TSTP Solution File: SWV180+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV180+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n009.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  : 300s
% DateTime : Thu Sep 29 15:10:16 EDT 2022

% Result   : Theorem 0.21s 0.45s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   55 (  12 unt;  21 typ;   0 def)
%            Number of atoms       :  344 (  95 equ)
%            Maximal formula atoms :   82 (  10 avg)
%            Number of connectives :  422 ( 127   ~; 107   |; 136   &)
%                                         (  20 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of FOOLs       :   15 (  15 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   19 (  19 usr;  16 con; 0-3 aty)
%            Number of variables   :   81 (  78   !;   0   ?;  81   :)

% Comments : 
%------------------------------------------------------------------------------
tff(init_type,type,
    init: $i ).

tff(a_select2_type,type,
    a_select2: ( $i * $i ) > $i ).

tff(pv86_type,type,
    pv86: $i ).

tff(muold_init_type,type,
    muold_init: $i ).

tff(sigmaold_init_type,type,
    sigmaold_init: $i ).

tff(leq_type,type,
    leq: ( $i * $i ) > $o ).

tff(n4_type,type,
    n4: $i ).

tff(n0_type,type,
    n0: $i ).

tff(rhoold_init_type,type,
    rhoold_init: $i ).

tff(gt_type,type,
    gt: ( $i * $i ) > $o ).

tff(n1_type,type,
    n1: $i ).

tff(loopcounter_type,type,
    loopcounter: $i ).

tff(a_select3_type,type,
    a_select3: ( $i * $i * $i ) > $i ).

tff(center_init_type,type,
    center_init: $i ).

tff(sigma_init_type,type,
    sigma_init: $i ).

tff(mu_init_type,type,
    mu_init: $i ).

tff(rho_init_type,type,
    rho_init: $i ).

tff(q_init_type,type,
    q_init: $i ).

tff(n135299_type,type,
    n135299: $i ).

tff(succ_type,type,
    succ: $i > $i ).

tff(tptp_minus_1_type,type,
    tptp_minus_1: $i ).

