%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL853-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:22:25 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.46s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named inputERROR: Could not build tree for root to_be_clausified_0ERROR: MakeTreeStats fails)
% 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(cls_App_I4_J_0,axiom,
c_InductTermi_OIT(v_ta____),
input ).
fof(cls_App_I4_J_0_0,plain,
( c_InductTermi_OIT(v_ta____)
| $false ),
inference(orientation,[status(thm)],[cls_App_I4_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_App_I2_J_0,axiom,
c_InductTermi_OIT(v_s____),
input ).
fof(cls_App_I2_J_0_0,plain,
( c_InductTermi_OIT(v_s____)
| $false ),
inference(orientation,[status(thm)],[cls_App_I2_J_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_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_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_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_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_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_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_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_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_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_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]) ).
fof(def_lhs_atom1,axiom,
! [V_u,V_t,V_s,V_k] :
( lhs_atom1(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_0,plain,
! [V_k,V_s,V_t,V_u] :
( lhs_atom1(V_u,V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__App_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom2(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_1,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom2(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I8_J_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom3(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_2,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom3(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I9_J_0_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [V_u,V_k] :
( lhs_atom4(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_3,plain,
! [V_k,V_u] :
( lhs_atom4(V_u,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__eq_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [V_n] :
( lhs_atom5(V_n)
<=> ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_4,plain,
! [V_n] :
( lhs_atom5(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_less__not__refl_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_x] :
( lhs_atom6(V_x)
<=> ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_5,plain,
! [V_x] :
( lhs_atom6(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__less__le_1_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom7(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_6,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom7(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I4_J_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_t,V_s,V_k] :
( lhs_atom8(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_7,plain,
! [V_k,V_s,V_t] :
( lhs_atom8(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_lift_Osimps_I2_J_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_t,V_s,V_k] :
( lhs_atom9(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_8,plain,
! [V_k,V_s,V_t] :
( lhs_atom9(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__lift_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom10(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_9,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom10(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I5_J_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [V_nat,V_dB_H] :
( lhs_atom11(V_nat,V_dB_H)
<=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_10,plain,
! [V_dB_H,V_nat] :
( lhs_atom11(V_nat,V_dB_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I6_J_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,
( lhs_atom13
<=> c_InductTermi_OIT(v_s____) ),
inference(definition,[],[]) ).
fof(to_be_clausified_12,plain,
( lhs_atom13
| $false ),
inference(fold_definition,[status(thm)],[cls_App_I2_J_0_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_n] :
( lhs_atom14(V_n)
<=> c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_13,plain,
! [V_n] :
( lhs_atom14(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__IT_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
( lhs_atom15
<=> c_InductTermi_OIT(v_ta____) ),
inference(definition,[],[]) ).
fof(to_be_clausified_14,plain,
( lhs_atom15
| $false ),
inference(fold_definition,[status(thm)],[cls_App_I4_J_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
( lhs_atom16
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_15,plain,
( lhs_atom16
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
( lhs_atom17
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_16,plain,
( lhs_atom17
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
( lhs_atom18
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_17,plain,
( lhs_atom18
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom18]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X1,X2,X3,X4] :
( lhs_atom1(X1,X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_1,axiom,
! [X10,X11,X12] :
( lhs_atom10(X10,X11,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_2,axiom,
! [X2,X3,X4] :
( lhs_atom9(X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_3,axiom,
! [X2,X3,X4] :
( lhs_atom8(X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_4,axiom,
! [X10,X11,X12] :
( lhs_atom7(X10,X11,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_5,axiom,
! [X5,X6,X7] :
( lhs_atom3(X5,X6,X7)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_6,axiom,
! [X5,X6,X7] :
( lhs_atom2(X5,X6,X7)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_7,axiom,
! [X10,X5] :
( lhs_atom12(X10,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_8,axiom,
! [X10,X5] :
( lhs_atom11(X10,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_9,axiom,
! [X1,X4] :
( lhs_atom4(X1,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_10,axiom,
! [X8] :
( lhs_atom14(X8)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_11,axiom,
! [X9] :
( lhs_atom6(X9)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_12,axiom,
! [X8] :
( lhs_atom5(X8)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_13,axiom,
( lhs_atom18
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_14,axiom,
( lhs_atom17
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_15,axiom,
( lhs_atom16
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_16,axiom,
( lhs_atom15
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_17,axiom,
( lhs_atom13
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_18,plain,
! [X1,X2,X3,X4] : lhs_atom1(X1,X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_19,plain,
! [X10,X11,X12] : lhs_atom10(X10,X11,X12),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_20,plain,
! [X2,X3,X4] : lhs_atom9(X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_21,plain,
! [X2,X3,X4] : lhs_atom8(X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_22,plain,
! [X10,X11,X12] : lhs_atom7(X10,X11,X12),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_23,plain,
! [X5,X6,X7] : lhs_atom3(X5,X6,X7),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_24,plain,
! [X5,X6,X7] : lhs_atom2(X5,X6,X7),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_25,plain,
! [X10,X5] : lhs_atom12(X10,X5),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_26,plain,
! [X10,X5] : lhs_atom11(X10,X5),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_27,plain,
! [X1,X4] : lhs_atom4(X1,X4),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_28,plain,
! [X8] : lhs_atom14(X8),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_29,plain,
! [X9] : lhs_atom6(X9),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_30,plain,
! [X8] : lhs_atom5(X8),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_31,plain,
lhs_atom18,
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_32,plain,
lhs_atom17,
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_33,plain,
lhs_atom16,
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_34,plain,
lhs_atom15,
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_35,plain,
lhs_atom13,
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_36,plain,
! [X5,X6,X7,X8] : lhs_atom1(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_18]) ).
fof(c_0_37,plain,
! [X13,X14,X15] : lhs_atom10(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_19]) ).
fof(c_0_38,plain,
! [X5,X6,X7] : lhs_atom9(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_20]) ).
fof(c_0_39,plain,
! [X5,X6,X7] : lhs_atom8(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_21]) ).
fof(c_0_40,plain,
! [X13,X14,X15] : lhs_atom7(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_22]) ).
fof(c_0_41,plain,
! [X8,X9,X10] : lhs_atom3(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_23]) ).
