TSTP Solution File: SWV199+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV199+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 20:30:28 EDT 2022

% Result   : Theorem 108.23s 108.42s
% Output   : CNFRefutation 108.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  131 (  51 unt;   0 def)
%            Number of atoms       :  454 ( 277 equ)
%            Maximal formula atoms :   51 (   3 avg)
%            Number of connectives :  471 ( 148   ~; 108   |; 194   &)
%                                         (   6 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   43 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;  18 con; 0-3 aty)
%            Number of variables   :   83 (   0 sgn  57   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(leq_gt2,axiom,
    ! [X,Y] :
      ( ( leq(X,Y)
        & X != Y )
     => gt(Y,X) ) ).

fof(leq_gt_pred,axiom,
    ! [X,Y] :
      ( leq(X,pred(Y))
    <=> gt(Y,X) ) ).

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

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

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

fof(quaternion_ds1_inuse_0010,conjecture,
    ( ( a_select2(rho_defuse,n0) = use
      & a_select2(rho_defuse,n1) = use
      & a_select2(rho_defuse,n2) = use
      & a_select2(sigma_defuse,n0) = use
      & a_select2(sigma_defuse,n1) = use
      & a_select2(sigma_defuse,n2) = use
      & a_select2(sigma_defuse,n3) = use
      & a_select2(sigma_defuse,n4) = use
      & a_select2(sigma_defuse,n5) = use
      & a_select3(u_defuse,n0,n0) = use
      & a_select3(u_defuse,n1,n0) = use
      & a_select3(u_defuse,n2,n0) = use
      & a_select2(xinit_defuse,n3) = use
      & a_select2(xinit_defuse,n4) = use
      & a_select2(xinit_defuse,n5) = use
      & a_select2(xinit_mean_defuse,n0) = use
      & a_select2(xinit_mean_defuse,n1) = use
      & a_select2(xinit_mean_defuse,n2) = use
      & a_select2(xinit_mean_defuse,n3) = use
      & a_select2(xinit_mean_defuse,n4) = use
      & a_select2(xinit_mean_defuse,n5) = use
      & a_select2(xinit_noise_defuse,n0) = use
      & a_select2(xinit_noise_defuse,n1) = use
      & a_select2(xinit_noise_defuse,n2) = use
      & a_select2(xinit_noise_defuse,n3) = use
      & a_select2(xinit_noise_defuse,n4) = use
      & a_select2(xinit_noise_defuse,n5) = use
      & leq(n0,pv5)
      & leq(pv5,n0)
      & leq(pv5,n998)
      & ! [A,B] :
          ( ( leq(n0,A)
            & leq(n0,B)
            & leq(A,n2)
            & leq(B,pred(pv5)) )
         => a_select3(u_defuse,A,B) = use )
      & ! [C,D] :
          ( ( leq(n0,C)
            & leq(n0,D)
            & leq(C,n2)
            & leq(D,pred(pv5)) )
         => a_select3(z_defuse,C,D) = use ) )
   => ! [E,F] :
        ( ( leq(n0,E)
          & leq(n0,F)
          & leq(E,n2)
          & leq(F,pv5) )
       => ( ( ~ ( n0 = E
                & pv5 = F )
            & ~ ( n1 = E
                & pv5 = F )
            & ~ ( n2 = E
                & pv5 = F ) )
         => a_select3(z_defuse,E,F) = use ) ) ) ).

