1:1:INP:Top: c_HOL_Oord__class_Oless(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) -> % 0.12/0.42 % 1169:1:1:INP:Top: c_HOL_Oord__class_Oless(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) -> % 0.12/0.42 % 1170:1:0:INP:: -> =(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1171:1:2:INP:TopTop: -> =(c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),x0,x1),x0) % 0.12/0.42 % 1172:1:1:INP:Top: -> =(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1173:1:1:INP:Top: -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat) % 0.12/0.42 % 1174:1:1:INP:Top: -> =(c_Nat_Osize__class_Osize(x0,tc_String_Ochar),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1175:1:3:INP:TopTopTop: -> =(c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),x0,x1),c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),x2,x1)) % 0.12/0.42 % 1176:1:1:INP:Top: -> =(c_Orderings_Oord__class_Omax(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),x0) % 0.12/0.42 % 1177:1:1:INP:Top: -> =(c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),x0) % 0.12/0.42 % 1178:3:5:INP:TopTopTopTopTop: =(c_List_Oreplicate(x0,x1,x2),c_List_Oreplicate(x3,x4,x2)) -> =(x1,x4),=(x0,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1179:1:1:INP:Top: -> =(x0,c_HOL_Oplus__class_Oplus(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)) % 0.12/0.42 % 1180:1:1:INP:Top: -> =(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),x0,tc_nat),x0) % 0.12/0.42 % 1181:1:1:INP:Top: -> =(c_HOL_Oplus__class_Oplus(x0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),x0) % 0.12/0.42 % 1182:1:3:INP:TopTopTop: -> =(c_Lambda_Osubstn(x0,x1,x2),c_Lambda_Osubst(x0,c_Lambda_Oliftn(x2,x1,c_HOL_Ozero__class_Ozero(tc_nat)),x2)) % 0.12/0.42 % 1183:1:3:INP:TopTopTop: -> =(c_Lambda_Osubst(c_Lambda_OdB_OAbs(x0),x1,x2),c_Lambda_OdB_OAbs(c_Lambda_Osubst(x0,c_Lambda_Olift(x1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(x2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) % 0.12/0.42 % 1184:1:4:INP:TopTopTopTop: -> =(c_Lambda_Osubst(c_Lambda_OdB_OApp(x0,x1),x2,x3),c_Lambda_OdB_OApp(c_Lambda_Osubst(x0,x2,x3),c_Lambda_Osubst(x1,x2,x3))) % 0.12/0.42 % 1185:1:2:INP:TopTop: -> =(c_Lambda_Osubst(c_Lambda_OdB_OVar(x0),x1,x0),x1) % 0.12/0.42 % 1186:2:4:INP:TopTopTopTop: c_Lambda_Obeta(x0,x1) -> c_Lambda_Obeta(c_Lambda_Osubst(x0,x2,x3),c_Lambda_Osubst(x1,x2,x3)) % 0.12/0.42 % 1187:1:3:INP:TopTopTop: -> =(c_Lambda_Olift(c_Lambda_OdB_OApp(x0,x1),x2),c_Lambda_OdB_OApp(c_Lambda_Olift(x0,x2),c_Lambda_Olift(x1,x2))) % 0.12/0.42 % 1188:2:3:INP:TopTopTop: c_Lambda_Obeta(x0,x1) -> c_Lambda_Obeta(c_Lambda_Olift(x0,x2),c_Lambda_Olift(x1,x2)) % 0.12/0.42 % 1189:1:1:INP:Top: -> c_InductTermi_OIT(c_Lambda_OdB_OVar(x0)) % 0.12/0.42 % 1190:1:0:INP:: -> c_InductTermi_OIT(v_ua______) % 0.12/0.42 % 1191:2:1:INP:Top: c_InductTermi_OIT(x0) -> c_InductTermi_OIT(c_Lambda_OdB_OAbs(x0)) % 0.12/0.42 % 1192:6:2:INP:TopTop: