TSTP Solution File: LCL843-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL843-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n010.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 11:40:39 EDT 2022
% Result : Unsatisfiable 0.55s 0.86s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Oorder]) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Olinorder_0,plain,
( class_Orderings_Olinorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Opreorder]) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
input ).
fof(clsarity_nat__Nat_Osemiring__char__0_0,plain,
( class_Nat_Osemiring__char__0(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0]) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Osemiring__1_0,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__semidom_0,plain,
( class_Ring__and__Field_Oordered__semidom(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom]) ).
cnf(cls_dB_Osimps_I5_J_0,axiom,
c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
input ).
fof(cls_dB_Osimps_I5_J_0_0,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I5_J_0]) ).
cnf(cls_Var__IT_0,axiom,
c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)),
input ).
fof(cls_Var__IT_0_0,plain,
! [V_n] :
( c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n))
| $false ),
inference(orientation,[status(thm)],[cls_Var__IT_0]) ).
cnf(cls_dB_Osimps_I6_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
input ).
fof(cls_dB_Osimps_I6_J_0_0,plain,
! [V_dB_H,V_nat] :
( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I6_J_0]) ).
cnf(cls_dB_Osimps_I4_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H),
input ).
fof(cls_dB_Osimps_I4_J_0_0,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I4_J_0]) ).
cnf(cls_beta__cases_I1_J_0,axiom,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t),
input ).
fof(cls_beta__cases_I1_J_0_0,plain,
! [V_i,V_t] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t)
| $false ),
inference(orientation,[status(thm)],[cls_beta__cases_I1_J_0]) ).
cnf(cls_Var_0,axiom,
v_env______(v_x______) = v_Ta______,
input ).
fof(cls_Var_0_0,plain,
( v_env______(v_x______) = v_Ta______
| $false ),
inference(orientation,[status(thm)],[cls_Var_0]) ).
cnf(cls_subst__eq_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u,
input ).
fof(cls_subst__eq_0_0,plain,
! [V_k,V_u] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u
| $false ),
inference(orientation,[status(thm)],[cls_subst__eq_0]) ).
cnf(cls_dB_Osimps_I7_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
input ).
fof(cls_dB_Osimps_I7_J_0_0,plain,
! [V_dB_H,V_nat] :
( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I7_J_0]) ).
cnf(cls_subst__App_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)),
input ).
fof(cls_subst__App_0_0,plain,
! [V_k,V_s,V_t,V_u] :
( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k))
| $false ),
inference(orientation,[status(thm)],[cls_subst__App_0]) ).
cnf(cls_dB_Osimps_I8_J_0,axiom,
c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
input ).
fof(cls_dB_Osimps_I8_J_0_0,plain,
! [V_dB1,V_dB2,V_dB_H] :
( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I8_J_0]) ).
cnf(cls_dB_Osimps_I9_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2),
input ).
fof(cls_dB_Osimps_I9_J_0_0,plain,
! [V_dB1,V_dB2,V_dB_H] :
( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I9_J_0]) ).
cnf(cls_beta_0,axiom,
c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(V_s),V_t),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat))),
input ).
fof(cls_beta_0_0,plain,
! [V_s,V_t] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(V_s),V_t),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat)))
| $false ),
inference(orientation,[status(thm)],[cls_beta_0]) ).
cnf(cls_lift_Osimps_I2_J_0,axiom,
c_Lambda_Olift(c_Lambda_OdB_OApp(V_s,V_t),V_k) = c_Lambda_OdB_OApp(c_Lambda_Olift(V_s,V_k),c_Lambda_Olift(V_t,V_k)),
input ).
fof(cls_lift_Osimps_I2_J_0_0,plain,
! [V_k,V_s,V_t] :
( c_Lambda_Olift(c_Lambda_OdB_OApp(V_s,V_t),V_k) = c_Lambda_OdB_OApp(c_Lambda_Olift(V_s,V_k),c_Lambda_Olift(V_t,V_k))
| $false ),
inference(orientation,[status(thm)],[cls_lift_Osimps_I2_J_0]) ).
cnf(cls_subst__lift_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t,
input ).
fof(cls_subst__lift_0_0,plain,
! [V_k,V_s,V_t] :
( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t
| $false ),
inference(orientation,[status(thm)],[cls_subst__lift_0]) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_not__less0_0_0,plain,
! [V_n] :
( ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_not__less0_0]) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_gr__implies__not0_0_0,plain,
! [V_m] :
( ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_gr__implies__not0_0]) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
input ).
fof(cls_nat__less__le_1_0,plain,
! [V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_nat__less__le_1]) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
input ).
fof(cls_less__not__refl_0_0,plain,
! [V_n] :
( ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_less__not__refl_0]) ).
cnf(cls_neq0__conv_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_neq0__conv_1_0,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_neq0__conv_1]) ).
fof(def_lhs_atom1,axiom,
( lhs_atom1
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
( lhs_atom1
| $false ),
inference(fold_definition,[status(thm)],[cls_neq0__conv_1_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [V_n] :
( lhs_atom2(V_n)
<=> ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [V_n] :
( lhs_atom2(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_less__not__refl_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_x] :
( lhs_atom3(V_x)
<=> ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [V_x] :
( lhs_atom3(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__less__le_1_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [V_m] :
( lhs_atom4(V_m)
<=> ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [V_m] :
( lhs_atom4(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_gr__implies__not0_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [V_n] :
( lhs_atom5(V_n)
<=> ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [V_n] :
( lhs_atom5(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__less0_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_t,V_s,V_k] :
( lhs_atom6(V_t,V_s,V_k)
<=> c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [V_k,V_s,V_t] :
( lhs_atom6(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__lift_0_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_t,V_s,V_k] :
( lhs_atom7(V_t,V_s,V_k)
<=> c_Lambda_Olift(c_Lambda_OdB_OApp(V_s,V_t),V_k) = c_Lambda_OdB_OApp(c_Lambda_Olift(V_s,V_k),c_Lambda_Olift(V_t,V_k)) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [V_k,V_s,V_t] :
( lhs_atom7(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_lift_Osimps_I2_J_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_t,V_s] :
( lhs_atom8(V_t,V_s)
<=> c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(V_s),V_t),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [V_s,V_t] :
( lhs_atom8(V_t,V_s)
| $false ),
inference(fold_definition,[status(thm)],[cls_beta_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom9(V_dB_H,V_dB2,V_dB1)
<=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom9(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I9_J_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom10(V_dB_H,V_dB2,V_dB1)
<=> c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom10(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I8_J_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [V_u,V_t,V_s,V_k] :
( lhs_atom11(V_u,V_t,V_s,V_k)
<=> c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [V_k,V_s,V_t,V_u] :
( lhs_atom11(V_u,V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__App_0_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [V_nat,V_dB_H] :
( lhs_atom12(V_nat,V_dB_H)
<=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [V_dB_H,V_nat] :
( lhs_atom12(V_nat,V_dB_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I7_J_0_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_u,V_k] :
( lhs_atom13(V_u,V_k)
<=> c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [V_k,V_u] :
( lhs_atom13(V_u,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__eq_0_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
( lhs_atom14
<=> v_env______(v_x______) = v_Ta______ ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
( lhs_atom14
| $false ),
inference(fold_definition,[status(thm)],[cls_Var_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_t,V_i] :
( lhs_atom15(V_t,V_i)
<=> ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [V_i,V_t] :
( lhs_atom15(V_t,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_beta__cases_I1_J_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom16(V_nat,V_dB2_H,V_dB1_H)
<=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom16(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I4_J_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V_nat,V_dB_H] :
( lhs_atom17(V_nat,V_dB_H)
<=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [V_dB_H,V_nat] :
( lhs_atom17(V_nat,V_dB_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I6_J_0_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [V_n] :
( lhs_atom18(V_n)
<=> c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
! [V_n] :
( lhs_atom18(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__IT_0_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom19(V_nat,V_dB2_H,V_dB1_H)
<=> c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom19(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I5_J_0_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
( lhs_atom20
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
( lhs_atom20
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
( lhs_atom21
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
( lhs_atom21
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
( lhs_atom22
<=> class_Nat_Osemiring__char__0(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
( lhs_atom22
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
( lhs_atom23
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
( lhs_atom23
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
( lhs_atom24
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
( lhs_atom24
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
( lhs_atom25
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
( lhs_atom25
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom25]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X10,X4,X5,X6] :
( lhs_atom11(X10,X4,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_1,axiom,
! [X11,X13,X14] :
( lhs_atom19(X11,X13,X14)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_2,axiom,
! [X11,X13,X14] :
( lhs_atom16(X11,X13,X14)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_3,axiom,
! [X7,X8,X9] :
( lhs_atom10(X7,X8,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_4,axiom,
! [X7,X8,X9] :
( lhs_atom9(X7,X8,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_5,axiom,
! [X4,X5,X6] :
( lhs_atom7(X4,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_6,axiom,
! [X4,X5,X6] :
( lhs_atom6(X4,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_7,axiom,
! [X11,X7] :
( lhs_atom17(X11,X7)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_8,axiom,
! [X4,X12] :
( lhs_atom15(X4,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_9,axiom,
! [X10,X6] :
( lhs_atom13(X10,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_10,axiom,
! [X11,X7] :
( lhs_atom12(X11,X7)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_11,axiom,
! [X4,X5] :
( lhs_atom8(X4,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_12,axiom,
! [X1] :
( lhs_atom18(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_13,axiom,
! [X1] :
( lhs_atom5(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_14,axiom,
! [X3] :
( lhs_atom4(X3)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_15,axiom,
! [X2] :
( lhs_atom3(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_16,axiom,
! [X1] :
( lhs_atom2(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_17,axiom,
( lhs_atom25
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_18,axiom,
( lhs_atom24
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_19,axiom,
( lhs_atom23
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_20,axiom,
( lhs_atom22
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_21,axiom,
( lhs_atom21
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_22,axiom,
( lhs_atom20
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_23,axiom,
( lhs_atom14
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_24,axiom,
( lhs_atom1
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_25,plain,
! [X10,X4,X5,X6] : lhs_atom11(X10,X4,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_26,plain,
! [X11,X13,X14] : lhs_atom19(X11,X13,X14),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_27,plain,
! [X11,X13,X14] : lhs_atom16(X11,X13,X14),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_28,plain,
! [X7,X8,X9] : lhs_atom10(X7,X8,X9),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_29,plain,
! [X7,X8,X9] : lhs_atom9(X7,X8,X9),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_30,plain,
! [X4,X5,X6] : lhs_atom7(X4,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_31,plain,
! [X4,X5,X6] : lhs_atom6(X4,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_32,plain,
! [X11,X7] : lhs_atom17(X11,X7),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_33,plain,
! [X4,X12] : lhs_atom15(X4,X12),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_34,plain,
! [X10,X6] : lhs_atom13(X10,X6),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_35,plain,
! [X11,X7] : lhs_atom12(X11,X7),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_36,plain,
! [X4,X5] : lhs_atom8(X4,X5),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_37,plain,
! [X1] : lhs_atom18(X1),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_38,plain,
! [X1] : lhs_atom5(X1),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_39,plain,
! [X3] : lhs_atom4(X3),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_40,plain,
! [X2] : lhs_atom3(X2),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_41,plain,
! [X1] : lhs_atom2(X1),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_42,plain,
lhs_atom25,
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_43,plain,
lhs_atom24,
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_44,plain,
lhs_atom23,
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_45,plain,
lhs_atom22,
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_46,plain,
lhs_atom21,
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_47,plain,
lhs_atom20,
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_48,plain,
lhs_atom14,
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_49,plain,
lhs_atom1,
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_50,plain,
! [X11,X12,X13,X14] : lhs_atom11(X11,X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_25]) ).
