TSTP Solution File: LCL748-1 by Etableau---0.67
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- Process Solution
%------------------------------------------------------------------------------
% File : Etableau---0.67
% Problem : LCL748-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 10:24:58 EDT 2022
% Result : Unsatisfiable 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL748-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 07:10:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.39 # No SInE strategy applied
% 0.12/0.39 # Auto-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y
% 0.12/0.39 # and selection function SelectMaxLComplexAvoidPosPred.
% 0.12/0.39 #
% 0.12/0.39 # Presaturation interreduction done
% 0.12/0.39 # Number of axioms: 368 Number of unprocessed: 281
% 0.12/0.39 # Tableaux proof search.
% 0.12/0.39 # APR header successfully linked.
% 0.12/0.39 # Hello from C++
% 0.18/0.49 # The folding up rule is enabled...
% 0.18/0.49 # Local unification is enabled...
% 0.18/0.49 # Any saturation attempts will use folding labels...
% 0.18/0.49 # 281 beginning clauses after preprocessing and clausification
% 0.18/0.49 # Creating start rules for all 3 conjectures.
% 0.18/0.49 # There are 3 start rule candidates:
% 0.18/0.49 # Found 71 unit axioms.
% 0.18/0.49 # Unsuccessfully attempted saturation on 1 start tableaux, moving on.
% 0.18/0.49 # 3 start rule tableaux created.
% 0.18/0.49 # 210 extension rule candidate clauses
% 0.18/0.49 # 71 unit axiom clauses
% 0.18/0.49
% 0.18/0.49 # Requested 8, 32 cores available to the main process.
% 0.18/0.49 # There are not enough tableaux to fork, creating more from the initial 3
% 0.18/0.50 # There were 1 total branch saturation attempts.
% 0.18/0.50 # There were 0 of these attempts blocked.
% 0.18/0.50 # There were 0 deferred branch saturation attempts.
% 0.18/0.50 # There were 0 free duplicated saturations.
% 0.18/0.50 # There were 1 total successful branch saturations.
% 0.18/0.50 # There were 0 successful branch saturations in interreduction.
% 0.18/0.50 # There were 0 successful branch saturations on the branch.
% 0.18/0.50 # There were 1 successful branch saturations after the branch.
% 0.18/0.50 # SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.50 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.50 # Begin clausification derivation
% 0.18/0.50
% 0.18/0.50 # End clausification derivation
% 0.18/0.50 # Begin listing active clauses obtained from FOF to CNF conversion
% 0.18/0.50 cnf(i_0_713, negated_conjecture, (c_InductTermi_OIT(v_r))).
% 0.18/0.50 cnf(i_0_714, negated_conjecture, (c_InductTermi_OIT(c_Lambda_Olift(v_r,X1)))).
% 0.18/0.50 cnf(i_0_725, plain, (class_Ring__and__Field_Ocomm__semiring__1(tc_nat))).
% 0.18/0.50 cnf(i_0_731, plain, (class_Ring__and__Field_Ozero__neq__one(tc_nat))).
% 0.18/0.50 cnf(i_0_724, plain, (class_Ring__and__Field_Oordered__semidom(tc_nat))).
% 0.18/0.50 cnf(i_0_719, plain, (class_Ring__and__Field_Oordered__semiring__strict(tc_nat))).
% 0.18/0.50 cnf(i_0_723, plain, (class_Ring__and__Field_Ono__zero__divisors(tc_nat))).
% 0.18/0.50 cnf(i_0_737, plain, (class_Nat_Osemiring__char__0(tc_nat))).
% 0.18/0.50 cnf(i_0_727, plain, (class_OrderedGroup_Ocomm__monoid__mult(tc_nat))).
% 0.18/0.50 cnf(i_0_734, plain, (class_OrderedGroup_Omonoid__mult(tc_nat))).
% 0.18/0.50 cnf(i_0_733, plain, (class_Ring__and__Field_Omult__zero(tc_nat))).
% 0.18/0.50 cnf(i_0_740, plain, (class_Orderings_Oorder(tc_nat))).
% 0.18/0.50 cnf(i_0_739, plain, (class_Orderings_Olinorder(tc_nat))).
% 0.18/0.50 cnf(i_0_738, plain, (class_Orderings_Opreorder(tc_nat))).
% 0.18/0.50 cnf(i_0_720, plain, (class_OrderedGroup_Opordered__comm__monoid__add(tc_nat))).
% 0.18/0.50 cnf(i_0_716, plain, (class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat))).
% 0.18/0.50 cnf(i_0_717, plain, (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat))).
% 0.18/0.50 cnf(i_0_726, plain, (class_OrderedGroup_Oab__semigroup__mult(tc_nat))).
% 0.18/0.50 cnf(i_0_729, plain, (class_Ring__and__Field_Ocomm__semiring(tc_nat))).
% 0.18/0.50 cnf(i_0_732, plain, (class_Ring__and__Field_Osemiring__1(tc_nat))).
% 0.18/0.50 cnf(i_0_735, plain, (class_Ring__and__Field_Osemiring(tc_nat))).
% 0.18/0.50 cnf(i_0_718, plain, (class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat))).
% 0.18/0.50 cnf(i_0_730, plain, (class_OrderedGroup_Ocomm__monoid__add(tc_nat))).