class_Ring__and__Field_Ozero__neq__one(x0),class_Ring__and__Field_Ono__zero__divisors(x0),class_Ring__and__Field_Omult__zero(x0),class_Power_Opower(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)),=(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1193:4:2:INP:TopTop: class_Ring__and__Field_Osemiring__0(x0),class_Power_Opower(x0) -> =(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(x0),x1,x0),c_HOL_Ozero__class_Ozero(x0)),=(x1,c_HOL_Ozero__class_Ozero(tc_nat)) % 0.12/0.42 % 1194:5:2:INP:TopTop: class_Ring__and__Field_Ozero__neq__one(x0),class_Ring__and__Field_Ono__zero__divisors(x0),class_Ring__and__Field_Omult__zero(x0),class_Power_Opower(x0),=(c_Power_Opower__class_Opower(x1,c_HOL_Ozero__class_Ozero(tc_nat),x0),c_HOL_Ozero__class_Ozero(x0)) -> % 0.12/0.42 % 1195:2:1:INP:Top: class_Ring__and__Field_Osemiring__1(x0) -> =(c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),x0),c_HOL_Ozero__class_Ozero(x0)) % 0.12/0.42 % 1196:1:2:INP:TopTop: -> =(c_Lambda_Osubstn(x0,x1,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(x0,x1,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.12/0.42 % 1197:2:3:INP:TopTopTop: c_InductTermi_OIT(x0) -> c_InductTermi_OIT(c_Lambda_Osubst(x0,c_Lambda_OdB_OVar(x1),x2)) % 0.12/0.42 % 1198:1:0:INP:: -> =(v_i____,v_n____) % 0.12/0.42 % 1199:2:2:INP:TopTop: c_InductTermi_OIT(x0) -> c_InductTermi_OIT(c_Lambda_Olift(x0,x1)) % 0.12/0.42 % 1200:1:0:INP:: -> c_InductTermi_OIT(v_u____) % 0.12/0.42 % 1201:1:3:INP:TopTopTop: -> =(c_Lambda_Osubst(c_Lambda_Olift(x0,x1),x2,x1),x0) % 0.12/0.42 % 1202:1:0:INP:: -> c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) % 0.12/0.42 % 1203:1:0:INP:: c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))) -> % 0.12/0.42 % 1204:1:0:INP:: -> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) % 0.12/0.42 % 1205:1:0:INP:: -> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) % 0.12/0.42 % 1206:1:0:INP:: -> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) % 0.12/0.42 % 1207:1:0:INP:: -> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) % 0.12/0.42 % 1208:1:0:INP:: -> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) % 0.12/0.42 % 1209:1:0:INP:: -> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) % 0.12/0.42 % 1210:1:0:INP:: -> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) % 0.12/0.42 % 1211:1:0:INP:: -> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) % 0.12/0.42 % 1212:1:0:INP:: -> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) % 0.12/0.42 % 1213:1:0:INP:: -> class_Ring__and__Field_Opordered__semiring(tc_nat) % 0.12/0.42 % 1214:1:0:INP:: -> class_Ring__and__Field_Oordered__semiring(tc_nat) % 0.12/0.42 % 1215:1:0:INP:: -> class_Ring__and__Field_Ono__zero__divisors(tc_nat) % 0.12/0.42 % 1216:1:0:INP:: -> class_Ring__and__Field_Oordered__semidom(tc_nat) % 0.12/0.42 % 1217:1:0:INP:: -> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) % 