fof(c_0_51,plain,
! [X15,X16,X17] : lhs_atom19(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_26]) ).
fof(c_0_52,plain,
! [X15,X16,X17] : lhs_atom16(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_27]) ).
fof(c_0_53,plain,
! [X10,X11,X12] : lhs_atom10(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_28]) ).
fof(c_0_54,plain,
! [X10,X11,X12] : lhs_atom9(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_29]) ).
fof(c_0_55,plain,
! [X7,X8,X9] : lhs_atom7(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_30]) ).
fof(c_0_56,plain,
! [X7,X8,X9] : lhs_atom6(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_31]) ).
fof(c_0_57,plain,
! [X12,X13] : lhs_atom17(X12,X13),
inference(variable_rename,[status(thm)],[c_0_32]) ).
fof(c_0_58,plain,
! [X13,X14] : lhs_atom15(X13,X14),
inference(variable_rename,[status(thm)],[c_0_33]) ).
fof(c_0_59,plain,
! [X11,X12] : lhs_atom13(X11,X12),
inference(variable_rename,[status(thm)],[c_0_34]) ).
fof(c_0_60,plain,
! [X12,X13] : lhs_atom12(X12,X13),
inference(variable_rename,[status(thm)],[c_0_35]) ).
fof(c_0_61,plain,
! [X6,X7] : lhs_atom8(X6,X7),
inference(variable_rename,[status(thm)],[c_0_36]) ).
fof(c_0_62,plain,
! [X2] : lhs_atom18(X2),
inference(variable_rename,[status(thm)],[c_0_37]) ).
fof(c_0_63,plain,
! [X2] : lhs_atom5(X2),
inference(variable_rename,[status(thm)],[c_0_38]) ).
fof(c_0_64,plain,
! [X4] : lhs_atom4(X4),
inference(variable_rename,[status(thm)],[c_0_39]) ).
fof(c_0_65,plain,
! [X3] : lhs_atom3(X3),
inference(variable_rename,[status(thm)],[c_0_40]) ).
fof(c_0_66,plain,
! [X2] : lhs_atom2(X2),
inference(variable_rename,[status(thm)],[c_0_41]) ).
fof(c_0_67,plain,
lhs_atom25,
c_0_42 ).
fof(c_0_68,plain,
lhs_atom24,
c_0_43 ).
fof(c_0_69,plain,
lhs_atom23,
c_0_44 ).
fof(c_0_70,plain,
lhs_atom22,
c_0_45 ).
fof(c_0_71,plain,
lhs_atom21,
c_0_46 ).
fof(c_0_72,plain,
lhs_atom20,
c_0_47 ).
fof(c_0_73,plain,
lhs_atom14,
c_0_48 ).
fof(c_0_74,plain,
lhs_atom1,
c_0_49 ).
cnf(c_0_75,plain,
lhs_atom11(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_76,plain,
lhs_atom19(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_77,plain,
lhs_atom16(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_78,plain,
lhs_atom10(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_79,plain,
lhs_atom9(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_80,plain,
lhs_atom7(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_81,plain,
lhs_atom6(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_82,plain,
lhs_atom17(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_83,plain,
lhs_atom15(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_84,plain,
lhs_atom13(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_85,plain,
lhs_atom12(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_86,plain,
lhs_atom8(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_87,plain,
lhs_atom18(X1),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_88,plain,
lhs_atom5(X1),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_89,plain,
lhs_atom4(X1),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_90,plain,
lhs_atom3(X1),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_91,plain,
lhs_atom2(X1),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_92,plain,
lhs_atom25,
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_93,plain,
lhs_atom24,
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_94,plain,
lhs_atom23,
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_95,plain,
lhs_atom22,
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_96,plain,
lhs_atom21,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_97,plain,
lhs_atom20,
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_98,plain,
lhs_atom14,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_99,plain,
lhs_atom1,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_100,plain,
lhs_atom11(X1,X2,X3,X4),
c_0_75,
[final] ).
cnf(c_0_101,plain,
lhs_atom19(X1,X2,X3),
c_0_76,
[final] ).
cnf(c_0_102,plain,
lhs_atom16(X1,X2,X3),
c_0_77,
[final] ).
cnf(c_0_103,plain,
lhs_atom10(X1,X2,X3),
c_0_78,
[final] ).
cnf(c_0_104,plain,
lhs_atom9(X1,X2,X3),
c_0_79,
[final] ).
cnf(c_0_105,plain,
lhs_atom7(X1,X2,X3),
c_0_80,
[final] ).
cnf(c_0_106,plain,
lhs_atom6(X1,X2,X3),
c_0_81,
[final] ).
cnf(c_0_107,plain,
lhs_atom17(X1,X2),
c_0_82,
[final] ).
cnf(c_0_108,plain,
lhs_atom15(X1,X2),
c_0_83,
[final] ).
cnf(c_0_109,plain,
lhs_atom13(X1,X2),
c_0_84,
[final] ).
cnf(c_0_110,plain,
lhs_atom12(X1,X2),
c_0_85,
[final] ).
cnf(c_0_111,plain,
lhs_atom8(X1,X2),
c_0_86,
[final] ).
cnf(c_0_112,plain,
lhs_atom18(X1),
c_0_87,
[final] ).
cnf(c_0_113,plain,
lhs_atom5(X1),
c_0_88,
[final] ).
cnf(c_0_114,plain,
lhs_atom4(X1),
c_0_89,
[final] ).
cnf(c_0_115,plain,
lhs_atom3(X1),
c_0_90,
[final] ).
cnf(c_0_116,plain,
lhs_atom2(X1),
c_0_91,
[final] ).
cnf(c_0_117,plain,
lhs_atom25,
c_0_92,
[final] ).
cnf(c_0_118,plain,
lhs_atom24,
c_0_93,
[final] ).
cnf(c_0_119,plain,
lhs_atom23,
c_0_94,
[final] ).
cnf(c_0_120,plain,
lhs_atom22,
c_0_95,
[final] ).
cnf(c_0_121,plain,
lhs_atom21,
c_0_96,
[final] ).
cnf(c_0_122,plain,
lhs_atom20,
c_0_97,
[final] ).
cnf(c_0_123,plain,
lhs_atom14,
c_0_98,
[final] ).
cnf(c_0_124,plain,
lhs_atom1,
c_0_99,
[final] ).
% End CNF derivation
cnf(c_0_100_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OApp(X2,X1),X3,X4) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X2,X3,X4),c_Lambda_Osubst(X1,X3,X4)),
inference(unfold_definition,[status(thm)],[c_0_100,def_lhs_atom11]) ).
cnf(c_0_101_0,axiom,
c_Lambda_OdB_OApp(X3,X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_101,def_lhs_atom19]) ).
cnf(c_0_102_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OApp(X3,X2),
inference(unfold_definition,[status(thm)],[c_0_102,def_lhs_atom16]) ).
cnf(c_0_103_0,axiom,
c_Lambda_OdB_OApp(X3,X2) != c_Lambda_OdB_OAbs(X1),
inference(unfold_definition,[status(thm)],[c_0_103,def_lhs_atom10]) ).
cnf(c_0_104_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OApp(X3,X2),
inference(unfold_definition,[status(thm)],[c_0_104,def_lhs_atom9]) ).
cnf(c_0_105_0,axiom,
c_Lambda_Olift(c_Lambda_OdB_OApp(X2,X1),X3) = c_Lambda_OdB_OApp(c_Lambda_Olift(X2,X3),c_Lambda_Olift(X1,X3)),
inference(unfold_definition,[status(thm)],[c_0_105,def_lhs_atom7]) ).
cnf(c_0_106_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(X1,X3),X2,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_106,def_lhs_atom6]) ).
cnf(c_0_107_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(unfold_definition,[status(thm)],[c_0_107,def_lhs_atom17]) ).
cnf(c_0_108_0,axiom,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X2),X1),
inference(unfold_definition,[status(thm)],[c_0_108,def_lhs_atom15]) ).
cnf(c_0_109_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_109,def_lhs_atom13]) ).
cnf(c_0_110_0,axiom,
c_Lambda_OdB_OAbs(X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_110,def_lhs_atom12]) ).
cnf(c_0_111_0,axiom,
c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X2),X1),c_Lambda_Osubst(X2,X1,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(unfold_definition,[status(thm)],[c_0_111,def_lhs_atom8]) ).
cnf(c_0_112_0,axiom,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X1)),
inference(unfold_definition,[status(thm)],[c_0_112,def_lhs_atom18]) ).
cnf(c_0_113_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_113,def_lhs_atom5]) ).
cnf(c_0_114_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_114,def_lhs_atom4]) ).