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(subgoal_0,plain,
    ( ( a_select2(rho_defuse,n0) = use
      & a_select2(rho_defuse,n1) = use
      & a_select2(rho_defuse,n2) = use
      & a_select2(sigma_defuse,n0) = use
      & a_select2(sigma_defuse,n1) = use
      & a_select2(sigma_defuse,n2) = use
      & a_select2(sigma_defuse,n3) = use
      & a_select2(sigma_defuse,n4) = use
      & a_select2(sigma_defuse,n5) = use
      & a_select3(u_defuse,n0,n0) = use
      & a_select3(u_defuse,n1,n0) = use
      & a_select3(u_defuse,n2,n0) = use
      & a_select2(xinit_defuse,n3) = use
      & a_select2(xinit_defuse,n4) = use
      & a_select2(xinit_defuse,n5) = use
      & a_select2(xinit_mean_defuse,n0) = use
      & a_select2(xinit_mean_defuse,n1) = use
      & a_select2(xinit_mean_defuse,n2) = use
      & a_select2(xinit_mean_defuse,n3) = use
      & a_select2(xinit_mean_defuse,n4) = use
      & a_select2(xinit_mean_defuse,n5) = use
      & a_select2(xinit_noise_defuse,n0) = use
      & a_select2(xinit_noise_defuse,n1) = use
      & a_select2(xinit_noise_defuse,n2) = use
      & a_select2(xinit_noise_defuse,n3) = use
      & a_select2(xinit_noise_defuse,n4) = use
      & a_select2(xinit_noise_defuse,n5) = use
      & leq(n0,pv5)
      & leq(pv5,n0)
      & leq(pv5,n998)
      & ! [A,B] :
          ( ( leq(n0,A)
            & leq(n0,B)
            & leq(A,n2)
            & leq(B,pred(pv5)) )
         => a_select3(u_defuse,A,B) = use )
      & ! [C,D] :
          ( ( leq(n0,C)
            & leq(n0,D)
            & leq(C,n2)
            & leq(D,pred(pv5)) )
         => a_select3(z_defuse,C,D) = use ) )
   => ! [E,F] :
        ( ( leq(n0,E)
          & leq(n0,F)
          & leq(E,n2)
          & leq(F,pv5)
          & ~ ( n0 = E
              & pv5 = F )
          & ~ ( n1 = E
              & pv5 = F )
          & ~ ( n2 = E
              & pv5 = F ) )
       => a_select3(z_defuse,E,F) = use ) ),
    inference(strip,[],[quaternion_ds1_inuse_0010]) ).

fof(negate_0_0,plain,
    ~ ( ( a_select2(rho_defuse,n0) = use
        & a_select2(rho_defuse,n1) = use
        & a_select2(rho_defuse,n2) = use
        & a_select2(sigma_defuse,n0) = use
        & a_select2(sigma_defuse,n1) = use
        & a_select2(sigma_defuse,n2) = use
        & a_select2(sigma_defuse,n3) = use
        & a_select2(sigma_defuse,n4) = use
        & a_select2(sigma_defuse,n5) = use
        & a_select3(u_defuse,n0,n0) = use
        & a_select3(u_defuse,n1,n0) = use
        & a_select3(u_defuse,n2,n0) = use
        & a_select2(xinit_defuse,n3) = use
        & a_select2(xinit_defuse,n4) = use
        & a_select2(xinit_defuse,n5) = use
        & a_select2(xinit_mean_defuse,n0) = use
        & a_select2(xinit_mean_defuse,n1) = use
        & a_select2(xinit_mean_defuse,n2) = use
        & a_select2(xinit_mean_defuse,n3) = use
        & a_select2(xinit_mean_defuse,n4) = use
        & a_select2(xinit_mean_defuse,n5) = use
        & a_select2(xinit_noise_defuse,n0) = use
        & a_select2(xinit_noise_defuse,n1) = use
        & a_select2(xinit_noise_defuse,n2) = use
        & a_select2(xinit_noise_defuse,n3) = use
        & a_select2(xinit_noise_defuse,n4) = use
        & a_select2(xinit_noise_defuse,n5) = use
        & leq(n0,pv5)
        & leq(pv5,n0)
        & leq(pv5,n998)
        & ! [A,B] :
            ( ( leq(n0,A)
              & leq(n0,B)
              & leq(A,n2)
              & leq(B,pred(pv5)) )
           => a_select3(u_defuse,A,B) = use )
        & ! [C,D] :
            ( ( leq(n0,C)
              & leq(n0,D)
              & leq(C,n2)
              & leq(D,pred(pv5)) )
           => a_select3(z_defuse,C,D) = use ) )
     => ! [E,F] :
          ( ( leq(n0,E)
            & leq(n0,F)
            & leq(E,n2)
            & leq(F,pv5)
            & ~ ( n0 = E
                & pv5 = F )
            & ~ ( n1 = E
                & pv5 = F )
            & ~ ( n2 = E
                & pv5 = F ) )
         => a_select3(z_defuse,E,F) = use ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [X] : succ(pred(X)) = X,
    inference(canonicalize,[],[succ_pred]) ).