% 0.18/0.50 cnf(i_0_736, plain, (class_OrderedGroup_Omonoid__add(tc_nat))).
% 0.18/0.50 cnf(i_0_722, plain, (class_OrderedGroup_Ocancel__semigroup__add(tc_nat))).
% 0.18/0.50 cnf(i_0_721, plain, (class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat))).
% 0.18/0.50 cnf(i_0_728, plain, (class_OrderedGroup_Oab__semigroup__add(tc_nat))).
% 0.18/0.50 cnf(i_0_410, plain, (c_HOL_Ominus__class_Ominus(X1,X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))).
% 0.18/0.50 cnf(i_0_620, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=X1)).
% 0.18/0.50 cnf(i_0_409, plain, (c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=X1)).
% 0.18/0.50 cnf(i_0_621, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)=X1)).
% 0.18/0.50 cnf(i_0_485, plain, (c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2)=X1)).
% 0.18/0.50 cnf(i_0_698, plain, (c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1)=X2)).
% 0.18/0.50 cnf(i_0_710, plain, (c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2)=X1)).
% 0.18/0.50 cnf(i_0_571, plain, (c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))).
% 0.18/0.50 cnf(i_0_631, plain, (c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat)=X1)).
% 0.18/0.50 cnf(i_0_632, plain, (c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat)=X2)).
% 0.18/0.50 cnf(i_0_702, plain, (c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))=c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X2))).
% 0.18/0.50 cnf(i_0_562, plain, (c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))).
% 0.18/0.50 cnf(i_0_477, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_708, plain, (c_Lambda_OdB_OApp(c_Lambda_Olift(X1,X2),c_Lambda_Olift(X3,X2))=c_Lambda_Olift(c_Lambda_OdB_OApp(X1,X3),X2))).
% 0.18/0.50 cnf(i_0_574, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_688, plain, (c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X1),X2),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))))).
% 0.18/0.50 cnf(i_0_394, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_408, plain, (c_Lambda_Olift(c_Lambda_Oliftn(X1,X2,X3),X3)=c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,X3))).
% 0.18/0.50 cnf(i_0_689, plain, (c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))=c_Lambda_Oliftn(X1,c_Lambda_OdB_OAbs(X2),X3))).
% 0.18/0.50 cnf(i_0_555, plain, (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_563, plain, (c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)=c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_671, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)=c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_572, plain, (c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(X1,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_573, plain, (c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_594, plain, (c_Lambda_OdB_OApp(c_Lambda_Oliftn(X1,X2,X3),c_Lambda_Oliftn(X1,X4,X3))=c_Lambda_Oliftn(X1,c_Lambda_OdB_OApp(X2,X4),X3))).
% 0.18/0.50 cnf(i_0_700, plain, (c_Lambda_OdB_OApp(c_Lambda_Osubst(X1,X2,X3),c_Lambda_Osubst(X4,X2,X3))=c_Lambda_Osubst(c_Lambda_OdB_OApp(X1,X4),X2,X3))).
% 0.18/0.50 cnf(i_0_651, plain, (c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))=c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3))).
% 0.18/0.50 cnf(i_0_587, plain, (c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_679, plain, (c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))=c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),c_Lambda_Oliftn(X2,X3,c_HOL_Ozero__class_Ozero(tc_nat)),X2))).
% 0.18/0.50 cnf(i_0_428, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_429, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_682, plain, (c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)=c_HOL_Oplus__class_Oplus(X2,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_672, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_715, negated_conjecture, (~c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)))).
% 0.18/0.50 cnf(i_0_692, plain, (~c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2))).
% 0.18/0.50 cnf(i_0_452, plain, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_707, plain, (c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OVar(X2))).
% 0.18/0.50 cnf(i_0_705, plain, (c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OApp(X2,X3))).
% 0.18/0.50 cnf(i_0_559, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_685, plain, (c_Lambda_OdB_OVar(X1)!=c_Lambda_OdB_OApp(X2,X3))).
% 0.18/0.50 cnf(i_0_500, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)!=X1)).
% 0.18/0.50 cnf(i_0_434, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat))).
% 0.18/0.50 cnf(i_0_493, plain, (~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat))).
% 0.18/0.50 cnf(i_0_492, plain, (~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat))).
% 0.18/0.50 cnf(i_0_709, plain, (c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))|~c_InductTermi_OIT(X1))).
% 0.18/0.50 cnf(i_0_381, plain, (c_HOL_Oone__class_Oone(X1)!=c_HOL_Ozero__class_Ozero(X1)|~class_Ring__and__Field_Ozero__neq__one(X1))).
% 0.18/0.50 cnf(i_0_706, plain, (X1=X2|c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OAbs(X2))).
% 0.18/0.50 cnf(i_0_699, plain, (X1=X2|c_Lambda_OdB_OVar(X1)!=c_Lambda_OdB_OVar(X2))).
% 0.18/0.50 cnf(i_0_454, plain, (~class_Orderings_Oorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1))).
% 0.18/0.50 cnf(i_0_577, plain, (c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1)=c_HOL_Ozero__class_Ozero(X1)|~class_Ring__and__Field_Osemiring__1(X1))).
% 0.18/0.50 cnf(i_0_455, plain, (~class_Orderings_Olinorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1))).
% 0.18/0.50 cnf(i_0_456, plain, (~class_Orderings_Opreorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1))).