cnf(c_0_115_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_115,def_lhs_atom3]) ).
cnf(c_0_116_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_116,def_lhs_atom2]) ).
cnf(c_0_117_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_117,def_lhs_atom25]) ).
cnf(c_0_118_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_118,def_lhs_atom24]) ).
cnf(c_0_119_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_119,def_lhs_atom23]) ).
cnf(c_0_120_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_120,def_lhs_atom22]) ).
cnf(c_0_121_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_121,def_lhs_atom21]) ).
cnf(c_0_122_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_122,def_lhs_atom20]) ).
cnf(c_0_123_0,axiom,
v_env______(v_x______) = v_Ta______,
inference(unfold_definition,[status(thm)],[c_0_123,def_lhs_atom14]) ).
cnf(c_0_124_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_124,def_lhs_atom1]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X1,X8,X3,X2] :
( c_Lambda_Obeta(c_Lambda_Osubst(X3,X1,X2),c_Lambda_Osubst(X8,X1,X2))
| ~ c_Lambda_Obeta(X3,X8) ),
file('<stdin>',cls_subst__preserves__beta_0) ).
fof(c_0_1_002,axiom,
! [X17,X18,X16,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_HOL_Oord__class_Oless(X16,X17,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19)
| ~ c_HOL_Oord__class_Oless(X16,X18,X19) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_2_003,axiom,
! [X17,X18,X16,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X17,X16,X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19)
| ~ c_HOL_Oord__class_Oless(X18,X16,X19) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_3_004,axiom,
! [X20,X21,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X19),c_Nat_Osemiring__1__class_Oof__nat(X20,X19),X19) ),
file('<stdin>',cls_of__nat__less__iff_0) ).
fof(c_0_4_005,axiom,
! [X20,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),c_Nat_Osemiring__1__class_Oof__nat(X20,X19),X19) ),
file('<stdin>',cls_of__nat__0__less__iff_0) ).
fof(c_0_5_006,axiom,
! [X20,X21,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X19),c_Nat_Osemiring__1__class_Oof__nat(X20,X19),X19)
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat) ),
file('<stdin>',cls_of__nat__less__iff_1) ).
fof(c_0_6_007,axiom,
! [X20,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),c_Nat_Osemiring__1__class_Oof__nat(X20,X19),X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
file('<stdin>',cls_of__nat__0__less__iff_1) ).
fof(c_0_7_008,axiom,
! [X22,X23,X19] :
( ~ class_Orderings_Opreorder(X19)
| ~ c_HOL_Oord__class_Oless(X22,X23,X19)
| ~ c_HOL_Oord__class_Oless(X23,X22,X19) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_8_009,axiom,
! [X18,X16,X19] :
( ~ class_Orderings_Opreorder(X19)
| ~ c_HOL_Oord__class_Oless(X18,X16,X19)
| ~ c_HOL_Oord__class_Oless(X16,X18,X19) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_9_010,axiom,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| ~ c_HOL_Oord__class_Oless(X16,X18,X19)
| ~ c_HOL_Oord__class_Oless(X18,X16,X19) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_10_011,axiom,
! [X22,X23,X19] :
( ~ class_Orderings_Oorder(X19)
| ~ c_HOL_Oord__class_Oless(X23,X22,X19)
| ~ c_HOL_Oord__class_Oless(X22,X23,X19) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_11_012,axiom,
! [X7,X4,X2] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X4),X7,X2) = c_Lambda_OdB_OVar(X4)
| ~ c_HOL_Oord__class_Oless(X4,X2,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_12_013,axiom,
! [X21,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X19),c_HOL_Ozero__class_Ozero(X19),X19) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_13_014,axiom,
! [X3,X4,X2] :
( c_InductTermi_OIT(c_Lambda_Osubst(X3,c_Lambda_OdB_OVar(X2),X4))
| ~ c_InductTermi_OIT(X3) ),
file('<stdin>',cls_subst__Var__IT_0) ).
fof(c_0_14_015,axiom,
! [X8,X15,X2] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X8,X15) = c_Lambda_OdB_OVar(X2)
| X2 = X15
| c_HOL_Oord__class_Oless(X15,X2,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_15_016,axiom,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| X16 = X18
| c_HOL_Oord__class_Oless(X16,X18,X19)
| c_HOL_Oord__class_Oless(X18,X16,X19) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_16_017,axiom,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| X16 = X18
| c_HOL_Oord__class_Oless(X16,X18,X19) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_17_018,axiom,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| X16 = X18 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_18_019,axiom,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| X16 = X18
| c_HOL_Oord__class_Oless(X18,X16,X19)
| c_HOL_Oord__class_Oless(X16,X18,X19) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_19_020,axiom,
! [X18,X16,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| X16 = X18 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_20_021,axiom,
! [X16,X8] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X16),X8,X16) = X8 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_21_022,axiom,
! [X18,X16] :
( c_HOL_Oord__class_Oless(X18,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X18,tc_nat)
| X16 = X18 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_22_023,axiom,
! [X20,X21] :
( c_HOL_Oord__class_Oless(X20,X21,tc_nat)
| c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| X21 = X20 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_23_024,axiom,
! [X15,X2] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X2),X15) = c_Lambda_OdB_OVar(X2)
| ~ c_HOL_Oord__class_Oless(X2,X15,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_24_025,axiom,
! [X16,X19] :
( ~ class_Orderings_Opreorder(X19)
| ~ c_HOL_Oord__class_Oless(X16,X16,X19) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_25_026,axiom,
! [X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| ~ c_HOL_Oord__class_Oless(X16,X16,X19) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_26_027,axiom,
! [X16,X19] :
( ~ class_Orderings_Oorder(X19)
| ~ c_HOL_Oord__class_Oless(X16,X16,X19) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_27_028,axiom,
! [X8,X3,X2] :
( c_Lambda_Obeta(c_Lambda_Olift(X3,X2),c_Lambda_Olift(X8,X2))
| ~ c_Lambda_Obeta(X3,X8) ),
file('<stdin>',cls_lift__preserves__beta_0) ).
fof(c_0_28_029,axiom,
! [X7,X1,X8] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X8,X7),c_Lambda_OdB_OApp(X1,X7))
| ~ c_Lambda_Obeta(X8,X1) ),
file('<stdin>',cls_appL_0) ).
fof(c_0_29_030,axiom,
! [X7,X1,X8] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X7,X8),c_Lambda_OdB_OApp(X7,X1))
| ~ c_Lambda_Obeta(X8,X1) ),
file('<stdin>',cls_appR_0) ).
fof(c_0_30_031,axiom,
! [X8,X3] :
( c_Lambda_Obeta(X3,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X3,X8))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X3),X8) ),
file('<stdin>',cls_beta__cases_I2_J_1) ).
fof(c_0_31_032,axiom,
! [X8,X3] :
( X8 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X3,X8))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X3),X8) ),
file('<stdin>',cls_beta__cases_I2_J_0) ).
fof(c_0_32_033,axiom,
! [X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_33_034,axiom,
! [X20,X21,X19] :
( ~ class_Nat_Osemiring__char__0(X19)
| c_Nat_Osemiring__1__class_Oof__nat(X21,X19) != c_Nat_Osemiring__1__class_Oof__nat(X20,X19)
| X21 = X20 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_34_035,axiom,
! [X1,X2] :
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X1,c_Lambda_OdB_OVar(X2)))
| ~ c_InductTermi_OIT(X1) ),
file('<stdin>',cls_app__Var__IT_0) ).
fof(c_0_35_036,axiom,
! [X1,X8] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X8),c_Lambda_OdB_OAbs(X1))
| ~ c_Lambda_Obeta(X8,X1) ),
file('<stdin>',cls_abs_0) ).
fof(c_0_36_037,axiom,
! [X9,X10,X11,X12] :
( c_Lambda_OdB_OApp(X12,X10) != c_Lambda_OdB_OApp(X11,X9)
| X10 = X9 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_37_038,axiom,
! [X9,X10,X11,X12] :
( c_Lambda_OdB_OApp(X12,X10) != c_Lambda_OdB_OApp(X11,X9)
| X12 = X11 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_38_039,axiom,
! [X1,X2] :
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_39_040,axiom,
! [X19] :
( ~ class_Ring__and__Field_Osemiring__1(X19)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X19) = c_HOL_Ozero__class_Ozero(X19) ),
file('<stdin>',cls_of__nat__0_0) ).
fof(c_0_40_041,axiom,
! [X3] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X3))
| ~ c_InductTermi_OIT(X3) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_41_042,axiom,
! [X13,X14] :
( c_Lambda_OdB_OAbs(X14) != c_Lambda_OdB_OAbs(X13)
| X14 = X13 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_42_043,axiom,
! [X5,X6] :
( c_Lambda_OdB_OVar(X6) != c_Lambda_OdB_OVar(X5)
| X6 = X5 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_43_044,plain,
! [X1,X8,X3,X2] :
( c_Lambda_Obeta(c_Lambda_Osubst(X3,X1,X2),c_Lambda_Osubst(X8,X1,X2))
| ~ c_Lambda_Obeta(X3,X8) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_44_045,plain,
! [X17,X18,X16,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_HOL_Oord__class_Oless(X16,X17,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19)
| ~ c_HOL_Oord__class_Oless(X16,X18,X19) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_45_046,plain,
! [X17,X18,X16,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X17,X16,X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19)
| ~ c_HOL_Oord__class_Oless(X18,X16,X19) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_46_047,plain,
! [X20,X21,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X19),c_Nat_Osemiring__1__class_Oof__nat(X20,X19),X19) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_47_048,plain,
! [X20,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),c_Nat_Osemiring__1__class_Oof__nat(X20,X19),X19) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_48_049,plain,
! [X20,X21,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X19),c_Nat_Osemiring__1__class_Oof__nat(X20,X19),X19)
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_49_050,plain,
! [X20,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),c_Nat_Osemiring__1__class_Oof__nat(X20,X19),X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_50_051,plain,
! [X22,X23,X19] :
( ~ class_Orderings_Opreorder(X19)
| ~ c_HOL_Oord__class_Oless(X22,X23,X19)
| ~ c_HOL_Oord__class_Oless(X23,X22,X19) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_51_052,plain,
! [X18,X16,X19] :
( ~ class_Orderings_Opreorder(X19)
| ~ c_HOL_Oord__class_Oless(X18,X16,X19)
| ~ c_HOL_Oord__class_Oless(X16,X18,X19) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_52_053,plain,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| ~ c_HOL_Oord__class_Oless(X16,X18,X19)
| ~ c_HOL_Oord__class_Oless(X18,X16,X19) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_53_054,plain,
! [X22,X23,X19] :
( ~ class_Orderings_Oorder(X19)
| ~ c_HOL_Oord__class_Oless(X23,X22,X19)
| ~ c_HOL_Oord__class_Oless(X22,X23,X19) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_54_055,plain,
! [X7,X4,X2] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X4),X7,X2) = c_Lambda_OdB_OVar(X4)
| ~ c_HOL_Oord__class_Oless(X4,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_55_056,plain,
! [X21,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X19),c_HOL_Ozero__class_Ozero(X19),X19) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_56_057,plain,
! [X3,X4,X2] :
( c_InductTermi_OIT(c_Lambda_Osubst(X3,c_Lambda_OdB_OVar(X2),X4))
| ~ c_InductTermi_OIT(X3) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_57_058,axiom,
! [X8,X15,X2] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X8,X15) = c_Lambda_OdB_OVar(X2)
| X2 = X15
| c_HOL_Oord__class_Oless(X15,X2,tc_nat) ),
c_0_14 ).