fof(c_0_42,plain,
! [X8,X9,X10] : lhs_atom2(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_24]) ).
fof(c_0_43,plain,
! [X11,X12] : lhs_atom12(X11,X12),
inference(variable_rename,[status(thm)],[c_0_25]) ).
fof(c_0_44,plain,
! [X11,X12] : lhs_atom11(X11,X12),
inference(variable_rename,[status(thm)],[c_0_26]) ).
fof(c_0_45,plain,
! [X5,X6] : lhs_atom4(X5,X6),
inference(variable_rename,[status(thm)],[c_0_27]) ).
fof(c_0_46,plain,
! [X9] : lhs_atom14(X9),
inference(variable_rename,[status(thm)],[c_0_28]) ).
fof(c_0_47,plain,
! [X10] : lhs_atom6(X10),
inference(variable_rename,[status(thm)],[c_0_29]) ).
fof(c_0_48,plain,
! [X9] : lhs_atom5(X9),
inference(variable_rename,[status(thm)],[c_0_30]) ).
fof(c_0_49,plain,
lhs_atom18,
c_0_31 ).
fof(c_0_50,plain,
lhs_atom17,
c_0_32 ).
fof(c_0_51,plain,
lhs_atom16,
c_0_33 ).
fof(c_0_52,plain,
lhs_atom15,
c_0_34 ).
fof(c_0_53,plain,
lhs_atom13,
c_0_35 ).
cnf(c_0_54,plain,
lhs_atom1(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_55,plain,
lhs_atom10(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_56,plain,
lhs_atom9(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_57,plain,
lhs_atom8(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_58,plain,
lhs_atom7(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_59,plain,
lhs_atom3(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_60,plain,
lhs_atom2(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_61,plain,
lhs_atom12(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_62,plain,
lhs_atom11(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_63,plain,
lhs_atom4(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_64,plain,
lhs_atom14(X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_65,plain,
lhs_atom6(X1),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_66,plain,
lhs_atom5(X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_67,plain,
lhs_atom18,
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_68,plain,
lhs_atom17,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_69,plain,
lhs_atom16,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_70,plain,
lhs_atom15,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_71,plain,
lhs_atom13,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_72,plain,
lhs_atom1(X1,X2,X3,X4),
c_0_54,
[final] ).
cnf(c_0_73,plain,
lhs_atom10(X1,X2,X3),
c_0_55,
[final] ).
cnf(c_0_74,plain,
lhs_atom9(X1,X2,X3),
c_0_56,
[final] ).
cnf(c_0_75,plain,
lhs_atom8(X1,X2,X3),
c_0_57,
[final] ).
cnf(c_0_76,plain,
lhs_atom7(X1,X2,X3),
c_0_58,
[final] ).
cnf(c_0_77,plain,
lhs_atom3(X1,X2,X3),
c_0_59,
[final] ).
cnf(c_0_78,plain,
lhs_atom2(X1,X2,X3),
c_0_60,
[final] ).
cnf(c_0_79,plain,
lhs_atom12(X1,X2),
c_0_61,
[final] ).
cnf(c_0_80,plain,
lhs_atom11(X1,X2),
c_0_62,
[final] ).
cnf(c_0_81,plain,
lhs_atom4(X1,X2),
c_0_63,
[final] ).
cnf(c_0_82,plain,
lhs_atom14(X1),
c_0_64,
[final] ).
cnf(c_0_83,plain,
lhs_atom6(X1),
c_0_65,
[final] ).
cnf(c_0_84,plain,
lhs_atom5(X1),
c_0_66,
[final] ).
cnf(c_0_85,plain,
lhs_atom18,
c_0_67,
[final] ).
cnf(c_0_86,plain,
lhs_atom17,
c_0_68,
[final] ).
cnf(c_0_87,plain,
lhs_atom16,
c_0_69,
[final] ).
cnf(c_0_88,plain,
lhs_atom15,
c_0_70,
[final] ).
cnf(c_0_89,plain,
lhs_atom13,
c_0_71,
[final] ).
% End CNF derivation
cnf(c_0_72_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_72,def_lhs_atom1]) ).
cnf(c_0_73_0,axiom,
c_Lambda_OdB_OApp(X3,X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_73,def_lhs_atom10]) ).
cnf(c_0_74_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(X1,X3),X2,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_74,def_lhs_atom9]) ).
cnf(c_0_75_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_75,def_lhs_atom8]) ).
cnf(c_0_76_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OApp(X3,X2),
inference(unfold_definition,[status(thm)],[c_0_76,def_lhs_atom7]) ).
cnf(c_0_77_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OApp(X3,X2),
inference(unfold_definition,[status(thm)],[c_0_77,def_lhs_atom3]) ).
cnf(c_0_78_0,axiom,
c_Lambda_OdB_OApp(X3,X2) != c_Lambda_OdB_OAbs(X1),
inference(unfold_definition,[status(thm)],[c_0_78,def_lhs_atom2]) ).
cnf(c_0_79_0,axiom,
c_Lambda_OdB_OAbs(X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_79,def_lhs_atom12]) ).
cnf(c_0_80_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(unfold_definition,[status(thm)],[c_0_80,def_lhs_atom11]) ).
cnf(c_0_81_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_81,def_lhs_atom4]) ).
cnf(c_0_82_0,axiom,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X1)),
inference(unfold_definition,[status(thm)],[c_0_82,def_lhs_atom14]) ).
cnf(c_0_83_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_83,def_lhs_atom6]) ).
cnf(c_0_84_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_84,def_lhs_atom5]) ).
cnf(c_0_85_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_85,def_lhs_atom18]) ).
cnf(c_0_86_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_86,def_lhs_atom17]) ).
cnf(c_0_87_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_87,def_lhs_atom16]) ).
cnf(c_0_88_0,axiom,
c_InductTermi_OIT(v_ta____),
inference(unfold_definition,[status(thm)],[c_0_88,def_lhs_atom15]) ).