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

fof(normalize_0_2,plain,
    ! [X] :
      ( ~ leq(X,n0)
      | ~ leq(n0,X)
      | X = n0 ),
    inference(canonicalize,[],[finite_domain_0]) ).

fof(normalize_0_3,plain,
    ! [X] :
      ( ~ leq(X,n0)
      | ~ leq(n0,X)
      | X = n0 ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
    <=> ~ leq(succ(X),succ(Y)) ),
    inference(canonicalize,[],[leq_succ_succ]) ).

fof(normalize_0_5,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
    <=> ~ leq(succ(X),succ(Y)) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Y] :
      ( ( ~ leq(X,Y)
        | leq(succ(X),succ(Y)) )
      & ( ~ leq(succ(X),succ(Y))
        | leq(X,Y) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( ~ leq(succ(X),succ(Y))
      | leq(X,Y) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    succ(n0) = n1,
    inference(canonicalize,[],[successor_1]) ).

fof(normalize_0_9,plain,
    ! [X,Y] :
      ( ~ gt(Y,X)
    <=> ~ leq(X,pred(Y)) ),
    inference(canonicalize,[],[leq_gt_pred]) ).

fof(normalize_0_10,plain,
    ! [X,Y] :
      ( ~ gt(Y,X)
    <=> ~ leq(X,pred(Y)) ),
    inference(specialize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X,Y] :
      ( ( ~ gt(Y,X)
        | leq(X,pred(Y)) )
      & ( ~ leq(X,pred(Y))
        | gt(Y,X) ) ),
    inference(clausify,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X,Y] :
      ( ~ gt(Y,X)
      | leq(X,pred(Y)) ),
    inference(conjunct,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ( a_select2(rho_defuse,n0) = use
    & a_select2(rho_defuse,n1) = use
    & a_select2(rho_defuse,n2) = use
    & a_select2(sigma_defuse,n0) = use
    & a_select2(sigma_defuse,n1) = use
    & a_select2(sigma_defuse,n2) = use
    & a_select2(sigma_defuse,n3) = use
    & a_select2(sigma_defuse,n4) = use
    & a_select2(sigma_defuse,n5) = use
    & a_select2(xinit_defuse,n3) = use
    & a_select2(xinit_defuse,n4) = use
    & a_select2(xinit_defuse,n5) = use
    & a_select2(xinit_mean_defuse,n0) = use
    & a_select2(xinit_mean_defuse,n1) = use
    & a_select2(xinit_mean_defuse,n2) = use
    & a_select2(xinit_mean_defuse,n3) = use
    & a_select2(xinit_mean_defuse,n4) = use
    & a_select2(xinit_mean_defuse,n5) = use
    & a_select2(xinit_noise_defuse,n0) = use
    & a_select2(xinit_noise_defuse,n1) = use
    & a_select2(xinit_noise_defuse,n2) = use
    & a_select2(xinit_noise_defuse,n3) = use
    & a_select2(xinit_noise_defuse,n4) = use
    & a_select2(xinit_noise_defuse,n5) = use
    & a_select3(u_defuse,n0,n0) = use
    & a_select3(u_defuse,n1,n0) = use
    & a_select3(u_defuse,n2,n0) = use
    & leq(n0,pv5)
    & leq(pv5,n0)
    & leq(pv5,n998)
    & ? [E,F] :
        ( a_select3(z_defuse,E,F) != use
        & leq(E,n2)
        & leq(F,pv5)
        & leq(n0,E)
        & leq(n0,F)
        & ( n0 != E
          | pv5 != F )
        & ( n1 != E
          | pv5 != F )
        & ( n2 != E
          | pv5 != F ) )
    & ! [A,B] :
        ( ~ leq(A,n2)
        | ~ leq(B,pred(pv5))
        | ~ leq(n0,A)
        | ~ leq(n0,B)
        | a_select3(u_defuse,A,B) = use )
    & ! [C,D] :
        ( ~ leq(C,n2)
        | ~ leq(D,pred(pv5))
        | ~ leq(n0,C)
        | ~ leq(n0,D)
        | a_select3(z_defuse,C,D) = use ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_14,plain,
    ? [E,F] :
      ( a_select3(z_defuse,E,F) != use
      & leq(E,n2)
      & leq(F,pv5)
      & leq(n0,E)
      & leq(n0,F)
      & ( n0 != E
        | pv5 != F )
      & ( n1 != E
        | pv5 != F )
      & ( n2 != E
        | pv5 != F ) ),
    inference(conjunct,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ( a_select3(z_defuse,skolemFOFtoCNF_E,skolemFOFtoCNF_F) != use
    & leq(n0,skolemFOFtoCNF_E)
    & leq(n0,skolemFOFtoCNF_F)
    & leq(skolemFOFtoCNF_E,n2)
    & leq(skolemFOFtoCNF_F,pv5)
    & ( n0 != skolemFOFtoCNF_E
      | pv5 != skolemFOFtoCNF_F )
    & ( n1 != skolemFOFtoCNF_E
      | pv5 != skolemFOFtoCNF_F )
    & ( n2 != skolemFOFtoCNF_E
      | pv5 != skolemFOFtoCNF_F ) ),
    inference(skolemize,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    leq(skolemFOFtoCNF_E,n2),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
      | X = Y
      | gt(Y,X) ),
    inference(canonicalize,[],[leq_gt2]) ).

