TSTP Solution File: SWV282-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV282-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Wed Jul 20 20:30:51 EDT 2022
% Result : Unsatisfiable 1.22s 1.44s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 102
% Number of leaves : 66
% Syntax : Number of clauses : 314 ( 90 unt; 103 nHn; 206 RR)
% Number of literals : 720 ( 472 equ; 228 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 274 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
( V_U = V_W
| V_V = V_W
| V_U = V_V
| c_in(c_Message_Omsg_ONonce(V_W),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_V),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg) ) ).
cnf(cls_Binomial_Obinomial__1_0,axiom,
c_Binomial_Obinomial(V_y,c_Suc(c_0)) = V_y ).
cnf(cls_Binomial_Obinomial__Suc__Suc_0,axiom,
c_Binomial_Obinomial(c_Suc(V_n),c_Suc(V_k)) = c_plus(c_Binomial_Obinomial(V_n,V_k),c_Binomial_Obinomial(V_n,c_Suc(V_k)),tc_nat) ).
cnf(cls_Binomial_Obinomial__n__0_0,axiom,
c_Binomial_Obinomial(V_n,c_0) = c_1 ).
cnf(cls_Nat_OOne__nat__def_0,axiom,
c_1 = c_Suc(c_0) ).
cnf(cls_Nat_Odiff__is__0__eq_0,axiom,
( c_minus(V_m,V_n,tc_nat) != c_0
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Odiff__self__eq__0_0,axiom,
c_minus(V_m,V_m,tc_nat) = c_0 ).
cnf(cls_Nat_Ole__add1_0,axiom,
c_lessequals(V_n,c_plus(V_n,V_m,tc_nat),tc_nat) ).
cnf(cls_Nat_OlessI_0,axiom,
c_less(V_n,c_Suc(V_n),tc_nat) ).
cnf(cls_Nat_Oless__Suc__eq__le_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_less(V_m,c_Suc(V_n),tc_nat) ) ).
cnf(cls_Nat_Onat__add__left__cancel__le_0,axiom,
( ~ c_lessequals(c_plus(V_k,V_m,tc_nat),c_plus(V_k,V_n,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_Nat_Onot__add__less2_0,axiom,
~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat) ).
cnf(cls_Public_ONonce__supply__lemma_0,axiom,
( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(V_evs),V_U,tc_nat) ) ).
cnf(refute_0_0,plain,
c_lessequals(V_n,c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat),tc_nat),
inference(subst,[],[cls_Nat_Ole__add1_0:[bind(V_m,$fot(c_Binomial_Obinomial(V_n,c_Suc(c_1))))]]) ).
cnf(refute_0_1,plain,
c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_1)) = c_plus(c_Binomial_Obinomial(X_10,c_1),c_Binomial_Obinomial(X_10,c_Suc(c_1)),tc_nat),
inference(subst,[],[cls_Binomial_Obinomial__Suc__Suc_0:[bind(V_k,$fot(c_1)),bind(V_n,$fot(X_10))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( c_1 != c_Suc(c_0)
| c_Suc(c_0) = c_1 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(c_1)),bind(Y,$fot(c_Suc(c_0)))]]) ).
cnf(refute_0_6,plain,
c_Suc(c_0) = c_1,
inference(resolve,[$cnf( $equal(c_1,c_Suc(c_0)) )],[cls_Nat_OOne__nat__def_0,refute_0_5]) ).
cnf(refute_0_7,plain,
c_Binomial_Obinomial(V_y,c_Suc(c_0)) = c_Binomial_Obinomial(V_y,c_Suc(c_0)),
introduced(tautology,[refl,[$fot(c_Binomial_Obinomial(V_y,c_Suc(c_0)))]]) ).
cnf(refute_0_8,plain,
( c_Binomial_Obinomial(V_y,c_Suc(c_0)) != c_Binomial_Obinomial(V_y,c_Suc(c_0))
| c_Suc(c_0) != c_1
| c_Binomial_Obinomial(V_y,c_Suc(c_0)) = c_Binomial_Obinomial(V_y,c_1) ),
introduced(tautology,[equality,[$cnf( $equal(c_Binomial_Obinomial(V_y,c_Suc(c_0)),c_Binomial_Obinomial(V_y,c_Suc(c_0))) ),[1,1],$fot(c_1)]]) ).
cnf(refute_0_9,plain,
( c_Suc(c_0) != c_1
| c_Binomial_Obinomial(V_y,c_Suc(c_0)) = c_Binomial_Obinomial(V_y,c_1) ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(V_y,c_Suc(c_0)),c_Binomial_Obinomial(V_y,c_Suc(c_0))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
c_Binomial_Obinomial(V_y,c_Suc(c_0)) = c_Binomial_Obinomial(V_y,c_1),
inference(resolve,[$cnf( $equal(c_Suc(c_0),c_1) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( c_Binomial_Obinomial(V_y,c_Suc(c_0)) != V_y
| c_Binomial_Obinomial(V_y,c_Suc(c_0)) != c_Binomial_Obinomial(V_y,c_1)
| c_Binomial_Obinomial(V_y,c_1) = V_y ),
introduced(tautology,[equality,[$cnf( $equal(c_Binomial_Obinomial(V_y,c_Suc(c_0)),V_y) ),[0],$fot(c_Binomial_Obinomial(V_y,c_1))]]) ).
cnf(refute_0_12,plain,
( c_Binomial_Obinomial(V_y,c_Suc(c_0)) != V_y
| c_Binomial_Obinomial(V_y,c_1) = V_y ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(V_y,c_Suc(c_0)),c_Binomial_Obinomial(V_y,c_1)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
c_Binomial_Obinomial(V_y,c_1) = V_y,
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(V_y,c_Suc(c_0)),V_y) )],[cls_Binomial_Obinomial__1_0,refute_0_12]) ).
cnf(refute_0_14,plain,
c_Binomial_Obinomial(X_10,c_1) = X_10,
inference(subst,[],[refute_0_13:[bind(V_y,$fot(X_10))]]) ).
cnf(refute_0_15,plain,
( c_Binomial_Obinomial(X_10,c_1) != X_10
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_1)) != c_plus(c_Binomial_Obinomial(X_10,c_1),c_Binomial_Obinomial(X_10,c_Suc(c_1)),tc_nat)
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_1)) = c_plus(X_10,c_Binomial_Obinomial(X_10,c_Suc(c_1)),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_1)),c_plus(c_Binomial_Obinomial(X_10,c_1),c_Binomial_Obinomial(X_10,c_Suc(c_1)),tc_nat)) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_16,plain,
( c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_1)) != c_plus(c_Binomial_Obinomial(X_10,c_1),c_Binomial_Obinomial(X_10,c_Suc(c_1)),tc_nat)
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_1)) = c_plus(X_10,c_Binomial_Obinomial(X_10,c_Suc(c_1)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(X_10,c_1),X_10) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_1)) = c_plus(X_10,c_Binomial_Obinomial(X_10,c_Suc(c_1)),tc_nat),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_1)),c_plus(c_Binomial_Obinomial(X_10,c_1),c_Binomial_Obinomial(X_10,c_Suc(c_1)),tc_nat)) )],[refute_0_1,refute_0_16]) ).
cnf(refute_0_18,plain,
c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)) = c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat),
inference(subst,[],[refute_0_17:[bind(X_10,$fot(V_n))]]) ).
cnf(refute_0_19,plain,
( c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)) != c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat)
| c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat) = c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)))),bind(Y,$fot(c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat)))]]) ).
cnf(refute_0_20,plain,
c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat) = c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)),c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat) != c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1))
| ~ c_lessequals(V_n,c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat),tc_nat)
| c_lessequals(V_n,c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)),tc_nat) ),
introduced(tautology,[equality,[$cnf( c_lessequals(V_n,c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat),tc_nat) ),[1],$fot(c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)))]]) ).
cnf(refute_0_22,plain,
( ~ c_lessequals(V_n,c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat),tc_nat)
| c_lessequals(V_n,c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat),c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
c_lessequals(V_n,c_Binomial_Obinomial(c_Suc(V_n),c_Suc(c_1)),tc_nat),
inference(resolve,[$cnf( c_lessequals(V_n,c_plus(V_n,c_Binomial_Obinomial(V_n,c_Suc(c_1)),tc_nat),tc_nat) )],[refute_0_0,refute_0_22]) ).