fof(c_0_58_059,plain,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| X16 = X18
| c_HOL_Oord__class_Oless(X16,X18,X19)
| c_HOL_Oord__class_Oless(X18,X16,X19) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_59_060,plain,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| X16 = X18
| c_HOL_Oord__class_Oless(X16,X18,X19) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_60_061,plain,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| X16 = X18 ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_61_062,plain,
! [X18,X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| X16 = X18
| c_HOL_Oord__class_Oless(X18,X16,X19)
| c_HOL_Oord__class_Oless(X16,X18,X19) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_62_063,plain,
! [X18,X16,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| X16 = X18 ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_63_064,axiom,
! [X16,X8] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X16),X8,X16) = X8 ),
c_0_20 ).
fof(c_0_64_065,axiom,
! [X18,X16] :
( c_HOL_Oord__class_Oless(X18,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X18,tc_nat)
| X16 = X18 ),
c_0_21 ).
fof(c_0_65_066,axiom,
! [X20,X21] :
( c_HOL_Oord__class_Oless(X20,X21,tc_nat)
| c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| X21 = X20 ),
c_0_22 ).
fof(c_0_66_067,plain,
! [X15,X2] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X2),X15) = c_Lambda_OdB_OVar(X2)
| ~ c_HOL_Oord__class_Oless(X2,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_67_068,plain,
! [X16,X19] :
( ~ class_Orderings_Opreorder(X19)
| ~ c_HOL_Oord__class_Oless(X16,X16,X19) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_68_069,plain,
! [X16,X19] :
( ~ class_Orderings_Olinorder(X19)
| ~ c_HOL_Oord__class_Oless(X16,X16,X19) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_69_070,plain,
! [X16,X19] :
( ~ class_Orderings_Oorder(X19)
| ~ c_HOL_Oord__class_Oless(X16,X16,X19) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_70_071,plain,
! [X8,X3,X2] :
( c_Lambda_Obeta(c_Lambda_Olift(X3,X2),c_Lambda_Olift(X8,X2))
| ~ c_Lambda_Obeta(X3,X8) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_71_072,plain,
! [X7,X1,X8] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X8,X7),c_Lambda_OdB_OApp(X1,X7))
| ~ c_Lambda_Obeta(X8,X1) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_72_073,plain,
! [X7,X1,X8] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X7,X8),c_Lambda_OdB_OApp(X7,X1))
| ~ c_Lambda_Obeta(X8,X1) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_73_074,plain,
! [X8,X3] :
( c_Lambda_Obeta(X3,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X3,X8))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X3),X8) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_74_075,plain,
! [X8,X3] :
( X8 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X3,X8))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X3),X8) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_75_076,axiom,
! [X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_32 ).
fof(c_0_76_077,plain,
! [X20,X21,X19] :
( ~ class_Nat_Osemiring__char__0(X19)
| c_Nat_Osemiring__1__class_Oof__nat(X21,X19) != c_Nat_Osemiring__1__class_Oof__nat(X20,X19)
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_77_078,plain,
! [X1,X2] :
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X1,c_Lambda_OdB_OVar(X2)))
| ~ c_InductTermi_OIT(X1) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_78_079,plain,
! [X1,X8] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X8),c_Lambda_OdB_OAbs(X1))
| ~ c_Lambda_Obeta(X8,X1) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_79_080,axiom,
! [X9,X10,X11,X12] :
( c_Lambda_OdB_OApp(X12,X10) != c_Lambda_OdB_OApp(X11,X9)
| X10 = X9 ),
c_0_36 ).
fof(c_0_80_081,axiom,
! [X9,X10,X11,X12] :
( c_Lambda_OdB_OApp(X12,X10) != c_Lambda_OdB_OApp(X11,X9)
| X12 = X11 ),
c_0_37 ).
fof(c_0_81_082,plain,
! [X1,X2] :
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_82_083,plain,
! [X19] :
( ~ class_Ring__and__Field_Osemiring__1(X19)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X19) = c_HOL_Ozero__class_Ozero(X19) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_83_084,plain,
! [X3] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X3))
| ~ c_InductTermi_OIT(X3) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_84_085,axiom,
! [X13,X14] :
( c_Lambda_OdB_OAbs(X14) != c_Lambda_OdB_OAbs(X13)
| X14 = X13 ),
c_0_41 ).
fof(c_0_85_086,axiom,
! [X5,X6] :
( c_Lambda_OdB_OVar(X6) != c_Lambda_OdB_OVar(X5)
| X6 = X5 ),
c_0_42 ).
fof(c_0_86_087,plain,
! [X9,X10,X11,X12] :
( c_Lambda_Obeta(c_Lambda_Osubst(X11,X9,X12),c_Lambda_Osubst(X10,X9,X12))
| ~ c_Lambda_Obeta(X11,X10) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_43])])]) ).
fof(c_0_87_088,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Opreorder(X23)
| c_HOL_Oord__class_Oless(X22,X20,X23)
| ~ c_HOL_Oord__class_Oless(X21,X20,X23)
| ~ c_HOL_Oord__class_Oless(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_44]) ).
fof(c_0_88_089,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| c_HOL_Oord__class_Oless(X20,X22,X23)
| ~ c_HOL_Oord__class_Oless(X20,X21,X23)
| ~ c_HOL_Oord__class_Oless(X21,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_45]) ).
fof(c_0_89_090,plain,
! [X22,X23,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X24)
| c_HOL_Oord__class_Oless(X23,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X23,X24),c_Nat_Osemiring__1__class_Oof__nat(X22,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_46]) ).
fof(c_0_90_091,plain,
! [X21,X22] :
( ~ class_Ring__and__Field_Oordered__semidom(X22)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),c_Nat_Osemiring__1__class_Oof__nat(X21,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_47]) ).
fof(c_0_91_092,plain,
! [X22,X23,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X24)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X23,X24),c_Nat_Osemiring__1__class_Oof__nat(X22,X24),X24)
| ~ c_HOL_Oord__class_Oless(X23,X22,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_48]) ).
fof(c_0_92_093,plain,
! [X21,X22] :
( ~ class_Ring__and__Field_Oordered__semidom(X22)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),c_Nat_Osemiring__1__class_Oof__nat(X21,X22),X22)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_49]) ).
fof(c_0_93_094,plain,
! [X24,X25,X26] :
( ~ class_Orderings_Opreorder(X26)
| ~ c_HOL_Oord__class_Oless(X24,X25,X26)
| ~ c_HOL_Oord__class_Oless(X25,X24,X26) ),
inference(variable_rename,[status(thm)],[c_0_50]) ).
fof(c_0_94_095,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Opreorder(X22)
| ~ c_HOL_Oord__class_Oless(X20,X21,X22)
| ~ c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_51]) ).
fof(c_0_95_096,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| ~ c_HOL_Oord__class_Oless(X21,X20,X22)
| ~ c_HOL_Oord__class_Oless(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_52]) ).
fof(c_0_96_097,plain,
! [X24,X25,X26] :
( ~ class_Orderings_Oorder(X26)
| ~ c_HOL_Oord__class_Oless(X25,X24,X26)
| ~ c_HOL_Oord__class_Oless(X24,X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_53]) ).
fof(c_0_97_098,plain,
! [X8,X9,X10] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X9),X8,X10) = c_Lambda_OdB_OVar(X9)
| ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_54]) ).
fof(c_0_98_099,plain,
! [X22,X23] :
( ~ class_Ring__and__Field_Oordered__semidom(X23)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X22,X23),c_HOL_Ozero__class_Ozero(X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_55]) ).
fof(c_0_99_100,plain,
! [X5,X6,X7] :
( c_InductTermi_OIT(c_Lambda_Osubst(X5,c_Lambda_OdB_OVar(X7),X6))
| ~ c_InductTermi_OIT(X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_56])])]) ).
fof(c_0_100_101,plain,
! [X16,X17,X18] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X18),X16,X17) = c_Lambda_OdB_OVar(X18)
| X18 = X17
| c_HOL_Oord__class_Oless(X17,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_57]) ).
fof(c_0_101_102,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| X21 = X20
| c_HOL_Oord__class_Oless(X21,X20,X22)
| c_HOL_Oord__class_Oless(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_58]) ).
fof(c_0_102_103,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_HOL_Oord__class_Oless(X20,X21,X22)
| X21 = X20
| c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_59]) ).
fof(c_0_103_104,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_HOL_Oord__class_Oless(X20,X21,X22)
| c_HOL_Oord__class_Oless(X21,X20,X22)
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_60]) ).
fof(c_0_104_105,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| X21 = X20
| c_HOL_Oord__class_Oless(X20,X21,X22)
| c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_61]) ).
fof(c_0_105_106,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__idom(X22)
| c_HOL_Oord__class_Oless(X20,X21,X22)
| c_HOL_Oord__class_Oless(X21,X20,X22)
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_62]) ).
