TSTP Solution File: SWV163+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV163+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n006.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 20:30:20 EDT 2022

% Result   : Theorem 19.43s 19.60s
% Output   : CNFRefutation 19.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   55
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  205 ( 103 unt;   0 def)
%            Number of atoms       :  375 ( 257 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  315 ( 145   ~; 133   |;  23   &)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;  13 con; 0-3 aty)
%            Number of variables   :  139 (   0 sgn  47   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
    ! [X] : ~ gt(X,X) ).

fof(reflexivity_leq,axiom,
    ! [X] : leq(X,X) ).

fof(gt_succ,axiom,
    ! [X] : gt(succ(X),X) ).

fof(leq_succ,axiom,
    ! [X,Y] :
      ( leq(X,Y)
     => leq(X,succ(Y)) ) ).

fof(succ_tptp_minus_1,axiom,
    succ(tptp_minus_1) = n0 ).

fof(succ_plus_1_r,axiom,
    ! [X] : plus(X,n1) = succ(X) ).

fof(succ_plus_2_r,axiom,
    ! [X] : plus(X,n2) = succ(succ(X)) ).

fof(succ_plus_3_r,axiom,
    ! [X] : plus(X,n3) = succ(succ(succ(X))) ).

fof(pred_succ,axiom,
    ! [X] : pred(succ(X)) = X ).

fof(leq_succ_succ,axiom,
    ! [X,Y] :
      ( leq(succ(X),succ(Y))
    <=> leq(X,Y) ) ).

fof(cl5_nebula_norm_0013,conjecture,
    ( ( leq(n0,pv10)
      & leq(pv10,n135299)
      & ! [A] :
          ( ( leq(n0,A)
            & leq(A,pred(pv10)) )
         => sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ) )
   => ! [B] :
        ( ( leq(n0,B)
          & leq(B,tptp_minus_1) )
       => a_select3(q,pv10,B) = divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ).

fof(finite_domain_0,axiom,
    ! [X] :
      ( ( leq(n0,X)
        & leq(X,n0) )
     => X = n0 ) ).

fof(successor_1,axiom,
    succ(n0) = n1 ).

fof(successor_2,axiom,
    succ(succ(n0)) = n2 ).

fof(successor_3,axiom,
    succ(succ(succ(n0))) = n3 ).

fof(subgoal_0,plain,
    ( ( leq(n0,pv10)
      & leq(pv10,n135299)
      & ! [A] :
          ( ( leq(n0,A)
            & leq(A,pred(pv10)) )
         => sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ) )
   => ! [B] :
        ( ( leq(n0,B)
          & leq(B,tptp_minus_1) )
       => a_select3(q,pv10,B) = divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
    inference(strip,[],[cl5_nebula_norm_0013]) ).

fof(negate_0_0,plain,
    ~ ( ( leq(n0,pv10)
        & leq(pv10,n135299)
        & ! [A] :
            ( ( leq(n0,A)
              & leq(A,pred(pv10)) )
           => sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ) )
     => ! [B] :
          ( ( leq(n0,B)
            & leq(B,tptp_minus_1) )
         => a_select3(q,pv10,B) = divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [X] : gt(succ(X),X),
    inference(canonicalize,[],[gt_succ]) ).

fof(normalize_0_1,plain,
    ! [X] : gt(succ(X),X),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X] : pred(succ(X)) = X,
    inference(canonicalize,[],[pred_succ]) ).

fof(normalize_0_3,plain,
    ! [X] : pred(succ(X)) = X,
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X] : plus(X,n3) = succ(succ(succ(X))),
    inference(canonicalize,[],[succ_plus_3_r]) ).

fof(normalize_0_5,plain,
    ! [X] : plus(X,n3) = succ(succ(succ(X))),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X] : plus(X,n1) = succ(X),
    inference(canonicalize,[],[succ_plus_1_r]) ).

fof(normalize_0_7,plain,
    ! [X] : plus(X,n1) = succ(X),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ( leq(n0,pv10)
    & leq(pv10,n135299)
    & ? [B] :
        ( a_select3(q,pv10,B) != divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
        & leq(B,tptp_minus_1)
        & leq(n0,B) )
    & ! [A] :
        ( ~ leq(A,pred(pv10))
        | ~ leq(n0,A)
        | sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_9,plain,
    ? [B] :
      ( a_select3(q,pv10,B) != divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
      & leq(B,tptp_minus_1)
      & leq(n0,B) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ( a_select3(q,pv10,skolemFOFtoCNF_B) != divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_B,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
    & leq(n0,skolemFOFtoCNF_B)
    & leq(skolemFOFtoCNF_B,tptp_minus_1) ),
    inference(skolemize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    leq(skolemFOFtoCNF_B,tptp_minus_1),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
    <=> ~ leq(succ(X),succ(Y)) ),
    inference(canonicalize,[],[leq_succ_succ]) ).

fof(normalize_0_13,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
    <=> ~ leq(succ(X),succ(Y)) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [X,Y] :
      ( ( ~ leq(X,Y)
        | leq(succ(X),succ(Y)) )
      & ( ~ leq(succ(X),succ(Y))
        | leq(X,Y) ) ),
    inference(clausify,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
      | leq(succ(X),succ(Y)) ),
    inference(conjunct,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    succ(tptp_minus_1) = n0,
    inference(canonicalize,[],[succ_tptp_minus_1]) ).