tff(1,plain,
    ( ( a_select2(muold_init,pv86) != init )
  <=> ( a_select2(muold_init,pv86) != init ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ~ ( ( leq(n0,pv86)
          & leq(pv86,n4)
          & ! [A: $i] :
              ( ( leq(n0,A)
                & leq(A,n135299) )
             => ! [B: $i] :
                  ( ( leq(n0,B)
                    & leq(B,n4) )
                 => ( a_select3(q_init,A,B) = init ) ) )
          & ! [C: $i] :
              ( ( leq(n0,C)
                & leq(C,n4) )
             => ( a_select2(rho_init,C) = init ) )
          & ! [D: $i] :
              ( ( leq(n0,D)
                & leq(D,n4) )
             => ( a_select2(mu_init,D) = init ) )
          & ! [E: $i] :
              ( ( leq(n0,E)
                & leq(E,n4) )
             => ( a_select2(sigma_init,E) = init ) )
          & ! [F: $i] :
              ( ( leq(n0,F)
                & leq(F,n4) )
             => ( a_select3(center_init,F,n0) = init ) )
          & ( gt(loopcounter,n1)
           => ! [G: $i] :
                ( ( leq(n0,G)
                  & leq(G,n4) )
               => ( a_select2(muold_init,G) = init ) ) )
          & ( gt(loopcounter,n1)
           => ! [H: $i] :
                ( ( leq(n0,H)
                  & leq(H,n4) )
               => ( a_select2(rhoold_init,H) = init ) ) )
          & ( gt(loopcounter,n1)
           => ! [I: $i] :
                ( ( leq(n0,I)
                  & leq(I,n4) )
               => ( a_select2(sigmaold_init,I) = init ) ) )
          & ! [J: $i] :
              ( ( leq(n0,J)
                & leq(J,n4) )
             => ( a_select2(muold_init,J) = init ) )
          & ! [K: $i] :
              ( ( leq(n0,K)
                & leq(K,n4) )
             => ( a_select2(rhoold_init,K) = init ) )
          & ! [L: $i] :
              ( ( leq(n0,L)
                & leq(L,n4) )
             => ( a_select2(sigmaold_init,L) = init ) ) )
       => ( a_select2(muold_init,pv86) = init ) )
  <=> ~ ( ~ ( leq(n0,pv86)
            & leq(pv86,n4)
            & ! [A: $i] :
                ( ~ ( leq(n0,A)
                    & leq(A,n135299) )
                | ! [B: $i] :
                    ( ~ ( leq(n0,B)
                        & leq(B,n4) )
                    | ( a_select3(q_init,A,B) = init ) ) )
            & ! [C: $i] :
                ( ~ ( leq(n0,C)
                    & leq(C,n4) )
                | ( a_select2(rho_init,C) = init ) )
            & ! [D: $i] :
                ( ~ ( leq(n0,D)
                    & leq(D,n4) )
                | ( a_select2(mu_init,D) = init ) )
            & ! [E: $i] :
                ( ~ ( leq(n0,E)
                    & leq(E,n4) )
                | ( a_select2(sigma_init,E) = init ) )
            & ! [F: $i] :
                ( ~ ( leq(n0,F)
                    & leq(F,n4) )
                | ( a_select3(center_init,F,n0) = init ) )
            & ( ~ gt(loopcounter,n1)
              | ! [G: $i] :
                  ( ~ ( leq(n0,G)
                      & leq(G,n4) )
                  | ( a_select2(muold_init,G) = init ) ) )
            & ( ~ gt(loopcounter,n1)
              | ! [H: $i] :
                  ( ~ ( leq(n0,H)
                      & leq(H,n4) )
                  | ( a_select2(rhoold_init,H) = init ) ) )
            & ( ~ gt(loopcounter,n1)
              | ! [I: $i] :
                  ( ~ ( leq(n0,I)
                      & leq(I,n4) )
                  | ( a_select2(sigmaold_init,I) = init ) ) )
            & ! [J: $i] :
                ( ~ ( leq(n0,J)
                    & leq(J,n4) )
                | ( a_select2(muold_init,J) = init ) )
            & ! [K: $i] :
                ( ~ ( leq(n0,K)
                    & leq(K,n4) )
                | ( a_select2(rhoold_init,K) = init ) )
            & ! [L: $i] :
                ( ~ ( leq(n0,L)
                    & leq(L,n4) )
                | ( a_select2(sigmaold_init,L) = init ) ) )
        | ( a_select2(muold_init,pv86) = init ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    ~ ( ( leq(n0,pv86)
        & leq(pv86,n4)
        & ! [A: $i] :
            ( ( leq(n0,A)
              & leq(A,n135299) )
           => ! [B: $i] :
                ( ( leq(n0,B)
                  & leq(B,n4) )
               => ( a_select3(q_init,A,B) = init ) ) )
        & ! [C: $i] :
            ( ( leq(n0,C)
              & leq(C,n4) )
           => ( a_select2(rho_init,C) = init ) )
        & ! [D: $i] :
            ( ( leq(n0,D)
              & leq(D,n4) )
           => ( a_select2(mu_init,D) = init ) )
        & ! [E: $i] :
            ( ( leq(n0,E)
              & leq(E,n4) )
           => ( a_select2(sigma_init,E) = init ) )
        & ! [F: $i] :
            ( ( leq(n0,F)
              & leq(F,n4) )
           => ( a_select3(center_init,F,n0) = init ) )
        & ( gt(loopcounter,n1)
         => ! [G: $i] :
              ( ( leq(n0,G)
                & leq(G,n4) )
             => ( a_select2(muold_init,G) = init ) ) )
        & ( gt(loopcounter,n1)
         => ! [H: $i] :
              ( ( leq(n0,H)
                & leq(H,n4) )
             => ( a_select2(rhoold_init,H) = init ) ) )
        & ( gt(loopcounter,n1)
         => ! [I: $i] :
              ( ( leq(n0,I)
                & leq(I,n4) )
             => ( a_select2(sigmaold_init,I) = init ) ) )
        & ! [J: $i] :
            ( ( leq(n0,J)
              & leq(J,n4) )
           => ( a_select2(muold_init,J) = init ) )
        & ! [K: $i] :
            ( ( leq(n0,K)
              & leq(K,n4) )
           => ( a_select2(rhoold_init,K) = init ) )
        & ! [L: $i] :
            ( ( leq(n0,L)
              & leq(L,n4) )
           => ( a_select2(sigmaold_init,L) = init ) ) )
     => ( a_select2(muold_init,pv86) = init ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0076) ).