fof(c_0_106_107,plain,
! [X17,X18] :
( c_HOL_Oord__class_Oless(X17,X17,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X17),X18,X17) = X18 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_63])])]) ).
fof(c_0_107_108,plain,
! [X19,X20] :
( c_HOL_Oord__class_Oless(X19,X20,tc_nat)
| c_HOL_Oord__class_Oless(X20,X19,tc_nat)
| X20 = X19 ),
inference(variable_rename,[status(thm)],[c_0_64]) ).
fof(c_0_108_109,plain,
! [X22,X23] :
( c_HOL_Oord__class_Oless(X22,X23,tc_nat)
| c_HOL_Oord__class_Oless(X23,X22,tc_nat)
| X23 = X22 ),
inference(variable_rename,[status(thm)],[c_0_65]) ).
fof(c_0_109_110,plain,
! [X16,X17] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X17),X16) = c_Lambda_OdB_OVar(X17)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_66]) ).
fof(c_0_110_111,plain,
! [X20,X21] :
( ~ class_Orderings_Opreorder(X21)
| ~ c_HOL_Oord__class_Oless(X20,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_67]) ).
fof(c_0_111_112,plain,
! [X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| ~ c_HOL_Oord__class_Oless(X20,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_68]) ).
fof(c_0_112_113,plain,
! [X20,X21] :
( ~ class_Orderings_Oorder(X21)
| ~ c_HOL_Oord__class_Oless(X20,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_69]) ).
fof(c_0_113_114,plain,
! [X9,X10,X11] :
( c_Lambda_Obeta(c_Lambda_Olift(X10,X11),c_Lambda_Olift(X9,X11))
| ~ c_Lambda_Obeta(X10,X9) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_70])])]) ).
fof(c_0_114_115,plain,
! [X9,X10,X11] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X11,X9),c_Lambda_OdB_OApp(X10,X9))
| ~ c_Lambda_Obeta(X11,X10) ),
inference(variable_rename,[status(thm)],[c_0_71]) ).
fof(c_0_115_116,plain,
! [X9,X10,X11] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X9,X11),c_Lambda_OdB_OApp(X9,X10))
| ~ c_Lambda_Obeta(X11,X10) ),
inference(variable_rename,[status(thm)],[c_0_72]) ).
fof(c_0_116_117,plain,
! [X9,X10] :
( c_Lambda_Obeta(X10,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X10,X9))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X10),X9) ),
inference(variable_rename,[status(thm)],[c_0_73]) ).
fof(c_0_117_118,plain,
! [X9,X10] :
( X9 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X10,X9))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X10),X9) ),
inference(variable_rename,[status(thm)],[c_0_74]) ).
fof(c_0_118_119,plain,
! [X21] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
| X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_75]) ).
fof(c_0_119_120,plain,
! [X22,X23,X24] :
( ~ class_Nat_Osemiring__char__0(X24)
| c_Nat_Osemiring__1__class_Oof__nat(X23,X24) != c_Nat_Osemiring__1__class_Oof__nat(X22,X24)
| X23 = X22 ),
inference(variable_rename,[status(thm)],[c_0_76]) ).
fof(c_0_120_121,plain,
! [X3,X4] :
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X3,c_Lambda_OdB_OVar(X4)))
| ~ c_InductTermi_OIT(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_77])])]) ).
fof(c_0_121_122,plain,
! [X9,X10] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X10),c_Lambda_OdB_OAbs(X9))
| ~ c_Lambda_Obeta(X10,X9) ),
inference(variable_rename,[status(thm)],[c_0_78]) ).
fof(c_0_122_123,plain,
! [X13,X14,X15,X16] :
( c_Lambda_OdB_OApp(X16,X14) != c_Lambda_OdB_OApp(X15,X13)
| X14 = X13 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_79])])]) ).
fof(c_0_123_124,plain,
! [X13,X14,X15,X16] :
( c_Lambda_OdB_OApp(X16,X14) != c_Lambda_OdB_OApp(X15,X13)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_80]) ).
fof(c_0_124_125,plain,
! [X3,X4] :
( c_InductTermi_OIT(c_Lambda_Olift(X3,X4))
| ~ c_InductTermi_OIT(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_81])])]) ).
fof(c_0_125,plain,
! [X20] :
( ~ class_Ring__and__Field_Osemiring__1(X20)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X20) = c_HOL_Ozero__class_Ozero(X20) ),
inference(variable_rename,[status(thm)],[c_0_82]) ).
fof(c_0_126,plain,
! [X4] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X4))
| ~ c_InductTermi_OIT(X4) ),
inference(variable_rename,[status(thm)],[c_0_83]) ).
fof(c_0_127,plain,
! [X15,X16] :
( c_Lambda_OdB_OAbs(X16) != c_Lambda_OdB_OAbs(X15)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_84]) ).
fof(c_0_128,plain,
! [X7,X8] :
( c_Lambda_OdB_OVar(X8) != c_Lambda_OdB_OVar(X7)
| X8 = X7 ),
inference(variable_rename,[status(thm)],[c_0_85]) ).
cnf(c_0_129,plain,
( c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_130,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_131,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_132,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_133,plain,
( 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(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_134,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_135,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_136,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_137,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_138,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_139,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_140,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_141,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_142,plain,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))
| ~ c_InductTermi_OIT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_143,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_144,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_145,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_146,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_147,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_148,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) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_149,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_150,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_151,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_152,plain,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_153,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_154,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_155,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_156,plain,
( c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_157,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_158,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_159,plain,
( c_Lambda_Obeta(X1,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_160,plain,
( X2 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_161,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_162,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) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_163,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X1,c_Lambda_OdB_OVar(X2)))
| ~ c_InductTermi_OIT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_164,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_165,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_166,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_167,plain,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_168,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) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_169,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_170,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_171,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_172,plain,
( c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_129,
[final] ).
cnf(c_0_173,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_130,
[final] ).
cnf(c_0_174,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_131,
[final] ).
cnf(c_0_175,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ 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_0_132,
[final] ).
cnf(c_0_176,plain,
( 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(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_133,
[final] ).
cnf(c_0_177,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_134,
[final] ).
cnf(c_0_178,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_135,
[final] ).
cnf(c_0_179,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_136,
[final] ).
cnf(c_0_180,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_137,
[final] ).
cnf(c_0_181,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_138,
[final] ).
cnf(c_0_182,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_139,
[final] ).
cnf(c_0_183,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_140,
[final] ).
cnf(c_0_184,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_141,
[final] ).
cnf(c_0_185,plain,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))
| ~ c_InductTermi_OIT(X1) ),
c_0_142,
[final] ).
cnf(c_0_186,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
c_0_143,
[final] ).
cnf(c_0_187,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
c_0_144,
[final] ).
cnf(c_0_188,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_145,
[final] ).
cnf(c_0_189,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_146,
[final] ).
cnf(c_0_190,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
c_0_147,
[final] ).
cnf(c_0_191,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) ),
c_0_148,
[final] ).
cnf(c_0_192,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_149,
[final] ).
cnf(c_0_193,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_150,
[final] ).
cnf(c_0_194,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_151,
[final] ).
cnf(c_0_195,plain,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_152,
[final] ).
cnf(c_0_196,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_153,
[final] ).
cnf(c_0_197,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_154,
[final] ).
cnf(c_0_198,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_155,
[final] ).
cnf(c_0_199,plain,
( c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_156,
[final] ).
cnf(c_0_200,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_157,
[final] ).
cnf(c_0_201,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_158,
[final] ).
cnf(c_0_202,plain,
( c_Lambda_Obeta(X1,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
c_0_159,
[final] ).
cnf(c_0_203,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) ),
c_0_160,
[final] ).
cnf(c_0_204,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_161,
[final] ).
cnf(c_0_205,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) ),
c_0_162,
[final] ).
cnf(c_0_206,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X1,c_Lambda_OdB_OVar(X2)))
| ~ c_InductTermi_OIT(X1) ),
c_0_163,
[final] ).
cnf(c_0_207,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_164,
[final] ).
cnf(c_0_208,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
c_0_165,
[final] ).
cnf(c_0_209,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
c_0_166,
[final] ).
cnf(c_0_210,plain,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
c_0_167,
[final] ).
cnf(c_0_211,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) ),
c_0_168,
[final] ).
cnf(c_0_212,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
c_0_169,
[final] ).
cnf(c_0_213,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_170,
[final] ).
cnf(c_0_214,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_171,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_172_0,axiom,
( c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_172]) ).
cnf(c_0_172_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_172]) ).
cnf(c_0_173_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_173]) ).
cnf(c_0_173_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_173]) ).
cnf(c_0_173_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_173]) ).
cnf(c_0_173_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_173]) ).
cnf(c_0_174_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_174]) ).
cnf(c_0_174_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_174]) ).
cnf(c_0_174_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_174]) ).
cnf(c_0_174_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_174]) ).
cnf(c_0_175_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_175]) ).
cnf(c_0_175_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_175]) ).
cnf(c_0_175_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_175]) ).
cnf(c_0_176_0,axiom,
( 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(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_176]) ).
cnf(c_0_176_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_176]) ).
cnf(c_0_176_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_176]) ).
cnf(c_0_177_0,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_177]) ).
cnf(c_0_177_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_177]) ).
cnf(c_0_177_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_177]) ).
cnf(c_0_178_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_178]) ).
cnf(c_0_178_1,axiom,
( ~ 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(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_178]) ).
cnf(c_0_178_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ 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(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_178]) ).
cnf(c_0_179_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_179]) ).
cnf(c_0_179_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_179]) ).
cnf(c_0_179_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_179]) ).
cnf(c_0_180_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_180]) ).
cnf(c_0_180_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_180]) ).
cnf(c_0_180_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_180]) ).
cnf(c_0_181_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_181]) ).
cnf(c_0_181_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_181]) ).
cnf(c_0_181_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_181]) ).
cnf(c_0_182_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_182]) ).
cnf(c_0_182_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_182]) ).
cnf(c_0_182_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_182]) ).
cnf(c_0_183_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_183]) ).
cnf(c_0_183_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_183]) ).
cnf(c_0_184_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_184]) ).