fof(normalize_0_17,plain,
    ! [X] :
      ( ~ leq(X,n0)
      | ~ leq(n0,X)
      | X = n0 ),
    inference(canonicalize,[],[finite_domain_0]) ).

fof(normalize_0_18,plain,
    ! [X] :
      ( ~ leq(X,n0)
      | ~ leq(n0,X)
      | X = n0 ),
    inference(specialize,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    succ(n0) = n1,
    inference(canonicalize,[],[successor_1]) ).

fof(normalize_0_20,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
      | leq(X,succ(Y)) ),
    inference(canonicalize,[],[leq_succ]) ).

fof(normalize_0_21,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
      | leq(X,succ(Y)) ),
    inference(specialize,[],[normalize_0_20]) ).

fof(normalize_0_22,plain,
    leq(n0,skolemFOFtoCNF_B),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_23,plain,
    ! [X] : leq(X,X),
    inference(canonicalize,[],[reflexivity_leq]) ).

fof(normalize_0_24,plain,
    ! [X] : leq(X,X),
    inference(specialize,[],[normalize_0_23]) ).

fof(normalize_0_25,plain,
    succ(succ(succ(n0))) = n3,
    inference(canonicalize,[],[successor_3]) ).

fof(normalize_0_26,plain,
    ! [X] : plus(X,n2) = succ(succ(X)),
    inference(canonicalize,[],[succ_plus_2_r]) ).

fof(normalize_0_27,plain,
    ! [X] : plus(X,n2) = succ(succ(X)),
    inference(specialize,[],[normalize_0_26]) ).

fof(normalize_0_28,plain,
    succ(succ(n0)) = n2,
    inference(canonicalize,[],[successor_2]) ).

fof(normalize_0_29,plain,
    ! [X] : ~ gt(X,X),
    inference(canonicalize,[],[irreflexivity_gt]) ).

fof(normalize_0_30,plain,
    ! [X] : ~ gt(X,X),
    inference(specialize,[],[normalize_0_29]) ).

cnf(refute_0_0,plain,
    gt(succ(X),X),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    pred(succ(X)) = X,
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    pred(succ(succ(succ(X_9)))) = succ(succ(X_9)),
    inference(subst,[],[refute_0_1:[bind(X,$fot(succ(succ(X_9))))]]) ).

cnf(refute_0_3,plain,
    plus(X,n3) = succ(succ(succ(X))),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_4,plain,
    plus(X_9,n3) = succ(succ(succ(X_9))),
    inference(subst,[],[refute_0_3:[bind(X,$fot(X_9))]]) ).

cnf(refute_0_5,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_6,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_7,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( plus(X_9,n3) != succ(succ(succ(X_9)))
    | succ(succ(succ(X_9))) = plus(X_9,n3) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(plus(X_9,n3))),bind(Y0,$fot(succ(succ(succ(X_9)))))]]) ).

cnf(refute_0_9,plain,
    succ(succ(succ(X_9))) = plus(X_9,n3),
    inference(resolve,[$cnf( $equal(plus(X_9,n3),succ(succ(succ(X_9)))) )],[refute_0_4,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( pred(succ(succ(succ(X_9)))) != succ(succ(X_9))
    | succ(succ(succ(X_9))) != plus(X_9,n3)
    | pred(plus(X_9,n3)) = succ(succ(X_9)) ),
    introduced(tautology,[equality,[$cnf( $equal(pred(succ(succ(succ(X_9)))),succ(succ(X_9))) ),[0,0],$fot(plus(X_9,n3))]]) ).

cnf(refute_0_11,plain,
    ( pred(succ(succ(succ(X_9)))) != succ(succ(X_9))
    | pred(plus(X_9,n3)) = succ(succ(X_9)) ),
    inference(resolve,[$cnf( $equal(succ(succ(succ(X_9))),plus(X_9,n3)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    pred(plus(X_9,n3)) = succ(succ(X_9)),
    inference(resolve,[$cnf( $equal(pred(succ(succ(succ(X_9)))),succ(succ(X_9))) )],[refute_0_2,refute_0_11]) ).

cnf(refute_0_13,plain,
    pred(succ(X_9)) = X_9,
    inference(subst,[],[refute_0_1:[bind(X,$fot(X_9))]]) ).

cnf(refute_0_14,plain,
    plus(X,n1) = succ(X),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_15,plain,
    leq(skolemFOFtoCNF_B,tptp_minus_1),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_16,plain,
    ( ~ leq(X,Y)
    | leq(succ(X),succ(Y)) ),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_17,plain,
    ( ~ leq(skolemFOFtoCNF_B,tptp_minus_1)
    | leq(succ(skolemFOFtoCNF_B),succ(tptp_minus_1)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(tptp_minus_1))]]) ).

cnf(refute_0_18,plain,
    leq(succ(skolemFOFtoCNF_B),succ(tptp_minus_1)),
    inference(resolve,[$cnf( leq(skolemFOFtoCNF_B,tptp_minus_1) )],[refute_0_15,refute_0_17]) ).

cnf(refute_0_19,plain,
    succ(tptp_minus_1) = n0,
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_20,plain,
    ( succ(tptp_minus_1) != n0
    | ~ leq(succ(skolemFOFtoCNF_B),succ(tptp_minus_1))
    | leq(succ(skolemFOFtoCNF_B),n0) ),
    introduced(tautology,[equality,[$cnf( leq(succ(skolemFOFtoCNF_B),succ(tptp_minus_1)) ),[1],$fot(n0)]]) ).