tff(4,plain,
    ~ ( ~ ( leq(n0,pv86)
          & leq(pv86,n4)
          & ! [A: $i] :
              ( ~ ( leq(n0,A)
                  & leq(A,n135299) )
              | ! [B: $i] :
                  ( ~ ( leq(n0,B)
                      & leq(B,n4) )
                  | ( a_select3(q_init,A,B) = init ) ) )
          & ! [C: $i] :
              ( ~ ( leq(n0,C)
                  & leq(C,n4) )
              | ( a_select2(rho_init,C) = init ) )
          & ! [D: $i] :
              ( ~ ( leq(n0,D)
                  & leq(D,n4) )
              | ( a_select2(mu_init,D) = init ) )
          & ! [E: $i] :
              ( ~ ( leq(n0,E)
                  & leq(E,n4) )
              | ( a_select2(sigma_init,E) = init ) )
          & ! [F: $i] :
              ( ~ ( leq(n0,F)
                  & leq(F,n4) )
              | ( a_select3(center_init,F,n0) = init ) )
          & ( ~ gt(loopcounter,n1)
            | ! [G: $i] :
                ( ~ ( leq(n0,G)
                    & leq(G,n4) )
                | ( a_select2(muold_init,G) = init ) ) )
          & ( ~ gt(loopcounter,n1)
            | ! [H: $i] :
                ( ~ ( leq(n0,H)
                    & leq(H,n4) )
                | ( a_select2(rhoold_init,H) = init ) ) )
          & ( ~ gt(loopcounter,n1)
            | ! [I: $i] :
                ( ~ ( leq(n0,I)
                    & leq(I,n4) )
                | ( a_select2(sigmaold_init,I) = init ) ) )
          & ! [J: $i] :
              ( ~ ( leq(n0,J)
                  & leq(J,n4) )
              | ( a_select2(muold_init,J) = init ) )
          & ! [K: $i] :
              ( ~ ( leq(n0,K)
                  & leq(K,n4) )
              | ( a_select2(rhoold_init,K) = init ) )
          & ! [L: $i] :
              ( ~ ( leq(n0,L)
                  & leq(L,n4) )
              | ( a_select2(sigmaold_init,L) = init ) ) )
      | ( a_select2(muold_init,pv86) = init ) ),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    a_select2(muold_init,pv86) != init,
    inference(or_elim,[status(thm)],[4]) ).

tff(6,plain,
    a_select2(muold_init,pv86) != init,
    inference(modus_ponens,[status(thm)],[5,1]) ).

tff(7,plain,
    ^ [J: $i] :
      refl(
        ( ( ( a_select2(muold_init,J) = init )
          | ~ leq(succ(tptp_minus_1),J)
          | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
      <=> ( ( a_select2(muold_init,J) = init )
          | ~ leq(succ(tptp_minus_1),J)
          | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
    inference(bind,[status(th)],]) ).

tff(8,plain,
    ( ! [J: $i] :
        ( ( a_select2(muold_init,J) = init )
        | ~ leq(succ(tptp_minus_1),J)
        | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
  <=> ! [J: $i] :
        ( ( a_select2(muold_init,J) = init )
        | ~ leq(succ(tptp_minus_1),J)
        | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) ),
    inference(quant_intro,[status(thm)],[7]) ).

tff(9,plain,
    ^ [J: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( leq(succ(tptp_minus_1),J)
                  & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
              <=> ~ ( ~ leq(succ(tptp_minus_1),J)
                    | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
              ( ~ ( leq(succ(tptp_minus_1),J)
                  & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
            <=> ~ ~ ( ~ leq(succ(tptp_minus_1),J)
                    | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
            rewrite(
              ( ~ ~ ( ~ leq(succ(tptp_minus_1),J)
                    | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
            <=> ( ~ leq(succ(tptp_minus_1),J)
                | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
            ( ~ ( leq(succ(tptp_minus_1),J)
                & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
          <=> ( ~ leq(succ(tptp_minus_1),J)
              | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
          ( ( ~ ( leq(succ(tptp_minus_1),J)
                & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
            | ( a_select2(muold_init,J) = init ) )
        <=> ( ~ leq(succ(tptp_minus_1),J)
            | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1))))))
            | ( a_select2(muold_init,J) = init ) ) )),
        rewrite(
          ( ( ~ leq(succ(tptp_minus_1),J)
            | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1))))))
            | ( a_select2(muold_init,J) = init ) )
        <=> ( ( a_select2(muold_init,J) = init )
            | ~ leq(succ(tptp_minus_1),J)
            | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
        ( ( ~ ( leq(succ(tptp_minus_1),J)
              & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
          | ( a_select2(muold_init,J) = init ) )
      <=> ( ( a_select2(muold_init,J) = init )
          | ~ leq(succ(tptp_minus_1),J)
          | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
    inference(bind,[status(th)],]) ).

