%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG350-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:08:31 PM UTC 2026
% Result : Unsatisfiable 0.27s 1.54s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 426)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_abs__diff__triangle__ineq_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X4,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
cnf(cls_norm__diff__triangle__ineq_0,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1),X1),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X4,X1),X1),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__diff__triangle__ineq_0) ).
cnf(cls_min__max_Odistrib__inf__le_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),c_Orderings_Oord__class_Omin(X2,X4,X1),X1),c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
cnf(cls_distrib__inf__le_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
cnf(cls_min__max_Odistrib__sup__le_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),c_Orderings_Oord__class_Omax(X2,X4,X1),X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
cnf(cls_distrib__sup__le_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
cnf(cls_abs__diff__less__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
cnf(cls_abs__triangle__ineq3_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
cnf(cls_norm__add__less_0,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(X4,X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X1),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__add__less_0) ).
cnf(cls_abs__diff__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X2,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
cnf(cls_abs__diff__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_Deriv_Oadd__diff__add_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
cnf(cls_abs__triangle__ineq2_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
cnf(cls_abs__triangle__ineq_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
cnf(cls_abs__triangle__ineq4_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
cnf(cls_le__add__right__mono_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(cls_norm__triangle__ineq_0,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__triangle__ineq_0) ).
cnf(cls_norm__triangle__ineq4_0,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__triangle__ineq4_0) ).
cnf(cls_add__less__cancel__right_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
cnf(cls_add__less__cancel__left_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_add__le__cancel__right_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
cnf(cls_add__le__cancel__left_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
cnf(cls_estimate__by__abs_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oabs__class_Oabs(X4,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
cnf(cls_add__strict__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
cnf(cls_add__le__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
cnf(cls_add__less__le__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
cnf(cls_add__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
cnf(cls_min__max_Osup__inf__distrib2_0,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X4,X1),c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
cnf(cls_min__max_Oinf__sup__distrib2_0,axiom,
( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X4,X1),c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
cnf(cls_max__add__distrib__left_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
cnf(cls_min__add__distrib__left_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
cnf(cls_add__inf__distrib__right_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
cnf(cls_add__sup__distrib__right_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
cnf(cls_max__diff__distrib__left_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
cnf(cls_min__diff__distrib__left_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
cnf(cls_min__max_Osup__inf__distrib1_0,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
cnf(cls_min__max_Oinf__sup__distrib1_0,axiom,
( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),c_Orderings_Oord__class_Omin(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
cnf(cls_add__inf__distrib__left_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
cnf(cls_add__sup__distrib__left_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
cnf(cls_add__cancel__21_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_min__less__iff__disj_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
cnf(cls_min__le__iff__disj_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X4,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
cnf(cls_less__max__iff__disj_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
cnf(cls_le__max__iff__disj_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
cnf(cls_add__less__cancel__left_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
cnf(cls_add__strict__left__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
cnf(cls_add__less__cancel__right_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_add__strict__right__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
cnf(cls_add__le__cancel__left_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
cnf(cls_add__left__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
cnf(cls_add__le__cancel__right_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
cnf(cls_add__right__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
cnf(cls_real__add__left__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
cnf(cls_max__less__iff__conj_2,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
cnf(cls_min__max_Ole__supI_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
cnf(cls_min__max_Osup__least_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
cnf(cls_min__max_Ole__sup__iff_2,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
cnf(cls_le__supI_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
cnf(cls_sup__least_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
cnf(cls_le__sup__iff_2,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
cnf(cls_min__less__iff__conj_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
cnf(cls_min__max_Ole__infI_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
cnf(cls_min__max_Ole__inf__iff_2,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
cnf(cls_min__max_Oinf__greatest_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
cnf(cls_le__infI_0,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).
cnf(cls_le__inf__iff_2,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
cnf(cls_inf__greatest_0,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
cnf(cls_abs__add__abs_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_min__max_Osup__assoc_0,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
cnf(cls_min__max_Oinf__assoc_0,axiom,
( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
cnf(cls_inf__assoc_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
cnf(cls_sup__assoc_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_min__max_Osup__left__commute_0,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
cnf(cls_min__max_Oinf__left__commute_0,axiom,
( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
cnf(cls_inf__left__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
cnf(cls_sup__left__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
cnf(cls_add__cancel__21_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_add__eq__inf__sup_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).
cnf(cls_less__eqI_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
cnf(cls_less__eqI_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_le__eqI_1,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
cnf(cls_le__eqI_0,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
cnf(cls_max__less__iff__conj_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
cnf(cls_max__less__iff__conj_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
cnf(cls_min__max_Ole__supE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
cnf(cls_min__max_Ole__sup__iff_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
cnf(cls_min__max_Ole__supE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
cnf(cls_min__max_Ole__sup__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
cnf(cls_le__supE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
cnf(cls_le__sup__iff_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
cnf(cls_le__supE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
cnf(cls_le__sup__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
cnf(cls_min__less__iff__conj_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
cnf(cls_min__less__iff__conj_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
cnf(cls_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(cls_le__inf__iff_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
cnf(cls_le__infE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
cnf(cls_le__inf__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
cnf(cls_min__max_Ole__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
cnf(cls_min__max_Ole__inf__iff_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
cnf(cls_min__max_Ole__infE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
cnf(cls_min__max_Ole__inf__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
cnf(cls_abs__less__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
cnf(cls_abs__le__iff_2,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
cnf(cls_abs__leI_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__leI_0) ).
cnf(cls_inf__eq__neg__sup_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
cnf(cls_sup__eq__neg__inf_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
cnf(cls_add__cancel__end_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
cnf(cls_min__max_Oless__infI1_0,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
cnf(cls_min__less__iff__disj_1,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
cnf(cls_min__max_Oless__infI2_0,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
cnf(cls_min__less__iff__disj_2,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
cnf(cls_less__infI1_0,axiom,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).
cnf(cls_less__infI2_0,axiom,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).
cnf(cls_min__max_Ole__infI1_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
cnf(cls_min__le__iff__disj_1,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
cnf(cls_min__max_Ole__infI2_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
cnf(cls_min__le__iff__disj_2,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
cnf(cls_le__infI1_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
cnf(cls_le__infI2_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
cnf(cls_min__max_Oless__supI1_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
cnf(cls_less__max__iff__disj_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
cnf(cls_min__max_Oless__supI2_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
cnf(cls_less__max__iff__disj_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
cnf(cls_less__supI1_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).
cnf(cls_less__supI2_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).
cnf(cls_min__max_Ole__supI1_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
cnf(cls_le__max__iff__disj_1,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
cnf(cls_min__max_Ole__supI2_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
cnf(cls_le__max__iff__disj_2,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
cnf(cls_le__supI1_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
cnf(cls_le__supI2_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
cnf(cls_abs__minus__commute_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
cnf(cls_norm__minus__commute_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__commute_0) ).
cnf(cls_xt1_I10_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_xt1_I8_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
cnf(cls_order__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
cnf(cls_order__le__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
cnf(cls_order__less__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(cls_xt1_I6_J_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_order__trans_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
cnf(cls_Lim_Ominus__diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
cnf(cls_compl__inf_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf_0) ).
cnf(cls_neg__inf__eq__sup_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
cnf(cls_compl__sup_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup_0) ).