cnf(c_0_184_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_184]) ).
cnf(c_0_185_0,axiom,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))
| ~ c_InductTermi_OIT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_185]) ).
cnf(c_0_185_1,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_185]) ).
cnf(c_0_186_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_186]) ).
cnf(c_0_186_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_186]) ).
cnf(c_0_186_2,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_186]) ).
cnf(c_0_187_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_187]) ).
cnf(c_0_187_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_187]) ).
cnf(c_0_187_2,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_187]) ).
cnf(c_0_187_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_187]) ).
cnf(c_0_188_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_188]) ).
cnf(c_0_188_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_188]) ).
cnf(c_0_188_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_188]) ).
cnf(c_0_188_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_188]) ).
cnf(c_0_189_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_189]) ).
cnf(c_0_189_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_189]) ).
cnf(c_0_189_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_189]) ).
cnf(c_0_189_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_189]) ).
cnf(c_0_190_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_190]) ).
cnf(c_0_190_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_190]) ).
cnf(c_0_190_2,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_190]) ).
cnf(c_0_190_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_190]) ).
cnf(c_0_191_0,axiom,
( 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) ),
inference(literals_permutation,[status(thm)],[c_0_191]) ).
cnf(c_0_191_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_191]) ).
cnf(c_0_191_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_191]) ).
cnf(c_0_191_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_191]) ).
cnf(c_0_192_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_192]) ).
cnf(c_0_192_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_192]) ).
cnf(c_0_193_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_193]) ).
cnf(c_0_193_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_193]) ).
cnf(c_0_193_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_193]) ).
cnf(c_0_194_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_194]) ).
cnf(c_0_194_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_194]) ).
cnf(c_0_194_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_194]) ).
cnf(c_0_195_0,axiom,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_195]) ).
cnf(c_0_195_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_195]) ).
cnf(c_0_196_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_196]) ).
cnf(c_0_196_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_196]) ).
cnf(c_0_197_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_197]) ).
cnf(c_0_197_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_197]) ).
cnf(c_0_198_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_198]) ).
cnf(c_0_198_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_198]) ).
cnf(c_0_199_0,axiom,
( c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_199]) ).
cnf(c_0_199_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_199]) ).
cnf(c_0_200_0,axiom,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_200]) ).
cnf(c_0_200_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_200]) ).
cnf(c_0_201_0,axiom,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_201]) ).
cnf(c_0_201_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_201]) ).
cnf(c_0_202_0,axiom,
( c_Lambda_Obeta(X1,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_202]) ).
cnf(c_0_202_1,axiom,
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2)
| c_Lambda_Obeta(X1,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_202]) ).
cnf(c_0_203_0,axiom,
( c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) = X2
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_203]) ).
cnf(c_0_203_1,axiom,
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2)
| c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_203]) ).
cnf(c_0_204_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_204]) ).
cnf(c_0_204_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_204]) ).
cnf(c_0_205_0,axiom,
( 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) ),
inference(literals_permutation,[status(thm)],[c_0_205]) ).
cnf(c_0_205_1,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_205]) ).
cnf(c_0_205_2,axiom,
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_205]) ).
cnf(c_0_206_0,axiom,
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X1,c_Lambda_OdB_OVar(X2)))
| ~ c_InductTermi_OIT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_206]) ).
cnf(c_0_206_1,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(X1,c_Lambda_OdB_OVar(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_206]) ).
cnf(c_0_207_0,axiom,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_207]) ).
cnf(c_0_207_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_207]) ).
cnf(c_0_208_0,axiom,
( X1 = X2
| c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_208]) ).
cnf(c_0_208_1,axiom,
( c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_208]) ).
cnf(c_0_209_0,axiom,
( X1 = X2
| c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_209]) ).
cnf(c_0_209_1,axiom,
( c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_209]) ).
cnf(c_0_210_0,axiom,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_210]) ).
cnf(c_0_210_1,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_Olift(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_210]) ).
cnf(c_0_211_0,axiom,
( 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) ),
inference(literals_permutation,[status(thm)],[c_0_211]) ).
cnf(c_0_211_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_211]) ).
cnf(c_0_212_0,axiom,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_212]) ).
cnf(c_0_212_1,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_212]) ).
cnf(c_0_213_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_213]) ).
cnf(c_0_213_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_213]) ).
cnf(c_0_214_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_214]) ).
cnf(c_0_214_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_214]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_126,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_127,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_2_128,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
c_0_1 ).
cnf(c_0_3_129,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_130,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_137,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
file('/export/starexec/sandbox/tmp/iprover_modulo_0311ed.p',c_0_4) ).
cnf(c_174,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
inference(copy,[status(esa)],[c_137]) ).
cnf(c_178,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
inference(copy,[status(esa)],[c_174]) ).
cnf(c_179,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
inference(copy,[status(esa)],[c_178]) ).
cnf(c_180,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
inference(copy,[status(esa)],[c_179]) ).
cnf(c_588,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
inference(copy,[status(esa)],[c_180]) ).
cnf(c_124,plain,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X0)),
file('/export/starexec/sandbox/tmp/iprover_modulo_0311ed.p',c_0_112_0) ).
cnf(c_566,plain,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X0)),
inference(copy,[status(esa)],[c_124]) ).
cnf(c_591,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_588,c_566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL843-1 : TPTP v8.1.0. Released v4.1.0.
% 0.13/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 08:41:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.35 % Running in mono-core mode
% 0.19/0.41 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.41 % Orientation found
% 0.19/0.41 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_dc3c1d.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_0311ed.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_567cb8 | grep -v "SZS"
% 0.20/0.43