cnf(c_0_89_0,axiom,
c_InductTermi_OIT(v_s____),
inference(unfold_definition,[status(thm)],[c_0_89,def_lhs_atom13]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X12,X13,X10,X14] :
( ~ class_Orderings_Opreorder(X14)
| c_HOL_Oord__class_Oless(X10,X12,X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(X10,X13,X14) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_1_002,axiom,
! [X12,X13,X10,X14] :
( ~ class_Orderings_Oorder(X14)
| c_HOL_Oord__class_Oless(X12,X10,X14)
| ~ c_HOL_Oord__class_Oless(X12,X13,X14)
| ~ c_HOL_Oord__class_Oless(X13,X10,X14) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_2_003,axiom,
! [X22,X23,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_HOL_Oord__class_Oless(X22,X23,X14)
| ~ c_HOL_Oord__class_Oless(X23,X22,X14) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_3_004,axiom,
! [X13,X10,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_HOL_Oord__class_Oless(X13,X10,X14)
| ~ c_HOL_Oord__class_Oless(X10,X13,X14) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_4_005,axiom,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| ~ c_HOL_Oord__class_Oless(X10,X13,X14)
| ~ c_HOL_Oord__class_Oless(X13,X10,X14) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_5_006,axiom,
! [X22,X23,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_HOL_Oord__class_Oless(X23,X22,X14)
| ~ c_HOL_Oord__class_Oless(X22,X23,X14) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_6_007,axiom,
! [X21,X6,X3] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X6),X21,X3) = c_Lambda_OdB_OVar(X6)
| ~ c_HOL_Oord__class_Oless(X6,X3,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_7_008,axiom,
! [X1,X6,X3] :
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X3),X6))
| ~ c_InductTermi_OIT(X1) ),
file('<stdin>',cls_subst__Var__IT_0) ).
fof(c_0_8_009,axiom,
! [X11,X9,X3] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X3),X11,X9) = c_Lambda_OdB_OVar(X3)
| X3 = X9
| c_HOL_Oord__class_Oless(X9,X3,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_9_010,axiom,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| X10 = X13
| c_HOL_Oord__class_Oless(X10,X13,X14)
| c_HOL_Oord__class_Oless(X13,X10,X14) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_10_011,axiom,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_HOL_Oord__class_Oless(X13,X10,X14)
| X10 = X13
| c_HOL_Oord__class_Oless(X10,X13,X14) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_11_012,axiom,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_HOL_Oord__class_Oless(X13,X10,X14)
| c_HOL_Oord__class_Oless(X10,X13,X14)
| X10 = X13 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_12_013,axiom,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| X10 = X13
| c_HOL_Oord__class_Oless(X13,X10,X14)
| c_HOL_Oord__class_Oless(X10,X13,X14) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_13_014,axiom,
! [X13,X10,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_HOL_Oord__class_Oless(X13,X10,X14)
| c_HOL_Oord__class_Oless(X10,X13,X14)
| X10 = X13 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_14_015,axiom,
! [X10,X11] :
( c_HOL_Oord__class_Oless(X10,X10,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X10),X11,X10) = X11 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_15_016,axiom,
! [X13,X10] :
( c_HOL_Oord__class_Oless(X13,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,X13,tc_nat)
| X10 = X13 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_16_017,axiom,
! [X15,X16] :
( c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| X16 = X15 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_17_018,axiom,
! [X9,X3] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X3),X9) = c_Lambda_OdB_OVar(X3)
| ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_18_019,axiom,
! [X10,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_HOL_Oord__class_Oless(X10,X10,X14) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_19_020,axiom,
! [X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| ~ c_HOL_Oord__class_Oless(X10,X10,X14) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_20_021,axiom,
! [X10,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_HOL_Oord__class_Oless(X10,X10,X14) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_21_022,axiom,
! [X2,X3] :
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X2,c_Lambda_OdB_OVar(X3)))
| ~ c_InductTermi_OIT(X2) ),
file('<stdin>',cls_app__Var__IT_0) ).
fof(c_0_22_023,axiom,
! [X17,X18,X19,X20] :
( c_Lambda_OdB_OApp(X20,X18) != c_Lambda_OdB_OApp(X19,X17)
| X20 = X19 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_23_024,axiom,
! [X17,X18,X19,X20] :
( c_Lambda_OdB_OApp(X20,X18) != c_Lambda_OdB_OApp(X19,X17)
| X18 = X17 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_24_025,axiom,
! [X2,X3] :
( c_InductTermi_OIT(c_Lambda_Olift(X2,X3))
| ~ c_InductTermi_OIT(X2) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_25_026,axiom,
! [X1] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_26_027,axiom,
! [X7,X8] :
( c_Lambda_OdB_OAbs(X8) != c_Lambda_OdB_OAbs(X7)
| X8 = X7 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_27_028,axiom,
! [X4,X5] :
( c_Lambda_OdB_OVar(X5) != c_Lambda_OdB_OVar(X4)
| X5 = X4 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_28_029,plain,
! [X12,X13,X10,X14] :
( ~ class_Orderings_Opreorder(X14)
| c_HOL_Oord__class_Oless(X10,X12,X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(X10,X13,X14) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_29_030,plain,
! [X12,X13,X10,X14] :
( ~ class_Orderings_Oorder(X14)
| c_HOL_Oord__class_Oless(X12,X10,X14)
| ~ c_HOL_Oord__class_Oless(X12,X13,X14)
| ~ c_HOL_Oord__class_Oless(X13,X10,X14) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_30_031,plain,
! [X22,X23,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_HOL_Oord__class_Oless(X22,X23,X14)
| ~ c_HOL_Oord__class_Oless(X23,X22,X14) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_31_032,plain,
! [X13,X10,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_HOL_Oord__class_Oless(X13,X10,X14)
| ~ c_HOL_Oord__class_Oless(X10,X13,X14) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_32_033,plain,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| ~ c_HOL_Oord__class_Oless(X10,X13,X14)
| ~ c_HOL_Oord__class_Oless(X13,X10,X14) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_33_034,plain,
! [X22,X23,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_HOL_Oord__class_Oless(X23,X22,X14)
| ~ c_HOL_Oord__class_Oless(X22,X23,X14) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_34_035,plain,
! [X21,X6,X3] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X6),X21,X3) = c_Lambda_OdB_OVar(X6)
| ~ c_HOL_Oord__class_Oless(X6,X3,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_35_036,plain,
! [X1,X6,X3] :
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X3),X6))
| ~ c_InductTermi_OIT(X1) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_36_037,axiom,
! [X11,X9,X3] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X3),X11,X9) = c_Lambda_OdB_OVar(X3)
| X3 = X9
| c_HOL_Oord__class_Oless(X9,X3,tc_nat) ),
c_0_8 ).