cnf(cls_neg__sup__eq__inf_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
cnf(cls_minus__add__distrib_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
cnf(cls_minus__add_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
cnf(cls_neg__less__iff__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
cnf(cls_neg__le__iff__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
cnf(cls_min__max_Osup__left__idem_0,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = c_Orderings_Oord__class_Omax(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
cnf(cls_min__max_Oinf__left__idem_0,axiom,
( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X2,X3,X1),X1) = c_Orderings_Oord__class_Omin(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
cnf(cls_inf__left__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
cnf(cls_sup__left__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
cnf(cls_add__minus__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
cnf(cls_real__le__trans_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
cnf(cls_minus__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
cnf(cls_minus__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
cnf(cls_abs__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
cnf(cls_minus__le__iff_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
cnf(cls_minus__le__iff_1,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
cnf(cls_abs__le__D2_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
cnf(cls_less__minus__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
cnf(cls_less__minus__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
cnf(cls_le__minus__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
cnf(cls_le__minus__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
cnf(cls_exp__less__cancel_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),c_Transcendental_Oexp(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__less__cancel_0) ).
cnf(cls_exp__le__cancel__iff_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),c_Transcendental_Oexp(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__le__cancel__iff_0) ).
cnf(cls_compl__unique_0,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__unique_0) ).
cnf(cls_less__le__not__le_2,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_neg__less__iff__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
cnf(cls_le__imp__neg__le_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
cnf(cls_minus__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
cnf(cls_add__cancel__end_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X3,X2,X1),X1) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
cnf(cls_abs__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
cnf(cls_abs__le__D1_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_exp__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),c_Transcendental_Oexp(X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__less__mono_0) ).
cnf(cls_exp__le__cancel__iff_1,axiom,
( c_lessequals(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),c_Transcendental_Oexp(X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__le__cancel__iff_1) ).
cnf(cls_minus__diff__eq_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(cls_order__antisym_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_eq__eqI_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_add__left__cancel_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_eq__eqI_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_abs__le__interval__iff_1,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
cnf(cls_real__le__antisym_0,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_add__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_min__max_Osup__inf__absorb_0,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X2,X3,X1),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
cnf(cls_min__max_Oinf__sup__absorb_0,axiom,
( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
cnf(cls_inf__sup__absorb_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_sup__inf__absorb_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(cls_min__max_Oinf__le1_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
cnf(cls_min__max_Oinf__le2_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
cnf(cls_inf__le1_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
cnf(cls_inf__le2_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
cnf(cls_le__maxI1_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
cnf(cls_le__maxI2_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X2,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
cnf(cls_sup__ge1_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
cnf(cls_sup__ge2_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
cnf(cls_real__sqrt__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).
cnf(cls_real__sqrt__le__iff_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
cnf(cls_order__less__le_2,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
cnf(cls_order__le__less_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
cnf(cls_order__le__neq__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
cnf(cls_order__neq__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(cls_xt1_I12_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_min__max_Ole__iff__sup_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Omax(X2,X3,X1) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
cnf(cls_min__max_Ole__iff__inf_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Omin(X2,X3,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
cnf(cls_le__iff__inf_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
cnf(cls_le__iff__sup_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
cnf(cls_arctan__monotone_0,axiom,
( c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X2),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__monotone_0) ).
cnf(cls_real__sqrt__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).
cnf(cls_arctan__monotone_H_0,axiom,
( c_lessequals(c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X2),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__monotone_H_0) ).
cnf(cls_real__sqrt__le__iff_1,axiom,
( c_lessequals(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).
cnf(cls_min__max_Osup__absorb1_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
cnf(cls_min__max_Ole__iff__sup_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
cnf(cls_min__max_Ole__iff__inf_0,axiom,
( c_Orderings_Oord__class_Omin(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
cnf(cls_min__max_Oinf__absorb2_0,axiom,
( c_Orderings_Oord__class_Omin(X2,X3,X1) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
cnf(cls_le__iff__inf_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_inf__absorb2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(cls_sup__absorb1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
cnf(cls_le__iff__sup_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(cls_order__le__less_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
cnf(cls_order__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
cnf(cls_diff__minus__eq__add_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
cnf(cls_diff__eq_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__eq_0) ).
cnf(cls_class__ring_Osub__add_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
cnf(cls_ab__diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
cnf(cls_diff__def_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
cnf(cls_diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
cnf(cls_real__less__def_2,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
cnf(cls_real__less__def_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
cnf(cls_linorder__less__linear_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
cnf(cls_linorder__neqE_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( c_HOL_Oord__class_Oless(X2,X2,X1)
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
cnf(cls_linorder__not__less_0,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
cnf(cls_linorder__not__le_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
cnf(cls_not__leE_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_min__max_Osup__commute_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = c_Orderings_Oord__class_Omax(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
cnf(cls_min__max_Oinf__commute_0,axiom,
( c_Orderings_Oord__class_Omin(X2,X3,X1) = c_Orderings_Oord__class_Omin(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
cnf(cls_inf__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_sup__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_abs__ge__minus__self_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
cnf(cls_real__le__linear_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
cnf(cls_inf__eq__top__eq1_0,axiom,
( X2 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
cnf(cls_inf__eq__top__eq2_0,axiom,
( X3 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
cnf(cls_abs__lattice_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__lattice_0) ).
cnf(cls_CHAINED_0,axiom,
( c_HOL_Oord__class_Oless(X1,v_Y____,tc_RealDef_Oreal)
| ~ hBOOL(hAPP(v_P,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_Y_0,axiom,
( c_HOL_Oord__class_Oless(X1,v_Y____,tc_RealDef_Oreal)
| ~ hBOOL(hAPP(v_P,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Y_0) ).
cnf(cls_L_H_0,axiom,
( c_lessequals(X1,v_L____,tc_RealDef_Oreal)
| ~ hBOOL(hAPP(v_P,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_L_H_0) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_compl__inf__bot_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
cnf(cls_compl__sup__top_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
cnf(cls_inf__compl__bot_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
cnf(cls_sup__compl__top_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
cnf(cls_abs__ge__self_0,axiom,
( c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
cnf(cls_real__less__def_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_inf__bot__left_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
cnf(cls_sup__top__left_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(cls_inf__bot__right_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
cnf(cls_sup__top__right_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(cls_inf__top__left_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
cnf(cls_sup__bot__left_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
cnf(cls_inf__top__right_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
cnf(cls_sup__bot__right_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_top__greatest_0,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
cnf(cls_min__max_Osup__idem_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X2,X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
cnf(cls_min__max_Oinf__idem_0,axiom,
( c_Orderings_Oord__class_Omin(X2,X2,X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
cnf(cls_inf__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_sup__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_abs__idempotent_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
cnf(cls_abs__minus__cancel_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
cnf(cls_norm__minus__cancel_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
cnf(cls_abs__norm__cancel_0,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
cnf(cls_real__le__refl_0,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
cnf(cls_xY_0,axiom,
c_HOL_Oord__class_Oless(v_x____,v_Y____,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xY_0) ).
cnf(cls_double__compl_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_minus__minus_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
cnf(cls_minus__equation__iff_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
cnf(cls_equation__minus__iff_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
cnf(cls_equation__minus__iff_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_abs__exp__cancel_0,axiom,
c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__exp__cancel_0) ).
cnf(cls_exp__inj__iff_0,axiom,
( X1 = X2
| c_Transcendental_Oexp(X1,tc_RealDef_Oreal) != c_Transcendental_Oexp(X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__inj__iff_0) ).
cnf(cls_compl__top__eq_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
cnf(cls_compl__bot__eq_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
cnf(cls_conjecture_0,negated_conjecture,
hBOOL(hAPP(v_P,v_xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_x_0,axiom,
hBOOL(hAPP(v_P,v_x____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_x_0) ).