cnf(refute_0_24,plain,
c_lessequals(X_23,c_Binomial_Obinomial(c_Suc(X_23),c_Suc(c_1)),tc_nat),
inference(subst,[],[refute_0_23:[bind(V_n,$fot(X_23))]]) ).
cnf(refute_0_25,plain,
( ~ c_lessequals(X_23,c_Binomial_Obinomial(c_Suc(X_23),c_Suc(c_1)),tc_nat)
| c_less(X_23,c_Suc(c_Binomial_Obinomial(c_Suc(X_23),c_Suc(c_1))),tc_nat) ),
inference(subst,[],[cls_Nat_Oless__Suc__eq__le_1:[bind(V_m,$fot(X_23)),bind(V_n,$fot(c_Binomial_Obinomial(c_Suc(X_23),c_Suc(c_1))))]]) ).
cnf(refute_0_26,plain,
c_less(X_23,c_Suc(c_Binomial_Obinomial(c_Suc(X_23),c_Suc(c_1))),tc_nat),
inference(resolve,[$cnf( c_lessequals(X_23,c_Binomial_Obinomial(c_Suc(X_23),c_Suc(c_1)),tc_nat) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
c_less(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),
inference(subst,[],[refute_0_26:[bind(X_23,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_28,plain,
~ c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat),
inference(subst,[],[cls_Nat_Onot__add__less2_0:[bind(V_j,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_29,plain,
( ~ c_in(c_Message_Omsg_ONonce(c_plus(v_sko__urX(v_evs),X_221,tc_nat)),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat) ),
inference(subst,[],[cls_Public_ONonce__supply__lemma_0:[bind(V_U,$fot(c_plus(v_sko__urX(v_evs),X_221,tc_nat))),bind(V_evs,$fot(v_evs_H))]]) ).
cnf(refute_0_30,plain,
c_lessequals(X_23,c_plus(X_23,V_m,tc_nat),tc_nat),
inference(subst,[],[cls_Nat_Ole__add1_0:[bind(V_n,$fot(X_23))]]) ).
cnf(refute_0_31,plain,
( ~ c_lessequals(X_23,c_plus(X_23,V_m,tc_nat),tc_nat)
| c_less(X_23,c_Suc(c_plus(X_23,V_m,tc_nat)),tc_nat) ),
inference(subst,[],[cls_Nat_Oless__Suc__eq__le_1:[bind(V_m,$fot(X_23)),bind(V_n,$fot(c_plus(X_23,V_m,tc_nat)))]]) ).
cnf(refute_0_32,plain,
c_less(X_23,c_Suc(c_plus(X_23,V_m,tc_nat)),tc_nat),
inference(resolve,[$cnf( c_lessequals(X_23,c_plus(X_23,V_m,tc_nat),tc_nat) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),V_m,tc_nat)),tc_nat),
inference(subst,[],[refute_0_32:[bind(X_23,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_34,plain,
~ c_less(c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat),c_Suc(X_199),tc_nat),
inference(subst,[],[cls_Nat_Onot__add__less2_0:[bind(V_i,$fot(c_Suc(X_199))),bind(V_j,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_35,plain,
c_less(X_192,c_Suc(X_192),tc_nat),
inference(subst,[],[cls_Nat_OlessI_0:[bind(V_n,$fot(X_192))]]) ).
cnf(refute_0_36,plain,
c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),tc_nat),
inference(subst,[],[cls_Nat_Ole__add1_0:[bind(V_n,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_37,plain,
( ~ c_in(c_Message_Omsg_ONonce(X_78),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X_78,tc_nat) ),
inference(subst,[],[cls_Public_ONonce__supply__lemma_0:[bind(V_U,$fot(X_78)),bind(V_evs,$fot(v_evs_H_H))]]) ).
cnf(refute_0_38,plain,
( c_minus(X_33,X_33,tc_nat) != c_0
| c_lessequals(X_33,X_33,tc_nat) ),
inference(subst,[],[cls_Nat_Odiff__is__0__eq_0:[bind(V_m,$fot(X_33)),bind(V_n,$fot(X_33))]]) ).
cnf(refute_0_39,plain,
c_minus(X_33,X_33,tc_nat) = c_0,
inference(subst,[],[cls_Nat_Odiff__self__eq__0_0:[bind(V_m,$fot(X_33))]]) ).
cnf(refute_0_40,plain,
( c_0 != c_0
| c_minus(X_33,X_33,tc_nat) != c_0
| c_minus(X_33,X_33,tc_nat) = c_0 ),
introduced(tautology,[equality,[$cnf( $equal(c_minus(X_33,X_33,tc_nat),c_0) ),[1],$fot(c_0)]]) ).
cnf(refute_0_41,plain,
( c_0 != c_0
| c_minus(X_33,X_33,tc_nat) = c_0 ),
inference(resolve,[$cnf( $equal(c_minus(X_33,X_33,tc_nat),c_0) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( c_0 != c_0
| c_lessequals(X_33,X_33,tc_nat) ),
inference(resolve,[$cnf( $equal(c_minus(X_33,X_33,tc_nat),c_0) )],[refute_0_41,refute_0_38]) ).
cnf(refute_0_43,plain,
c_0 = c_0,
introduced(tautology,[refl,[$fot(c_0)]]) ).
cnf(refute_0_44,plain,
c_lessequals(X_33,X_33,tc_nat),
inference(resolve,[$cnf( $equal(c_0,c_0) )],[refute_0_43,refute_0_42]) ).
cnf(refute_0_45,plain,
c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat),
inference(subst,[],[refute_0_44:[bind(X_33,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_46,plain,
( ~ c_in(c_Message_Omsg_ONonce(X_71),c_Event_Oused(v_evs),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(v_evs),X_71,tc_nat) ),
inference(subst,[],[cls_Public_ONonce__supply__lemma_0:[bind(V_U,$fot(X_71)),bind(V_evs,$fot(v_evs))]]) ).
cnf(refute_0_47,plain,
( X_71 = X_72
| X_71 = X_73
| X_72 = X_73
| c_in(c_Message_Omsg_ONonce(X_71),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X_72),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X_73),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(X_71)),bind(V_V,$fot(X_72)),bind(V_W,$fot(X_73))]]) ).
cnf(refute_0_48,plain,
( ~ c_lessequals(v_sko__urX(v_evs),X_71,tc_nat)
| X_71 = X_72
| X_71 = X_73
| X_72 = X_73
| c_in(c_Message_Omsg_ONonce(X_72),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X_73),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(X_71),c_Event_Oused(v_evs),tc_Message_Omsg) )],[refute_0_47,refute_0_46]) ).
cnf(refute_0_49,plain,
( ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat)
| X_75 = X_76
| v_sko__urX(v_evs) = X_75
| v_sko__urX(v_evs) = X_76
| c_in(c_Message_Omsg_ONonce(X_75),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X_76),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_48:[bind(X_71,$fot(v_sko__urX(v_evs))),bind(X_72,$fot(X_75)),bind(X_73,$fot(X_76))]]) ).
cnf(refute_0_50,plain,
( X_75 = X_76
| v_sko__urX(v_evs) = X_75
| v_sko__urX(v_evs) = X_76
| c_in(c_Message_Omsg_ONonce(X_75),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X_76),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
( X_77 = X_78
| v_sko__urX(v_evs) = X_77
| v_sko__urX(v_evs) = X_78
| c_in(c_Message_Omsg_ONonce(X_77),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X_78),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_50:[bind(X_75,$fot(X_77)),bind(X_76,$fot(X_78))]]) ).
cnf(refute_0_52,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H_H),X_78,tc_nat)
| X_77 = X_78
| v_sko__urX(v_evs) = X_77
| v_sko__urX(v_evs) = X_78
| c_in(c_Message_Omsg_ONonce(X_77),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(X_78),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) )],[refute_0_51,refute_0_37]) ).
cnf(refute_0_53,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),tc_nat)
| X_131 = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| v_sko__urX(v_evs) = X_131
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| c_in(c_Message_Omsg_ONonce(X_131),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_52:[bind(X_77,$fot(X_131)),bind(X_78,$fot(c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)))]]) ).