fof(c_0_37_038,plain,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| X10 = X13
| c_HOL_Oord__class_Oless(X10,X13,X14)
| c_HOL_Oord__class_Oless(X13,X10,X14) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_38_039,plain,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_HOL_Oord__class_Oless(X13,X10,X14)
| X10 = X13
| c_HOL_Oord__class_Oless(X10,X13,X14) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_39_040,plain,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_HOL_Oord__class_Oless(X13,X10,X14)
| c_HOL_Oord__class_Oless(X10,X13,X14)
| X10 = X13 ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_40_041,plain,
! [X13,X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| X10 = X13
| c_HOL_Oord__class_Oless(X13,X10,X14)
| c_HOL_Oord__class_Oless(X10,X13,X14) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_41_042,plain,
! [X13,X10,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_HOL_Oord__class_Oless(X13,X10,X14)
| c_HOL_Oord__class_Oless(X10,X13,X14)
| X10 = X13 ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_42_043,axiom,
! [X10,X11] :
( c_HOL_Oord__class_Oless(X10,X10,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X10),X11,X10) = X11 ),
c_0_14 ).
fof(c_0_43_044,axiom,
! [X13,X10] :
( c_HOL_Oord__class_Oless(X13,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,X13,tc_nat)
| X10 = X13 ),
c_0_15 ).
fof(c_0_44_045,axiom,
! [X15,X16] :
( c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| X16 = X15 ),
c_0_16 ).
fof(c_0_45_046,plain,
! [X9,X3] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X3),X9) = c_Lambda_OdB_OVar(X3)
| ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_46_047,plain,
! [X10,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_HOL_Oord__class_Oless(X10,X10,X14) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_47_048,plain,
! [X10,X14] :
( ~ class_Orderings_Olinorder(X14)
| ~ c_HOL_Oord__class_Oless(X10,X10,X14) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_48_049,plain,
! [X10,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_HOL_Oord__class_Oless(X10,X10,X14) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_49_050,plain,
! [X2,X3] :
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X2,c_Lambda_OdB_OVar(X3)))
| ~ c_InductTermi_OIT(X2) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_50_051,axiom,
! [X17,X18,X19,X20] :
( c_Lambda_OdB_OApp(X20,X18) != c_Lambda_OdB_OApp(X19,X17)
| X20 = X19 ),
c_0_22 ).
fof(c_0_51_052,axiom,
! [X17,X18,X19,X20] :
( c_Lambda_OdB_OApp(X20,X18) != c_Lambda_OdB_OApp(X19,X17)
| X18 = X17 ),
c_0_23 ).
fof(c_0_52_053,plain,
! [X2,X3] :
( c_InductTermi_OIT(c_Lambda_Olift(X2,X3))
| ~ c_InductTermi_OIT(X2) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_53_054,plain,
! [X1] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_54_055,axiom,
! [X7,X8] :
( c_Lambda_OdB_OAbs(X8) != c_Lambda_OdB_OAbs(X7)
| X8 = X7 ),
c_0_26 ).
fof(c_0_55_056,axiom,
! [X4,X5] :
( c_Lambda_OdB_OVar(X5) != c_Lambda_OdB_OVar(X4)
| X5 = X4 ),
c_0_27 ).
fof(c_0_56_057,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Opreorder(X18)
| c_HOL_Oord__class_Oless(X17,X15,X18)
| ~ c_HOL_Oord__class_Oless(X16,X15,X18)
| ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_28]) ).
fof(c_0_57_058,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Oorder(X18)
| c_HOL_Oord__class_Oless(X15,X17,X18)
| ~ c_HOL_Oord__class_Oless(X15,X16,X18)
| ~ c_HOL_Oord__class_Oless(X16,X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_29]) ).
fof(c_0_58_059,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_30]) ).
fof(c_0_59_060,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| ~ c_HOL_Oord__class_Oless(X15,X16,X17)
| ~ c_HOL_Oord__class_Oless(X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_31]) ).
fof(c_0_60_061,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| ~ c_HOL_Oord__class_Oless(X16,X15,X17)
| ~ c_HOL_Oord__class_Oless(X15,X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_32]) ).
fof(c_0_61_062,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_33]) ).
fof(c_0_62_063,plain,
! [X22,X23,X24] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X23),X22,X24) = c_Lambda_OdB_OVar(X23)
| ~ c_HOL_Oord__class_Oless(X23,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_34]) ).
fof(c_0_63_064,plain,
! [X7,X8,X9] :
( c_InductTermi_OIT(c_Lambda_Osubst(X7,c_Lambda_OdB_OVar(X9),X8))
| ~ c_InductTermi_OIT(X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_35])])]) ).
fof(c_0_64_065,plain,
! [X12,X13,X14] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X12,X13) = c_Lambda_OdB_OVar(X14)
| X14 = X13
| c_HOL_Oord__class_Oless(X13,X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_36]) ).
fof(c_0_65_066,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| X16 = X15
| c_HOL_Oord__class_Oless(X16,X15,X17)
| c_HOL_Oord__class_Oless(X15,X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_37]) ).
fof(c_0_66_067,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_HOL_Oord__class_Oless(X15,X16,X17)
| X16 = X15
| c_HOL_Oord__class_Oless(X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_38]) ).
fof(c_0_67_068,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_HOL_Oord__class_Oless(X15,X16,X17)
| c_HOL_Oord__class_Oless(X16,X15,X17)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_39]) ).
fof(c_0_68_069,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| X16 = X15
| c_HOL_Oord__class_Oless(X15,X16,X17)
| c_HOL_Oord__class_Oless(X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_40]) ).
fof(c_0_69_070,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X17)
| c_HOL_Oord__class_Oless(X15,X16,X17)
| c_HOL_Oord__class_Oless(X16,X15,X17)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_41]) ).
fof(c_0_70_071,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(X12,X12,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X13,X12) = X13 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_42])])]) ).