0.12/0.42 % 1218:1:0:INP:: -> class_OrderedGroup_Oab__semigroup__mult(tc_nat) % 0.12/0.42 % 1219:1:0:INP:: -> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) % 0.12/0.42 % 1220:1:0:INP:: -> class_OrderedGroup_Oab__semigroup__add(tc_nat) % 0.12/0.42 % 1221:1:0:INP:: -> class_Ring__and__Field_Ocomm__semiring(tc_nat) % 0.12/0.42 % 1222:1:0:INP:: -> class_OrderedGroup_Ocomm__monoid__add(tc_nat) % 0.12/0.42 % 1223:1:0:INP:: -> class_Ring__and__Field_Ozero__neq__one(tc_nat) % 0.12/0.42 % 1224:1:0:INP:: -> class_Ring__and__Field_Osemiring__1(tc_nat) % 0.12/0.42 % 1225:1:0:INP:: -> class_Ring__and__Field_Osemiring__0(tc_nat) % 0.12/0.42 % 1226:1:0:INP:: -> class_Ring__and__Field_Omult__mono1(tc_nat) % 0.12/0.42 % 1227:1:0:INP:: -> class_Ring__and__Field_Omult__zero(tc_nat) % 0.12/0.42 % 1228:1:0:INP:: -> class_Ring__and__Field_Omult__mono(tc_nat) % 0.12/0.42 % 1229:1:0:INP:: -> class_OrderedGroup_Omonoid__mult(tc_nat) % 0.12/0.42 % 1230:1:0:INP:: -> class_Ring__and__Field_Osemiring(tc_nat) % 0.12/0.42 % 1231:1:0:INP:: -> class_OrderedGroup_Omonoid__add(tc_nat) % 0.12/0.42 % 1232:1:0:INP:: -> class_Divides_Osemiring__div(tc_nat) % 0.12/0.42 % 1233:1:0:INP:: -> class_Nat_Osemiring__char__0(tc_nat) % 0.12/0.42 % 1234:1:0:INP:: -> class_Ring__and__Field_Odvd(tc_nat) % 0.12/0.42 % 1235:1:0:INP:: -> class_Orderings_Opreorder(tc_nat) % 0.12/0.42 % 1236:1:0:INP:: -> class_Orderings_Olinorder(tc_nat) % 0.12/0.42 % 1237:1:0:INP:: -> class_Orderings_Oorder(tc_nat) % 0.12/0.42 % 1238:1:0:INP:: -> class_Orderings_Obot(tc_nat) % 0.12/0.42 % 1239:1:0:INP:: -> class_Power_Opower(tc_nat) % 0.12/0.42 % 0.12/0.42 % Predicates: class_Ring__and__Field_Oordered__field c_lessequals c_HOL_Oord__class_Oless class_Ring__and__Field_Oidom c_Ring__and__Field_Odvd__class_Odvd class_Divides_Osemiring__div = class_Ring__and__Field_Ofield class_Int_Onumber__ring class_Ring__and__Field_Oordered__semiring__strict class_OrderedGroup_Opordered__ab__group__add__abs class_Ring__and__Field_Oordered__semidom class_Ring__and__Field_Osemiring__0 class_Power_Opower class_Ring__and__Field_Olordered__ring class_OrderedGroup_Opordered__ab__group__add class_Ring__and__Field_Oring class_Orderings_Olinorder class_Orderings_Obot class_OrderedGroup_Opordered__ab__semigroup__add__imp__le class_OrderedGroup_Ocomm__monoid__add class_Ring__and__Field_Ocomm__semiring__1 class_OrderedGroup_Olordered__ab__group__add class_Ring__and__Field_Odivision__by__zero class_Ring__and__Field_Opordered__ring class_Ring__and__Field_Oordered__ring__strict class_Ring__and__Field_Oordered__idom class_Ring__and__Field_Oring__1 class_Nat_Osemiring__char__0 class_Ring__and__Field_Oordered__semiring class_OrderedGroup_Oordered__ab__group__add class_OrderedGroup_Ocomm__monoid__mult class_OrderedGroup_Omonoid__mult class_Ring__and__Field_Odvd class_OrderedGroup_Ogroup__add class_Ring__and__Field_Odivision__ring