cnf(refute_0_54,plain,
( X_131 = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| v_sko__urX(v_evs) = X_131
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| c_in(c_Message_Omsg_ONonce(X_131),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),tc_nat) )],[refute_0_36,refute_0_53]) ).
cnf(refute_0_55,plain,
~ c_less(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat),
inference(subst,[],[cls_Nat_Onot__add__less2_0:[bind(V_i,$fot(c_Suc(v_sko__urX(v_evs_H_H)))),bind(V_j,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_56,plain,
c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),V_m,tc_nat),tc_nat),
inference(subst,[],[cls_Nat_Ole__add1_0:[bind(V_n,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_57,plain,
( ~ c_in(c_Message_Omsg_ONonce(X_133),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(v_evs_H),X_133,tc_nat) ),
inference(subst,[],[cls_Public_ONonce__supply__lemma_0:[bind(V_U,$fot(X_133)),bind(V_evs,$fot(v_evs_H))]]) ).
cnf(refute_0_58,plain,
c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat),
inference(subst,[],[refute_0_44:[bind(X_33,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_59,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat)
| X_131 = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = X_131
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_in(c_Message_Omsg_ONonce(X_131),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_52:[bind(X_77,$fot(X_131)),bind(X_78,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_60,plain,
( X_131 = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = X_131
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_in(c_Message_Omsg_ONonce(X_131),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( X_133 = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = X_133
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_in(c_Message_Omsg_ONonce(X_133),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_60:[bind(X_131,$fot(X_133))]]) ).
cnf(refute_0_62,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),X_133,tc_nat)
| X_133 = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = X_133
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(X_133),c_Event_Oused(v_evs_H),tc_Message_Omsg) )],[refute_0_61,refute_0_57]) ).
cnf(refute_0_63,plain,
~ c_less(c_plus(v_sko__urX(v_evs),c_1,tc_nat),c_1,tc_nat),
inference(subst,[],[cls_Nat_Onot__add__less2_0:[bind(V_i,$fot(c_1)),bind(V_j,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_64,plain,
( ~ c_lessequals(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_0,tc_nat)
| c_less(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_Suc(c_0),tc_nat) ),
inference(subst,[],[cls_Nat_Oless__Suc__eq__le_1:[bind(V_m,$fot(c_plus(v_sko__urX(v_evs),X_100,tc_nat))),bind(V_n,$fot(c_0))]]) ).
cnf(refute_0_65,plain,
( ~ c_lessequals(c_plus(c_1,X_38,tc_nat),c_plus(c_1,X_39,tc_nat),tc_nat)
| c_lessequals(X_38,X_39,tc_nat) ),
inference(subst,[],[cls_Nat_Onat__add__left__cancel__le_0:[bind(V_k,$fot(c_1)),bind(V_m,$fot(X_38)),bind(V_n,$fot(X_39))]]) ).
cnf(refute_0_66,plain,
c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_Suc(c_0)),tc_nat),
inference(subst,[],[cls_Binomial_Obinomial__Suc__Suc_0:[bind(V_k,$fot(c_0)),bind(V_n,$fot(X_10))]]) ).
cnf(refute_0_67,plain,
( c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) != c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_Suc(c_0)),tc_nat)
| c_Suc(c_0) != c_1
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)),c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_Suc(c_0)),tc_nat)) ),[1,1,1],$fot(c_1)]]) ).
cnf(refute_0_68,plain,
( c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) != c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_Suc(c_0)),tc_nat)
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) ),
inference(resolve,[$cnf( $equal(c_Suc(c_0),c_1) )],[refute_0_6,refute_0_67]) ).
cnf(refute_0_69,plain,
c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)),c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_Suc(c_0)),tc_nat)) )],[refute_0_66,refute_0_68]) ).
cnf(refute_0_70,plain,
c_Binomial_Obinomial(c_Suc(X_10),c_1) = c_Suc(X_10),
inference(subst,[],[refute_0_13:[bind(V_y,$fot(c_Suc(X_10)))]]) ).
cnf(refute_0_71,plain,
c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)),
introduced(tautology,[refl,[$fot(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)))]]) ).
cnf(refute_0_72,plain,
( c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) != c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0))
| c_Suc(c_0) != c_1
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_Binomial_Obinomial(c_Suc(X_10),c_1) ),
introduced(tautology,[equality,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)),c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0))) ),[1,1],$fot(c_1)]]) ).
cnf(refute_0_73,plain,
( c_Suc(c_0) != c_1
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_Binomial_Obinomial(c_Suc(X_10),c_1) ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)),c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_Binomial_Obinomial(c_Suc(X_10),c_1),
inference(resolve,[$cnf( $equal(c_Suc(c_0),c_1) )],[refute_0_6,refute_0_73]) ).
cnf(refute_0_75,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_76,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_75]) ).
cnf(refute_0_77,plain,
( c_Binomial_Obinomial(c_Suc(X_10),c_1) != c_Suc(X_10)
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) != c_Binomial_Obinomial(c_Suc(X_10),c_1)
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_Suc(X_10) ),
inference(subst,[],[refute_0_76:[bind(X,$fot(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)))),bind(Y,$fot(c_Binomial_Obinomial(c_Suc(X_10),c_1))),bind(Z,$fot(c_Suc(X_10)))]]) ).
cnf(refute_0_78,plain,
( c_Binomial_Obinomial(c_Suc(X_10),c_1) != c_Suc(X_10)
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_Suc(X_10) ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)),c_Binomial_Obinomial(c_Suc(X_10),c_1)) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) = c_Suc(X_10),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_1),c_Suc(X_10)) )],[refute_0_70,refute_0_78]) ).
cnf(refute_0_80,plain,
( c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) != c_Suc(X_10)
| c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) != c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)
| c_Suc(X_10) = c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)),c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)) ),[0],$fot(c_Suc(X_10))]]) ).
cnf(refute_0_81,plain,
( c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) != c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)
| c_Suc(X_10) = c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)),c_Suc(X_10)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat),
introduced(tautology,[refl,[$fot(c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat))]]) ).
cnf(refute_0_83,plain,
( c_Binomial_Obinomial(X_10,c_1) != X_10
| c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat) != c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat)
| c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,X_10,tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat),c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat)) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_84,plain,
( c_Binomial_Obinomial(X_10,c_1) != X_10
| c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,X_10,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat),c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,X_10,tc_nat),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(X_10,c_1),X_10) )],[refute_0_14,refute_0_84]) ).
cnf(refute_0_86,plain,
c_Binomial_Obinomial(X_10,c_0) = c_1,
inference(subst,[],[cls_Binomial_Obinomial__n__0_0:[bind(V_n,$fot(X_10))]]) ).
cnf(refute_0_87,plain,
c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat),
introduced(tautology,[refl,[$fot(c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat))]]) ).
cnf(refute_0_88,plain,
( c_Binomial_Obinomial(X_10,c_0) != c_1
| c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) != c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)
| c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat),c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)) ),[1,0],$fot(c_1)]]) ).
cnf(refute_0_89,plain,
( c_Binomial_Obinomial(X_10,c_0) != c_1
| c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat),c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(X_10,c_0),c_1) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat) != c_plus(c_1,X_10,tc_nat)
| c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) != c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat)
| c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,X_10,tc_nat) ),
inference(subst,[],[refute_0_76:[bind(X,$fot(c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat))),bind(Y,$fot(c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat))),bind(Z,$fot(c_plus(c_1,X_10,tc_nat)))]]) ).
cnf(refute_0_92,plain,
( c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat) != c_plus(c_1,X_10,tc_nat)
| c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,X_10,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat),c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) = c_plus(c_1,X_10,tc_nat),
inference(resolve,[$cnf( $equal(c_plus(c_1,c_Binomial_Obinomial(X_10,c_1),tc_nat),c_plus(c_1,X_10,tc_nat)) )],[refute_0_85,refute_0_92]) ).
cnf(refute_0_94,plain,
( c_Suc(X_10) != c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)
| c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat) != c_plus(c_1,X_10,tc_nat)
| c_Suc(X_10) = c_plus(c_1,X_10,tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_Suc(X_10),c_plus(c_1,X_10,tc_nat)) ),[0],$fot(c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat))]]) ).