cnf(cls_real__sqrt__eq__iff_0,axiom,
( X1 = X2
| c_NthRoot_Osqrt(X1) != c_NthRoot_Osqrt(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet,axiom,
class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
cnf(clsarity_RealDef__Oreal__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).
cnf(clsarity_RealDef__Oreal__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olattice) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(clsarity_RealDef__Oreal__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Odistrib__lattice) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join,axiom,
class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
cnf(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
cnf(i_0_378,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X4,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__diff__triangle__ineq_0,
[final] ).
cnf(i_0_379,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1),X1),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X4,X1),X1),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__diff__triangle__ineq_0,
[final] ).
cnf(i_0_380,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),c_Orderings_Oord__class_Omin(X2,X4,X1),X1),c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Odistrib__inf__le_0,
[final] ).
cnf(i_0_381,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_distrib__inf__le_0,
[final] ).
cnf(i_0_382,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),c_Orderings_Oord__class_Omax(X2,X4,X1),X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Odistrib__sup__le_0,
[final] ).
cnf(i_0_383,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_distrib__sup__le_0,
[final] ).
cnf(i_0_384,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X1),X2,X1) ),
cls_abs__diff__less__iff_2,
[final] ).
cnf(i_0_385,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq3_0,
[final] ).
cnf(i_0_386,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(X4,X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X1),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),X4,tc_RealDef_Oreal) ),
cls_norm__add__less_0,
[final] ).
cnf(i_0_387,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X2,X1),X1),X3,X1) ),
cls_abs__diff__less__iff_0,
[final] ).
cnf(i_0_388,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1) ),
cls_abs__diff__less__iff_1,
[final] ).
cnf(i_0_389,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_390,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_Deriv_Oadd__diff__add_0,
[final] ).
cnf(i_0_391,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq2_0,
[final] ).
cnf(i_0_392,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq_0,
[final] ).
cnf(i_0_393,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq4_0,
[final] ).
cnf(i_0_394,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
cls_le__add__right__mono_0,
[final] ).
cnf(i_0_395,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__triangle__ineq_0,
[final] ).
cnf(i_0_396,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__triangle__ineq4_0,
[final] ).
cnf(i_0_397,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
cls_add__less__cancel__right_0,
[final] ).
cnf(i_0_398,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
cls_add__less__cancel__left_0,
[final] ).
cnf(i_0_399,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
cls_add__le__cancel__right_0,
[final] ).
cnf(i_0_400,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
cls_add__le__cancel__left_0,
[final] ).
cnf(i_0_401,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oabs__class_Oabs(X4,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1) ),
cls_estimate__by__abs_0,
[final] ).
cnf(i_0_402,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__mono_0,
[final] ).
cnf(i_0_403,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__less__mono_0,
[final] ).
cnf(i_0_404,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__less__le__mono_0,
[final] ).
cnf(i_0_405,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__mono_0,
[final] ).
cnf(i_0_406,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X4,X1),c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__inf__distrib2_0,
[final] ).
cnf(i_0_407,axiom,
( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X4,X1),c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__sup__distrib2_0,
[final] ).
cnf(i_0_408,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_inf__sup__distrib2_0,
[final] ).
cnf(i_0_409,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_sup__inf__distrib2_0,
[final] ).
cnf(i_0_410,axiom,
( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
cls_max__add__distrib__left_0,
[final] ).
cnf(i_0_411,axiom,
( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
cls_min__add__distrib__left_0,
[final] ).
cnf(i_0_412,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
cls_add__inf__distrib__right_0,
[final] ).
cnf(i_0_413,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,
[final] ).
cnf(i_0_414,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
cls_add__sup__distrib__right_0,
[final] ).
cnf(i_0_415,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,
[final] ).
cnf(i_0_416,axiom,
( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
cls_max__diff__distrib__left_0,
[final] ).
cnf(i_0_417,axiom,
( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
cls_min__diff__distrib__left_0,
[final] ).
cnf(i_0_418,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__inf__distrib1_0,
[final] ).
cnf(i_0_419,axiom,
( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),c_Orderings_Oord__class_Omin(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__sup__distrib1_0,
[final] ).
cnf(i_0_420,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_inf__sup__distrib1_0,
[final] ).
cnf(i_0_421,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_sup__inf__distrib1_0,
[final] ).
cnf(i_0_422,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
cls_add__inf__distrib__left_0,
[final] ).
cnf(i_0_423,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,
[final] ).
cnf(i_0_424,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
cls_add__sup__distrib__left_0,
[final] ).
cnf(i_0_425,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,
[final] ).
cnf(i_0_426,axiom,
( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
cls_add__cancel__21_0,
[final] ).
cnf(i_0_427,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X2,X1),X3,X1) ),
cls_min__less__iff__disj_0,
[final] ).
cnf(i_0_428,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X4,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X4,X2,X1),X3,X1) ),
cls_min__le__iff__disj_0,
[final] ).
cnf(i_0_429,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
cls_less__max__iff__disj_0,
[final] ).
cnf(i_0_430,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
cls_le__max__iff__disj_0,
[final] ).
cnf(i_0_431,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__less__cancel__left_1,
[final] ).
cnf(i_0_432,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__strict__left__mono_0,
[final] ).
cnf(i_0_433,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__less__cancel__right_1,
[final] ).
cnf(i_0_434,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__right__mono_0,
[final] ).
cnf(i_0_435,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__le__cancel__left_1,
[final] ).
cnf(i_0_436,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__left__mono_0,
[final] ).
cnf(i_0_437,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__cancel__right_1,
[final] ).
cnf(i_0_438,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__right__mono_0,
[final] ).
cnf(i_0_439,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal) ),
cls_real__add__left__mono_0,
[final] ).
cnf(i_0_440,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_max__less__iff__conj_2,
[final] ).
cnf(i_0_441,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__max_Ole__supI_0,
[final] ).
cnf(i_0_442,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__max_Osup__least_0,
[final] ).
cnf(i_0_443,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__max_Ole__sup__iff_2,
[final] ).
cnf(i_0_444,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__supI_0,
[final] ).
cnf(i_0_445,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_sup__least_0,
[final] ).
cnf(i_0_446,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__sup__iff_2,
[final] ).
cnf(i_0_447,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_min__less__iff__conj_2,
[final] ).
cnf(i_0_448,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Ole__infI_0,
[final] ).
cnf(i_0_449,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Ole__inf__iff_2,
[final] ).
cnf(i_0_450,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Oinf__greatest_0,
[final] ).
cnf(i_0_451,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__infI_0,
[final] ).
cnf(i_0_452,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__inf__iff_2,
[final] ).
cnf(i_0_453,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_inf__greatest_0,
[final] ).
cnf(i_0_454,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__add__abs_0,
[final] ).
cnf(i_0_455,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_456,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__assoc_0,
[final] ).
cnf(i_0_457,axiom,
( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__assoc_0,
[final] ).
cnf(i_0_458,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__assoc_0,
[final] ).
cnf(i_0_459,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I2_J_0,
[final] ).
cnf(i_0_460,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I6_J_0,
[final] ).
cnf(i_0_461,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__assoc_0,
[final] ).
cnf(i_0_462,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
[final] ).
cnf(i_0_463,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_464,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__assoc_0,
[final] ).
cnf(i_0_465,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_466,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0,
[final] ).
cnf(i_0_467,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__left__commute_0,
[final] ).