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

fof(normalize_0_19,plain,
    ( n2 != skolemFOFtoCNF_E
    | pv5 != skolemFOFtoCNF_F ),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_20,plain,
    leq(pv5,n0),
    inference(conjunct,[],[normalize_0_13]) ).

fof(normalize_0_21,plain,
    leq(n0,pv5),
    inference(conjunct,[],[normalize_0_13]) ).

fof(normalize_0_22,plain,
    leq(skolemFOFtoCNF_F,pv5),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_23,plain,
    leq(n0,skolemFOFtoCNF_F),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_24,plain,
    ! [X] : pred(succ(X)) = X,
    inference(canonicalize,[],[pred_succ]) ).

fof(normalize_0_25,plain,
    ! [X] : pred(succ(X)) = X,
    inference(specialize,[],[normalize_0_24]) ).

fof(normalize_0_26,plain,
    succ(succ(n0)) = n2,
    inference(canonicalize,[],[successor_2]) ).

fof(normalize_0_27,plain,
    leq(n0,skolemFOFtoCNF_E),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_28,plain,
    ( n0 != skolemFOFtoCNF_E
    | pv5 != skolemFOFtoCNF_F ),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_29,plain,
    ( n1 != skolemFOFtoCNF_E
    | pv5 != skolemFOFtoCNF_F ),
    inference(conjunct,[],[normalize_0_15]) ).

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

cnf(refute_0_1,plain,
    succ(pred(skolemFOFtoCNF_E)) = skolemFOFtoCNF_E,
    inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_E))]]) ).

cnf(refute_0_2,plain,
    ( ~ leq(X,n0)
    | ~ leq(n0,X)
    | X = n0 ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    ( ~ leq(n0,pred(skolemFOFtoCNF_E))
    | ~ leq(pred(skolemFOFtoCNF_E),n0)
    | pred(skolemFOFtoCNF_E) = n0 ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(pred(skolemFOFtoCNF_E)))]]) ).

cnf(refute_0_4,plain,
    ( ~ leq(succ(X),succ(Y))
    | leq(X,Y) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_5,plain,
    ( ~ leq(succ(X_7564),succ(n0))
    | leq(X_7564,n0) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(X_7564)),bind(Y,$fot(n0))]]) ).

cnf(refute_0_6,plain,
    succ(n0) = n1,
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_7,plain,
    ( succ(n0) != n1
    | ~ leq(succ(X_7564),n1)
    | leq(succ(X_7564),succ(n0)) ),
    introduced(tautology,[equality,[$cnf( ~ leq(succ(X_7564),succ(n0)) ),[1],$fot(n1)]]) ).