cnf(refute_0_21,plain,
    ( ~ leq(succ(skolemFOFtoCNF_B),succ(tptp_minus_1))
    | leq(succ(skolemFOFtoCNF_B),n0) ),
    inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n0) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    leq(succ(skolemFOFtoCNF_B),n0),
    inference(resolve,[$cnf( leq(succ(skolemFOFtoCNF_B),succ(tptp_minus_1)) )],[refute_0_18,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( ~ leq(X,n0)
    | ~ leq(n0,X)
    | X = n0 ),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_24,plain,
    ( ~ leq(n0,succ(skolemFOFtoCNF_B))
    | ~ leq(succ(skolemFOFtoCNF_B),n0)
    | succ(skolemFOFtoCNF_B) = n0 ),
    inference(subst,[],[refute_0_23:[bind(X,$fot(succ(skolemFOFtoCNF_B)))]]) ).

cnf(refute_0_25,plain,
    ( ~ leq(n0,succ(skolemFOFtoCNF_B))
    | succ(skolemFOFtoCNF_B) = n0 ),
    inference(resolve,[$cnf( leq(succ(skolemFOFtoCNF_B),n0) )],[refute_0_22,refute_0_24]) ).

cnf(refute_0_26,plain,
    succ(n0) = n1,
    inference(canonicalize,[],[normalize_0_19]) ).

cnf(refute_0_27,plain,
    ( ~ leq(X,Y)
    | leq(X,succ(Y)) ),
    inference(canonicalize,[],[normalize_0_21]) ).

cnf(refute_0_28,plain,
    ( ~ leq(skolemFOFtoCNF_B,tptp_minus_1)
    | leq(skolemFOFtoCNF_B,succ(tptp_minus_1)) ),
    inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(tptp_minus_1))]]) ).

cnf(refute_0_29,plain,
    leq(skolemFOFtoCNF_B,succ(tptp_minus_1)),
    inference(resolve,[$cnf( leq(skolemFOFtoCNF_B,tptp_minus_1) )],[refute_0_15,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( succ(tptp_minus_1) != n0
    | ~ leq(skolemFOFtoCNF_B,succ(tptp_minus_1))
    | leq(skolemFOFtoCNF_B,n0) ),
    introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_B,succ(tptp_minus_1)) ),[1],$fot(n0)]]) ).

cnf(refute_0_31,plain,
    ( ~ leq(skolemFOFtoCNF_B,succ(tptp_minus_1))
    | leq(skolemFOFtoCNF_B,n0) ),
    inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n0) )],[refute_0_19,refute_0_30]) ).

cnf(refute_0_32,plain,
    leq(skolemFOFtoCNF_B,n0),
    inference(resolve,[$cnf( leq(skolemFOFtoCNF_B,succ(tptp_minus_1)) )],[refute_0_29,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( ~ leq(n0,skolemFOFtoCNF_B)
    | ~ leq(skolemFOFtoCNF_B,n0)
    | skolemFOFtoCNF_B = n0 ),
    inference(subst,[],[refute_0_23:[bind(X,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_34,plain,
    ( ~ leq(n0,skolemFOFtoCNF_B)
    | skolemFOFtoCNF_B = n0 ),
    inference(resolve,[$cnf( leq(skolemFOFtoCNF_B,n0) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    leq(n0,skolemFOFtoCNF_B),
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_36,plain,
    skolemFOFtoCNF_B = n0,
    inference(resolve,[$cnf( leq(n0,skolemFOFtoCNF_B) )],[refute_0_35,refute_0_34]) ).

cnf(refute_0_37,plain,
    succ(skolemFOFtoCNF_B) = succ(skolemFOFtoCNF_B),
    introduced(tautology,[refl,[$fot(succ(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_38,plain,
    ( skolemFOFtoCNF_B != n0
    | succ(skolemFOFtoCNF_B) != succ(skolemFOFtoCNF_B)
    | succ(skolemFOFtoCNF_B) = succ(n0) ),
    introduced(tautology,[equality,[$cnf( $equal(succ(skolemFOFtoCNF_B),succ(skolemFOFtoCNF_B)) ),[1,0],$fot(n0)]]) ).

cnf(refute_0_39,plain,
    ( skolemFOFtoCNF_B != n0
    | succ(skolemFOFtoCNF_B) = succ(n0) ),
    inference(resolve,[$cnf( $equal(succ(skolemFOFtoCNF_B),succ(skolemFOFtoCNF_B)) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    succ(skolemFOFtoCNF_B) = succ(n0),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,n0) )],[refute_0_36,refute_0_39]) ).

cnf(refute_0_41,plain,
    ( Y0 != X0
    | Y0 != Z
    | X0 = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).

cnf(refute_0_42,plain,
    ( X0 != Y0
    | Y0 != Z
    | X0 = Z ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_41]) ).

cnf(refute_0_43,plain,
    ( succ(n0) != n1
    | succ(skolemFOFtoCNF_B) != succ(n0)
    | succ(skolemFOFtoCNF_B) = n1 ),
    inference(subst,[],[refute_0_42:[bind(X0,$fot(succ(skolemFOFtoCNF_B))),bind(Y0,$fot(succ(n0))),bind(Z,$fot(n1))]]) ).