% 0.18/0.50 cnf(i_0_712, plain, (c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))|~c_Lambda_Obeta(X1,X2))).
% 0.18/0.50 cnf(i_0_660, plain, (c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1)=c_HOL_Oone__class_Oone(X1)|~class_Ring__and__Field_Osemiring__1(X1))).
% 0.18/0.50 cnf(i_0_382, plain, (~class_Ring__and__Field_Oordered__semidom(X1)|~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1))).
% 0.18/0.50 cnf(i_0_591, plain, (~class_Ring__and__Field_Oordered__semidom(X1)|~c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1))).
% 0.18/0.50 cnf(i_0_583, plain, (~class_Ring__and__Field_Oordered__ring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1))).
% 0.18/0.50 cnf(i_0_416, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)!=X2)).
% 0.18/0.50 cnf(i_0_643, plain, (c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))=X2|~c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2))).
% 0.18/0.50 cnf(i_0_690, plain, (X1=X2|c_Lambda_OdB_OApp(X3,X1)!=c_Lambda_OdB_OApp(X4,X2))).
% 0.18/0.50 cnf(i_0_691, plain, (X1=X2|c_Lambda_OdB_OApp(X1,X3)!=c_Lambda_OdB_OApp(X2,X4))).
% 0.18/0.50 cnf(i_0_538, plain, (~class_Orderings_Oorder(X1)|~c_HOL_Oord__class_Oless(X2,X3,X1)|~c_HOL_Oord__class_Oless(X3,X2,X1))).
% 0.18/0.50 cnf(i_0_539, plain, (~class_Orderings_Olinorder(X1)|~c_HOL_Oord__class_Oless(X2,X3,X1)|~c_HOL_Oord__class_Oless(X3,X2,X1))).
% 0.18/0.50 cnf(i_0_540, plain, (~class_Orderings_Opreorder(X1)|~c_HOL_Oord__class_Oless(X2,X3,X1)|~c_HOL_Oord__class_Oless(X3,X2,X1))).
% 0.18/0.50 cnf(i_0_406, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat))).
% 0.18/0.50 cnf(i_0_407, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat))).
% 0.18/0.50 cnf(i_0_511, plain, (c_HOL_Otimes__class_Otimes(X1,X1,X2)=X1|~class_OrderedGroup_Oab__semigroup__idem__mult(X2))).
% 0.18/0.50 cnf(i_0_419, plain, (X1=X2|c_Nat_Osemiring__1__class_Oof__nat(X1,X3)!=c_Nat_Osemiring__1__class_Oof__nat(X2,X3)|~class_Nat_Osemiring__char__0(X3))).
% 0.18/0.50 cnf(i_0_601, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X2,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_580, plain, (X1=X2|c_HOL_Ominus__class_Ominus(X1,X2,X3)!=c_HOL_Ozero__class_Ozero(X3)|~class_OrderedGroup_Ogroup__add(X3))).
% 0.18/0.50 cnf(i_0_581, plain, (X1=X2|c_HOL_Ominus__class_Ominus(X1,X2,X3)!=c_HOL_Ozero__class_Ozero(X3)|~class_OrderedGroup_Oab__group__add(X3))).
% 0.18/0.50 cnf(i_0_656, plain, (X1=X2|c_HOL_Oplus__class_Oplus(X3,X1,tc_nat)!=c_HOL_Oplus__class_Oplus(X3,X2,tc_nat))).
% 0.18/0.50 cnf(i_0_543, plain, (c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2)=X1|~class_Ring__and__Field_Ocomm__semiring__1(X2))).
% 0.18/0.50 cnf(i_0_646, plain, (c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2)=c_Lambda_OdB_OVar(X1)|~c_HOL_Oord__class_Oless(X1,X2,tc_nat))).
% 0.18/0.50 cnf(i_0_694, plain, (c_Lambda_Obeta(X1,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))|~c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2))).
% 0.18/0.50 cnf(i_0_439, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1)=X2|~class_Ring__and__Field_Ocomm__semiring__1(X1))).
% 0.18/0.50 cnf(i_0_484, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat))).
% 0.18/0.50 cnf(i_0_657, plain, (X1=X2|c_HOL_Oplus__class_Oplus(X1,X3,tc_nat)!=c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_405, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|c_HOL_Oplus__class_Oplus(X1,X1,X2)!=c_HOL_Ozero__class_Ozero(X2)|~class_OrderedGroup_Olordered__ab__group__add(X2))).
% 0.18/0.50 cnf(i_0_579, plain, (X1=X2|c_HOL_Ominus__class_Ominus(X1,X2,X3)!=c_HOL_Ozero__class_Ozero(X3)|~class_Int_Onumber__ring(X3)|~class_Ring__and__Field_Oidom(X3))).
% 0.18/0.50 cnf(i_0_711, plain, (c_Lambda_Obeta(c_Lambda_Olift(X1,X2),c_Lambda_Olift(X3,X2))|~c_Lambda_Obeta(X1,X3))).
% 0.18/0.50 cnf(i_0_412, plain, (c_HOL_Ominus__class_Ominus(X1,X1,X2)=c_HOL_Ozero__class_Ozero(X2)|~class_OrderedGroup_Ogroup__add(X2))).