cnf(i_0_468,axiom,
( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__left__commute_0,
[final] ).
cnf(i_0_469,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__left__commute_0,
[final] ).
cnf(i_0_470,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I3_J_0,
[final] ).
cnf(i_0_471,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I7_J_0,
[final] ).
cnf(i_0_472,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__left__commute_0,
[final] ).
cnf(i_0_473,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__21_1,
[final] ).
cnf(i_0_474,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_475,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__left__commute_0,
[final] ).
cnf(i_0_476,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_add__eq__inf__sup_0,
[final] ).
cnf(i_0_477,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
cls_less__eqI_1,
[final] ).
cnf(i_0_478,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__eqI_0,
[final] ).
cnf(i_0_479,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
cls_le__eqI_1,
[final] ).
cnf(i_0_480,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__eqI_0,
[final] ).
cnf(i_0_481,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
cls_max__less__iff__conj_0,
[final] ).
cnf(i_0_482,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
cls_max__less__iff__conj_1,
[final] ).
cnf(i_0_483,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
cls_min__max_Ole__supE_0,
[final] ).
cnf(i_0_484,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
cls_min__max_Ole__sup__iff_0,
[final] ).
cnf(i_0_485,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
cls_min__max_Ole__supE_1,
[final] ).
cnf(i_0_486,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
cls_min__max_Ole__sup__iff_1,
[final] ).
cnf(i_0_487,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
cls_le__supE_0,
[final] ).
cnf(i_0_488,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
cls_le__sup__iff_0,
[final] ).
cnf(i_0_489,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
cls_le__supE_1,
[final] ).
cnf(i_0_490,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
cls_le__sup__iff_1,
[final] ).
cnf(i_0_491,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
cls_min__less__iff__conj_0,
[final] ).
cnf(i_0_492,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
cls_min__less__iff__conj_1,
[final] ).
cnf(i_0_493,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
cls_le__infE_0,
[final] ).
cnf(i_0_494,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
cls_le__inf__iff_0,
[final] ).
cnf(i_0_495,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
cls_le__infE_1,
[final] ).
cnf(i_0_496,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
cls_le__inf__iff_1,
[final] ).
cnf(i_0_497,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
cls_min__max_Ole__infE_0,
[final] ).
cnf(i_0_498,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
cls_min__max_Ole__inf__iff_0,
[final] ).
cnf(i_0_499,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
cls_min__max_Ole__infE_1,
[final] ).
cnf(i_0_500,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
cls_min__max_Ole__inf__iff_1,
[final] ).
cnf(i_0_501,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_abs__less__iff_2,
[final] ).
cnf(i_0_502,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_abs__le__iff_2,
[final] ).
cnf(i_0_503,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_abs__leI_0,
[final] ).
cnf(i_0_504,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_inf__eq__neg__sup_0,
[final] ).
cnf(i_0_505,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_sup__eq__neg__inf_0,
[final] ).
cnf(i_0_506,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != X3 ),
cls_add__cancel__end_0,
[final] ).
cnf(i_0_507,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_min__max_Oless__infI1_0,
[final] ).
cnf(i_0_508,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_min__less__iff__disj_1,
[final] ).
cnf(i_0_509,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_min__max_Oless__infI2_0,
[final] ).
cnf(i_0_510,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_min__less__iff__disj_2,
[final] ).
cnf(i_0_511,axiom,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_less__infI1_0,
[final] ).
cnf(i_0_512,axiom,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_less__infI2_0,
[final] ).
cnf(i_0_513,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__max_Ole__infI1_0,
[final] ).
cnf(i_0_514,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__le__iff__disj_1,
[final] ).
cnf(i_0_515,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_min__max_Ole__infI2_0,
[final] ).
cnf(i_0_516,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_min__le__iff__disj_2,
[final] ).
cnf(i_0_517,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__infI1_0,
[final] ).
cnf(i_0_518,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_le__infI2_0,
[final] ).
cnf(i_0_519,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_min__max_Oless__supI1_0,
[final] ).
cnf(i_0_520,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__max__iff__disj_1,
[final] ).
cnf(i_0_521,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_min__max_Oless__supI2_0,
[final] ).
cnf(i_0_522,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_less__max__iff__disj_2,
[final] ).
cnf(i_0_523,axiom,
( c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__supI1_0,
[final] ).
cnf(i_0_524,axiom,
( c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_less__supI2_0,
[final] ).
cnf(i_0_525,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Ole__supI1_0,
[final] ).
cnf(i_0_526,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__max__iff__disj_1,
[final] ).
cnf(i_0_527,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__max_Ole__supI2_0,
[final] ).
cnf(i_0_528,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__max__iff__disj_2,
[final] ).
cnf(i_0_529,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__supI1_0,
[final] ).
cnf(i_0_530,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__supI2_0,
[final] ).
cnf(i_0_531,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__commute_0,
[final] ).
cnf(i_0_532,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__minus__commute_0,
[final] ).
cnf(i_0_533,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I10_J_0,
[final] ).
cnf(i_0_534,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I7_J_0,
[final] ).
cnf(i_0_535,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I8_J_0,
[final] ).
cnf(i_0_536,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__trans_0,
[final] ).
cnf(i_0_537,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__le__less__trans_0,
[final] ).
cnf(i_0_538,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__le__trans_0,
[final] ).
cnf(i_0_539,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I6_J_0,
[final] ).
cnf(i_0_540,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__trans_0,
[final] ).
cnf(i_0_541,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_Lim_Ominus__diff__minus_0,
[final] ).
cnf(i_0_542,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf_0,
[final] ).
cnf(i_0_543,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_neg__inf__eq__sup_0,
[final] ).
cnf(i_0_544,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup_0,
[final] ).
cnf(i_0_545,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_neg__sup__eq__inf_0,
[final] ).
cnf(i_0_546,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__add__distrib_0,
[final] ).
cnf(i_0_547,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add_0,
[final] ).
cnf(i_0_548,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__less__iff__less_0,
[final] ).
cnf(i_0_549,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__le__iff__le_0,
[final] ).
cnf(i_0_550,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = c_Orderings_Oord__class_Omax(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__left__idem_0,
[final] ).
cnf(i_0_551,axiom,
( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X2,X3,X1),X1) = c_Orderings_Oord__class_Omin(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__left__idem_0,
[final] ).
cnf(i_0_552,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__left__idem_0,
[final] ).
cnf(i_0_553,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I4_J_0,
[final] ).
cnf(i_0_554,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I8_J_0,
[final] ).
cnf(i_0_555,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__left__idem_0,
[final] ).
cnf(i_0_556,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__minus__cancel_0,
[final] ).
cnf(i_0_557,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
cls_real__le__trans_0,
[final] ).
cnf(i_0_558,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__less__iff_0,
[final] ).
cnf(i_0_559,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__less__iff_1,
[final] ).
cnf(i_0_560,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__less__iff_1,
[final] ).
cnf(i_0_561,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__le__iff_0,
[final] ).
cnf(i_0_562,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__le__iff_1,
[final] ).
cnf(i_0_563,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__le__D2_0,
[final] ).
cnf(i_0_564,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__minus__iff_0,
[final] ).
cnf(i_0_565,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__minus__iff_1,
[final] ).
cnf(i_0_566,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_le__minus__iff_0,
[final] ).
cnf(i_0_567,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_le__minus__iff_1,
[final] ).
cnf(i_0_568,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),c_Transcendental_Oexp(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_exp__less__cancel_0,
[final] ).