cnf(refute_0_95,plain,
( c_Suc(X_10) != c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)
| c_Suc(X_10) = c_plus(c_1,X_10,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat),c_plus(c_1,X_10,tc_nat)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)) != c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)
| c_Suc(X_10) = c_plus(c_1,X_10,tc_nat) ),
inference(resolve,[$cnf( $equal(c_Suc(X_10),c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)) )],[refute_0_81,refute_0_95]) ).
cnf(refute_0_97,plain,
c_Suc(X_10) = c_plus(c_1,X_10,tc_nat),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(X_10),c_Suc(c_0)),c_plus(c_Binomial_Obinomial(X_10,c_0),c_Binomial_Obinomial(X_10,c_1),tc_nat)) )],[refute_0_69,refute_0_96]) ).
cnf(refute_0_98,plain,
c_Suc(X_38) = c_plus(c_1,X_38,tc_nat),
inference(subst,[],[refute_0_97:[bind(X_10,$fot(X_38))]]) ).
cnf(refute_0_99,plain,
( c_Suc(X_38) != c_plus(c_1,X_38,tc_nat)
| c_plus(c_1,X_38,tc_nat) = c_Suc(X_38) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(c_Suc(X_38))),bind(Y,$fot(c_plus(c_1,X_38,tc_nat)))]]) ).
cnf(refute_0_100,plain,
c_plus(c_1,X_38,tc_nat) = c_Suc(X_38),
inference(resolve,[$cnf( $equal(c_Suc(X_38),c_plus(c_1,X_38,tc_nat)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( c_plus(c_1,X_38,tc_nat) != c_Suc(X_38)
| ~ c_lessequals(c_Suc(X_38),c_plus(c_1,X_39,tc_nat),tc_nat)
| c_lessequals(c_plus(c_1,X_38,tc_nat),c_plus(c_1,X_39,tc_nat),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_plus(c_1,X_38,tc_nat),c_plus(c_1,X_39,tc_nat),tc_nat) ),[0],$fot(c_Suc(X_38))]]) ).
cnf(refute_0_102,plain,
( ~ c_lessequals(c_Suc(X_38),c_plus(c_1,X_39,tc_nat),tc_nat)
| c_lessequals(c_plus(c_1,X_38,tc_nat),c_plus(c_1,X_39,tc_nat),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(c_1,X_38,tc_nat),c_Suc(X_38)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( ~ c_lessequals(c_Suc(X_38),c_plus(c_1,X_39,tc_nat),tc_nat)
| c_lessequals(X_38,X_39,tc_nat) ),
inference(resolve,[$cnf( c_lessequals(c_plus(c_1,X_38,tc_nat),c_plus(c_1,X_39,tc_nat),tc_nat) )],[refute_0_102,refute_0_65]) ).
cnf(refute_0_104,plain,
( c_Suc(X_10) != c_plus(c_1,X_10,tc_nat)
| c_plus(c_1,X_10,tc_nat) = c_Suc(X_10) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(c_Suc(X_10))),bind(Y,$fot(c_plus(c_1,X_10,tc_nat)))]]) ).
cnf(refute_0_105,plain,
c_plus(c_1,X_10,tc_nat) = c_Suc(X_10),
inference(resolve,[$cnf( $equal(c_Suc(X_10),c_plus(c_1,X_10,tc_nat)) )],[refute_0_97,refute_0_104]) ).
cnf(refute_0_106,plain,
c_plus(c_1,X_39,tc_nat) = c_Suc(X_39),
inference(subst,[],[refute_0_105:[bind(X_10,$fot(X_39))]]) ).
cnf(refute_0_107,plain,
( c_plus(c_1,X_39,tc_nat) != c_Suc(X_39)
| ~ c_lessequals(c_Suc(X_38),c_Suc(X_39),tc_nat)
| c_lessequals(c_Suc(X_38),c_plus(c_1,X_39,tc_nat),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_Suc(X_38),c_plus(c_1,X_39,tc_nat),tc_nat) ),[1],$fot(c_Suc(X_39))]]) ).
cnf(refute_0_108,plain,
( ~ c_lessequals(c_Suc(X_38),c_Suc(X_39),tc_nat)
| c_lessequals(c_Suc(X_38),c_plus(c_1,X_39,tc_nat),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(c_1,X_39,tc_nat),c_Suc(X_39)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
( ~ c_lessequals(c_Suc(X_38),c_Suc(X_39),tc_nat)
| c_lessequals(X_38,X_39,tc_nat) ),
inference(resolve,[$cnf( c_lessequals(c_Suc(X_38),c_plus(c_1,X_39,tc_nat),tc_nat) )],[refute_0_108,refute_0_103]) ).
cnf(refute_0_110,plain,
( ~ c_lessequals(c_Suc(X_40),c_Suc(c_0),tc_nat)
| c_lessequals(X_40,c_0,tc_nat) ),
inference(subst,[],[refute_0_109:[bind(X_38,$fot(X_40)),bind(X_39,$fot(c_0))]]) ).
cnf(refute_0_111,plain,
( c_Suc(c_0) != c_1
| ~ c_lessequals(c_Suc(X_40),c_1,tc_nat)
| c_lessequals(c_Suc(X_40),c_Suc(c_0),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_Suc(X_40),c_Suc(c_0),tc_nat) ),[1],$fot(c_1)]]) ).
cnf(refute_0_112,plain,
( ~ c_lessequals(c_Suc(X_40),c_1,tc_nat)
| c_lessequals(c_Suc(X_40),c_Suc(c_0),tc_nat) ),
inference(resolve,[$cnf( $equal(c_Suc(c_0),c_1) )],[refute_0_6,refute_0_111]) ).
cnf(refute_0_113,plain,
( ~ c_lessequals(c_Suc(X_40),c_1,tc_nat)
| c_lessequals(X_40,c_0,tc_nat) ),
inference(resolve,[$cnf( c_lessequals(c_Suc(X_40),c_Suc(c_0),tc_nat) )],[refute_0_112,refute_0_110]) ).
cnf(refute_0_114,plain,
( ~ c_lessequals(c_Suc(c_plus(v_sko__urX(v_evs),X_99,tc_nat)),c_1,tc_nat)
| c_lessequals(c_plus(v_sko__urX(v_evs),X_99,tc_nat),c_0,tc_nat) ),
inference(subst,[],[refute_0_113:[bind(X_40,$fot(c_plus(v_sko__urX(v_evs),X_99,tc_nat)))]]) ).
cnf(refute_0_115,plain,
( ~ c_lessequals(c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),V_n,tc_nat) ),
inference(subst,[],[cls_Nat_Onat__add__left__cancel__le_0:[bind(V_k,$fot(v_sko__urX(v_evs_H))),bind(V_m,$fot(c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat))))]]) ).
cnf(refute_0_116,plain,
~ c_less(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),V_i,tc_nat),
inference(subst,[],[cls_Nat_Onot__add__less2_0:[bind(V_j,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_117,plain,
( ~ c_in(c_Message_Omsg_ONonce(X_83),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X_83,tc_nat) ),
inference(subst,[],[cls_Public_ONonce__supply__lemma_0:[bind(V_U,$fot(X_83)),bind(V_evs,$fot(v_evs_H_H))]]) ).
cnf(refute_0_118,plain,
c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),tc_nat),
inference(subst,[],[refute_0_44:[bind(X_33,$fot(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_119,plain,
( ~ c_in(c_Message_Omsg_ONonce(X_77),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(v_evs_H),X_77,tc_nat) ),
inference(subst,[],[cls_Public_ONonce__supply__lemma_0:[bind(V_U,$fot(X_77)),bind(V_evs,$fot(v_evs_H))]]) ).
cnf(refute_0_120,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),X_77,tc_nat)
| X_77 = X_78
| v_sko__urX(v_evs) = X_77
| v_sko__urX(v_evs) = X_78
| c_in(c_Message_Omsg_ONonce(X_78),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(X_77),c_Event_Oused(v_evs_H),tc_Message_Omsg) )],[refute_0_51,refute_0_119]) ).