cnf(refute_0_44,plain,
    ( succ(n0) != n1
    | succ(skolemFOFtoCNF_B) = n1 ),
    inference(resolve,[$cnf( $equal(succ(skolemFOFtoCNF_B),succ(n0)) )],[refute_0_40,refute_0_43]) ).

cnf(refute_0_45,plain,
    succ(skolemFOFtoCNF_B) = n1,
    inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_26,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( succ(skolemFOFtoCNF_B) != n1
    | ~ leq(n0,n1)
    | leq(n0,succ(skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( ~ leq(n0,succ(skolemFOFtoCNF_B)) ),[1],$fot(n1)]]) ).

cnf(refute_0_47,plain,
    ( ~ leq(n0,n1)
    | leq(n0,succ(skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(succ(skolemFOFtoCNF_B),n1) )],[refute_0_45,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( ~ leq(n0,n1)
    | succ(skolemFOFtoCNF_B) = n0 ),
    inference(resolve,[$cnf( leq(n0,succ(skolemFOFtoCNF_B)) )],[refute_0_47,refute_0_25]) ).

cnf(refute_0_49,plain,
    ( succ(skolemFOFtoCNF_B) != n0
    | succ(skolemFOFtoCNF_B) != n1
    | n1 = n0 ),
    introduced(tautology,[equality,[$cnf( $equal(succ(skolemFOFtoCNF_B),n0) ),[0],$fot(n1)]]) ).

cnf(refute_0_50,plain,
    ( succ(skolemFOFtoCNF_B) != n0
    | n1 = n0 ),
    inference(resolve,[$cnf( $equal(succ(skolemFOFtoCNF_B),n1) )],[refute_0_45,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( ~ leq(n0,n1)
    | n1 = n0 ),
    inference(resolve,[$cnf( $equal(succ(skolemFOFtoCNF_B),n0) )],[refute_0_48,refute_0_50]) ).

cnf(refute_0_52,plain,
    leq(X,X),
    inference(canonicalize,[],[normalize_0_24]) ).

cnf(refute_0_53,plain,
    leq(X_71,X_71),
    inference(subst,[],[refute_0_52:[bind(X,$fot(X_71))]]) ).

cnf(refute_0_54,plain,
    ( ~ leq(X_71,X_71)
    | leq(X_71,succ(X_71)) ),
    inference(subst,[],[refute_0_27:[bind(X,$fot(X_71)),bind(Y,$fot(X_71))]]) ).

cnf(refute_0_55,plain,
    leq(X_71,succ(X_71)),
    inference(resolve,[$cnf( leq(X_71,X_71) )],[refute_0_53,refute_0_54]) ).

cnf(refute_0_56,plain,
    leq(n0,succ(n0)),
    inference(subst,[],[refute_0_55:[bind(X_71,$fot(n0))]]) ).

cnf(refute_0_57,plain,
    ( succ(n0) != n1
    | ~ leq(n0,succ(n0))
    | leq(n0,n1) ),
    introduced(tautology,[equality,[$cnf( leq(n0,succ(n0)) ),[1],$fot(n1)]]) ).

cnf(refute_0_58,plain,
    ( ~ leq(n0,succ(n0))
    | leq(n0,n1) ),
    inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_26,refute_0_57]) ).

cnf(refute_0_59,plain,
    leq(n0,n1),
    inference(resolve,[$cnf( leq(n0,succ(n0)) )],[refute_0_56,refute_0_58]) ).

cnf(refute_0_60,plain,
    n1 = n0,
    inference(resolve,[$cnf( leq(n0,n1) )],[refute_0_59,refute_0_51]) ).

cnf(refute_0_61,plain,
    plus(X,n1) = plus(X,n1),
    introduced(tautology,[refl,[$fot(plus(X,n1))]]) ).

cnf(refute_0_62,plain,
    ( n1 != n0
    | plus(X,n1) != plus(X,n1)
    | plus(X,n1) = plus(X,n0) ),
    introduced(tautology,[equality,[$cnf( $equal(plus(X,n1),plus(X,n1)) ),[1,1],$fot(n0)]]) ).

cnf(refute_0_63,plain,
    ( n1 != n0
    | plus(X,n1) = plus(X,n0) ),
    inference(resolve,[$cnf( $equal(plus(X,n1),plus(X,n1)) )],[refute_0_61,refute_0_62]) ).

cnf(refute_0_64,plain,
    plus(X,n1) = plus(X,n0),
    inference(resolve,[$cnf( $equal(n1,n0) )],[refute_0_60,refute_0_63]) ).

cnf(refute_0_65,plain,
    ( plus(X,n1) != plus(X,n0)
    | plus(X,n1) != succ(X)
    | plus(X,n0) = succ(X) ),
    introduced(tautology,[equality,[$cnf( $equal(plus(X,n1),succ(X)) ),[0],$fot(plus(X,n0))]]) ).

cnf(refute_0_66,plain,
    ( plus(X,n1) != succ(X)
    | plus(X,n0) = succ(X) ),
    inference(resolve,[$cnf( $equal(plus(X,n1),plus(X,n0)) )],[refute_0_64,refute_0_65]) ).

cnf(refute_0_67,plain,
    plus(X,n0) = succ(X),
    inference(resolve,[$cnf( $equal(plus(X,n1),succ(X)) )],[refute_0_14,refute_0_66]) ).