fof(c_0_71_072,plain,
! [X14,X15] :
( c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_43]) ).
fof(c_0_72_073,plain,
! [X17,X18] :
( c_HOL_Oord__class_Oless(X17,X18,tc_nat)
| c_HOL_Oord__class_Oless(X18,X17,tc_nat)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_44]) ).
fof(c_0_73_074,plain,
! [X10,X11] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X10) = c_Lambda_OdB_OVar(X11)
| ~ c_HOL_Oord__class_Oless(X11,X10,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_45]) ).
fof(c_0_74_075,plain,
! [X15,X16] :
( ~ class_Orderings_Opreorder(X16)
| ~ c_HOL_Oord__class_Oless(X15,X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_46]) ).
fof(c_0_75_076,plain,
! [X15,X16] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_HOL_Oord__class_Oless(X15,X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_47]) ).
fof(c_0_76_077,plain,
! [X15,X16] :
( ~ class_Orderings_Oorder(X16)
| ~ c_HOL_Oord__class_Oless(X15,X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_48]) ).
fof(c_0_77_078,plain,
! [X4,X5] :
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X4,c_Lambda_OdB_OVar(X5)))
| ~ c_InductTermi_OIT(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_49])])]) ).
fof(c_0_78_079,plain,
! [X21,X22,X23,X24] :
( c_Lambda_OdB_OApp(X24,X22) != c_Lambda_OdB_OApp(X23,X21)
| X24 = X23 ),
inference(variable_rename,[status(thm)],[c_0_50]) ).
fof(c_0_79_080,plain,
! [X21,X22,X23,X24] :
( c_Lambda_OdB_OApp(X24,X22) != c_Lambda_OdB_OApp(X23,X21)
| X22 = X21 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_51])])]) ).
fof(c_0_80_081,plain,
! [X4,X5] :
( c_InductTermi_OIT(c_Lambda_Olift(X4,X5))
| ~ c_InductTermi_OIT(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_52])])]) ).
fof(c_0_81_082,plain,
! [X2] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X2))
| ~ c_InductTermi_OIT(X2) ),
inference(variable_rename,[status(thm)],[c_0_53]) ).
fof(c_0_82_083,plain,
! [X9,X10] :
( c_Lambda_OdB_OAbs(X10) != c_Lambda_OdB_OAbs(X9)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_54]) ).
fof(c_0_83_084,plain,
! [X6,X7] :
( c_Lambda_OdB_OVar(X7) != c_Lambda_OdB_OVar(X6)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_55]) ).
cnf(c_0_84_085,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_56]) ).
cnf(c_0_85_086,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_57]) ).
cnf(c_0_86_087,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_58]) ).
cnf(c_0_87_088,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_59]) ).
cnf(c_0_88_089,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_60]) ).
cnf(c_0_89_090,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_61]) ).
cnf(c_0_90,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_62]) ).
cnf(c_0_91,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_63]) ).
cnf(c_0_92,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_64]) ).
cnf(c_0_93,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_65]) ).
cnf(c_0_94,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_66]) ).
cnf(c_0_95,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_67]) ).
cnf(c_0_96,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_68]) ).
cnf(c_0_97,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_69]) ).
cnf(c_0_98,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_70]) ).
cnf(c_0_99,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_71]) ).
cnf(c_0_100,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_72]) ).
cnf(c_0_101,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_73]) ).
cnf(c_0_102,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_103,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_104,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_105,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_77]) ).
cnf(c_0_106,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_107,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_108,plain,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_109,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_110,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_111,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_112,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_84,
[final] ).
cnf(c_0_113,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_85,
[final] ).
cnf(c_0_114,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_86,
[final] ).
cnf(c_0_115,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_87,
[final] ).
cnf(c_0_116,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_88,
[final] ).
cnf(c_0_117,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_89,
[final] ).
cnf(c_0_118,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_90,
[final] ).
cnf(c_0_119,plain,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))
| ~ c_InductTermi_OIT(X1) ),
c_0_91,
[final] ).
cnf(c_0_120,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_92,
[final] ).
cnf(c_0_121,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_93,
[final] ).
cnf(c_0_122,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_94,
[final] ).
cnf(c_0_123,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_95,
[final] ).
cnf(c_0_124,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_96,
[final] ).
cnf(c_0_125,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_97,
[final] ).
cnf(c_0_126,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_98,
[final] ).
cnf(c_0_127,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_99,
[final] ).
cnf(c_0_128,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_100,
[final] ).
cnf(c_0_129,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_101,
[final] ).
cnf(c_0_130,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_102,
[final] ).
cnf(c_0_131,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_103,
[final] ).
cnf(c_0_132,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_104,
[final] ).
cnf(c_0_133,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OApp(X1,c_Lambda_OdB_OVar(X2)))
| ~ c_InductTermi_OIT(X1) ),
c_0_105,
[final] ).
cnf(c_0_134,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
c_0_106,
[final] ).
cnf(c_0_135,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
c_0_107,
[final] ).
cnf(c_0_136,plain,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
c_0_108,
[final] ).
cnf(c_0_137,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
c_0_109,
[final] ).
cnf(c_0_138,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_110,
[final] ).
cnf(c_0_139,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_111,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_112_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_112]) ).
cnf(c_0_112_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_112]) ).
cnf(c_0_112_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_112]) ).
cnf(c_0_112_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_112]) ).
cnf(c_0_113_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_113]) ).
cnf(c_0_113_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_113]) ).
cnf(c_0_113_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_113]) ).
cnf(c_0_113_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_113]) ).
cnf(c_0_114_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_114]) ).
cnf(c_0_114_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_114]) ).
cnf(c_0_114_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_114]) ).
cnf(c_0_115_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_115]) ).
cnf(c_0_115_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_115]) ).
cnf(c_0_115_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_115]) ).
cnf(c_0_116_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_116]) ).
cnf(c_0_116_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_116]) ).
cnf(c_0_116_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_116]) ).
cnf(c_0_117_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_117]) ).
cnf(c_0_117_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_117]) ).
cnf(c_0_117_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_117]) ).
cnf(c_0_118_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_118]) ).
cnf(c_0_118_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_118]) ).
cnf(c_0_119_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_119]) ).