cnf(refute_0_121,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),tc_nat)
| v_sko__urX(v_evs) = X_82
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = X_82
| c_in(c_Message_Omsg_ONonce(X_82),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_120:[bind(X_77,$fot(v_sko__urX(v_evs_H))),bind(X_78,$fot(X_82))]]) ).
cnf(refute_0_122,plain,
( v_sko__urX(v_evs) = X_82
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = X_82
| c_in(c_Message_Omsg_ONonce(X_82),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),tc_nat) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
( v_sko__urX(v_evs) = X_83
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = X_83
| c_in(c_Message_Omsg_ONonce(X_83),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_122:[bind(X_82,$fot(X_83))]]) ).
cnf(refute_0_124,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H_H),X_83,tc_nat)
| v_sko__urX(v_evs) = X_83
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = X_83 ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(X_83),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) )],[refute_0_123,refute_0_117]) ).
cnf(refute_0_125,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) ),
inference(subst,[],[refute_0_124:[bind(X_83,$fot(c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)))]]) ).
cnf(refute_0_126,plain,
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),tc_nat) )],[refute_0_36,refute_0_125]) ).
cnf(refute_0_127,plain,
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) ),
inference(subst,[],[refute_0_126:[bind(V_m,$fot(V_i))]]) ).
cnf(refute_0_128,plain,
( v_sko__urX(v_evs) != c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)
| c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) = v_sko__urX(v_evs) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs))),bind(Y,$fot(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)))]]) ).
cnf(refute_0_129,plain,
( c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) = v_sko__urX(v_evs)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
( c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) != v_sko__urX(v_evs)
| ~ c_less(v_sko__urX(v_evs),V_i,tc_nat)
| c_less(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),V_i,tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_less(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),V_i,tc_nat) ),[0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_131,plain,
( ~ c_less(v_sko__urX(v_evs),V_i,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)
| c_less(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),V_i,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),v_sko__urX(v_evs)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( ~ c_less(v_sko__urX(v_evs),V_i,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) ),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),V_i,tc_nat) )],[refute_0_131,refute_0_116]) ).
cnf(refute_0_133,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),V_m,tc_nat)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs),V_m,tc_nat)),tc_nat) ),
inference(subst,[],[refute_0_132:[bind(V_i,$fot(c_Suc(c_plus(v_sko__urX(v_evs),V_m,tc_nat))))]]) ).
cnf(refute_0_134,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs),V_m,tc_nat)),tc_nat) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),V_m,tc_nat)),tc_nat) )],[refute_0_33,refute_0_133]) ).
cnf(refute_0_135,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs),X_90,tc_nat)),tc_nat) ),
inference(subst,[],[refute_0_134:[bind(V_m,$fot(X_90))]]) ).
cnf(refute_0_136,plain,
~ c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H)),tc_nat),
inference(subst,[],[cls_Nat_Onot__add__less2_0:[bind(V_i,$fot(c_Suc(v_sko__urX(v_evs_H)))),bind(V_j,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_137,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
inference(subst,[],[refute_0_132:[bind(V_i,$fot(c_Suc(v_sko__urX(v_evs_H))))]]) ).
cnf(refute_0_138,plain,
c_less(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat),
inference(subst,[],[refute_0_32:[bind(V_m,$fot(c_Suc(v_sko__urX(v_evs)))),bind(X_23,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_139,plain,
c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat),
inference(subst,[],[cls_Nat_OlessI_0:[bind(V_n,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_140,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(subst,[],[refute_0_132:[bind(V_i,$fot(c_Suc(v_sko__urX(v_evs))))]]) ).
cnf(refute_0_141,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
( v_sko__urX(v_evs_H) != c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat)
| c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat) = v_sko__urX(v_evs_H) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs_H))),bind(Y,$fot(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat)))]]) ).
cnf(refute_0_143,plain,
( c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat) != v_sko__urX(v_evs_H)
| ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat)
| c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
introduced(tautology,[equality,[$cnf( c_less(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat) ),[1,0],$fot(v_sko__urX(v_evs_H))]]) ).
cnf(refute_0_145,plain,
( ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat),v_sko__urX(v_evs_H)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat) )],[refute_0_138,refute_0_145]) ).
cnf(refute_0_147,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
inference(subst,[],[refute_0_124:[bind(X_83,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_148,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat) )],[refute_0_58,refute_0_147]) ).
cnf(refute_0_149,plain,
( v_sko__urX(v_evs) != v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs))),bind(Y,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_150,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H_H)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( v_sko__urX(v_evs_H_H) != v_sko__urX(v_evs)
| ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat)
| c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
introduced(tautology,[equality,[$cnf( c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),[0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_152,plain,
( ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) )],[refute_0_146,refute_0_152]) ).
cnf(refute_0_154,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H)),tc_nat) )],[refute_0_153,refute_0_137]) ).
cnf(refute_0_155,plain,
( v_sko__urX(v_evs_H) != c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat)
| c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) = v_sko__urX(v_evs_H) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs_H))),bind(Y,$fot(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat)))]]) ).
cnf(refute_0_156,plain,
( c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
( c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) != v_sko__urX(v_evs_H)
| ~ c_less(v_sko__urX(v_evs_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat)
| c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),[0],$fot(v_sko__urX(v_evs_H))]]) ).
cnf(refute_0_158,plain,
( ~ c_less(v_sko__urX(v_evs_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat),v_sko__urX(v_evs_H)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
( ~ c_less(v_sko__urX(v_evs_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H)),tc_nat) )],[refute_0_158,refute_0_136]) ).
cnf(refute_0_160,plain,
c_less(v_sko__urX(v_evs_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat),
inference(subst,[],[cls_Nat_OlessI_0:[bind(V_n,$fot(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_161,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) )],[refute_0_160,refute_0_159]) ).
cnf(refute_0_162,plain,
( v_sko__urX(v_evs_H) != v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs_H) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs_H))),bind(Y,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_163,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs_H) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H_H)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( v_sko__urX(v_evs_H) != c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs),X_90,tc_nat)),tc_nat)
| v_sko__urX(v_evs_H_H) != v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_90,tc_nat)),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs),X_90,tc_nat)),tc_nat)) ),[1,0],$fot(v_sko__urX(v_evs_H))]]) ).
cnf(refute_0_165,plain,
( v_sko__urX(v_evs_H) != c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs),X_90,tc_nat)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_90,tc_nat)),tc_nat) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H)) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_90,tc_nat)),tc_nat) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs),X_90,tc_nat)),tc_nat)) )],[refute_0_135,refute_0_165]) ).
cnf(refute_0_167,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat) ),
inference(subst,[],[refute_0_166:[bind(X_90,$fot(X_91))]]) ).
cnf(refute_0_168,plain,
( v_sko__urX(v_evs_H) != c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat)
| c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat) = v_sko__urX(v_evs_H) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs_H))),bind(Y,$fot(c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat)))]]) ).
cnf(refute_0_169,plain,
( c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
( c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat) != v_sko__urX(v_evs_H)
| ~ c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat)
| c_lessequals(c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat) ),[0],$fot(v_sko__urX(v_evs_H))]]) ).
cnf(refute_0_171,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_lessequals(c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat),v_sko__urX(v_evs_H)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_lessequals(c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),V_n,tc_nat) ),
inference(resolve,[$cnf( c_lessequals(c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),tc_nat),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat) )],[refute_0_171,refute_0_115]) ).
cnf(refute_0_173,plain,
c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat),
inference(subst,[],[cls_Nat_Ole__add1_0:[bind(V_m,$fot(V_n)),bind(V_n,$fot(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_174,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_lessequals(c_Suc(c_plus(v_sko__urX(v_evs),X_91,tc_nat)),V_n,tc_nat) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H),V_n,tc_nat),tc_nat) )],[refute_0_173,refute_0_172]) ).
cnf(refute_0_175,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_lessequals(c_Suc(c_plus(v_sko__urX(v_evs),X_99,tc_nat)),c_1,tc_nat) ),
inference(subst,[],[refute_0_174:[bind(V_n,$fot(c_1)),bind(X_91,$fot(X_99))]]) ).