% 0.20/0.43 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.43
% 0.20/0.43 %
% 0.20/0.43 % ------ iProver source info
% 0.20/0.43
% 0.20/0.43 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.43 % git: non_committed_changes: true
% 0.20/0.43 % git: last_make_outside_of_git: true
% 0.20/0.43
% 0.20/0.43 %
% 0.20/0.43 % ------ Input Options
% 0.20/0.43
% 0.20/0.43 % --out_options all
% 0.20/0.43 % --tptp_safe_out true
% 0.20/0.43 % --problem_path ""
% 0.20/0.43 % --include_path ""
% 0.20/0.43 % --clausifier .//eprover
% 0.20/0.43 % --clausifier_options --tstp-format
% 0.20/0.43 % --stdin false
% 0.20/0.43 % --dbg_backtrace false
% 0.20/0.43 % --dbg_dump_prop_clauses false
% 0.20/0.43 % --dbg_dump_prop_clauses_file -
% 0.20/0.43 % --dbg_out_stat false
% 0.20/0.43
% 0.20/0.43 % ------ General Options
% 0.20/0.43
% 0.20/0.43 % --fof false
% 0.20/0.43 % --time_out_real 150.
% 0.20/0.43 % --time_out_prep_mult 0.2
% 0.20/0.43 % --time_out_virtual -1.
% 0.20/0.43 % --schedule none
% 0.20/0.43 % --ground_splitting input
% 0.20/0.43 % --splitting_nvd 16
% 0.20/0.43 % --non_eq_to_eq false
% 0.20/0.43 % --prep_gs_sim true
% 0.20/0.43 % --prep_unflatten false
% 0.20/0.43 % --prep_res_sim true
% 0.20/0.43 % --prep_upred true
% 0.20/0.43 % --res_sim_input true
% 0.20/0.43 % --clause_weak_htbl true
% 0.20/0.43 % --gc_record_bc_elim false
% 0.20/0.43 % --symbol_type_check false
% 0.20/0.43 % --clausify_out false
% 0.20/0.43 % --large_theory_mode false
% 0.20/0.43 % --prep_sem_filter none
% 0.20/0.43 % --prep_sem_filter_out false
% 0.20/0.43 % --preprocessed_out false
% 0.20/0.43 % --sub_typing false
% 0.20/0.43 % --brand_transform false
% 0.20/0.43 % --pure_diseq_elim true
% 0.20/0.43 % --min_unsat_core false
% 0.20/0.43 % --pred_elim true
% 0.20/0.43 % --add_important_lit false
% 0.20/0.43 % --soft_assumptions false
% 0.20/0.43 % --reset_solvers false
% 0.20/0.43 % --bc_imp_inh []
% 0.20/0.43 % --conj_cone_tolerance 1.5
% 0.20/0.43 % --prolific_symb_bound 500
% 0.20/0.43 % --lt_threshold 2000
% 0.20/0.43
% 0.20/0.43 % ------ SAT Options
% 0.20/0.43
% 0.20/0.43 % --sat_mode false
% 0.20/0.43 % --sat_fm_restart_options ""
% 0.20/0.43 % --sat_gr_def false
% 0.20/0.43 % --sat_epr_types true
% 0.20/0.43 % --sat_non_cyclic_types false
% 0.20/0.43 % --sat_finite_models false
% 0.20/0.43 % --sat_fm_lemmas false
% 0.20/0.43 % --sat_fm_prep false
% 0.20/0.43 % --sat_fm_uc_incr true
% 0.20/0.43 % --sat_out_model small
% 0.20/0.43 % --sat_out_clauses false
% 0.20/0.43
% 0.20/0.43 % ------ QBF Options
% 0.20/0.43
% 0.20/0.43 % --qbf_mode false
% 0.20/0.43 % --qbf_elim_univ true
% 0.20/0.43 % --qbf_sk_in true
% 0.20/0.43 % --qbf_pred_elim true
% 0.20/0.43 % --qbf_split 32
% 0.20/0.43
% 0.20/0.43 % ------ BMC1 Options
% 0.20/0.43
% 0.20/0.43 % --bmc1_incremental false
% 0.20/0.43 % --bmc1_axioms reachable_all
% 0.20/0.43 % --bmc1_min_bound 0
% 0.20/0.43 % --bmc1_max_bound -1
% 0.20/0.43 % --bmc1_max_bound_default -1
% 0.20/0.43 % --bmc1_symbol_reachability true
% 0.20/0.43 % --bmc1_property_lemmas false
% 0.20/0.43 % --bmc1_k_induction false
% 0.20/0.43 % --bmc1_non_equiv_states false
% 0.20/0.43 % --bmc1_deadlock false
% 0.20/0.43 % --bmc1_ucm false
% 0.20/0.43 % --bmc1_add_unsat_core none
% 0.20/0.43 % --bmc1_unsat_core_children false
% 0.20/0.43 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.43 % --bmc1_out_stat full
% 0.20/0.43 % --bmc1_ground_init false
% 0.20/0.43 % --bmc1_pre_inst_next_state false
% 0.20/0.43 % --bmc1_pre_inst_state false
% 0.20/0.43 % --bmc1_pre_inst_reach_state false
% 0.20/0.43 % --bmc1_out_unsat_core false
% 0.20/0.43 % --bmc1_aig_witness_out false
% 0.20/0.43 % --bmc1_verbose false
% 0.20/0.43 % --bmc1_dump_clauses_tptp false
% 0.55/0.85 % --bmc1_dump_unsat_core_tptp false
% 0.55/0.85 % --bmc1_dump_file -
% 0.55/0.85 % --bmc1_ucm_expand_uc_limit 128
% 0.55/0.85 % --bmc1_ucm_n_expand_iterations 6
% 0.55/0.85 % --bmc1_ucm_extend_mode 1
% 0.55/0.85 % --bmc1_ucm_init_mode 2
% 0.55/0.85 % --bmc1_ucm_cone_mode none
% 0.55/0.85 % --bmc1_ucm_reduced_relation_type 0
% 0.55/0.85 % --bmc1_ucm_relax_model 4
% 0.55/0.85 % --bmc1_ucm_full_tr_after_sat true
% 0.55/0.85 % --bmc1_ucm_expand_neg_assumptions false
% 0.55/0.85 % --bmc1_ucm_layered_model none
% 0.55/0.85 % --bmc1_ucm_max_lemma_size 10
% 0.55/0.85
% 0.55/0.85 % ------ AIG Options
% 0.55/0.85
% 0.55/0.85 % --aig_mode false
% 0.55/0.85
% 0.55/0.85 % ------ Instantiation Options
% 0.55/0.85
% 0.55/0.85 % --instantiation_flag true
% 0.55/0.85 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.55/0.85 % --inst_solver_per_active 750
% 0.55/0.85 % --inst_solver_calls_frac 0.5
% 0.55/0.85 % --inst_passive_queue_type priority_queues
% 0.55/0.85 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.55/0.85 % --inst_passive_queues_freq [25;2]
% 0.55/0.85 % --inst_dismatching true
% 0.55/0.85 % --inst_eager_unprocessed_to_passive true
% 0.55/0.85 % --inst_prop_sim_given true
% 0.55/0.85 % --inst_prop_sim_new false
% 0.55/0.85 % --inst_orphan_elimination true
% 0.55/0.85 % --inst_learning_loop_flag true
% 0.55/0.85 % --inst_learning_start 3000
% 0.55/0.85 % --inst_learning_factor 2
% 0.55/0.85 % --inst_start_prop_sim_after_learn 3
% 0.55/0.85 % --inst_sel_renew solver
% 0.55/0.85 % --inst_lit_activity_flag true
% 0.55/0.85 % --inst_out_proof true
% 0.55/0.85
% 0.55/0.85 % ------ Resolution Options
% 0.55/0.85
% 0.55/0.85 % --resolution_flag true
% 0.55/0.85 % --res_lit_sel kbo_max
% 0.55/0.85 % --res_to_prop_solver none
% 0.55/0.85 % --res_prop_simpl_new false
% 0.55/0.85 % --res_prop_simpl_given false
% 0.55/0.85 % --res_passive_queue_type priority_queues
% 0.55/0.85 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.55/0.85 % --res_passive_queues_freq [15;5]
% 0.55/0.85 % --res_forward_subs full
% 0.55/0.85 % --res_backward_subs full
% 0.55/0.85 % --res_forward_subs_resolution true
% 0.55/0.85 % --res_backward_subs_resolution true
% 0.55/0.85 % --res_orphan_elimination false
% 0.55/0.85 % --res_time_limit 1000.
% 0.55/0.85 % --res_out_proof true
% 0.55/0.85 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_dc3c1d.s
% 0.55/0.85 % --modulo true
% 0.55/0.85
% 0.55/0.85 % ------ Combination Options
% 0.55/0.85
% 0.55/0.85 % --comb_res_mult 1000
% 0.55/0.85 % --comb_inst_mult 300
% 0.55/0.85 % ------
% 0.55/0.85
% 0.55/0.85 % ------ Parsing...% successful
% 0.55/0.85
% 0.55/0.85 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.55/0.85
% 0.55/0.85 % ------ Proving...
% 0.55/0.85 % ------ Problem Properties
% 0.55/0.85
% 0.55/0.85 %
% 0.55/0.85 % EPR false
% 0.55/0.85 % Horn false
% 0.55/0.85 % Has equality true
% 0.55/0.85
% 0.55/0.85 % % ------ Input Options Time Limit: Unbounded
% 0.55/0.85
% 0.55/0.85
% 0.55/0.85 Compiling...
% 0.55/0.85 Loading plugin: done.
% 0.55/0.85 Compiling...
% 0.55/0.85 Loading plugin: done.
% 0.55/0.85 Compiling...
% 0.55/0.85 Loading plugin: done.
% 0.55/0.85 Compiling...
% 0.55/0.85 Loading plugin: done.
% 0.55/0.85 % % ------ Current options:
% 0.55/0.85
% 0.55/0.85 % ------ Input Options
% 0.55/0.85
% 0.55/0.85 % --out_options all
% 0.55/0.85 % --tptp_safe_out true
% 0.55/0.85 % --problem_path ""
% 0.55/0.85 % --include_path ""
% 0.55/0.85 % --clausifier .//eprover
% 0.55/0.85 % --clausifier_options --tstp-format
% 0.55/0.85 % --stdin false
% 0.55/0.85 % --dbg_backtrace false
% 0.55/0.85 % --dbg_dump_prop_clauses false
% 0.55/0.85 % --dbg_dump_prop_clauses_file -
% 0.55/0.85 % --dbg_out_stat false
% 0.55/0.85
% 0.55/0.85 % ------ General Options
% 0.55/0.85
% 0.55/0.85 % --fof false
% 0.55/0.85 % --time_out_real 150.
% 0.55/0.85 % --time_out_prep_mult 0.2
% 0.55/0.85 % --time_out_virtual -1.
% 0.55/0.85 % --schedule none
% 0.55/0.85 % --ground_splitting input
% 0.55/0.85 % --splitting_nvd 16
% 0.55/0.85 % --non_eq_to_eq false
% 0.55/0.85 % --prep_gs_sim true
% 0.55/0.85 % --prep_unflatten false
% 0.55/0.85 % --prep_res_sim true
% 0.55/0.85 % --prep_upred true
% 0.55/0.85 % --res_sim_input true
% 0.55/0.85 % --clause_weak_htbl true
% 0.55/0.85 % --gc_record_bc_elim false
% 0.55/0.85 % --symbol_type_check false
% 0.55/0.85 % --clausify_out false
% 0.55/0.85 % --large_theory_mode false
% 0.55/0.85 % --prep_sem_filter none
% 0.55/0.85 % --prep_sem_filter_out false
% 0.55/0.85 % --preprocessed_out false
% 0.55/0.85 % --sub_typing false
% 0.55/0.85 % --brand_transform false
% 0.55/0.85 % --pure_diseq_elim true
% 0.55/0.85 % --min_unsat_core false
% 0.55/0.85 % --pred_elim true
% 0.55/0.85 % --add_important_lit false