cnf(c_0_119_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_119]) ).
cnf(c_0_120_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_120]) ).
cnf(c_0_120_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_120]) ).
cnf(c_0_120_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_120]) ).
cnf(c_0_121_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_121]) ).
cnf(c_0_121_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_121]) ).
cnf(c_0_121_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_121]) ).
cnf(c_0_121_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_121]) ).
cnf(c_0_122_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_122]) ).
cnf(c_0_122_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_122]) ).
cnf(c_0_122_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_122]) ).
cnf(c_0_122_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_122]) ).
cnf(c_0_123_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_123]) ).
cnf(c_0_123_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_123]) ).
cnf(c_0_123_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_123]) ).
cnf(c_0_123_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_123]) ).
cnf(c_0_124_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_124]) ).
cnf(c_0_124_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_124]) ).
cnf(c_0_124_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_124]) ).
cnf(c_0_124_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_124]) ).
cnf(c_0_125_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_125]) ).
cnf(c_0_125_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_125]) ).
cnf(c_0_125_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_125]) ).
cnf(c_0_125_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_125]) ).
cnf(c_0_126_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_126]) ).
cnf(c_0_126_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_126]) ).
cnf(c_0_127_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_127]) ).
cnf(c_0_127_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_127]) ).
cnf(c_0_127_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_127]) ).
cnf(c_0_128_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_128]) ).
cnf(c_0_128_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_128]) ).
cnf(c_0_128_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_128]) ).
cnf(c_0_129_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_129]) ).
cnf(c_0_129_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_129]) ).
cnf(c_0_130_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_130]) ).
cnf(c_0_130_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_130]) ).
cnf(c_0_131_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_131]) ).
cnf(c_0_131_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_131]) ).
cnf(c_0_132_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_132]) ).
cnf(c_0_132_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_132]) ).
cnf(c_0_133_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_133]) ).
cnf(c_0_133_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_133]) ).
cnf(c_0_134_0,axiom,
( X1 = X2
| c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_134]) ).
cnf(c_0_134_1,axiom,
( c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_134]) ).
cnf(c_0_135_0,axiom,
( X1 = X2
| c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_135]) ).
cnf(c_0_135_1,axiom,
( c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_135]) ).
cnf(c_0_136_0,axiom,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_136]) ).
cnf(c_0_136_1,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_Olift(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_136]) ).
cnf(c_0_137_0,axiom,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_137]) ).
cnf(c_0_137_1,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_137]) ).
cnf(c_0_138_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_138]) ).
cnf(c_0_138_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_138]) ).
cnf(c_0_139_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_139]) ).
cnf(c_0_139_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_139]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_091,negated_conjecture,
~ c_InductTermi_OIT(v_s____),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_092,negated_conjecture,
~ c_InductTermi_OIT(v_s____),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_2_093,negated_conjecture,
~ c_InductTermi_OIT(v_s____),
c_0_1 ).
cnf(c_0_3_094,negated_conjecture,
~ c_InductTermi_OIT(v_s____),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_095,negated_conjecture,
~ c_InductTermi_OIT(v_s____),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_77,plain,
c_InductTermi_OIT(v_s____),
file('/export/starexec/sandbox2/tmp/iprover_modulo_2155f5.p',c_0_89_0) ).
cnf(c_95,negated_conjecture,
~ c_InductTermi_OIT(v_s____),
file('/export/starexec/sandbox2/tmp/iprover_modulo_2155f5.p',c_0_4) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_77,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL853-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : iprover_modulo %s %d
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 00:39:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Running in mono-core mode
% 0.09/0.44 % Orienting using strategy Equiv(ClausalAll)
% 0.09/0.44 % Orientation found
% 0.09/0.44 % 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/sandbox2/tmp/iprover_proof_224355.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_2155f5.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_a299b5 | grep -v "SZS"
% 0.20/0.46
% 0.20/0.46 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.46
% 0.20/0.46 %
% 0.20/0.46 % ------ iProver source info
% 0.20/0.46
% 0.20/0.46 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.46 % git: non_committed_changes: true
% 0.20/0.46 % git: last_make_outside_of_git: true
% 0.20/0.46
% 0.20/0.46 %
% 0.20/0.46 % ------ Input Options
% 0.20/0.46
% 0.20/0.46 % --out_options all
% 0.20/0.46 % --tptp_safe_out true
% 0.20/0.46 % --problem_path ""
% 0.20/0.46 % --include_path ""
% 0.20/0.46 % --clausifier .//eprover
% 0.20/0.46 % --clausifier_options --tstp-format
% 0.20/0.46 % --stdin false
% 0.20/0.46 % --dbg_backtrace false
% 0.20/0.46 % --dbg_dump_prop_clauses false
% 0.20/0.46 % --dbg_dump_prop_clauses_file -
% 0.20/0.46 % --dbg_out_stat false
% 0.20/0.46
% 0.20/0.46 % ------ General Options
% 0.20/0.46
% 0.20/0.46 % --fof false
% 0.20/0.46 % --time_out_real 150.
% 0.20/0.46 % --time_out_prep_mult 0.2
% 0.20/0.46 % --time_out_virtual -1.