cnf(refute_0_176,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_lessequals(c_plus(v_sko__urX(v_evs),X_99,tc_nat),c_0,tc_nat) ),
inference(resolve,[$cnf( c_lessequals(c_Suc(c_plus(v_sko__urX(v_evs),X_99,tc_nat)),c_1,tc_nat) )],[refute_0_175,refute_0_114]) ).
cnf(refute_0_177,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_lessequals(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_0,tc_nat) ),
inference(subst,[],[refute_0_176:[bind(X_99,$fot(X_100))]]) ).
cnf(refute_0_178,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_less(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_Suc(c_0),tc_nat) ),
inference(resolve,[$cnf( c_lessequals(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_0,tc_nat) )],[refute_0_177,refute_0_64]) ).
cnf(refute_0_179,plain,
( c_Suc(c_0) != c_1
| ~ c_less(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_Suc(c_0),tc_nat)
| c_less(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_1,tc_nat) ),
introduced(tautology,[equality,[$cnf( c_less(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_Suc(c_0),tc_nat) ),[1],$fot(c_1)]]) ).
cnf(refute_0_180,plain,
( ~ c_less(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_Suc(c_0),tc_nat)
| c_less(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_1,tc_nat) ),
inference(resolve,[$cnf( $equal(c_Suc(c_0),c_1) )],[refute_0_6,refute_0_179]) ).
cnf(refute_0_181,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_less(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_1,tc_nat) ),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs),X_100,tc_nat),c_Suc(c_0),tc_nat) )],[refute_0_178,refute_0_180]) ).
cnf(refute_0_182,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_less(c_plus(v_sko__urX(v_evs),c_1,tc_nat),c_1,tc_nat) ),
inference(subst,[],[refute_0_181:[bind(X_100,$fot(c_1))]]) ).
cnf(refute_0_183,plain,
v_sko__urX(v_evs) = v_sko__urX(v_evs_H),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs),c_1,tc_nat),c_1,tc_nat) )],[refute_0_182,refute_0_63]) ).
cnf(refute_0_184,plain,
( v_sko__urX(v_evs) != v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs))),bind(Y,$fot(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_185,plain,
v_sko__urX(v_evs_H) = v_sko__urX(v_evs),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
( v_sko__urX(v_evs_H) != v_sko__urX(v_evs)
| ~ c_lessequals(v_sko__urX(v_evs),X_133,tc_nat)
| c_lessequals(v_sko__urX(v_evs_H),X_133,tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(v_sko__urX(v_evs_H),X_133,tc_nat) ),[0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_187,plain,
( ~ c_lessequals(v_sko__urX(v_evs),X_133,tc_nat)
| c_lessequals(v_sko__urX(v_evs_H),X_133,tc_nat) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H),v_sko__urX(v_evs)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
( ~ c_lessequals(v_sko__urX(v_evs),X_133,tc_nat)
| X_133 = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = X_133
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H),X_133,tc_nat) )],[refute_0_187,refute_0_62]) ).
cnf(refute_0_189,plain,
( ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),V_m,tc_nat),tc_nat)
| c_plus(v_sko__urX(v_evs),V_m,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_m,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(subst,[],[refute_0_188:[bind(X_133,$fot(c_plus(v_sko__urX(v_evs),V_m,tc_nat)))]]) ).
cnf(refute_0_190,plain,
( c_plus(v_sko__urX(v_evs),V_m,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_m,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),V_m,tc_nat),tc_nat) )],[refute_0_56,refute_0_189]) ).
cnf(refute_0_191,plain,
( c_plus(v_sko__urX(v_evs),V_i,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_i,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(subst,[],[refute_0_190:[bind(V_m,$fot(V_i))]]) ).
cnf(refute_0_192,plain,
( v_sko__urX(v_evs) != c_plus(v_sko__urX(v_evs),V_i,tc_nat)
| c_plus(v_sko__urX(v_evs),V_i,tc_nat) = v_sko__urX(v_evs) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs))),bind(Y,$fot(c_plus(v_sko__urX(v_evs),V_i,tc_nat)))]]) ).
cnf(refute_0_193,plain,
( c_plus(v_sko__urX(v_evs),V_i,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs),V_i,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),V_i,tc_nat)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
( c_plus(v_sko__urX(v_evs),V_i,tc_nat) != v_sko__urX(v_evs)
| ~ c_less(v_sko__urX(v_evs),V_i,tc_nat)
| c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) ),[0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_195,plain,
( ~ c_less(v_sko__urX(v_evs),V_i,tc_nat)
| c_plus(v_sko__urX(v_evs),V_i,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs),V_i,tc_nat),v_sko__urX(v_evs)) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
( ~ c_less(v_sko__urX(v_evs),V_i,tc_nat)
| c_plus(v_sko__urX(v_evs),V_i,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) )],[refute_0_195,refute_0_28]) ).
cnf(refute_0_197,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat)
| c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(subst,[],[refute_0_196:[bind(V_i,$fot(c_Suc(v_sko__urX(v_evs_H_H))))]]) ).
cnf(refute_0_198,plain,
c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat),
inference(subst,[],[refute_0_32:[bind(V_m,$fot(c_Suc(v_sko__urX(v_evs)))),bind(X_23,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_199,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)
| c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(subst,[],[refute_0_196:[bind(V_i,$fot(c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))))]]) ).
cnf(refute_0_200,plain,
( c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) )],[refute_0_27,refute_0_199]) ).
cnf(refute_0_201,plain,
~ c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),
inference(subst,[],[cls_Nat_Onot__add__less2_0:[bind(V_i,$fot(c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))))),bind(V_j,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_202,plain,
c_less(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),
inference(subst,[],[cls_Nat_OlessI_0:[bind(V_n,$fot(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))))]]) ).
cnf(refute_0_203,plain,
( ~ c_in(c_Message_Omsg_ONonce(X_112),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X_112,tc_nat) ),
inference(subst,[],[cls_Public_ONonce__supply__lemma_0:[bind(V_U,$fot(X_112)),bind(V_evs,$fot(v_evs_H_H))]]) ).
cnf(refute_0_204,plain,
c_lessequals(v_sko__urX(v_evs_H),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),tc_nat),
inference(subst,[],[refute_0_23:[bind(V_n,$fot(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_205,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),tc_nat)
| c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) = X_82
| v_sko__urX(v_evs) = X_82
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))
| c_in(c_Message_Omsg_ONonce(X_82),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_120:[bind(X_77,$fot(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)))),bind(X_78,$fot(X_82))]]) ).
cnf(refute_0_206,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) = X_82
| v_sko__urX(v_evs) = X_82
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))
| c_in(c_Message_Omsg_ONonce(X_82),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),tc_nat) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
c_Suc(v_sko__urX(v_evs_H)) = c_Suc(v_sko__urX(v_evs_H)),
introduced(tautology,[refl,[$fot(c_Suc(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_208,plain,
( c_Suc(v_sko__urX(v_evs_H)) != c_Suc(v_sko__urX(v_evs_H))
| v_sko__urX(v_evs_H) != v_sko__urX(v_evs)
| c_Suc(v_sko__urX(v_evs_H)) = c_Suc(v_sko__urX(v_evs)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Suc(v_sko__urX(v_evs_H)),c_Suc(v_sko__urX(v_evs_H))) ),[1,0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_209,plain,
( v_sko__urX(v_evs_H) != v_sko__urX(v_evs)
| c_Suc(v_sko__urX(v_evs_H)) = c_Suc(v_sko__urX(v_evs)) ),
inference(resolve,[$cnf( $equal(c_Suc(v_sko__urX(v_evs_H)),c_Suc(v_sko__urX(v_evs_H))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
c_Suc(v_sko__urX(v_evs_H)) = c_Suc(v_sko__urX(v_evs)),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H),v_sko__urX(v_evs)) )],[refute_0_185,refute_0_209]) ).
cnf(refute_0_211,plain,
c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),
introduced(tautology,[refl,[$fot(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)))]]) ).
cnf(refute_0_212,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) != c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))
| c_Suc(v_sko__urX(v_evs_H)) != c_Suc(v_sko__urX(v_evs))
| c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))) ),[1,0],$fot(c_Suc(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_213,plain,
( c_Suc(v_sko__urX(v_evs_H)) != c_Suc(v_sko__urX(v_evs))
| c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),
inference(resolve,[$cnf( $equal(c_Suc(v_sko__urX(v_evs_H)),c_Suc(v_sko__urX(v_evs))) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) != X_82
| c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) != c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = X_82 ),
introduced(tautology,[equality,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),X_82) ),[0],$fot(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))]]) ).