cnf(refute_0_8,plain,
    ( ~ leq(succ(X_7564),n1)
    | leq(succ(X_7564),succ(n0)) ),
    inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ leq(succ(X_7564),n1)
    | leq(X_7564,n0) ),
    inference(resolve,[$cnf( leq(succ(X_7564),succ(n0)) )],[refute_0_8,refute_0_5]) ).

cnf(refute_0_10,plain,
    ( ~ leq(succ(pred(X)),n1)
    | leq(pred(X),n0) ),
    inference(subst,[],[refute_0_9:[bind(X_7564,$fot(pred(X)))]]) ).

cnf(refute_0_11,plain,
    ( succ(pred(X)) != X
    | ~ leq(X,n1)
    | leq(succ(pred(X)),n1) ),
    introduced(tautology,[equality,[$cnf( ~ leq(succ(pred(X)),n1) ),[0],$fot(X)]]) ).

cnf(refute_0_12,plain,
    ( ~ leq(X,n1)
    | leq(succ(pred(X)),n1) ),
    inference(resolve,[$cnf( $equal(succ(pred(X)),X) )],[refute_0_0,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ leq(X,n1)
    | leq(pred(X),n0) ),
    inference(resolve,[$cnf( leq(succ(pred(X)),n1) )],[refute_0_12,refute_0_10]) ).

cnf(refute_0_14,plain,
    ( ~ leq(skolemFOFtoCNF_E,n1)
    | leq(pred(skolemFOFtoCNF_E),n0) ),
    inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_E))]]) ).

cnf(refute_0_15,plain,
    ( ~ gt(Y,X)
    | leq(X,pred(Y)) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_16,plain,
    ( ~ gt(n2,skolemFOFtoCNF_E)
    | leq(skolemFOFtoCNF_E,pred(n2)) ),
    inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_E)),bind(Y,$fot(n2))]]) ).

cnf(refute_0_17,plain,
    leq(skolemFOFtoCNF_E,n2),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_18,plain,
    ( ~ leq(X,Y)
    | X = Y
    | gt(Y,X) ),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_19,plain,
    ( ~ leq(skolemFOFtoCNF_E,n2)
    | skolemFOFtoCNF_E = n2
    | gt(n2,skolemFOFtoCNF_E) ),
    inference(subst,[],[refute_0_18:[bind(X,$fot(skolemFOFtoCNF_E)),bind(Y,$fot(n2))]]) ).

cnf(refute_0_20,plain,
    ( skolemFOFtoCNF_E = n2
    | gt(n2,skolemFOFtoCNF_E) ),
    inference(resolve,[$cnf( leq(skolemFOFtoCNF_E,n2) )],[refute_0_17,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( n2 != skolemFOFtoCNF_E
    | pv5 != skolemFOFtoCNF_F ),
    inference(canonicalize,[],[normalize_0_19]) ).

cnf(refute_0_22,plain,
    leq(pv5,n0),
    inference(canonicalize,[],[normalize_0_20]) ).

cnf(refute_0_23,plain,
    ( ~ leq(n0,pv5)
    | ~ leq(pv5,n0)
    | pv5 = n0 ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(pv5))]]) ).

cnf(refute_0_24,plain,
    ( ~ leq(n0,pv5)
    | pv5 = n0 ),
    inference(resolve,[$cnf( leq(pv5,n0) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    leq(n0,pv5),
    inference(canonicalize,[],[normalize_0_21]) ).

cnf(refute_0_26,plain,
    pv5 = n0,
    inference(resolve,[$cnf( leq(n0,pv5) )],[refute_0_25,refute_0_24]) ).

cnf(refute_0_27,plain,
    ( n0 != skolemFOFtoCNF_F
    | pv5 != n0
    | pv5 = skolemFOFtoCNF_F ),
    introduced(tautology,[equality,[$cnf( $equal(pv5,n0) ),[1],$fot(skolemFOFtoCNF_F)]]) ).

cnf(refute_0_28,plain,
    ( n0 != skolemFOFtoCNF_F
    | pv5 = skolemFOFtoCNF_F ),
    inference(resolve,[$cnf( $equal(pv5,n0) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( n0 != skolemFOFtoCNF_F
    | n2 != skolemFOFtoCNF_E ),
    inference(resolve,[$cnf( $equal(pv5,skolemFOFtoCNF_F) )],[refute_0_28,refute_0_21]) ).