% 0.18/0.50 cnf(i_0_415, plain, (c_HOL_Ominus__class_Ominus(X1,X1,X2)=c_HOL_Ozero__class_Ozero(X2)|~class_OrderedGroup_Oab__group__add(X2))).
% 0.18/0.50 cnf(i_0_542, plain, (c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2)=X1|~class_OrderedGroup_Omonoid__mult(X2))).
% 0.18/0.50 cnf(i_0_425, plain, (c_HOL_Oord__class_Oless(X1,X2,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat))).
% 0.18/0.50 cnf(i_0_418, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|c_HOL_Oplus__class_Oplus(X3,X1,X2)!=X3|~class_Int_Onumber__ring(X2)|~class_Ring__and__Field_Oidom(X2))).
% 0.18/0.50 cnf(i_0_512, plain, (c_HOL_Oord__class_Oless(X1,X2,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_413, plain, (c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2)=X1|~class_OrderedGroup_Ogroup__add(X2))).
% 0.18/0.50 cnf(i_0_627, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2)=X1|~class_Ring__and__Field_Ocomm__semiring__1(X2))).
% 0.18/0.50 cnf(i_0_624, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2)=X1|~class_OrderedGroup_Ocomm__monoid__add(X2))).
% 0.18/0.50 cnf(i_0_626, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2)=X1|~class_OrderedGroup_Omonoid__add(X2))).
% 0.18/0.50 cnf(i_0_440, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1)=X2|~class_OrderedGroup_Ocomm__monoid__mult(X1))).
% 0.18/0.50 cnf(i_0_443, plain, (c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2)=c_HOL_Ozero__class_Ozero(X2)|~class_Ring__and__Field_Ocomm__semiring__1(X2))).
% 0.18/0.50 cnf(i_0_548, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|~c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_565, plain, (X1=X2|c_HOL_Ominus__class_Ominus(X3,X3,X4)!=c_HOL_Ominus__class_Ominus(X1,X2,X4)|~class_OrderedGroup_Oab__group__add(X4))).
% 0.18/0.50 cnf(i_0_442, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1)=c_HOL_Ozero__class_Ozero(X1)|~class_Ring__and__Field_Ocomm__semiring__1(X1))).
% 0.18/0.50 cnf(i_0_441, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1)=X2|~class_OrderedGroup_Omonoid__mult(X1))).
% 0.18/0.50 cnf(i_0_618, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1)=X2|~class_Ring__and__Field_Ocomm__semiring__1(X1))).
% 0.18/0.50 cnf(i_0_619, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1)=X2|~class_OrderedGroup_Ocomm__monoid__add(X1))).
% 0.18/0.50 cnf(i_0_625, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1)=X2|~class_OrderedGroup_Omonoid__add(X1))).
% 0.18/0.50 cnf(i_0_653, plain, (X1=X2|c_HOL_Oplus__class_Oplus(X3,X1,X4)!=c_HOL_Oplus__class_Oplus(X3,X2,X4)|~class_OrderedGroup_Ocancel__semigroup__add(X4))).
% 0.18/0.50 cnf(i_0_654, plain, (X1=X2|c_HOL_Oplus__class_Oplus(X3,X1,X4)!=c_HOL_Oplus__class_Oplus(X3,X2,X4)|~class_OrderedGroup_Ocancel__ab__semigroup__add(X4))).
% 0.18/0.50 cnf(i_0_652, plain, (X1=X2|c_HOL_Oplus__class_Oplus(X1,X3,X4)!=c_HOL_Oplus__class_Oplus(X2,X3,X4)|~class_OrderedGroup_Ocancel__semigroup__add(X4))).
% 0.18/0.50 cnf(i_0_480, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)|~class_Ring__and__Field_Oordered__semidom(X1))).
% 0.18/0.50 cnf(i_0_411, plain, (c_HOL_Ominus__class_Ominus(X1,X1,X2)=c_HOL_Ozero__class_Ozero(X2)|~class_Int_Onumber__ring(X2)|~class_Ring__and__Field_Oidom(X2))).
% 0.18/0.50 cnf(i_0_444, plain, (c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2)=c_HOL_Ozero__class_Ozero(X2)|~class_Ring__and__Field_Oring__no__zero__divisors(X2))).
% 0.18/0.50 cnf(i_0_446, plain, (c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2)=c_HOL_Ozero__class_Ozero(X2)|~class_Ring__and__Field_Omult__zero(X2))).
% 0.18/0.50 cnf(i_0_462, plain, (X1=X2|c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat))).
% 0.18/0.50 cnf(i_0_476, plain, (c_HOL_Oord__class_Oless(X1,X2,tc_nat)|~class_Ring__and__Field_Oordered__semidom(X3)|~c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3))).
% 0.18/0.50 cnf(i_0_445, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1)=c_HOL_Ozero__class_Ozero(X1)|~class_Ring__and__Field_Oring__no__zero__divisors(X1))).
% 0.18/0.50 cnf(i_0_447, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1)=c_HOL_Ozero__class_Ozero(X1)|~class_Ring__and__Field_Omult__zero(X1))).
% 0.18/0.50 cnf(i_0_623, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2)=X1|~class_Int_Onumber__ring(X2)|~class_Ring__and__Field_Oidom(X2))).