cnf(refute_0_216,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) != X_82
| c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = X_82 ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = X_82
| v_sko__urX(v_evs) = X_82
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))
| c_in(c_Message_Omsg_ONonce(X_82),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),X_82) )],[refute_0_206,refute_0_216]) ).
cnf(refute_0_218,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)) != c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) != c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) ),
introduced(tautology,[equality,[$cnf( $equal(v_sko__urX(v_evs),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))) ),[1],$fot(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))]]) ).
cnf(refute_0_219,plain,
( v_sko__urX(v_evs) != c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1)),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) )],[refute_0_214,refute_0_218]) ).
cnf(refute_0_220,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = X_82
| v_sko__urX(v_evs) = X_82
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| c_in(c_Message_Omsg_ONonce(X_82),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H)),c_Suc(c_1))) )],[refute_0_217,refute_0_219]) ).
cnf(refute_0_221,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = X_112
| v_sko__urX(v_evs) = X_112
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| c_in(c_Message_Omsg_ONonce(X_112),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_220:[bind(X_82,$fot(X_112))]]) ).
cnf(refute_0_222,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H_H),X_112,tc_nat)
| c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = X_112
| v_sko__urX(v_evs) = X_112
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(X_112),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) )],[refute_0_221,refute_0_203]) ).
cnf(refute_0_223,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),tc_nat)
| c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) ),
inference(subst,[],[refute_0_222:[bind(X_112,$fot(c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)))]]) ).
cnf(refute_0_224,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),tc_nat) )],[refute_0_36,refute_0_223]) ).
cnf(refute_0_225,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) ),
inference(subst,[],[refute_0_224:[bind(V_m,$fot(V_i))]]) ).
cnf(refute_0_226,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) != c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)
| c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))),bind(Y,$fot(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)))]]) ).
cnf(refute_0_227,plain,
( c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) ),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
( c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) != c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| ~ c_less(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),V_i,tc_nat)
| c_less(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),V_i,tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_less(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),V_i,tc_nat) ),[0],$fot(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))]]) ).
cnf(refute_0_229,plain,
( ~ c_less(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),V_i,tc_nat)
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat)
| c_less(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),V_i,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
( ~ c_less(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),V_i,tc_nat)
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat) ),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs_H_H),V_i,tc_nat),V_i,tc_nat) )],[refute_0_229,refute_0_116]) ).
cnf(refute_0_231,plain,
( ~ c_less(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) ),
inference(subst,[],[refute_0_230:[bind(V_i,$fot(c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))))]]) ).
cnf(refute_0_232,plain,
( v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) ),
inference(resolve,[$cnf( c_less(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) )],[refute_0_202,refute_0_231]) ).
cnf(refute_0_233,plain,
( v_sko__urX(v_evs) != c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)
| c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) = v_sko__urX(v_evs) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs))),bind(Y,$fot(c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)))]]) ).
cnf(refute_0_234,plain,
( c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) = v_sko__urX(v_evs)
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
( c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) != v_sko__urX(v_evs)
| ~ c_less(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)
| c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) ),[0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_236,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),v_sko__urX(v_evs)) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)
| v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) ),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) )],[refute_0_236,refute_0_201]) ).
cnf(refute_0_238,plain,
v_sko__urX(v_evs) = c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) )],[refute_0_27,refute_0_237]) ).
cnf(refute_0_239,plain,
( v_sko__urX(v_evs) != c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))
| c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = v_sko__urX(v_evs) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs))),bind(Y,$fot(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))))]]) ).
cnf(refute_0_240,plain,
c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) = v_sko__urX(v_evs),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) = c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),
introduced(tautology,[refl,[$fot(c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))))]]) ).
cnf(refute_0_242,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) != v_sko__urX(v_evs)
| c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) != c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))
| c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) = c_Suc(v_sko__urX(v_evs)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))) ),[1,0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_243,plain,
( c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)) != v_sko__urX(v_evs)
| c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) = c_Suc(v_sko__urX(v_evs)) ),
inference(resolve,[$cnf( $equal(c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) = c_Suc(v_sko__urX(v_evs)),
inference(resolve,[$cnf( $equal(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)),v_sko__urX(v_evs)) )],[refute_0_240,refute_0_243]) ).
cnf(refute_0_245,plain,
c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) = c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),
introduced(tautology,[refl,[$fot(c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat))]]) ).
cnf(refute_0_246,plain,
( c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) != c_Suc(v_sko__urX(v_evs))
| c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) != c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)
| c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) = c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)) ),[1,1],$fot(c_Suc(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_247,plain,
( c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))) != c_Suc(v_sko__urX(v_evs))
| c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) = c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat)) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) = c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat),
inference(resolve,[$cnf( $equal(c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),c_Suc(v_sko__urX(v_evs))) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
( c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) != c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat)
| c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) != v_sko__urX(v_evs_H_H)
| c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat) = v_sko__urX(v_evs_H_H) ),
introduced(tautology,[equality,[$cnf( $equal(c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),v_sko__urX(v_evs_H_H)) ),[0],$fot(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat))]]) ).
cnf(refute_0_250,plain,
( c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) != v_sko__urX(v_evs_H_H)
| c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
( c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),v_sko__urX(v_evs_H_H)) )],[refute_0_200,refute_0_250]) ).
cnf(refute_0_252,plain,
( c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat) != v_sko__urX(v_evs_H_H)
| ~ c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat)
| c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) ),
introduced(tautology,[equality,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat) ),[1,0],$fot(v_sko__urX(v_evs_H_H))]]) ).
cnf(refute_0_253,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat),v_sko__urX(v_evs_H_H)) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat)),tc_nat) )],[refute_0_198,refute_0_253]) ).
cnf(refute_0_255,plain,
( c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) )],[refute_0_254,refute_0_197]) ).
cnf(refute_0_256,plain,
( c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) != v_sko__urX(v_evs_H_H)
| ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat)
| c_less(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_less(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) ),[0],$fot(v_sko__urX(v_evs_H_H))]]) ).
cnf(refute_0_257,plain,
( ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_less(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat),v_sko__urX(v_evs_H_H)) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
( ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) )],[refute_0_257,refute_0_55]) ).
cnf(refute_0_259,plain,
c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat),
inference(subst,[],[cls_Nat_OlessI_0:[bind(V_n,$fot(v_sko__urX(v_evs_H_H)))]]) ).
cnf(refute_0_260,plain,
v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) )],[refute_0_259,refute_0_258]) ).
cnf(refute_0_261,plain,
v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H_H)) )],[refute_0_260,refute_0_149]) ).
cnf(refute_0_262,plain,
c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),
introduced(tautology,[refl,[$fot(c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat))]]) ).
cnf(refute_0_263,plain,
( c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) != c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| v_sko__urX(v_evs_H_H) != v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) = c_plus(v_sko__urX(v_evs),V_m,tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)) ),[1,0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_264,plain,
( v_sko__urX(v_evs_H_H) != v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) = c_plus(v_sko__urX(v_evs),V_m,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) = c_plus(v_sko__urX(v_evs),V_m,tc_nat),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs)) )],[refute_0_261,refute_0_264]) ).
cnf(refute_0_266,plain,
( X_131 != c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) != c_plus(v_sko__urX(v_evs),V_m,tc_nat)
| X_131 = c_plus(v_sko__urX(v_evs),V_m,tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_131,c_plus(v_sko__urX(v_evs),V_m,tc_nat)) ),[0],$fot(c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat))]]) ).
cnf(refute_0_267,plain,
( X_131 != c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| X_131 = c_plus(v_sko__urX(v_evs),V_m,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),c_plus(v_sko__urX(v_evs),V_m,tc_nat)) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
( X_131 = c_plus(v_sko__urX(v_evs),V_m,tc_nat)
| v_sko__urX(v_evs) = X_131
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| c_in(c_Message_Omsg_ONonce(X_131),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( $equal(X_131,c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)) )],[refute_0_54,refute_0_267]) ).