cnf(refute_0_30,plain,
    ( ~ leq(n0,skolemFOFtoCNF_F)
    | ~ leq(skolemFOFtoCNF_F,n0)
    | skolemFOFtoCNF_F = n0 ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_F))]]) ).

cnf(refute_0_31,plain,
    leq(skolemFOFtoCNF_F,pv5),
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_32,plain,
    ( pv5 != n0
    | ~ leq(skolemFOFtoCNF_F,pv5)
    | leq(skolemFOFtoCNF_F,n0) ),
    introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_F,pv5) ),[1],$fot(n0)]]) ).

cnf(refute_0_33,plain,
    ( ~ leq(skolemFOFtoCNF_F,pv5)
    | leq(skolemFOFtoCNF_F,n0) ),
    inference(resolve,[$cnf( $equal(pv5,n0) )],[refute_0_26,refute_0_32]) ).

cnf(refute_0_34,plain,
    leq(skolemFOFtoCNF_F,n0),
    inference(resolve,[$cnf( leq(skolemFOFtoCNF_F,pv5) )],[refute_0_31,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( ~ leq(n0,skolemFOFtoCNF_F)
    | skolemFOFtoCNF_F = n0 ),
    inference(resolve,[$cnf( leq(skolemFOFtoCNF_F,n0) )],[refute_0_34,refute_0_30]) ).

cnf(refute_0_36,plain,
    leq(n0,skolemFOFtoCNF_F),
    inference(canonicalize,[],[normalize_0_23]) ).

cnf(refute_0_37,plain,
    skolemFOFtoCNF_F = n0,
    inference(resolve,[$cnf( leq(n0,skolemFOFtoCNF_F) )],[refute_0_36,refute_0_35]) ).

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

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

cnf(refute_0_40,plain,
    ( n0 != n0
    | n2 != skolemFOFtoCNF_E ),
    inference(resolve,[$cnf( $equal(n0,skolemFOFtoCNF_F) )],[refute_0_39,refute_0_29]) ).

cnf(refute_0_41,plain,
    n0 = n0,
    introduced(tautology,[refl,[$fot(n0)]]) ).

cnf(refute_0_42,plain,
    n2 != skolemFOFtoCNF_E,
    inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_41,refute_0_40]) ).

cnf(refute_0_43,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_44,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_45,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_43,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( skolemFOFtoCNF_E != n2
    | n2 = skolemFOFtoCNF_E ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(skolemFOFtoCNF_E)),bind(Y0,$fot(n2))]]) ).

cnf(refute_0_47,plain,
    skolemFOFtoCNF_E != n2,
    inference(resolve,[$cnf( $equal(n2,skolemFOFtoCNF_E) )],[refute_0_46,refute_0_42]) ).

cnf(refute_0_48,plain,
    gt(n2,skolemFOFtoCNF_E),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_E,n2) )],[refute_0_20,refute_0_47]) ).

cnf(refute_0_49,plain,
    leq(skolemFOFtoCNF_E,pred(n2)),
    inference(resolve,[$cnf( gt(n2,skolemFOFtoCNF_E) )],[refute_0_48,refute_0_16]) ).

cnf(refute_0_50,plain,
    pred(succ(X)) = X,
    inference(canonicalize,[],[normalize_0_25]) ).

cnf(refute_0_51,plain,
    pred(succ(n1)) = n1,
    inference(subst,[],[refute_0_50:[bind(X,$fot(n1))]]) ).

cnf(refute_0_52,plain,
    succ(succ(n0)) = n2,
    inference(canonicalize,[],[normalize_0_26]) ).

cnf(refute_0_53,plain,
    succ(succ(n0)) = succ(succ(n0)),
    introduced(tautology,[refl,[$fot(succ(succ(n0)))]]) ).

cnf(refute_0_54,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_55,plain,
    ( succ(n0) != n1
    | succ(succ(n0)) = succ(n1) ),
    inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) )],[refute_0_53,refute_0_54]) ).