cnf(i_0_569,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),c_Transcendental_Oexp(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_exp__le__cancel__iff_0,
[final] ).
cnf(i_0_570,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
cls_compl__unique_0,
[final] ).
cnf(i_0_571,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_less__le__not__le_2,
[final] ).
cnf(i_0_572,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_neg__less__iff__less_1,
[final] ).
cnf(i_0_573,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__imp__neg__le_0,
[final] ).
cnf(i_0_574,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add__cancel_0,
[final] ).
cnf(i_0_575,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X3,X2,X1),X1) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__end_1,
[final] ).
cnf(i_0_576,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__less__iff_0,
[final] ).
cnf(i_0_577,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__le__D1_0,
[final] ).
cnf(i_0_578,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_class__ringb_Oadd__cancel_0,
[final] ).
cnf(i_0_579,axiom,
( c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),c_Transcendental_Oexp(X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
cls_exp__less__mono_0,
[final] ).
cnf(i_0_580,axiom,
( c_lessequals(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),c_Transcendental_Oexp(X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_exp__le__cancel__iff_1,
[final] ).
cnf(i_0_581,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__diff__eq_0,
[final] ).
cnf(i_0_582,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__antisym_0,
[final] ).
cnf(i_0_583,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__eq__iff_2,
[final] ).
cnf(i_0_584,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_order__antisym__conv_0,
[final] ).
cnf(i_0_585,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
cls_eq__eqI_1,
[final] ).
cnf(i_0_586,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
cls_add__right__cancel_0,
[final] ).
cnf(i_0_587,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_add__left__cancel_0,
[final] ).
cnf(i_0_588,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_add__imp__eq_0,
[final] ).
cnf(i_0_589,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
cls_eq__eqI_0,
[final] ).
cnf(i_0_590,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_not__less__iff__gr__or__eq_1,
[final] ).
cnf(i_0_591,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__antisym__conv2_1,
[final] ).
cnf(i_0_592,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_linorder__not__le_1,
[final] ).
cnf(i_0_593,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_linorder__not__less_1,
[final] ).
cnf(i_0_594,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_xt1_I9_J_0,
[final] ).
cnf(i_0_595,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_0,
[final] ).
cnf(i_0_596,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_H_0,
[final] ).
cnf(i_0_597,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_less__le__not__le_1,
[final] ).
cnf(i_0_598,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_abs__le__interval__iff_1,
[final] ).
cnf(i_0_599,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__le__antisym_0,
[final] ).
cnf(i_0_600,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__add__cancel_0,
[final] ).
cnf(i_0_601,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__diff__cancel_0,
[final] ).
cnf(i_0_602,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X2,X3,X1),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__inf__absorb_0,
[final] ).
cnf(i_0_603,axiom,
( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__sup__absorb_0,
[final] ).
cnf(i_0_604,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__absorb_0,
[final] ).
cnf(i_0_605,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_sup__inf__absorb_0,
[final] ).
cnf(i_0_606,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__le1_0,
[final] ).
cnf(i_0_607,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__le2_0,
[final] ).
cnf(i_0_608,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__le1_0,
[final] ).
cnf(i_0_609,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I1_J_0,
[final] ).
cnf(i_0_610,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__le2_0,
[final] ).
cnf(i_0_611,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I2_J_0,
[final] ).
cnf(i_0_612,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_le__maxI1_0,
[final] ).
cnf(i_0_613,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X2,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_le__maxI2_0,
[final] ).
cnf(i_0_614,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I3_J_0,
[final] ).
cnf(i_0_615,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__ge1_0,
[final] ).
cnf(i_0_616,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I4_J_0,
[final] ).
cnf(i_0_617,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__ge2_0,
[final] ).
cnf(i_0_618,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
cls_real__sqrt__less__iff_0,
[final] ).
cnf(i_0_619,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
cls_real__sqrt__le__iff_0,
[final] ).
cnf(i_0_620,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv1_0,
[final] ).
cnf(i_0_621,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv2_0,
[final] ).
cnf(i_0_622,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__less__le_2,
[final] ).
cnf(i_0_623,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__less_0,
[final] ).
cnf(i_0_624,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__neq__trans_0,
[final] ).
cnf(i_0_625,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__neq__le__trans_0,
[final] ).
cnf(i_0_626,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I12_J_0,
[final] ).
cnf(i_0_627,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I11_J_0,
[final] ).
cnf(i_0_628,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Omax(X2,X3,X1) != X3 ),
cls_min__max_Ole__iff__sup_1,
[final] ).
cnf(i_0_629,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Omin(X2,X3,X1) != X2 ),
cls_min__max_Ole__iff__inf_1,
[final] ).
cnf(i_0_630,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
cls_le__iff__inf_1,
[final] ).
cnf(i_0_631,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
cls_le__iff__sup_1,
[final] ).
cnf(i_0_632,axiom,
( c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X2),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
cls_arctan__monotone_0,
[final] ).
cnf(i_0_633,axiom,
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
cls_real__sqrt__less__iff_1,
[final] ).
cnf(i_0_634,axiom,
( c_lessequals(c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X2),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_arctan__monotone_H_0,
[final] ).
cnf(i_0_635,axiom,
( c_lessequals(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__sqrt__le__iff_1,
[final] ).
cnf(i_0_636,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_min__max_Osup__absorb1_0,
[final] ).
cnf(i_0_637,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Ole__iff__sup_0,
[final] ).
cnf(i_0_638,axiom,
( c_Orderings_Oord__class_Omin(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Ole__iff__inf_0,
[final] ).
cnf(i_0_639,axiom,
( c_Orderings_Oord__class_Omin(X2,X3,X1) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_min__max_Oinf__absorb2_0,
[final] ).
cnf(i_0_640,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__inf_0,
[final] ).
cnf(i_0_641,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_inf__absorb2_0,
[final] ).
cnf(i_0_642,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_sup__absorb1_0,
[final] ).
cnf(i_0_643,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__sup_0,
[final] ).
cnf(i_0_644,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_order__le__less_1,
[final] ).
cnf(i_0_645,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_order__less__imp__le_0,
[final] ).
cnf(i_0_646,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus__eq__add_0,
[final] ).
cnf(i_0_647,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_diff__eq_0,
[final] ).
cnf(i_0_648,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ring_Osub__add_0,
[final] ).
cnf(i_0_649,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_ab__diff__minus_0,
[final] ).
cnf(i_0_650,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_diff__def_0,
[final] ).
cnf(i_0_651,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus_0,
[final] ).
cnf(i_0_652,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_2,
[final] ).
cnf(i_0_653,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_0,
[final] ).
cnf(i_0_654,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_linorder__neqE__ordered__idom_0,
[final] ).
cnf(i_0_655,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__less__iff__gr__or__eq_0,
[final] ).
cnf(i_0_656,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv3_0,
[final] ).
cnf(i_0_657,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__less__linear_0,
[final] ).
cnf(i_0_658,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__neqE_0,
[final] ).
cnf(i_0_659,axiom,
( c_HOL_Oord__class_Oless(X2,X2,X1)
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv1_1,
[final] ).
cnf(i_0_660,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__less_0,
[final] ).
cnf(i_0_661,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__le_0,
[final] ).
cnf(i_0_662,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__leE_0,
[final] ).
cnf(i_0_663,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_664,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = c_Orderings_Oord__class_Omax(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__commute_0,
[final] ).