cnf(refute_0_68,plain,
    plus(X_9,n0) = succ(X_9),
    inference(subst,[],[refute_0_67:[bind(X,$fot(X_9))]]) ).

cnf(refute_0_69,plain,
    succ(succ(succ(n0))) = n3,
    inference(canonicalize,[],[normalize_0_25]) ).

cnf(refute_0_70,plain,
    ( plus(X,n3) != succ(succ(succ(X)))
    | succ(succ(succ(X))) = plus(X,n3) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(plus(X,n3))),bind(Y0,$fot(succ(succ(succ(X)))))]]) ).

cnf(refute_0_71,plain,
    succ(succ(succ(X))) = plus(X,n3),
    inference(resolve,[$cnf( $equal(plus(X,n3),succ(succ(succ(X)))) )],[refute_0_3,refute_0_70]) ).

cnf(refute_0_72,plain,
    succ(succ(succ(n0))) = plus(n0,n3),
    inference(subst,[],[refute_0_71:[bind(X,$fot(n0))]]) ).

cnf(refute_0_73,plain,
    ( succ(succ(succ(n0))) != n3
    | succ(succ(succ(n0))) != plus(n0,n3)
    | plus(n0,n3) = n3 ),
    introduced(tautology,[equality,[$cnf( $equal(succ(succ(succ(n0))),n3) ),[0],$fot(plus(n0,n3))]]) ).

cnf(refute_0_74,plain,
    ( succ(succ(succ(n0))) != n3
    | plus(n0,n3) = n3 ),
    inference(resolve,[$cnf( $equal(succ(succ(succ(n0))),plus(n0,n3)) )],[refute_0_72,refute_0_73]) ).

cnf(refute_0_75,plain,
    plus(n0,n3) = n3,
    inference(resolve,[$cnf( $equal(succ(succ(succ(n0))),n3) )],[refute_0_69,refute_0_74]) ).

cnf(refute_0_76,plain,
    ( n1 != n0
    | succ(n0) != n1
    | succ(n0) = n0 ),
    introduced(tautology,[equality,[$cnf( $equal(succ(n0),n1) ),[1],$fot(n0)]]) ).

cnf(refute_0_77,plain,
    ( succ(n0) != n1
    | succ(n0) = n0 ),
    inference(resolve,[$cnf( $equal(n1,n0) )],[refute_0_60,refute_0_76]) ).

cnf(refute_0_78,plain,
    succ(n0) = n0,
    inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_26,refute_0_77]) ).

cnf(refute_0_79,plain,
    plus(X,n2) = succ(succ(X)),
    inference(canonicalize,[],[normalize_0_27]) ).

cnf(refute_0_80,plain,
    succ(succ(n0)) = n2,
    inference(canonicalize,[],[normalize_0_28]) ).

cnf(refute_0_81,plain,
    succ(succ(n0)) = succ(succ(n0)),
    introduced(tautology,[refl,[$fot(succ(succ(n0)))]]) ).

cnf(refute_0_82,plain,
    ( succ(n0) != n1
    | succ(succ(n0)) != succ(succ(n0))
    | succ(succ(n0)) = succ(n1) ),
    introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) ),[1,0],$fot(n1)]]) ).

cnf(refute_0_83,plain,
    ( succ(n0) != n1
    | succ(succ(n0)) = succ(n1) ),
    inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) )],[refute_0_81,refute_0_82]) ).

cnf(refute_0_84,plain,
    succ(succ(n0)) = succ(n1),
    inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_26,refute_0_83]) ).

cnf(refute_0_85,plain,
    ( succ(succ(n0)) != n2
    | succ(succ(n0)) != succ(n1)
    | succ(n1) = n2 ),
    introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),n2) ),[0],$fot(succ(n1))]]) ).

cnf(refute_0_86,plain,
    ( succ(succ(n0)) != n2
    | succ(n1) = n2 ),
    inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(n1)) )],[refute_0_84,refute_0_85]) ).

cnf(refute_0_87,plain,
    succ(n1) = n2,
    inference(resolve,[$cnf( $equal(succ(succ(n0)),n2) )],[refute_0_80,refute_0_86]) ).

cnf(refute_0_88,plain,
    succ(n1) = succ(n1),
    introduced(tautology,[refl,[$fot(succ(n1))]]) ).

cnf(refute_0_89,plain,
    ( n1 != n0
    | succ(n1) != succ(n1)
    | succ(n1) = succ(n0) ),
    introduced(tautology,[equality,[$cnf( $equal(succ(n1),succ(n1)) ),[1,0],$fot(n0)]]) ).

cnf(refute_0_90,plain,
    ( n1 != n0
    | succ(n1) = succ(n0) ),
    inference(resolve,[$cnf( $equal(succ(n1),succ(n1)) )],[refute_0_88,refute_0_89]) ).

cnf(refute_0_91,plain,
    succ(n1) = succ(n0),
    inference(resolve,[$cnf( $equal(n1,n0) )],[refute_0_60,refute_0_90]) ).

cnf(refute_0_92,plain,
    ( succ(n0) != n0
    | succ(n1) != succ(n0)
    | succ(n1) = n0 ),
    inference(subst,[],[refute_0_42:[bind(X0,$fot(succ(n1))),bind(Y0,$fot(succ(n0))),bind(Z,$fot(n0))]]) ).