cnf(refute_0_56,plain,
    succ(succ(n0)) = succ(n1),
    inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_6,refute_0_55]) ).

cnf(refute_0_57,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_58,plain,
    ( succ(succ(n0)) != n2
    | succ(n1) = n2 ),
    inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(n1)) )],[refute_0_56,refute_0_57]) ).

cnf(refute_0_59,plain,
    succ(n1) = n2,
    inference(resolve,[$cnf( $equal(succ(succ(n0)),n2) )],[refute_0_52,refute_0_58]) ).

cnf(refute_0_60,plain,
    ( pred(succ(n1)) != n1
    | succ(n1) != n2
    | pred(n2) = n1 ),
    introduced(tautology,[equality,[$cnf( $equal(pred(succ(n1)),n1) ),[0,0],$fot(n2)]]) ).

cnf(refute_0_61,plain,
    ( pred(succ(n1)) != n1
    | pred(n2) = n1 ),
    inference(resolve,[$cnf( $equal(succ(n1),n2) )],[refute_0_59,refute_0_60]) ).

cnf(refute_0_62,plain,
    pred(n2) = n1,
    inference(resolve,[$cnf( $equal(pred(succ(n1)),n1) )],[refute_0_51,refute_0_61]) ).

cnf(refute_0_63,plain,
    ( pred(n2) != n1
    | ~ leq(skolemFOFtoCNF_E,pred(n2))
    | leq(skolemFOFtoCNF_E,n1) ),
    introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_E,pred(n2)) ),[1],$fot(n1)]]) ).

cnf(refute_0_64,plain,
    ( ~ leq(skolemFOFtoCNF_E,pred(n2))
    | leq(skolemFOFtoCNF_E,n1) ),
    inference(resolve,[$cnf( $equal(pred(n2),n1) )],[refute_0_62,refute_0_63]) ).

cnf(refute_0_65,plain,
    leq(skolemFOFtoCNF_E,n1),
    inference(resolve,[$cnf( leq(skolemFOFtoCNF_E,pred(n2)) )],[refute_0_49,refute_0_64]) ).

cnf(refute_0_66,plain,
    leq(pred(skolemFOFtoCNF_E),n0),
    inference(resolve,[$cnf( leq(skolemFOFtoCNF_E,n1) )],[refute_0_65,refute_0_14]) ).

cnf(refute_0_67,plain,
    ( ~ leq(n0,pred(skolemFOFtoCNF_E))
    | pred(skolemFOFtoCNF_E) = n0 ),
    inference(resolve,[$cnf( leq(pred(skolemFOFtoCNF_E),n0) )],[refute_0_66,refute_0_3]) ).

cnf(refute_0_68,plain,
    ( ~ gt(skolemFOFtoCNF_E,n0)
    | leq(n0,pred(skolemFOFtoCNF_E)) ),
    inference(subst,[],[refute_0_15:[bind(X,$fot(n0)),bind(Y,$fot(skolemFOFtoCNF_E))]]) ).

cnf(refute_0_69,plain,
    leq(n0,skolemFOFtoCNF_E),
    inference(canonicalize,[],[normalize_0_27]) ).

cnf(refute_0_70,plain,
    ( ~ leq(n0,skolemFOFtoCNF_E)
    | n0 = skolemFOFtoCNF_E
    | gt(skolemFOFtoCNF_E,n0) ),
    inference(subst,[],[refute_0_18:[bind(X,$fot(n0)),bind(Y,$fot(skolemFOFtoCNF_E))]]) ).

cnf(refute_0_71,plain,
    ( n0 = skolemFOFtoCNF_E
    | gt(skolemFOFtoCNF_E,n0) ),
    inference(resolve,[$cnf( leq(n0,skolemFOFtoCNF_E) )],[refute_0_69,refute_0_70]) ).

cnf(refute_0_72,plain,
    ( n0 != skolemFOFtoCNF_E
    | pv5 != skolemFOFtoCNF_F ),
    inference(canonicalize,[],[normalize_0_28]) ).