% 0.20/0.46 % --schedule none
% 0.20/0.46 % --ground_splitting input
% 0.20/0.46 % --splitting_nvd 16
% 0.20/0.46 % --non_eq_to_eq false
% 0.20/0.46 % --prep_gs_sim true
% 0.20/0.46 % --prep_unflatten false
% 0.20/0.46 % --prep_res_sim true
% 0.20/0.46 % --prep_upred true
% 0.20/0.46 % --res_sim_input true
% 0.20/0.46 % --clause_weak_htbl true
% 0.20/0.46 % --gc_record_bc_elim false
% 0.20/0.46 % --symbol_type_check false
% 0.20/0.46 % --clausify_out false
% 0.20/0.46 % --large_theory_mode false
% 0.20/0.46 % --prep_sem_filter none
% 0.20/0.46 % --prep_sem_filter_out false
% 0.20/0.46 % --preprocessed_out false
% 0.20/0.46 % --sub_typing false
% 0.20/0.46 % --brand_transform false
% 0.20/0.46 % --pure_diseq_elim true
% 0.20/0.46 % --min_unsat_core false
% 0.20/0.46 % --pred_elim true
% 0.20/0.46 % --add_important_lit false
% 0.20/0.46 % --soft_assumptions false
% 0.20/0.46 % --reset_solvers false
% 0.20/0.46 % --bc_imp_inh []
% 0.20/0.46 % --conj_cone_tolerance 1.5
% 0.20/0.46 % --prolific_symb_bound 500
% 0.20/0.46 % --lt_threshold 2000
% 0.20/0.46
% 0.20/0.46 % ------ SAT Options
% 0.20/0.46
% 0.20/0.46 % --sat_mode false
% 0.20/0.46 % --sat_fm_restart_options ""
% 0.20/0.46 % --sat_gr_def false
% 0.20/0.46 % --sat_epr_types true
% 0.20/0.46 % --sat_non_cyclic_types false
% 0.20/0.46 % --sat_finite_models false
% 0.20/0.46 % --sat_fm_lemmas false
% 0.20/0.46 % --sat_fm_prep false
% 0.20/0.46 % --sat_fm_uc_incr true
% 0.20/0.46 % --sat_out_model small
% 0.20/0.46 % --sat_out_clauses false
% 0.20/0.46
% 0.20/0.46 % ------ QBF Options
% 0.20/0.46
% 0.20/0.46 % --qbf_mode false
% 0.20/0.46 % --qbf_elim_univ true
% 0.20/0.46 % --qbf_sk_in true
% 0.20/0.46 % --qbf_pred_elim true
% 0.20/0.46 % --qbf_split 32
% 0.20/0.46
% 0.20/0.46 % ------ BMC1 Options
% 0.20/0.46
% 0.20/0.46 % --bmc1_incremental false
% 0.20/0.46 % --bmc1_axioms reachable_all
% 0.20/0.46 % --bmc1_min_bound 0
% 0.20/0.46 % --bmc1_max_bound -1
% 0.20/0.46 % --bmc1_max_bound_default -1
% 0.20/0.46 % --bmc1_symbol_reachability true
% 0.20/0.46 % --bmc1_property_lemmas false
% 0.20/0.46 % --bmc1_k_induction false
% 0.20/0.46 % --bmc1_non_equiv_states false
% 0.20/0.46 % --bmc1_deadlock false
% 0.20/0.46 % --bmc1_ucm false
% 0.20/0.46 % --bmc1_add_unsat_core none
% 0.20/0.46 % --bmc1_unsat_core_children false
% 0.20/0.46 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.46 % --bmc1_out_stat full
% 0.20/0.46 % --bmc1_ground_init false
% 0.20/0.46 % --bmc1_pre_inst_next_state false
% 0.20/0.46 % --bmc1_pre_inst_state false
% 0.20/0.46 % --bmc1_pre_inst_reach_state false
% 0.20/0.46 % --bmc1_out_unsat_core false
% 0.20/0.46 % --bmc1_aig_witness_out false
% 0.20/0.46 % --bmc1_verbose false
% 0.20/0.46 % --bmc1_dump_clauses_tptp false
% 0.20/0.46 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.46 % --bmc1_dump_file -
% 0.20/0.46 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.46 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.46 % --bmc1_ucm_extend_mode 1
% 0.20/0.46 % --bmc1_ucm_init_mode 2
% 0.20/0.46 % --bmc1_ucm_cone_mode none
% 0.20/0.46 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.46 % --bmc1_ucm_relax_model 4
% 0.20/0.46 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.46 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.46 % --bmc1_ucm_layered_model none
% 0.20/0.46 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.46
% 0.20/0.46 % ------ AIG Options
% 0.20/0.46
% 0.20/0.46 % --aig_mode false
% 0.20/0.46
% 0.20/0.46 % ------ Instantiation Options
% 0.20/0.46
% 0.20/0.46 % --instantiation_flag true
% 0.20/0.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.46 % --inst_solver_per_active 750
% 0.20/0.46 % --inst_solver_calls_frac 0.5
% 0.20/0.46 % --inst_passive_queue_type priority_queues
% 0.20/0.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.46 % --inst_passive_queues_freq [25;2]
% 0.20/0.46 % --inst_dismatching true
% 0.20/0.46 % --inst_eager_unprocessed_to_passive true
% 0.20/0.46 % --inst_prop_sim_given true
% 0.20/0.46 % --inst_prop_sim_new false
% 0.20/0.46 % --inst_orphan_elimination true
% 0.20/0.46 % --inst_learning_loop_flag true
% 0.20/0.46 % --inst_learning_start 3000
% 0.20/0.46 % --inst_learning_factor 2
% 0.20/0.46 % --inst_start_prop_sim_after_learn 3
% 0.20/0.46 % --inst_sel_renew solver
% 0.20/0.46 % --inst_lit_activity_flag true
% 0.20/0.46 % --inst_out_proof true
% 0.20/0.46
% 0.20/0.46 % ------ Resolution Options
% 0.20/0.46
% 0.20/0.46 % --resolution_flag true
% 0.20/0.46 % --res_lit_sel kbo_max
% 0.20/0.46 % --res_to_prop_solver none
% 0.20/0.46 % --res_prop_simpl_new false
% 0.20/0.46 % --res_prop_simpl_given false
% 0.20/0.46 % --res_passive_queue_type priority_queues
% 0.20/0.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.46 % --res_passive_queues_freq [15;5]
% 0.20/0.46 % --res_forward_subs full
% 0.20/0.46 % --res_backward_subs full
% 0.20/0.46 % --res_forward_subs_resolution true
% 0.20/0.46 % --res_backward_subs_resolution true
% 0.20/0.46 % --res_orphan_elimination false
% 0.20/0.46 % --res_time_limit 1000.