cnf(i_0_665,axiom,
( c_Orderings_Oord__class_Omin(X2,X3,X1) = c_Orderings_Oord__class_Omin(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__commute_0,
[final] ).
cnf(i_0_666,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__commute_0,
[final] ).
cnf(i_0_667,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I1_J_0,
[final] ).
cnf(i_0_668,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I5_J_0,
[final] ).
cnf(i_0_669,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__commute_0,
[final] ).
cnf(i_0_670,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__c_0,
[final] ).
cnf(i_0_671,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_672,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__commute_0,
[final] ).
cnf(i_0_673,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__minus__self_0,
[final] ).
cnf(i_0_674,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
cls_real__le__linear_0,
[final] ).
cnf(i_0_675,axiom,
( X2 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
cls_inf__eq__top__eq1_0,
[final] ).
cnf(i_0_676,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq1_0,
[final] ).
cnf(i_0_677,axiom,
( X3 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
cls_inf__eq__top__eq2_0,
[final] ).
cnf(i_0_678,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq2_0,
[final] ).
cnf(i_0_679,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1) ),
cls_abs__lattice_0,
[final] ).
cnf(i_0_680,axiom,
( c_HOL_Oord__class_Oless(X1,v_Y____,tc_RealDef_Oreal)
| ~ hBOOL(hAPP(v_P,X1)) ),
cls_CHAINED_0,
[final] ).
cnf(i_0_681,axiom,
( c_HOL_Oord__class_Oless(X1,v_Y____,tc_RealDef_Oreal)
| ~ hBOOL(hAPP(v_P,X1)) ),
cls_Y_0,
[final] ).
cnf(i_0_682,axiom,
( c_lessequals(X1,v_L____,tc_RealDef_Oreal)
| ~ hBOOL(hAPP(v_P,X1)) ),
cls_L_H_0,
[final] ).
cnf(i_0_683,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_684,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_685,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_686,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf__bot_0,
[final] ).
cnf(i_0_687,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup__top_0,
[final] ).
cnf(i_0_688,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_inf__compl__bot_0,
[final] ).
cnf(i_0_689,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_sup__compl__top_0,
[final] ).
cnf(i_0_690,axiom,
( c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__self_0,
[final] ).
cnf(i_0_691,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
cls_real__less__def_1,
[final] ).
cnf(i_0_692,negated_conjecture,
~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal),
cls_conjecture_1,
[final] ).
cnf(i_0_693,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__left_0,
[final] ).
cnf(i_0_694,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__left_0,
[final] ).
cnf(i_0_695,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__right_0,
[final] ).
cnf(i_0_696,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__right_0,
[final] ).
cnf(i_0_697,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__left_0,
[final] ).
cnf(i_0_698,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__left_0,
[final] ).
cnf(i_0_699,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__right_0,
[final] ).
cnf(i_0_700,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0,
[final] ).
cnf(i_0_701,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0,
[final] ).
cnf(i_0_702,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__greatest_0,
[final] ).
cnf(i_0_703,axiom,
( c_Orderings_Oord__class_Omax(X2,X2,X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__idem_0,
[final] ).
cnf(i_0_704,axiom,
( c_Orderings_Oord__class_Omin(X2,X2,X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__idem_0,
[final] ).
cnf(i_0_705,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__idem_0,
[final] ).
cnf(i_0_706,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__idem_0,
[final] ).
cnf(i_0_707,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_708,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_709,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__idempotent_0,
[final] ).
cnf(i_0_710,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__cancel_0,
[final] ).
cnf(i_0_711,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__minus__cancel_0,
[final] ).
cnf(i_0_712,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_abs__norm__cancel_0,
[final] ).
cnf(i_0_713,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
cls_compl__eq__compl__iff_0,
[final] ).
cnf(i_0_714,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
cls_neg__equal__iff__equal_0,
[final] ).
cnf(i_0_715,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
cls_real__le__refl_0,
[final] ).
cnf(i_0_716,axiom,
c_HOL_Oord__class_Oless(v_x____,v_Y____,tc_RealDef_Oreal),
cls_xY_0,
[final] ).
cnf(i_0_717,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0,
[final] ).
cnf(i_0_718,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__minus_0,
[final] ).
cnf(i_0_719,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__equation__iff_1,
[final] ).
cnf(i_0_720,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_0,
[final] ).
cnf(i_0_721,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1,
[final] ).
cnf(i_0_722,axiom,
c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(X1,tc_RealDef_Oreal),
cls_abs__exp__cancel_0,
[final] ).
cnf(i_0_723,axiom,
( X1 = X2
| c_Transcendental_Oexp(X1,tc_RealDef_Oreal) != c_Transcendental_Oexp(X2,tc_RealDef_Oreal) ),
cls_exp__inj__iff_0,
[final] ).
cnf(i_0_724,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__top__eq_0,
[final] ).
cnf(i_0_725,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__bot__eq_0,
[final] ).
cnf(i_0_726,negated_conjecture,
hBOOL(hAPP(v_P,v_xa)),
cls_conjecture_0,
[final] ).
cnf(i_0_727,axiom,
hBOOL(hAPP(v_P,v_x____)),
cls_x_0,
[final] ).
cnf(i_0_728,axiom,
( X1 = X2
| c_NthRoot_Osqrt(X1) != c_NthRoot_Osqrt(X2) ),
cls_real__sqrt__eq__iff_0,
[final] ).
cnf(i_0_729,axiom,
class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet,
[final] ).
cnf(i_0_730,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_731,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_732,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_733,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber__ring,
[final] ).
cnf(i_0_734,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_735,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_736,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_737,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_738,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_739,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_740,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_741,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,
[final] ).
cnf(i_0_742,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,
[final] ).
cnf(i_0_743,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Lattices_Olower__semilattice,
[final] ).
cnf(i_0_744,axiom,
class_Lattices_Olattice(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Lattices_Olattice,
[final] ).
cnf(i_0_745,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_746,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_747,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Olinorder,
[final] ).
cnf(i_0_748,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_749,axiom,
class_Lattices_Odistrib__lattice(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Lattices_Odistrib__lattice,
[final] ).
cnf(i_0_750,axiom,
class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join,
[final] ).
cnf(i_0_751,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,
[final] ).
cnf(i_0_752,axiom,
class_Lattices_Oupper__semilattice(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Lattices_Oupper__semilattice,
[final] ).
cnf(i_0_753,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Oorder,
[final] ).
cnf(i_0_754,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Opreorder,
[final] ).
cnf(i_0_755,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_756,axiom,
X1 = X1 ).
cnf(i_0_757,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_758,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_759,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_760,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_761,axiom,
( X1 != X2
| c_Transcendental_Oexp(X1,X3) = c_Transcendental_Oexp(X2,X3) ) ).
cnf(i_0_762,axiom,
( X1 != X2
| c_Transcendental_Oexp(X3,X1) = c_Transcendental_Oexp(X3,X2) ) ).
cnf(i_0_763,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_764,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_765,axiom,
( X1 != X2
| c_NthRoot_Osqrt(X1) = c_NthRoot_Osqrt(X2) ) ).
cnf(i_0_766,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_767,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_768,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_769,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_770,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_771,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_772,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_773,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_774,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1,X3,X4) = c_Orderings_Oord__class_Omax(X2,X3,X4) ) ).
cnf(i_0_775,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X3,X1,X4) = c_Orderings_Oord__class_Omax(X3,X2,X4) ) ).
cnf(i_0_776,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X3,X4,X1) = c_Orderings_Oord__class_Omax(X3,X4,X2) ) ).