cnf(refute_0_73,plain,
    ( n0 != skolemFOFtoCNF_E
    | n0 != skolemFOFtoCNF_F ),
    inference(resolve,[$cnf( $equal(pv5,skolemFOFtoCNF_F) )],[refute_0_28,refute_0_72]) ).

cnf(refute_0_74,plain,
    ( n0 != n0
    | n0 != skolemFOFtoCNF_E ),
    inference(resolve,[$cnf( $equal(n0,skolemFOFtoCNF_F) )],[refute_0_39,refute_0_73]) ).

cnf(refute_0_75,plain,
    n0 != skolemFOFtoCNF_E,
    inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_41,refute_0_74]) ).

cnf(refute_0_76,plain,
    gt(skolemFOFtoCNF_E,n0),
    inference(resolve,[$cnf( $equal(n0,skolemFOFtoCNF_E) )],[refute_0_71,refute_0_75]) ).

cnf(refute_0_77,plain,
    leq(n0,pred(skolemFOFtoCNF_E)),
    inference(resolve,[$cnf( gt(skolemFOFtoCNF_E,n0) )],[refute_0_76,refute_0_68]) ).

cnf(refute_0_78,plain,
    pred(skolemFOFtoCNF_E) = n0,
    inference(resolve,[$cnf( leq(n0,pred(skolemFOFtoCNF_E)) )],[refute_0_77,refute_0_67]) ).

cnf(refute_0_79,plain,
    ( pred(skolemFOFtoCNF_E) != n0
    | succ(pred(skolemFOFtoCNF_E)) != skolemFOFtoCNF_E
    | succ(n0) = skolemFOFtoCNF_E ),
    introduced(tautology,[equality,[$cnf( $equal(succ(pred(skolemFOFtoCNF_E)),skolemFOFtoCNF_E) ),[0,0],$fot(n0)]]) ).

cnf(refute_0_80,plain,
    ( succ(pred(skolemFOFtoCNF_E)) != skolemFOFtoCNF_E
    | succ(n0) = skolemFOFtoCNF_E ),
    inference(resolve,[$cnf( $equal(pred(skolemFOFtoCNF_E),n0) )],[refute_0_78,refute_0_79]) ).

cnf(refute_0_81,plain,
    succ(n0) = skolemFOFtoCNF_E,
    inference(resolve,[$cnf( $equal(succ(pred(skolemFOFtoCNF_E)),skolemFOFtoCNF_E) )],[refute_0_1,refute_0_80]) ).

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

cnf(refute_0_83,plain,
    ( succ(n0) != skolemFOFtoCNF_E
    | n1 = skolemFOFtoCNF_E ),
    inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_6,refute_0_82]) ).

cnf(refute_0_84,plain,
    n1 = skolemFOFtoCNF_E,
    inference(resolve,[$cnf( $equal(succ(n0),skolemFOFtoCNF_E) )],[refute_0_81,refute_0_83]) ).

cnf(refute_0_85,plain,
    ( n1 != skolemFOFtoCNF_E
    | pv5 != skolemFOFtoCNF_F ),
    inference(canonicalize,[],[normalize_0_29]) ).

cnf(refute_0_86,plain,
    ( n0 != skolemFOFtoCNF_F
    | n1 != skolemFOFtoCNF_E ),
    inference(resolve,[$cnf( $equal(pv5,skolemFOFtoCNF_F) )],[refute_0_28,refute_0_85]) ).

cnf(refute_0_87,plain,
    ( n0 != n0
    | n1 != skolemFOFtoCNF_E ),
    inference(resolve,[$cnf( $equal(n0,skolemFOFtoCNF_F) )],[refute_0_39,refute_0_86]) ).

cnf(refute_0_88,plain,
    n1 != skolemFOFtoCNF_E,
    inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_41,refute_0_87]) ).

cnf(refute_0_89,plain,
    $false,
    inference(resolve,[$cnf( $equal(n1,skolemFOFtoCNF_E) )],[refute_0_84,refute_0_88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SWV199+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.04/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.36  % Computer : n029.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Wed Jun 15 16:25:26 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 108.23/108.42  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 108.23/108.42  
% 108.23/108.42  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 108.23/108.43  
%------------------------------------------------------------------------------