% 0.18/0.50 cnf(i_0_593, plain, (c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3)=c_Lambda_OdB_OVar(X2)|~c_HOL_Oord__class_Oless(X2,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_552, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)=c_HOL_Ozero__class_Ozero(X1)|~class_OrderedGroup_Olordered__ab__group__add(X1))).
% 0.18/0.50 cnf(i_0_483, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)|~class_Ring__and__Field_Oordered__semidom(X2)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2))).
% 0.18/0.50 cnf(i_0_655, plain, (X1=X2|c_HOL_Oplus__class_Oplus(X3,X1,X4)!=c_HOL_Oplus__class_Oplus(X3,X2,X4)|~class_Int_Onumber__ring(X4)|~class_Ring__and__Field_Oidom(X4))).
% 0.18/0.50 cnf(i_0_473, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_OrderedGroup_Opordered__ab__group__add(X3)|~c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3))).
% 0.18/0.50 cnf(i_0_508, plain, (c_HOL_Oord__class_Oless(X1,X2,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_697, plain, (c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3)=c_Lambda_OdB_OVar(X1)|~c_HOL_Oord__class_Oless(X1,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_647, plain, (c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X2),c_Lambda_OdB_OApp(X3,X2))|~c_Lambda_Obeta(X1,X3))).
% 0.18/0.50 cnf(i_0_648, plain, (c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X2),c_Lambda_OdB_OApp(X1,X3))|~c_Lambda_Obeta(X2,X3))).
% 0.18/0.50 cnf(i_0_423, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X1,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_461, plain, (X1=X2|c_HOL_Oord__class_Oless(X1,X2,tc_nat)|c_HOL_Oord__class_Oless(X2,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_380, plain, (~class_Ring__and__Field_Oordered__ring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1))).
% 0.18/0.50 cnf(i_0_497, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)|~c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_424, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X1,X2,tc_nat))).
% 0.18/0.50 cnf(i_0_450, plain, (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)|~c_HOL_Oord__class_Oless(X1,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_395, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|X3=c_HOL_Ozero__class_Ozero(X2)|c_HOL_Otimes__class_Otimes(X1,X3,X2)!=c_HOL_Ozero__class_Ozero(X2)|~class_Ring__and__Field_Ono__zero__divisors(X2))).
% 0.18/0.50 cnf(i_0_397, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|X3=c_HOL_Ozero__class_Ozero(X2)|c_HOL_Otimes__class_Otimes(X1,X3,X2)!=c_HOL_Ozero__class_Ozero(X2)|~class_Ring__and__Field_Oring__no__zero__divisors(X2))).
% 0.18/0.50 cnf(i_0_375, plain, (X1=X2|c_HOL_Oord__class_Oless(X2,X1,tc_nat)|~c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_391, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)|~class_Ring__and__Field_Oordered__idom(X2)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2))).
% 0.18/0.50 cnf(i_0_633, plain, (c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3)=X1|~class_OrderedGroup_Ogroup__add(X3))).
% 0.18/0.50 cnf(i_0_549, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3)=X1|~class_OrderedGroup_Ogroup__add(X3))).
% 0.18/0.50 cnf(i_0_551, plain, (c_HOL_Otimes__class_Otimes(X1,X2,X3)=c_HOL_Otimes__class_Otimes(X2,X1,X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_680, plain, (c_HOL_Oplus__class_Oplus(X1,X2,X3)=c_HOL_Oplus__class_Oplus(X2,X1,X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_392, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)|~class_OrderedGroup_Olordered__ab__group__add(X2)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2))).
% 0.18/0.50 cnf(i_0_640, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|~class_OrderedGroup_Olordered__ab__group__add(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1))).
% 0.18/0.50 cnf(i_0_636, plain, (c_HOL_Oord__class_Oless(X1,X2,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_506, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3))).
% 0.18/0.50 cnf(i_0_681, plain, (c_HOL_Oplus__class_Oplus(X1,X2,X3)=c_HOL_Oplus__class_Oplus(X2,X1,X3)|~class_OrderedGroup_Ocomm__monoid__add(X3))).
% 0.18/0.50 cnf(i_0_693, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)|~class_Ring__and__Field_Oordered__semidom(X2))).
% 0.18/0.50 cnf(i_0_662, plain, (c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2)=c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))|c_HOL_Oord__class_Oless(X1,X2,tc_nat))).
% 0.18/0.50 cnf(i_0_513, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X2,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_459, plain, (X1=X2|c_HOL_Oord__class_Oless(X1,X2,X3)|c_HOL_Oord__class_Oless(X2,X1,X3)|~class_Ring__and__Field_Oordered__idom(X3))).
% 0.18/0.50 cnf(i_0_503, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3))).
% 0.18/0.50 cnf(i_0_495, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2)!=c_HOL_Ozero__class_Ozero(X2)|~class_Ring__and__Field_Oordered__ring__strict(X2))).
% 0.18/0.50 cnf(i_0_496, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2)!=c_HOL_Ozero__class_Ozero(X2)|~class_Ring__and__Field_Oordered__ring__strict(X2))).
% 0.18/0.50 cnf(i_0_557, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X3)|~c_HOL_Oord__class_Oless(X4,X2,X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))).
% 0.18/0.50 cnf(i_0_675, plain, (c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3)=c_Lambda_OdB_OVar(X1)|X1=X3|c_HOL_Oord__class_Oless(X3,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_498, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat))).