cnf(i_0_777,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X1,X3,X4) = c_Orderings_Oord__class_Omin(X2,X3,X4) ) ).
cnf(i_0_778,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X3,X1,X4) = c_Orderings_Oord__class_Omin(X3,X2,X4) ) ).
cnf(i_0_779,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X3,X4,X1) = c_Orderings_Oord__class_Omin(X3,X4,X2) ) ).
cnf(i_0_780,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).
cnf(i_0_781,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).
cnf(i_0_782,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).
cnf(i_0_783,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_784,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_785,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_786,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_787,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_788,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_789,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_790,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_791,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_792,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_793,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_794,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_795,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_796,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_797,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
| class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).
cnf(i_0_798,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_799,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
| class_OrderedGroup_Olordered__ab__group__add__join(X2) ) ).
cnf(i_0_800,axiom,
( X1 != X2
| ~ class_Lattices_Oupper__semilattice(X1)
| class_Lattices_Oupper__semilattice(X2) ) ).
cnf(i_0_801,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_802,axiom,
( X1 != X2
| ~ class_Lattices_Olower__semilattice(X1)
| class_Lattices_Olower__semilattice(X2) ) ).
cnf(i_0_803,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_804,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_805,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_806,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_807,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_808,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_809,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_810,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_811,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_812,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_813,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_814,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_815,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_816,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_817,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_818,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_819,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_820,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_821,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_822,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_823,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_824,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_825,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_756_001,axiom,
X1 = X1 ).
cnf(i_0_757_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_758_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_759_004,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_760_005,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_761_006,axiom,
( X1 != X2
| c_Transcendental_Oexp(X1,X3) = c_Transcendental_Oexp(X2,X3) ) ).
cnf(i_0_762_007,axiom,
( X1 != X2
| c_Transcendental_Oexp(X3,X1) = c_Transcendental_Oexp(X3,X2) ) ).
cnf(i_0_763_008,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_764_009,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_765_010,axiom,
( X1 != X2
| c_NthRoot_Osqrt(X1) = c_NthRoot_Osqrt(X2) ) ).
cnf(i_0_766_011,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_767_012,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_768_013,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_769_014,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_770_015,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_771_016,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_772_017,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_773_018,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_774_019,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1,X3,X4) = c_Orderings_Oord__class_Omax(X2,X3,X4) ) ).
cnf(i_0_775_020,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X3,X1,X4) = c_Orderings_Oord__class_Omax(X3,X2,X4) ) ).
cnf(i_0_776_021,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X3,X4,X1) = c_Orderings_Oord__class_Omax(X3,X4,X2) ) ).
cnf(i_0_777_022,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X1,X3,X4) = c_Orderings_Oord__class_Omin(X2,X3,X4) ) ).
cnf(i_0_778_023,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X3,X1,X4) = c_Orderings_Oord__class_Omin(X3,X2,X4) ) ).
cnf(i_0_779_024,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X3,X4,X1) = c_Orderings_Oord__class_Omin(X3,X4,X2) ) ).
cnf(i_0_780_025,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).
cnf(i_0_781_026,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).
cnf(i_0_782_027,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).
cnf(i_0_783_028,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_784_029,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_785_030,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_786_031,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_787_032,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_788_033,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_789_034,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_790_035,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_791_036,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_792_037,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_793_038,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_794_039,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_795_040,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_796_041,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_797_042,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
| class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).
cnf(i_0_798_043,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_799_044,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
| class_OrderedGroup_Olordered__ab__group__add__join(X2) ) ).
cnf(i_0_800_045,axiom,
( X1 != X2
| ~ class_Lattices_Oupper__semilattice(X1)
| class_Lattices_Oupper__semilattice(X2) ) ).
cnf(i_0_801_046,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_802_047,axiom,
( X1 != X2
| ~ class_Lattices_Olower__semilattice(X1)
| class_Lattices_Olower__semilattice(X2) ) ).
cnf(i_0_803_048,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_804_049,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_805_050,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_806_051,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_807_052,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_808_053,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_809_054,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_810_055,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_811_056,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_812_057,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_813_058,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_814_059,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_815_060,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_816_061,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_817_062,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_818_063,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_819_064,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_820_065,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_821_066,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_822_067,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_823_068,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_824_069,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_825_070,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_826,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
inference(equality_inference,[],[426]) ).
cnf(i_0_827,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[578]) ).
cnf(i_0_828,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[585]) ).
cnf(i_0_829,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[586]) ).
cnf(i_0_830,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[587]) ).
cnf(i_0_831,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[588]) ).
cnf(i_0_832,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[589]) ).
cnf(i_0_833,plain,
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(equality_inference,[],[713]) ).
cnf(i_0_834,plain,
( X1 = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(equality_inference,[],[714]) ).
cnf(i_0_835,plain,
X1 = X1,
inference(equality_inference,[],[723]) ).
cnf(i_0_836,plain,
X1 = X1,
inference(equality_inference,[],[728]) ).
cnf(i_0_837,plain,
c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_715,i_0_598]) ).
cnf(i_0_838,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_839,plain,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(rename_variables,[],[i_0_598]) ).
cnf(i_0_840,plain,
c_lessequals(v_x____,v_Y____,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_715,i_0_716,i_0_598,i_0_653]) ).
cnf(i_0_841,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(rename_variables,[],[i_0_653]) ).
cnf(i_0_842,plain,
c_lessequals(v_Y____,v_xa,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_715,i_0_716,i_0_598,i_0_653,i_0_674]) ).
cnf(i_0_843,plain,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
inference(rename_variables,[],[i_0_674]) ).
cnf(i_0_844,plain,
c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_716,i_0_598,i_0_653,i_0_674,i_0_681]) ).
cnf(i_0_845,plain,
( ~ hBOOL(hAPP(v_P,X1))
| c_HOL_Oord__class_Oless(X1,v_Y____,tc_RealDef_Oreal) ),
inference(rename_variables,[],[i_0_681]) ).
cnf(i_0_846,plain,
c_lessequals(v_xa,v_L____,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_716,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682]) ).
cnf(i_0_847,plain,
( ~ hBOOL(hAPP(v_P,X1))
| c_lessequals(X1,v_L____,tc_RealDef_Oreal) ),
inference(rename_variables,[],[i_0_682]) ).
cnf(i_0_848,plain,
c_Transcendental_Oexp(X1,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_716,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757]) ).
cnf(i_0_849,plain,
c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_747,i_0_716,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484]) ).
cnf(i_0_850,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_851,plain,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3)
| c_lessequals(X1,X4,X3) ),
inference(rename_variables,[],[i_0_484]) ).
cnf(i_0_852,plain,
c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_747,i_0_716,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486]) ).
cnf(i_0_853,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_854,plain,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X4,X3) ),
inference(rename_variables,[],[i_0_486]) ).
cnf(i_0_855,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_747,i_0_716,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488]) ).
cnf(i_0_856,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_857,plain,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X1,X4,X3) ),
inference(rename_variables,[],[i_0_488]) ).
cnf(i_0_858,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_747,i_0_716,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490]) ).
cnf(i_0_859,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_860,plain,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X2,X4,X3) ),
inference(rename_variables,[],[i_0_490]) ).
cnf(i_0_861,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_747,i_0_716,i_0_743,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494]) ).
cnf(i_0_862,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_863,plain,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X1,X2,X4) ),
inference(rename_variables,[],[i_0_494]) ).
cnf(i_0_864,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_747,i_0_716,i_0_743,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496]) ).