class_OrderedGroup_Opordered__ab__semigroup__add class_OrderedGroup_Opordered__comm__monoid__add class_Orderings_Opreorder class_Orderings_Oorder class_Ring__and__Field_Osgn__if class_OrderedGroup_Olordered__ab__group__add__abs class_Ring__and__Field_Oabs__if class_Divides_Oring__div class_Ring__and__Field_Ocomm__ring__1 class_Ring__and__Field_Osemiring__1 class_OrderedGroup_Oab__group__add class_OrderedGroup_Oab__semigroup__add c_Lambda_Obeta class_Lattices_Oboolean__algebra class_OrderedGroup_Opordered__cancel__ab__semigroup__add class_Ring__and__Field_Osemiring class_Ring__and__Field_Opordered__cancel__semiring class_OrderedGroup_Ocancel__ab__semigroup__add class_OrderedGroup_Ocancel__semigroup__add class_Ring__and__Field_Opordered__ring__abs class_OrderedGroup_Oab__semigroup__idem__mult class_Ring__and__Field_Oordered__comm__semiring__strict c_InductTermi_OIT class_Ring__and__Field_Omult__mono class_Ring__and__Field_Omult__mono1 class_Ring__and__Field_Opordered__semiring class_Ring__and__Field_Ozero__neq__one class_Ring__and__Field_Ono__zero__divisors class_Ring__and__Field_Omult__zero class_Ring__and__Field_Oring__1__no__zero__divisors class_Ring__and__Field_Oring__no__zero__divisors class_Ring__and__Field_Ocomm__ring class_OrderedGroup_Oab__semigroup__mult class_Ring__and__Field_Ocomm__semiring class_OrderedGroup_Omonoid__add % 0.12/0.42 % Fol Constants: tc_nat tc_String_Ochar v_ua______ v_n____ v_i____ v_u____ v_b____ % 0.12/0.42 % Fol Functions: c_HOL_Oinverse__class_Odivide c_HOL_Ozero__class_Ozero c_HOL_Otimes__class_Otimes c_Divides_Odiv__class_Omod c_HOL_Oinverse__class_Oinverse c_HOL_Oone__class_Oone c_HOL_Oabs__class_Oabs c_Power_Opower__class_Opower c_Suc c_HOL_Oplus__class_Oplus c_HOL_Ouminus__class_Ouminus c_HOL_Ominus__class_Ominus c_Orderings_Oord__class_Omax c_Orderings_Obot__class_Obot c_Orderings_Oord__class_Omin c_OrderedGroup_Olordered__ab__group__add__class_Opprt c_Lambda_OdB_OAbs c_Lambda_Osubstn c_HOL_Osgn__class_Osgn c_Nat_Osemiring__1__class_Oof__nat c_List_Oreplicate c_Lambda_OdB_OVar c_Lambda_Osubst c_Lambda_Oliftn c_Lambda_Olift c_Nat_Osize__class_Osize c_Lambda_OdB_OApp c_List_Odrop c_nat_Onat__size c_Nitpick_Onat__gcd c_String_Ochar_Ochar__size % 0.12/0.42 % Problem Properties: % 0.12/0.42 % This is a full first-order problem with equality. The Problem is non-linear. % 0.12/0.42 % 0.12/0.42 % 0.12/0.42 % SZS status GaveUp % 0.12/0.42 % 0.12/0.42 % SPASS beiseite: SPASS does currently not support equality problems. % 0.12/0.42 % Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.12/0.42 % 0.12/0.42 % SPASS-SCL-FOL Statistics: % 0.12/0.42 % Number of learned clauses: 0 % 0.12/0.42 % Number of propagations: 0 % 0.12/0.42 % Number of decisions: 0 % 0.12/0.42 % Number of resolutions: 0 % 0.12/0.42 % Number of condensations: 0 % 0.12/0.42 % Number of sub resolutions: 0 %------------------------------------------------------------------------------