% 0.18/0.50 cnf(i_0_482, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)|~class_Ring__and__Field_Oordered__semidom(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))).
% 0.18/0.50 cnf(i_0_460, plain, (X1=X2|c_HOL_Oord__class_Oless(X1,X2,X3)|c_HOL_Oord__class_Oless(X2,X1,X3)|~class_Orderings_Olinorder(X3))).
% 0.18/0.50 cnf(i_0_525, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)=X2|c_HOL_Oord__class_Oless(X2,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_556, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Opreorder(X3)|~c_HOL_Oord__class_Oless(X4,X2,X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))).
% 0.18/0.50 cnf(i_0_523, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|c_HOL_Ominus__class_Ominus(X4,X5,X3)!=c_HOL_Ominus__class_Ominus(X1,X2,X3)|~class_OrderedGroup_Opordered__ab__group__add(X3)|~c_HOL_Oord__class_Oless(X4,X5,X3))).
% 0.18/0.50 cnf(i_0_676, plain, (c_Lambda_Obeta(c_Lambda_Osubst(X1,X2,X3),c_Lambda_Osubst(X4,X2,X3))|~c_Lambda_Obeta(X1,X4))).
% 0.18/0.50 cnf(i_0_528, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|X2=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat))).
% 0.18/0.50 cnf(i_0_602, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)|c_HOL_Oord__class_Oless(X2,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_629, plain, (~class_Ring__and__Field_Oordered__ring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1))).
% 0.18/0.50 cnf(i_0_475, plain, (c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)|~class_Ring__and__Field_Oordered__semidom(X2)|~c_HOL_Oord__class_Oless(X1,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_386, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|~class_Ring__and__Field_Oordered__semiring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1))).
% 0.18/0.50 cnf(i_0_387, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|~class_Ring__and__Field_Oordered__semiring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1))).
% 0.18/0.50 cnf(i_0_457, plain, (c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3)=c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat))|c_HOL_Oord__class_Oless(X2,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_616, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)|~class_Ring__and__Field_Oordered__semidom(X1))).
% 0.18/0.50 cnf(i_0_569, plain, (c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)|~class_Ring__and__Field_Osemiring__1(X2))).
% 0.18/0.50 cnf(i_0_603, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Ring__and__Field_Oordered__ring__strict(X3)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)|~c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3))).
% 0.18/0.50 cnf(i_0_605, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Ring__and__Field_Oordered__ring__strict(X3)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3))).
% 0.18/0.50 cnf(i_0_421, plain, (c_HOL_Oord__class_Oless(X1,X2,tc_nat)|c_HOL_Oplus__class_Oplus(X1,X3,tc_nat)!=c_HOL_Oplus__class_Oplus(X4,X2,tc_nat)|~c_HOL_Oord__class_Oless(X4,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_474, plain, (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)|~class_OrderedGroup_Opordered__ab__group__add(X3)|~c_HOL_Oord__class_Oless(X1,X2,X3))).
% 0.18/0.50 cnf(i_0_481, plain, (c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)=c_HOL_Otimes__class_Otimes(X1,X2,X3)|~class_OrderedGroup_Oab__semigroup__idem__mult(X3))).
% 0.18/0.50 cnf(i_0_522, plain, (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat))).
% 0.18/0.50 cnf(i_0_663, plain, (c_HOL_Oplus__class_Oplus(X1,X2,X3)=X4|c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3)!=c_HOL_Oplus__class_Oplus(X5,X4,X3)|~class_OrderedGroup_Oab__group__add(X3))).
% 0.18/0.50 cnf(i_0_641, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)|~class_OrderedGroup_Olordered__ab__group__add(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1))).
% 0.18/0.50 cnf(i_0_390, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)|~class_Ring__and__Field_Oordered__idom(X2)|~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2))).
% 0.18/0.50 cnf(i_0_393, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)|~class_OrderedGroup_Olordered__ab__group__add(X2)|~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2))).
% 0.18/0.50 cnf(i_0_507, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X1,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_509, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X2,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_468, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)=X1|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat))).
% 0.18/0.50 cnf(i_0_558, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_491, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)|~class_Ring__and__Field_Oordered__semidom(X4)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)|~c_HOL_Oord__class_Oless(X1,X3,X4))).
% 0.18/0.50 cnf(i_0_596, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|c_HOL_Oord__class_Oless(X2,X1,X3)|~class_Ring__and__Field_Oordered__ring__strict(X3)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3))).
% 0.18/0.50 cnf(i_0_598, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|c_HOL_Oord__class_Oless(X2,X1,X3)|~class_Ring__and__Field_Oordered__ring__strict(X3)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3))).
% 0.18/0.50 cnf(i_0_532, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)=c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_667, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)=c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_517, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)|c_HOL_Oord__class_Oless(X3,X4,X2)|~class_Ring__and__Field_Oordered__ring__strict(X2)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2))).
% 0.18/0.50 cnf(i_0_519, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)|c_HOL_Oord__class_Oless(X3,X4,X2)|~class_Ring__and__Field_Oordered__ring__strict(X2)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2))).
% 0.18/0.50 cnf(i_0_695, plain, (c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))|~c_HOL_Oord__class_Oless(X3,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_701, plain, (c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)=c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2)|~class_Ring__and__Field_Osemiring__1(X2))).