cnf(refute_0_93,plain,
    ( succ(n0) != n0
    | succ(n1) = n0 ),
    inference(resolve,[$cnf( $equal(succ(n1),succ(n0)) )],[refute_0_91,refute_0_92]) ).

cnf(refute_0_94,plain,
    succ(n1) = n0,
    inference(resolve,[$cnf( $equal(succ(n0),n0) )],[refute_0_78,refute_0_93]) ).

cnf(refute_0_95,plain,
    ( succ(n1) != n0
    | succ(n1) != n2
    | n0 = n2 ),
    introduced(tautology,[equality,[$cnf( $equal(succ(n1),n2) ),[0],$fot(n0)]]) ).

cnf(refute_0_96,plain,
    ( succ(n1) != n2
    | n0 = n2 ),
    inference(resolve,[$cnf( $equal(succ(n1),n0) )],[refute_0_94,refute_0_95]) ).

cnf(refute_0_97,plain,
    n0 = n2,
    inference(resolve,[$cnf( $equal(succ(n1),n2) )],[refute_0_87,refute_0_96]) ).

cnf(refute_0_98,plain,
    ( n0 != n2
    | n2 = n0 ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(n0)),bind(Y0,$fot(n2))]]) ).

cnf(refute_0_99,plain,
    n2 = n0,
    inference(resolve,[$cnf( $equal(n0,n2) )],[refute_0_97,refute_0_98]) ).

cnf(refute_0_100,plain,
    plus(X,n2) = plus(X,n2),
    introduced(tautology,[refl,[$fot(plus(X,n2))]]) ).

cnf(refute_0_101,plain,
    ( n2 != n0
    | plus(X,n2) != plus(X,n2)
    | plus(X,n2) = plus(X,n0) ),
    introduced(tautology,[equality,[$cnf( $equal(plus(X,n2),plus(X,n2)) ),[1,1],$fot(n0)]]) ).

cnf(refute_0_102,plain,
    ( n2 != n0
    | plus(X,n2) = plus(X,n0) ),
    inference(resolve,[$cnf( $equal(plus(X,n2),plus(X,n2)) )],[refute_0_100,refute_0_101]) ).

cnf(refute_0_103,plain,
    plus(X,n2) = plus(X,n0),
    inference(resolve,[$cnf( $equal(n2,n0) )],[refute_0_99,refute_0_102]) ).

cnf(refute_0_104,plain,
    ( plus(X,n0) != succ(X)
    | plus(X,n2) != plus(X,n0)
    | plus(X,n2) = succ(X) ),
    inference(subst,[],[refute_0_42:[bind(X0,$fot(plus(X,n2))),bind(Y0,$fot(plus(X,n0))),bind(Z,$fot(succ(X)))]]) ).

cnf(refute_0_105,plain,
    ( plus(X,n0) != succ(X)
    | plus(X,n2) = succ(X) ),
    inference(resolve,[$cnf( $equal(plus(X,n2),plus(X,n0)) )],[refute_0_103,refute_0_104]) ).

cnf(refute_0_106,plain,
    plus(X,n2) = succ(X),
    inference(resolve,[$cnf( $equal(plus(X,n0),succ(X)) )],[refute_0_67,refute_0_105]) ).

cnf(refute_0_107,plain,
    ( plus(X,n2) != succ(X)
    | plus(X,n2) != succ(succ(X))
    | succ(X) = succ(succ(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(plus(X,n2),succ(succ(X))) ),[0],$fot(succ(X))]]) ).

cnf(refute_0_108,plain,
    ( plus(X,n2) != succ(succ(X))
    | succ(X) = succ(succ(X)) ),
    inference(resolve,[$cnf( $equal(plus(X,n2),succ(X)) )],[refute_0_106,refute_0_107]) ).

cnf(refute_0_109,plain,
    succ(X) = succ(succ(X)),
    inference(resolve,[$cnf( $equal(plus(X,n2),succ(succ(X))) )],[refute_0_79,refute_0_108]) ).

cnf(refute_0_110,plain,
    ( succ(X) != succ(succ(X))
    | succ(succ(X)) = succ(X) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(succ(X))),bind(Y0,$fot(succ(succ(X))))]]) ).

cnf(refute_0_111,plain,
    succ(succ(X)) = succ(X),
    inference(resolve,[$cnf( $equal(succ(X),succ(succ(X))) )],[refute_0_109,refute_0_110]) ).

cnf(refute_0_112,plain,
    succ(succ(succ(X))) = succ(succ(X)),
    inference(subst,[],[refute_0_111:[bind(X,$fot(succ(X)))]]) ).

cnf(refute_0_113,plain,
    ( succ(succ(X)) != succ(X)
    | succ(succ(succ(X))) != succ(succ(X))
    | succ(succ(succ(X))) = succ(X) ),
    inference(subst,[],[refute_0_42:[bind(X0,$fot(succ(succ(succ(X))))),bind(Y0,$fot(succ(succ(X)))),bind(Z,$fot(succ(X)))]]) ).

cnf(refute_0_114,plain,
    ( succ(succ(X)) != succ(X)
    | succ(succ(succ(X))) = succ(X) ),
    inference(resolve,[$cnf( $equal(succ(succ(succ(X))),succ(succ(X))) )],[refute_0_112,refute_0_113]) ).