% 0.55/0.85 % --soft_assumptions false
% 0.55/0.85 % --reset_solvers false
% 0.55/0.85 % --bc_imp_inh []
% 0.55/0.85 % --conj_cone_tolerance 1.5
% 0.55/0.85 % --prolific_symb_bound 500
% 0.55/0.85 % --lt_threshold 2000
% 0.55/0.85
% 0.55/0.85 % ------ SAT Options
% 0.55/0.85
% 0.55/0.85 % --sat_mode false
% 0.55/0.85 % --sat_fm_restart_options ""
% 0.55/0.85 % --sat_gr_def false
% 0.55/0.85 % --sat_epr_types true
% 0.55/0.85 % --sat_non_cyclic_types false
% 0.55/0.85 % --sat_finite_models false
% 0.55/0.85 % --sat_fm_lemmas false
% 0.55/0.85 % --sat_fm_prep false
% 0.55/0.85 % --sat_fm_uc_incr true
% 0.55/0.85 % --sat_out_model small
% 0.55/0.85 % --sat_out_clauses false
% 0.55/0.85
% 0.55/0.85 % ------ QBF Options
% 0.55/0.85
% 0.55/0.85 % --qbf_mode false
% 0.55/0.85 % --qbf_elim_univ true
% 0.55/0.85 % --qbf_sk_in true
% 0.55/0.85 % --qbf_pred_elim true
% 0.55/0.85 % --qbf_split 32
% 0.55/0.85
% 0.55/0.85 % ------ BMC1 Options
% 0.55/0.85
% 0.55/0.85 % --bmc1_incremental false
% 0.55/0.85 % --bmc1_axioms reachable_all
% 0.55/0.85 % --bmc1_min_bound 0
% 0.55/0.85 % --bmc1_max_bound -1
% 0.55/0.85 % --bmc1_max_bound_default -1
% 0.55/0.85 % --bmc1_symbol_reachability true
% 0.55/0.85 % --bmc1_property_lemmas false
% 0.55/0.85 % --bmc1_k_induction false
% 0.55/0.85 % --bmc1_non_equiv_states false
% 0.55/0.85 % --bmc1_deadlock false
% 0.55/0.85 % --bmc1_ucm false
% 0.55/0.85 % --bmc1_add_unsat_core none
% 0.55/0.85 % --bmc1_unsat_core_children false
% 0.55/0.85 % --bmc1_unsat_core_extrapolate_axioms false
% 0.55/0.85 % --bmc1_out_stat full
% 0.55/0.85 % --bmc1_ground_init false
% 0.55/0.85 % --bmc1_pre_inst_next_state false
% 0.55/0.85 % --bmc1_pre_inst_state false
% 0.55/0.85 % --bmc1_pre_inst_reach_state false
% 0.55/0.85 % --bmc1_out_unsat_core false
% 0.55/0.85 % --bmc1_aig_witness_out false
% 0.55/0.85 % --bmc1_verbose false
% 0.55/0.85 % --bmc1_dump_clauses_tptp false
% 0.55/0.85 % --bmc1_dump_unsat_core_tptp false
% 0.55/0.85 % --bmc1_dump_file -
% 0.55/0.85 % --bmc1_ucm_expand_uc_limit 128
% 0.55/0.85 % --bmc1_ucm_n_expand_iterations 6
% 0.55/0.85 % --bmc1_ucm_extend_mode 1
% 0.55/0.85 % --bmc1_ucm_init_mode 2
% 0.55/0.85 % --bmc1_ucm_cone_mode none
% 0.55/0.85 % --bmc1_ucm_reduced_relation_type 0
% 0.55/0.85 % --bmc1_ucm_relax_model 4
% 0.55/0.85 % --bmc1_ucm_full_tr_after_sat true
% 0.55/0.85 % --bmc1_ucm_expand_neg_assumptions false
% 0.55/0.85 % --bmc1_ucm_layered_model none
% 0.55/0.85 % --bmc1_ucm_max_lemma_size 10
% 0.55/0.85
% 0.55/0.85 % ------ AIG Options
% 0.55/0.85
% 0.55/0.85 % --aig_mode false
% 0.55/0.85
% 0.55/0.85 % ------ Instantiation Options
% 0.55/0.85
% 0.55/0.85 % --instantiation_flag true
% 0.55/0.85 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.55/0.85 % --inst_solver_per_active 750
% 0.55/0.85 % --inst_solver_calls_frac 0.5
% 0.55/0.85 % --inst_passive_queue_type priority_queues
% 0.55/0.85 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.55/0.85 % --inst_passive_queues_freq [25;2]
% 0.55/0.85 % --inst_dismatching true
% 0.55/0.85 % --inst_eager_unprocessed_to_passive true
% 0.55/0.85 % --inst_prop_sim_given true
% 0.55/0.85 % --inst_prop_sim_new false
% 0.55/0.85 % --inst_orphan_elimination true
% 0.55/0.85 % --inst_learning_loop_flag true
% 0.55/0.85 % --inst_learning_start 3000
% 0.55/0.85 % --inst_learning_factor 2
% 0.55/0.85 % --inst_start_prop_sim_after_learn 3
% 0.55/0.85 % --inst_sel_renew solver
% 0.55/0.85 % --inst_lit_activity_flag true
% 0.55/0.85 % --inst_out_proof true
% 0.55/0.85
% 0.55/0.85 % ------ Resolution Options
% 0.55/0.85
% 0.55/0.85 % --resolution_flag true
% 0.55/0.85 % --res_lit_sel kbo_max
% 0.55/0.85 % --res_to_prop_solver none
% 0.55/0.85 % --res_prop_simpl_new false
% 0.55/0.85 % --res_prop_simpl_given false
% 0.55/0.85 % --res_passive_queue_type priority_queues
% 0.55/0.85 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.55/0.85 % --res_passive_queues_freq [15;5]
% 0.55/0.85 % --res_forward_subs full
% 0.55/0.85 % --res_backward_subs full
% 0.55/0.85 % --res_forward_subs_resolution true
% 0.55/0.85 % --res_backward_subs_resolution true
% 0.55/0.85 % --res_orphan_elimination false
% 0.55/0.85 % --res_time_limit 1000.
% 0.55/0.85 % --res_out_proof true
% 0.55/0.85 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_dc3c1d.s
% 0.55/0.85 % --modulo true
% 0.55/0.85
% 0.55/0.85 % ------ Combination Options
% 0.55/0.85
% 0.55/0.85 % --comb_res_mult 1000
% 0.55/0.85 % --comb_inst_mult 300
% 0.55/0.85 % ------
% 0.55/0.85
% 0.55/0.85
% 0.55/0.85
% 0.55/0.85 % ------ Proving...
% 0.55/0.85 %
% 0.55/0.85
% 0.55/0.85
% 0.55/0.85 % Resolution empty clause
% 0.55/0.85
% 0.55/0.85 % ------ Statistics
% 0.55/0.85
% 0.55/0.85 % ------ General
% 0.55/0.85
% 0.55/0.85 % num_of_input_clauses: 138
% 0.55/0.85 % num_of_input_neg_conjectures: 1
% 0.55/0.85 % num_of_splits: 0
% 0.55/0.85 % num_of_split_atoms: 0
% 0.55/0.85 % num_of_sem_filtered_clauses: 0
% 0.55/0.85 % num_of_subtypes: 0
% 0.55/0.85 % monotx_restored_types: 0
% 0.55/0.85 % sat_num_of_epr_types: 0
% 0.55/0.85 % sat_num_of_non_cyclic_types: 0
% 0.55/0.85 % sat_guarded_non_collapsed_types: 0
% 0.55/0.85 % is_epr: 0
% 0.55/0.85 % is_horn: 0
% 0.55/0.85 % has_eq: 1
% 0.55/0.85 % num_pure_diseq_elim: 0
% 0.55/0.85 % simp_replaced_by: 0
% 0.55/0.85 % res_preprocessed: 2
% 0.55/0.85 % prep_upred: 0
% 0.55/0.85 % prep_unflattend: 0
% 0.55/0.85 % pred_elim_cands: 0
% 0.55/0.85 % pred_elim: 0
% 0.55/0.85 % pred_elim_cl: 0
% 0.55/0.85 % pred_elim_cycles: 0
% 0.55/0.85 % forced_gc_time: 0
% 0.55/0.85 % gc_basic_clause_elim: 0
% 0.55/0.85 % parsing_time: 0.006
% 0.55/0.85 % sem_filter_time: 0.
% 0.55/0.85 % pred_elim_time: 0.
% 0.55/0.85 % out_proof_time: 0.
% 0.55/0.85 % monotx_time: 0.
% 0.55/0.85 % subtype_inf_time: 0.
% 0.55/0.85 % unif_index_cands_time: 0.
% 0.55/0.85 % unif_index_add_time: 0.
% 0.55/0.85 % total_time: 0.438
% 0.55/0.85 % num_of_symbols: 47
% 0.55/0.85 % num_of_terms: 420
% 0.55/0.85
% 0.55/0.85 % ------ Propositional Solver
% 0.55/0.85
% 0.55/0.85 % prop_solver_calls: 1
% 0.55/0.85 % prop_fast_solver_calls: 3
% 0.55/0.85 % prop_num_of_clauses: 126
% 0.55/0.85 % prop_preprocess_simplified: 416
% 0.55/0.85 % prop_fo_subsumed: 0
% 0.55/0.85 % prop_solver_time: 0.
% 0.55/0.85 % prop_fast_solver_time: 0.
% 0.55/0.85 % prop_unsat_core_time: 0.
% 0.55/0.85
% 0.55/0.85 % ------ QBF
% 0.55/0.85
% 0.55/0.85 % qbf_q_res: 0
% 0.55/0.85 % qbf_num_tautologies: 0
% 0.55/0.85 % qbf_prep_cycles: 0
% 0.55/0.85
% 0.55/0.85 % ------ BMC1
% 0.55/0.85
% 0.55/0.85 % bmc1_current_bound: -1
% 0.55/0.85 % bmc1_last_solved_bound: -1
% 0.55/0.85 % bmc1_unsat_core_size: -1
% 0.55/0.85 % bmc1_unsat_core_parents_size: -1
% 0.55/0.85 % bmc1_merge_next_fun: 0
% 0.55/0.85 % bmc1_unsat_core_clauses_time: 0.
% 0.55/0.85
% 0.55/0.85 % ------ Instantiation
% 0.55/0.85
% 0.55/0.85 % inst_num_of_clauses: 121
% 0.55/0.85 % inst_num_in_passive: 0
% 0.55/0.86 % inst_num_in_active: 0
% 0.55/0.86 % inst_num_in_unprocessed: 138
% 0.55/0.86 % inst_num_of_loops: 0
% 0.55/0.86 % inst_num_of_learning_restarts: 0
% 0.55/0.86 % inst_num_moves_active_passive: 0
% 0.55/0.86 % inst_lit_activity: 0
% 0.55/0.86 % inst_lit_activity_moves: 0
% 0.55/0.86 % inst_num_tautologies: 0
% 0.55/0.86 % inst_num_prop_implied: 0
% 0.55/0.86 % inst_num_existing_simplified: 0
% 0.55/0.86 % inst_num_eq_res_simplified: 0
% 0.55/0.86 % inst_num_child_elim: 0
% 0.55/0.86 % inst_num_of_dismatching_blockings: 0
% 0.55/0.86 % inst_num_of_non_proper_insts: 0
% 0.55/0.86 % inst_num_of_duplicates: 0
% 0.55/0.86 % inst_inst_num_from_inst_to_res: 0
% 0.55/0.86 % inst_dismatching_checking_time: 0.
% 0.55/0.86
% 0.55/0.86 % ------ Resolution
% 0.55/0.86
% 0.55/0.86 % res_num_of_clauses: 133
% 0.55/0.86 % res_num_in_passive: 0
% 0.55/0.86 % res_num_in_active: 63
% 0.55/0.86 % res_num_of_loops: 1
% 0.55/0.86 % res_forward_subset_subsumed: 69
% 0.55/0.86 % res_backward_subset_subsumed: 0
% 0.55/0.86 % res_forward_subsumed: 0
% 0.55/0.86 % res_backward_subsumed: 0
% 0.55/0.86 % res_forward_subsumption_resolution: 1
% 0.55/0.86 % res_backward_subsumption_resolution: 0
% 0.55/0.86 % res_clause_to_clause_subsumption: 1
% 0.55/0.86 % res_orphan_elimination: 0
% 0.55/0.86 % res_tautology_del: 0
% 0.55/0.86 % res_num_eq_res_simplified: 0
% 0.55/0.86 % res_num_sel_changes: 0
% 0.55/0.86 % res_moves_from_active_to_pass: 0
% 0.55/0.86
% 0.55/0.86 % Status Unsatisfiable
% 0.55/0.86 % SZS status Unsatisfiable
% 0.55/0.86 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------