% 0.18/0.50 cnf(i_0_644, plain, (c_Lambda_Olift(c_Lambda_Olift(X1,X2),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=c_Lambda_Olift(c_Lambda_Olift(X1,X3),X2)|~c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_520, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|c_HOL_Oord__class_Oless(X3,X4,X1)|~class_Ring__and__Field_Oordered__ring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1))).
% 0.18/0.50 cnf(i_0_518, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|c_HOL_Oord__class_Oless(X3,X4,X1)|~class_Ring__and__Field_Oordered__ring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1))).
% 0.18/0.50 cnf(i_0_529, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)=c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)|~class_OrderedGroup_Oab__semigroup__mult(X3))).
% 0.18/0.50 cnf(i_0_670, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)=c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)|~class_OrderedGroup_Ocomm__monoid__add(X3))).
% 0.18/0.50 cnf(i_0_668, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)=c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)|~class_OrderedGroup_Oab__semigroup__add(X3))).
% 0.18/0.50 cnf(i_0_501, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)|~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))).
% 0.18/0.50 cnf(i_0_502, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))).
% 0.18/0.50 cnf(i_0_479, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)|~c_HOL_Oord__class_Oless(X3,X2,tc_nat)|~c_HOL_Oord__class_Oless(X1,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_384, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)|~class_Ring__and__Field_Oordered__ring__strict(X1)|~c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)|~c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1))).
% 0.18/0.50 cnf(i_0_634, plain, (c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)|~class_Ring__and__Field_Oordered__semidom(X1)|~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)|~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1))).
% 0.18/0.50 cnf(i_0_504, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)|~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)|~c_HOL_Oord__class_Oless(X2,X4,X3))).
% 0.18/0.50 cnf(i_0_505, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)|~c_HOL_Oord__class_Oless(X2,X4,X3))).
% 0.18/0.50 cnf(i_0_526, plain, (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat))).
% 0.18/0.50 cnf(i_0_585, plain, (X1=c_HOL_Oone__class_Oone(tc_nat)|X1=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat))).
% 0.18/0.50 cnf(i_0_586, plain, (X1=c_HOL_Oone__class_Oone(tc_nat)|X1=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat))).
% 0.18/0.50 cnf(i_0_385, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)|~class_Ring__and__Field_Oordered__semiring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1))).
% 0.18/0.50 cnf(i_0_458, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)|~class_OrderedGroup_Opordered__comm__monoid__add(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1))).
% 0.18/0.50 cnf(i_0_578, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)|~class_OrderedGroup_Opordered__comm__monoid__add(X3)|~c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)|~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3))).
% 0.18/0.50 cnf(i_0_488, plain, (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)|~class_Ring__and__Field_Oordered__semiring__strict(X3)|~c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3))).
% 0.18/0.50 cnf(i_0_420, plain, (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X3,X2,tc_nat)|~c_HOL_Oord__class_Oless(X3,X1,tc_nat))).
% 0.18/0.50 cnf(i_0_470, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X2,X4,tc_nat)|~c_HOL_Oord__class_Oless(X1,X3,tc_nat))).
% 0.18/0.50 cnf(i_0_584, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=X2|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)|~c_HOL_Oord__class_Oless(X1,X2,tc_nat))).
% 0.18/0.50 cnf(i_0_684, plain, (c_HOL_Oplus__class_Oplus(X1,X1,X2)=c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)|~class_Ring__and__Field_Ocomm__semiring__1(X2))).
% 0.18/0.50 cnf(i_0_487, plain, (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)|~class_Ring__and__Field_Oordered__semiring__strict(X3)|~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3))).
% 0.18/0.50 cnf(i_0_597, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)|~class_Ring__and__Field_Oordered__ring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1))).
% 0.18/0.50 cnf(i_0_595, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)|~class_Ring__and__Field_Oordered__ring__strict(X1)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1))).
% 0.18/0.50 cnf(i_0_533, plain, (c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)=c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)|~class_Ring__and__Field_Ocomm__semiring__1(X4))).
% 0.18/0.50 cnf(i_0_527, plain, (X1=c_HOL_Oone__class_Oone(tc_nat)|X2=c_HOL_Oone__class_Oone(tc_nat)|c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat))).
% 0.18/0.50 cnf(i_0_665, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)=c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)|~class_Ring__and__Field_Ocomm__semiring__1(X4))).
% 0.18/0.50 cnf(i_0_494, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|X3=X4|c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)!=c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)|~class_Int_Onumber__ring(X2)|~class_Ring__and__Field_Oidom(X2))).
% 0.18/0.50 cnf(i_0_469, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)|~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)|~c_HOL_Oord__class_Oless(X2,X5,X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))).
% 0.18/0.50 cnf(i_0_611, plain, (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)|~class_Ring__and__Field_Oordered__ring__strict(X3)|~c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)|~c_HOL_Oord__class_Oless(X4,X1,X3))).
% 0.18/0.50 cnf(i_0_530, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_666, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_604, plain, (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)|~class_Ring__and__Field_Oordered__ring__strict(X3)|~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)|~c_HOL_Oord__class_Oless(X4,X2,X3))).
% 0.18/0.50 cnf(i_0_613, plain, (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)|~class_Ring__and__Field_Oordered__ring__strict(X3)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))).