cnf(i_0_865,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_866,plain,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X1,X3,X4) ),
inference(rename_variables,[],[i_0_496]) ).
cnf(i_0_867,plain,
c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_747,i_0_716,i_0_743,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498]) ).
cnf(i_0_868,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_869,plain,
( ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4)
| c_lessequals(X1,X2,X4) ),
inference(rename_variables,[],[i_0_498]) ).
cnf(i_0_870,plain,
c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_747,i_0_716,i_0_743,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500]) ).
cnf(i_0_871,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_872,plain,
( ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4)
| c_lessequals(X1,X3,X4) ),
inference(rename_variables,[],[i_0_500]) ).
cnf(i_0_873,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(v_xa,tc_RealDef_Oreal),v_Y____,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_747,i_0_716,i_0_743,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557]) ).
cnf(i_0_874,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal) ),
inference(rename_variables,[],[i_0_557]) ).
cnf(i_0_875,plain,
c_lessequals(X1,c_Orderings_Oord__class_Omax(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_747,i_0_716,i_0_743,i_0_746,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577]) ).
cnf(i_0_876,plain,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_lessequals(X1,X3,X2) ),
inference(rename_variables,[],[i_0_577]) ).
cnf(i_0_877,plain,
c_HOL_Oord__class_Oless(v_Y____,v_xa,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_747,i_0_716,i_0_743,i_0_746,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662]) ).
cnf(i_0_878,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(rename_variables,[],[i_0_662]) ).
cnf(i_0_879,plain,
c_lessequals(v_Y____,c_HOL_Oabs__class_Oabs(v_xa,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_747,i_0_716,i_0_743,i_0_746,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663]) ).
cnf(i_0_880,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3) ),
inference(rename_variables,[],[i_0_663]) ).
cnf(i_0_881,plain,
v_Y____ != v_xa,
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_747,i_0_716,i_0_743,i_0_746,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788]) ).
cnf(i_0_882,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_883,plain,
v_xa != v_Y____,
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_747,i_0_716,i_0_743,i_0_746,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789]) ).
cnf(i_0_884,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_885,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_747,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562]) ).
cnf(i_0_886,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_887,plain,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(rename_variables,[],[i_0_562]) ).
cnf(i_0_888,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_747,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563]) ).
cnf(i_0_889,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_890,plain,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(rename_variables,[],[i_0_563]) ).
cnf(i_0_891,plain,
c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_747,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567]) ).
cnf(i_0_892,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_715]) ).
cnf(i_0_893,plain,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(rename_variables,[],[i_0_567]) ).
cnf(i_0_894,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(v_xa,tc_RealDef_Oreal),v_xa,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_747,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593]) ).
cnf(i_0_895,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(rename_variables,[],[i_0_593]) ).
cnf(i_0_896,plain,
~ c_lessequals(v_Y____,v_x____,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_747,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597]) ).
cnf(i_0_897,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(rename_variables,[],[i_0_597]) ).
cnf(i_0_898,plain,
X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_747,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599]) ).
cnf(i_0_899,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| X2 = X1 ),
inference(rename_variables,[],[i_0_599]) ).
cnf(i_0_900,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792]) ).
cnf(i_0_901,plain,
class_Orderings_Olinorder(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818]) ).
cnf(i_0_902,plain,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508]) ).
cnf(i_0_903,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_691]) ).
cnf(i_0_904,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(rename_variables,[],[i_0_508]) ).
cnf(i_0_905,plain,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_903,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508,i_0_510]) ).
cnf(i_0_906,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_691]) ).
cnf(i_0_907,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(rename_variables,[],[i_0_510]) ).
cnf(i_0_908,plain,
~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_903,i_0_906,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508,i_0_510,i_0_511]) ).
cnf(i_0_909,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_691]) ).
cnf(i_0_910,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(rename_variables,[],[i_0_511]) ).
cnf(i_0_911,plain,
~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_903,i_0_906,i_0_909,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508,i_0_510,i_0_511,i_0_512]) ).
cnf(i_0_912,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_691]) ).
cnf(i_0_913,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(rename_variables,[],[i_0_512]) ).
cnf(i_0_914,plain,
~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_903,i_0_906,i_0_909,i_0_912,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508,i_0_510,i_0_511,i_0_512,i_0_520]) ).
cnf(i_0_915,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_691]) ).
cnf(i_0_916,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_520]) ).
cnf(i_0_917,plain,
~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_903,i_0_906,i_0_909,i_0_912,i_0_915,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508,i_0_510,i_0_511,i_0_512,i_0_520,i_0_522]) ).
cnf(i_0_918,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_691]) ).
cnf(i_0_919,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_920,plain,
~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_903,i_0_906,i_0_909,i_0_912,i_0_915,i_0_918,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508,i_0_510,i_0_511,i_0_512,i_0_520,i_0_522,i_0_523]) ).
cnf(i_0_921,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_691]) ).
cnf(i_0_922,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4)
| ~ c_HOL_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_523]) ).
cnf(i_0_923,plain,
~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_903,i_0_906,i_0_909,i_0_912,i_0_915,i_0_918,i_0_921,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508,i_0_510,i_0_511,i_0_512,i_0_520,i_0_522,i_0_523,i_0_524]) ).
cnf(i_0_924,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_691]) ).
cnf(i_0_925,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4)
| ~ c_HOL_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_524]) ).
cnf(i_0_926,plain,
~ c_HOL_Oord__class_Oless(v_Y____,v_x____,tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_903,i_0_906,i_0_909,i_0_912,i_0_915,i_0_918,i_0_921,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508,i_0_510,i_0_511,i_0_512,i_0_520,i_0_522,i_0_523,i_0_524,i_0_590]) ).
cnf(i_0_927,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(rename_variables,[],[i_0_590]) ).
cnf(i_0_928,plain,
$false,
inference(scs_inference,[],[i_0_692,i_0_726,i_0_715,i_0_838,i_0_850,i_0_853,i_0_856,i_0_859,i_0_862,i_0_865,i_0_868,i_0_871,i_0_882,i_0_884,i_0_886,i_0_889,i_0_734,i_0_747,i_0_691,i_0_903,i_0_906,i_0_909,i_0_912,i_0_915,i_0_918,i_0_921,i_0_716,i_0_742,i_0_743,i_0_746,i_0_752,i_0_753,i_0_754,i_0_722,i_0_598,i_0_653,i_0_674,i_0_681,i_0_682,i_0_757,i_0_484,i_0_486,i_0_488,i_0_490,i_0_494,i_0_496,i_0_498,i_0_500,i_0_557,i_0_577,i_0_662,i_0_663,i_0_788,i_0_789,i_0_562,i_0_563,i_0_567,i_0_593,i_0_597,i_0_599,i_0_792,i_0_818,i_0_508,i_0_510,i_0_511,i_0_512,i_0_520,i_0_522,i_0_523,i_0_524,i_0_590,i_0_594]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : ALG350-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.08/0.26 % Computer : n024.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Tue May 5 05:32:26 EDT 2026
% 0.08/0.26 % CPUTime :
% 0.08/0.27 % start to proof: theBenchmark
% 0.27/1.54 % Version : CSE_E---1.7
% 0.27/1.54 % Problem : theBenchmark.p
% 0.27/1.54 % SZS status Unsatisfiable for theBenchmark.p
% 0.27/1.54 % SZS output start CNFRefutation
% See solution above
% 0.65/1.95 % Total time : 1.268s
%------------------------------------------------------------------------------