cnf(refute_0_115,plain,
    succ(succ(succ(X))) = succ(X),
    inference(resolve,[$cnf( $equal(succ(succ(X)),succ(X)) )],[refute_0_111,refute_0_114]) ).

cnf(refute_0_116,plain,
    ( plus(X,n3) != succ(succ(succ(X)))
    | succ(succ(succ(X))) != succ(X)
    | plus(X,n3) = succ(X) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(plus(X,n3),succ(X)) ),[0],$fot(succ(succ(succ(X))))]]) ).

cnf(refute_0_117,plain,
    ( plus(X,n3) != succ(succ(succ(X)))
    | plus(X,n3) = succ(X) ),
    inference(resolve,[$cnf( $equal(succ(succ(succ(X))),succ(X)) )],[refute_0_115,refute_0_116]) ).

cnf(refute_0_118,plain,
    plus(X,n3) = succ(X),
    inference(resolve,[$cnf( $equal(plus(X,n3),succ(succ(succ(X)))) )],[refute_0_3,refute_0_117]) ).

cnf(refute_0_119,plain,
    plus(n0,n3) = succ(n0),
    inference(subst,[],[refute_0_118:[bind(X,$fot(n0))]]) ).

cnf(refute_0_120,plain,
    ( plus(n0,n3) != succ(n0)
    | succ(n0) != n0
    | plus(n0,n3) = n0 ),
    inference(subst,[],[refute_0_42:[bind(X0,$fot(plus(n0,n3))),bind(Y0,$fot(succ(n0))),bind(Z,$fot(n0))]]) ).

cnf(refute_0_121,plain,
    ( succ(n0) != n0
    | plus(n0,n3) = n0 ),
    inference(resolve,[$cnf( $equal(plus(n0,n3),succ(n0)) )],[refute_0_119,refute_0_120]) ).

cnf(refute_0_122,plain,
    plus(n0,n3) = n0,
    inference(resolve,[$cnf( $equal(succ(n0),n0) )],[refute_0_78,refute_0_121]) ).

cnf(refute_0_123,plain,
    ( plus(n0,n3) != n0
    | plus(n0,n3) != n3
    | n0 = n3 ),
    introduced(tautology,[equality,[$cnf( $equal(plus(n0,n3),n3) ),[0],$fot(n0)]]) ).

cnf(refute_0_124,plain,
    ( plus(n0,n3) != n3
    | n0 = n3 ),
    inference(resolve,[$cnf( $equal(plus(n0,n3),n0) )],[refute_0_122,refute_0_123]) ).

cnf(refute_0_125,plain,
    n0 = n3,
    inference(resolve,[$cnf( $equal(plus(n0,n3),n3) )],[refute_0_75,refute_0_124]) ).

cnf(refute_0_126,plain,
    ( n0 != n3
    | n3 = n0 ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(n0)),bind(Y0,$fot(n3))]]) ).

cnf(refute_0_127,plain,
    n3 = n0,
    inference(resolve,[$cnf( $equal(n0,n3) )],[refute_0_125,refute_0_126]) ).

cnf(refute_0_128,plain,
    plus(X_9,n3) = plus(X_9,n3),
    introduced(tautology,[refl,[$fot(plus(X_9,n3))]]) ).

cnf(refute_0_129,plain,
    ( n3 != n0
    | plus(X_9,n3) != plus(X_9,n3)
    | plus(X_9,n3) = plus(X_9,n0) ),
    introduced(tautology,[equality,[$cnf( $equal(plus(X_9,n3),plus(X_9,n3)) ),[1,1],$fot(n0)]]) ).

cnf(refute_0_130,plain,
    ( n3 != n0
    | plus(X_9,n3) = plus(X_9,n0) ),
    inference(resolve,[$cnf( $equal(plus(X_9,n3),plus(X_9,n3)) )],[refute_0_128,refute_0_129]) ).

cnf(refute_0_131,plain,
    plus(X_9,n3) = plus(X_9,n0),
    inference(resolve,[$cnf( $equal(n3,n0) )],[refute_0_127,refute_0_130]) ).

cnf(refute_0_132,plain,
    ( plus(X_9,n0) != succ(X_9)
    | plus(X_9,n3) != plus(X_9,n0)
    | plus(X_9,n3) = succ(X_9) ),
    inference(subst,[],[refute_0_42:[bind(X0,$fot(plus(X_9,n3))),bind(Y0,$fot(plus(X_9,n0))),bind(Z,$fot(succ(X_9)))]]) ).

cnf(refute_0_133,plain,
    ( plus(X_9,n0) != succ(X_9)
    | plus(X_9,n3) = succ(X_9) ),
    inference(resolve,[$cnf( $equal(plus(X_9,n3),plus(X_9,n0)) )],[refute_0_131,refute_0_132]) ).

cnf(refute_0_134,plain,
    plus(X_9,n3) = succ(X_9),
    inference(resolve,[$cnf( $equal(plus(X_9,n0),succ(X_9)) )],[refute_0_68,refute_0_133]) ).

cnf(refute_0_135,plain,
    pred(plus(X_9,n3)) = pred(plus(X_9,n3)),
    introduced(tautology,[refl,[$fot(pred(plus(X_9,n3)))]]) ).