% 0.18/0.50 cnf(i_0_606, plain, (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)|~class_Ring__and__Field_Oordered__ring__strict(X3)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)|~c_HOL_Oord__class_Oless(X2,X4,X3))).
% 0.18/0.50 cnf(i_0_612, plain, (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)|~class_Ring__and__Field_Oordered__semiring__strict(X3)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))).
% 0.18/0.50 cnf(i_0_537, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)=c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_673, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)=c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)|~class_OrderedGroup_Oab__group__add(X4))).
% 0.18/0.50 cnf(i_0_669, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)=c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)|~class_OrderedGroup_Ocomm__monoid__add(X4))).
% 0.18/0.50 cnf(i_0_608, plain, (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)|~class_Ring__and__Field_Oordered__semiring__strict(X3)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)|~c_HOL_Oord__class_Oless(X2,X4,X3))).
% 0.18/0.50 cnf(i_0_615, plain, (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)|~class_Ring__and__Field_Oordered__comm__semiring__strict(X3)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)|~c_HOL_Oord__class_Oless(X2,X4,X3))).
% 0.18/0.50 cnf(i_0_516, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1)=c_HOL_Ozero__class_Ozero(X1)|~class_Ring__and__Field_Oordered__ring__strict(X1))).
% 0.18/0.50 cnf(i_0_535, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)=c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_536, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)=c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)|~class_Ring__and__Field_Ocomm__semiring(X3))).
% 0.18/0.50 cnf(i_0_378, plain, (X1=X2|X3=X4|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)|~class_Int_Onumber__ring(X5)|~class_Ring__and__Field_Oidom(X5))).
% 0.18/0.50 cnf(i_0_687, plain, (c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)=c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_686, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3)=c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_449, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)|X1=c_HOL_Ozero__class_Ozero(tc_nat))).
% 0.18/0.50 cnf(i_0_590, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)|~class_Ring__and__Field_Oordered__ring__strict(X2))).
% 0.18/0.50 cnf(i_0_373, plain, (c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_589, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)|~class_Ring__and__Field_Oordered__ring__strict(X2))).
% 0.18/0.50 cnf(i_0_400, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)|~class_Ring__and__Field_Opordered__ring(X4)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4))).
% 0.18/0.50 cnf(i_0_398, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)|~class_Ring__and__Field_Opordered__ring(X3)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3))).
% 0.18/0.50 cnf(i_0_659, plain, (c_Lambda_Osubst(c_Lambda_Olift(X1,X2),c_Lambda_Olift(X3,X2),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=c_Lambda_Olift(c_Lambda_Osubst(X1,X3,X4),X2)|~c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_645, plain, (c_Lambda_Osubst(c_Lambda_Olift(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X3,X2),X4)=c_Lambda_Olift(c_Lambda_Osubst(X1,X3,X4),X2)|~c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 cnf(i_0_649, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)|~class_Ring__and__Field_Ocomm__semiring__1(X3))).
% 0.18/0.50 cnf(i_0_576, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)|~class_Ring__and__Field_Osemiring(X3))).
% 0.18/0.50 cnf(i_0_546, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)|~class_Int_Onumber__ring(X3)|~class_Ring__and__Field_Oidom(X3))).
% 0.18/0.50 cnf(i_0_432, plain, (X1=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)|~class_Ring__and__Field_Oring(X4))).
% 0.18/0.50 cnf(i_0_438, plain, (c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)|~class_Ring__and__Field_Oring(X3))).
% 0.18/0.50 cnf(i_0_401, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)|~class_Ring__and__Field_Opordered__ring(X3)|~c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3))).
% 0.18/0.50 cnf(i_0_399, plain, (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)|~class_Ring__and__Field_Opordered__ring(X3)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3))).
% 0.18/0.50 cnf(i_0_650, plain, (c_Lambda_Osubst(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,X3),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Osubst(X5,X2,X4),X3)=c_Lambda_Osubst(c_Lambda_Osubst(X1,X5,X3),X2,X4)|~c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))).
% 0.18/0.50 # End listing active clauses. There is an equivalent clause to each of these in the clausification!
% 0.18/0.50 # Begin printing tableau
% 0.18/0.50 # Found 4 steps
% 0.18/0.50 cnf(i_0_713, negated_conjecture, (c_InductTermi_OIT(v_r)), inference(start_rule)).
% 0.18/0.50 cnf(i_0_743, plain, (c_InductTermi_OIT(v_r)), inference(extension_rule, [i_0_709])).
% 0.18/0.50 cnf(i_0_1862, plain, (c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_r))), inference(extension_rule, [i_0_709])).
% 0.18/0.50 cnf(i_0_2421, plain, (c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(v_r)))), inference(etableau_closure_rule, [i_0_2421, ...])).
% 0.18/0.50 # End printing tableau
% 0.18/0.50 # SZS output end
% 0.18/0.50 # Branches closed with saturation will be marked with an "s"
% 0.18/0.50 # Returning from population with 2 new_tableaux and 0 remaining starting tableaux.
% 0.18/0.50 # We now have 2 tableaux to operate on
% 0.18/0.50 # Found closed tableau during pool population.
% 0.18/0.50 # Proof search is over...
% 0.18/0.50 # Freeing feature tree
%------------------------------------------------------------------------------