cnf(refute_0_269,plain,
( c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat) != c_plus(v_sko__urX(v_evs),V_m,tc_nat)
| v_sko__urX(v_evs) != c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_m,tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)) ),[1],$fot(c_plus(v_sko__urX(v_evs),V_m,tc_nat))]]) ).
cnf(refute_0_270,plain,
( v_sko__urX(v_evs) != c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_m,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat),c_plus(v_sko__urX(v_evs),V_m,tc_nat)) )],[refute_0_265,refute_0_269]) ).
cnf(refute_0_271,plain,
( X_131 = c_plus(v_sko__urX(v_evs),V_m,tc_nat)
| v_sko__urX(v_evs) = X_131
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_m,tc_nat)
| c_in(c_Message_Omsg_ONonce(X_131),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs_H_H),V_m,tc_nat)) )],[refute_0_268,refute_0_270]) ).
cnf(refute_0_272,plain,
( X_140 = c_plus(v_sko__urX(v_evs),V_i,tc_nat)
| v_sko__urX(v_evs) = X_140
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_i,tc_nat)
| c_in(c_Message_Omsg_ONonce(X_140),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_271:[bind(V_m,$fot(V_i)),bind(X_131,$fot(X_140))]]) ).
cnf(refute_0_273,plain,
( X_140 != c_plus(v_sko__urX(v_evs),V_i,tc_nat)
| c_plus(v_sko__urX(v_evs),V_i,tc_nat) = X_140 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_140)),bind(Y,$fot(c_plus(v_sko__urX(v_evs),V_i,tc_nat)))]]) ).
cnf(refute_0_274,plain,
( c_plus(v_sko__urX(v_evs),V_i,tc_nat) = X_140
| v_sko__urX(v_evs) = X_140
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_i,tc_nat)
| c_in(c_Message_Omsg_ONonce(X_140),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( $equal(X_140,c_plus(v_sko__urX(v_evs),V_i,tc_nat)) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
( c_plus(v_sko__urX(v_evs),V_i,tc_nat) != X_140
| ~ c_less(X_140,V_i,tc_nat)
| c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) ),[0],$fot(X_140)]]) ).
cnf(refute_0_276,plain,
( ~ c_less(X_140,V_i,tc_nat)
| v_sko__urX(v_evs) = X_140
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_i,tc_nat)
| c_in(c_Message_Omsg_ONonce(X_140),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs),V_i,tc_nat),X_140) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
( ~ c_less(X_140,V_i,tc_nat)
| v_sko__urX(v_evs) = X_140
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_i,tc_nat)
| c_in(c_Message_Omsg_ONonce(X_140),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) )],[refute_0_276,refute_0_28]) ).
cnf(refute_0_278,plain,
( ~ c_less(X_192,c_Suc(X_192),tc_nat)
| v_sko__urX(v_evs) = X_192
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),c_Suc(X_192),tc_nat)
| c_in(c_Message_Omsg_ONonce(X_192),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_277:[bind(V_i,$fot(c_Suc(X_192))),bind(X_140,$fot(X_192))]]) ).
cnf(refute_0_279,plain,
( v_sko__urX(v_evs) = X_192
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),c_Suc(X_192),tc_nat)
| c_in(c_Message_Omsg_ONonce(X_192),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_less(X_192,c_Suc(X_192),tc_nat) )],[refute_0_35,refute_0_278]) ).
cnf(refute_0_280,plain,
( v_sko__urX(v_evs) = X_199
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat)
| c_in(c_Message_Omsg_ONonce(X_199),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_279:[bind(X_192,$fot(X_199))]]) ).
cnf(refute_0_281,plain,
( v_sko__urX(v_evs) != c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat)
| c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat) = v_sko__urX(v_evs) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_sko__urX(v_evs))),bind(Y,$fot(c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat)))]]) ).
cnf(refute_0_282,plain,
( c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat) = v_sko__urX(v_evs)
| v_sko__urX(v_evs) = X_199
| c_in(c_Message_Omsg_ONonce(X_199),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat)) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
( c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat) != v_sko__urX(v_evs)
| ~ c_less(v_sko__urX(v_evs),c_Suc(X_199),tc_nat)
| c_less(c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat),c_Suc(X_199),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_less(c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat),c_Suc(X_199),tc_nat) ),[0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_284,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(X_199),tc_nat)
| v_sko__urX(v_evs) = X_199
| c_in(c_Message_Omsg_ONonce(X_199),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_less(c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat),c_Suc(X_199),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat),v_sko__urX(v_evs)) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(X_199),tc_nat)
| v_sko__urX(v_evs) = X_199
| c_in(c_Message_Omsg_ONonce(X_199),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs),c_Suc(X_199),tc_nat),c_Suc(X_199),tc_nat) )],[refute_0_284,refute_0_34]) ).
cnf(refute_0_286,plain,
( ~ c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),V_m,tc_nat)),tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_m,tc_nat)
| c_in(c_Message_Omsg_ONonce(c_plus(v_sko__urX(v_evs),V_m,tc_nat)),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_285:[bind(X_199,$fot(c_plus(v_sko__urX(v_evs),V_m,tc_nat)))]]) ).
cnf(refute_0_287,plain,
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_m,tc_nat)
| c_in(c_Message_Omsg_ONonce(c_plus(v_sko__urX(v_evs),V_m,tc_nat)),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(c_plus(v_sko__urX(v_evs),V_m,tc_nat)),tc_nat) )],[refute_0_33,refute_0_286]) ).
cnf(refute_0_288,plain,
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),X_221,tc_nat)
| c_in(c_Message_Omsg_ONonce(c_plus(v_sko__urX(v_evs),X_221,tc_nat)),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_287:[bind(V_m,$fot(X_221))]]) ).
cnf(refute_0_289,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),X_221,tc_nat) ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(c_plus(v_sko__urX(v_evs),X_221,tc_nat)),c_Event_Oused(v_evs_H),tc_Message_Omsg) )],[refute_0_288,refute_0_29]) ).
cnf(refute_0_290,plain,
( v_sko__urX(v_evs_H) != v_sko__urX(v_evs)
| ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat)
| c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat) ),[0],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_291,plain,
( ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat)
| c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat) ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H),v_sko__urX(v_evs)) )],[refute_0_185,refute_0_290]) ).
cnf(refute_0_292,plain,
( ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),X_221,tc_nat) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat) )],[refute_0_291,refute_0_289]) ).
cnf(refute_0_293,plain,
c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat),
inference(subst,[],[cls_Nat_Ole__add1_0:[bind(V_m,$fot(X_221)),bind(V_n,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_294,plain,
v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),X_221,tc_nat),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),X_221,tc_nat),tc_nat) )],[refute_0_293,refute_0_292]) ).
cnf(refute_0_295,plain,
v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),V_i,tc_nat),
inference(subst,[],[refute_0_294:[bind(X_221,$fot(V_i))]]) ).
cnf(refute_0_296,plain,
c_plus(v_sko__urX(v_evs),V_i,tc_nat) = v_sko__urX(v_evs),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),V_i,tc_nat)) )],[refute_0_295,refute_0_192]) ).
cnf(refute_0_297,plain,
( ~ c_less(v_sko__urX(v_evs),V_i,tc_nat)
| c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(v_sko__urX(v_evs),V_i,tc_nat),v_sko__urX(v_evs)) )],[refute_0_296,refute_0_194]) ).
cnf(refute_0_298,plain,
~ c_less(v_sko__urX(v_evs),V_i,tc_nat),
inference(resolve,[$cnf( c_less(c_plus(v_sko__urX(v_evs),V_i,tc_nat),V_i,tc_nat) )],[refute_0_297,refute_0_28]) ).
cnf(refute_0_299,plain,
~ c_less(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat),
inference(subst,[],[refute_0_298:[bind(V_i,$fot(c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1)))))]]) ).
cnf(refute_0_300,plain,
$false,
inference(resolve,[$cnf( c_less(v_sko__urX(v_evs),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) )],[refute_0_27,refute_0_299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV282-2 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 13:11:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.22/1.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.22/1.44
% 1.22/1.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.30/1.47
%------------------------------------------------------------------------------