% 0.20/0.46 % --res_out_proof true
% 0.20/0.46 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_224355.s
% 0.20/0.46 % --modulo true
% 0.20/0.46
% 0.20/0.46 % ------ Combination Options
% 0.20/0.46
% 0.20/0.46 % --comb_res_mult 1000
% 0.20/0.46 % --comb_inst_mult 300
% 0.20/0.46 % ------
% 0.20/0.46
% 0.20/0.46 % ------ Parsing...% successful
% 0.20/0.46
% 0.20/0.46 %
% 0.20/0.46
% 0.20/0.46
% 0.20/0.46 % ------ Statistics
% 0.20/0.46
% 0.20/0.46 % ------ General
% 0.20/0.46
% 0.20/0.46 % num_of_input_clauses: 96
% 0.20/0.46 % num_of_input_neg_conjectures: 1
% 0.20/0.46 % num_of_splits: 0
% 0.20/0.46 % num_of_split_atoms: 0
% 0.20/0.46 % num_of_sem_filtered_clauses: 0
% 0.20/0.46 % num_of_subtypes: 0
% 0.20/0.46 % monotx_restored_types: 0
% 0.20/0.46 % sat_num_of_epr_types: 0
% 0.20/0.46 % sat_num_of_non_cyclic_types: 0
% 0.20/0.46 % sat_guarded_non_collapsed_types: 0
% 0.20/0.46 % is_epr: 0
% 0.20/0.46 % is_horn: 0
% 0.20/0.46 % has_eq: 0
% 0.20/0.46 % num_pure_diseq_elim: 0
% 0.20/0.46 % simp_replaced_by: 0
% 0.20/0.46 % res_preprocessed: 0
% 0.20/0.46 % prep_upred: 0
% 0.20/0.46 % prep_unflattend: 0
% 0.20/0.46 % pred_elim_cands: 0
% 0.20/0.46 % pred_elim: 0
% 0.20/0.46 % pred_elim_cl: 0
% 0.20/0.46 % pred_elim_cycles: 0
% 0.20/0.46 % forced_gc_time: 0
% 0.20/0.46 % gc_basic_clause_elim: 0
% 0.20/0.46 % parsing_time: 0.002
% 0.20/0.46 % sem_filter_time: 0.
% 0.20/0.46 % pred_elim_time: 0.
% 0.20/0.46 % out_proof_time: 0.
% 0.20/0.46 % monotx_time: 0.
% 0.20/0.46 % subtype_inf_time: 0.
% 0.20/0.46 % unif_index_cands_time: 0.
% 0.20/0.46 % unif_index_add_time: 0.
% 0.20/0.46 % total_time: 0.017
% 0.20/0.46 % num_of_symbols: 39
% 0.20/0.46 % num_of_terms: 236
% 0.20/0.46
% 0.20/0.46 % ------ Propositional Solver
% 0.20/0.46
% 0.20/0.46 % prop_solver_calls: 0
% 0.20/0.46 % prop_fast_solver_calls: 0
% 0.20/0.46 % prop_num_of_clauses: 29
% 0.20/0.46 % prop_preprocess_simplified: 3
% 0.20/0.46 % prop_fo_subsumed: 0
% 0.20/0.46 % prop_solver_time: 0.
% 0.20/0.46 % prop_fast_solver_time: 0.
% 0.20/0.46 % prop_unsat_core_time: 0.
% 0.20/0.46
% 0.20/0.46 % ------ QBF
% 0.20/0.46
% 0.20/0.46 % qbf_q_res: 0
% 0.20/0.46 % qbf_num_tautologies: 0
% 0.20/0.46 % qbf_prep_cycles: 0
% 0.20/0.46
% 0.20/0.46 % ------ BMC1
% 0.20/0.46
% 0.20/0.46 % bmc1_current_bound: -1
% 0.20/0.46 % bmc1_last_solved_bound: -1
% 0.20/0.46 % bmc1_unsat_core_size: -1
% 0.20/0.46 % bmc1_unsat_core_parents_size: -1
% 0.20/0.46 % bmc1_merge_next_fun: 0
% 0.20/0.46 % bmc1_unsat_core_clauses_time: 0.
% 0.20/0.46
% 0.20/0.46 % ------ Instantiation
% 0.20/0.46
% 0.20/0.46 % inst_num_of_clauses: undef
% 0.20/0.46 % inst_num_in_passive: undef
% 0.20/0.46 % inst_num_in_active: 0
% 0.20/0.46 % inst_num_in_unprocessed: 0
% 0.20/0.46 % inst_num_of_loops: 0
% 0.20/0.46 % inst_num_of_learning_restarts: 0
% 0.20/0.46 % inst_num_moves_active_passive: 0
% 0.20/0.46 % inst_lit_activity: 0
% 0.20/0.46 % inst_lit_activity_moves: 0
% 0.20/0.46 % inst_num_tautologies: 0
% 0.20/0.46 % inst_num_prop_implied: 0
% 0.20/0.46 % inst_num_existing_simplified: 0
% 0.20/0.46 % inst_num_eq_res_simplified: 0
% 0.20/0.46 % inst_num_child_elim: 0
% 0.20/0.46 % inst_num_of_dismatching_blockings: 0
% 0.20/0.46 % inst_num_of_non_proper_insts: 0
% 0.20/0.46 % inst_num_of_duplicates: 0
% 0.20/0.46 % inst_inst_num_from_inst_to_res: 0
% 0.20/0.46 % inst_dismatching_checking_time: 0.
% 0.20/0.46
% 0.20/0.46 % ------ Resolution
% 0.20/0.46
% 0.20/0.46 % res_num_of_clauses: undef
% 0.20/0.46 % res_num_in_passive: undef
% 0.20/0.46 % res_num_in_active: 0
% 0.20/0.46 % res_num_of_loops: 0
% 0.20/0.46 % res_forward_subset_subsumed: 0
% 0.20/0.46 % res_backward_subset_subsumed: 0
% 0.20/0.46 % res_forward_subsumed: 0
% 0.20/0.46 % res_backward_subsumed: 0
% 0.20/0.46 % res_forward_subsumption_resolution: 0
% 0.20/0.46 % res_backward_subsumption_resolution: 0
% 0.20/0.46 % res_clause_to_clause_subsumption: 0
% 0.20/0.46 % res_orphan_elimination: 0
% 0.20/0.46 % res_tautology_del: 0
% 0.20/0.46 % res_num_eq_res_simplified: 0
% 0.20/0.46 % res_num_sel_changes: 0
% 0.20/0.46 % res_moves_from_active_to_pass: 0
% 0.20/0.46
% 0.20/0.46 % Status Unsatisfiable
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------