cnf(refute_0_136,plain,
    ( plus(X_9,n3) != succ(X_9)
    | pred(plus(X_9,n3)) != pred(plus(X_9,n3))
    | pred(plus(X_9,n3)) = pred(succ(X_9)) ),
    introduced(tautology,[equality,[$cnf( $equal(pred(plus(X_9,n3)),pred(plus(X_9,n3))) ),[1,0],$fot(succ(X_9))]]) ).

cnf(refute_0_137,plain,
    ( plus(X_9,n3) != succ(X_9)
    | pred(plus(X_9,n3)) = pred(succ(X_9)) ),
    inference(resolve,[$cnf( $equal(pred(plus(X_9,n3)),pred(plus(X_9,n3))) )],[refute_0_135,refute_0_136]) ).

cnf(refute_0_138,plain,
    pred(plus(X_9,n3)) = pred(succ(X_9)),
    inference(resolve,[$cnf( $equal(plus(X_9,n3),succ(X_9)) )],[refute_0_134,refute_0_137]) ).

cnf(refute_0_139,plain,
    ( pred(plus(X_9,n3)) != pred(succ(X_9))
    | pred(succ(X_9)) != X_9
    | pred(plus(X_9,n3)) = X_9 ),
    inference(subst,[],[refute_0_42:[bind(X0,$fot(pred(plus(X_9,n3)))),bind(Y0,$fot(pred(succ(X_9)))),bind(Z,$fot(X_9))]]) ).

cnf(refute_0_140,plain,
    ( pred(succ(X_9)) != X_9
    | pred(plus(X_9,n3)) = X_9 ),
    inference(resolve,[$cnf( $equal(pred(plus(X_9,n3)),pred(succ(X_9))) )],[refute_0_138,refute_0_139]) ).

cnf(refute_0_141,plain,
    pred(plus(X_9,n3)) = X_9,
    inference(resolve,[$cnf( $equal(pred(succ(X_9)),X_9) )],[refute_0_13,refute_0_140]) ).

cnf(refute_0_142,plain,
    ( pred(plus(X_9,n3)) != X_9
    | pred(plus(X_9,n3)) != succ(succ(X_9))
    | X_9 = succ(succ(X_9)) ),
    introduced(tautology,[equality,[$cnf( $equal(pred(plus(X_9,n3)),succ(succ(X_9))) ),[0],$fot(X_9)]]) ).

cnf(refute_0_143,plain,
    ( pred(plus(X_9,n3)) != succ(succ(X_9))
    | X_9 = succ(succ(X_9)) ),
    inference(resolve,[$cnf( $equal(pred(plus(X_9,n3)),X_9) )],[refute_0_141,refute_0_142]) ).

cnf(refute_0_144,plain,
    succ(succ(X_9)) = succ(X_9),
    inference(subst,[],[refute_0_111:[bind(X,$fot(X_9))]]) ).

cnf(refute_0_145,plain,
    ( X_9 != succ(succ(X_9))
    | succ(succ(X_9)) != succ(X_9)
    | X_9 = succ(X_9) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_9,succ(X_9)) ),[0],$fot(succ(succ(X_9)))]]) ).

cnf(refute_0_146,plain,
    ( X_9 != succ(succ(X_9))
    | X_9 = succ(X_9) ),
    inference(resolve,[$cnf( $equal(succ(succ(X_9)),succ(X_9)) )],[refute_0_144,refute_0_145]) ).

cnf(refute_0_147,plain,
    ( pred(plus(X_9,n3)) != succ(succ(X_9))
    | X_9 = succ(X_9) ),
    inference(resolve,[$cnf( $equal(X_9,succ(succ(X_9))) )],[refute_0_143,refute_0_146]) ).

cnf(refute_0_148,plain,
    X_9 = succ(X_9),
    inference(resolve,[$cnf( $equal(pred(plus(X_9,n3)),succ(succ(X_9))) )],[refute_0_12,refute_0_147]) ).

cnf(refute_0_149,plain,
    ( X_9 != succ(X_9)
    | succ(X_9) = X_9 ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(X_9)),bind(Y0,$fot(succ(X_9)))]]) ).

cnf(refute_0_150,plain,
    succ(X_9) = X_9,
    inference(resolve,[$cnf( $equal(X_9,succ(X_9)) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    succ(X) = X,
    inference(subst,[],[refute_0_150:[bind(X_9,$fot(X))]]) ).

cnf(refute_0_152,plain,
    ( succ(X) != X
    | ~ gt(succ(X),X)
    | gt(X,X) ),
    introduced(tautology,[equality,[$cnf( gt(succ(X),X) ),[0],$fot(X)]]) ).

cnf(refute_0_153,plain,
    ( ~ gt(succ(X),X)
    | gt(X,X) ),
    inference(resolve,[$cnf( $equal(succ(X),X) )],[refute_0_151,refute_0_152]) ).

cnf(refute_0_154,plain,
    gt(X,X),
    inference(resolve,[$cnf( gt(succ(X),X) )],[refute_0_0,refute_0_153]) ).

cnf(refute_0_155,plain,
    ~ gt(X,X),
    inference(canonicalize,[],[normalize_0_30]) ).

cnf(refute_0_156,plain,
    $false,
    inference(resolve,[$cnf( gt(X,X) )],[refute_0_154,refute_0_155]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWV163+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 14 18:36:11 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 19.43/19.60  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.43/19.60  
% 19.43/19.60  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.43/19.61  
%------------------------------------------------------------------------------