tff(10,plain,
    ( ! [J: $i] :
        ( ~ ( leq(succ(tptp_minus_1),J)
            & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
        | ( a_select2(muold_init,J) = init ) )
  <=> ! [J: $i] :
        ( ( a_select2(muold_init,J) = init )
        | ~ leq(succ(tptp_minus_1),J)
        | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) ),
    inference(quant_intro,[status(thm)],[9]) ).

tff(11,plain,
    ^ [J: $i] :
      rewrite(
        ( ( ~ ( leq(n0,J)
              & leq(J,n4) )
          | ( a_select2(muold_init,J) = init ) )
      <=> ( ~ ( leq(succ(tptp_minus_1),J)
              & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
          | ( a_select2(muold_init,J) = init ) ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [J: $i] :
        ( ~ ( leq(n0,J)
            & leq(J,n4) )
        | ( a_select2(muold_init,J) = init ) )
  <=> ! [J: $i] :
        ( ~ ( leq(succ(tptp_minus_1),J)
            & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
        | ( a_select2(muold_init,J) = init ) ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [J: $i] :
        ( ~ ( leq(n0,J)
            & leq(J,n4) )
        | ( a_select2(muold_init,J) = init ) )
  <=> ! [J: $i] :
        ( ~ ( leq(n0,J)
            & leq(J,n4) )
        | ( a_select2(muold_init,J) = init ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ( leq(n0,pv86)
    & leq(pv86,n4)
    & ! [A: $i] :
        ( ~ ( leq(n0,A)
            & leq(A,n135299) )
        | ! [B: $i] :
            ( ~ ( leq(n0,B)
                & leq(B,n4) )
            | ( a_select3(q_init,A,B) = init ) ) )
    & ! [C: $i] :
        ( ~ ( leq(n0,C)
            & leq(C,n4) )
        | ( a_select2(rho_init,C) = init ) )
    & ! [D: $i] :
        ( ~ ( leq(n0,D)
            & leq(D,n4) )
        | ( a_select2(mu_init,D) = init ) )
    & ! [E: $i] :
        ( ~ ( leq(n0,E)
            & leq(E,n4) )
        | ( a_select2(sigma_init,E) = init ) )
    & ! [F: $i] :
        ( ~ ( leq(n0,F)
            & leq(F,n4) )
        | ( a_select3(center_init,F,n0) = init ) )
    & ( ~ gt(loopcounter,n1)
      | ! [G: $i] :
          ( ~ ( leq(n0,G)
              & leq(G,n4) )
          | ( a_select2(muold_init,G) = init ) ) )
    & ( ~ gt(loopcounter,n1)
      | ! [H: $i] :
          ( ~ ( leq(n0,H)
              & leq(H,n4) )
          | ( a_select2(rhoold_init,H) = init ) ) )
    & ( ~ gt(loopcounter,n1)
      | ! [I: $i] :
          ( ~ ( leq(n0,I)
              & leq(I,n4) )
          | ( a_select2(sigmaold_init,I) = init ) ) )
    & ! [J: $i] :
        ( ~ ( leq(n0,J)
            & leq(J,n4) )
        | ( a_select2(muold_init,J) = init ) )
    & ! [K: $i] :
        ( ~ ( leq(n0,K)
            & leq(K,n4) )
        | ( a_select2(rhoold_init,K) = init ) )
    & ! [L: $i] :
        ( ~ ( leq(n0,L)
            & leq(L,n4) )
        | ( a_select2(sigmaold_init,L) = init ) ) ),
    inference(or_elim,[status(thm)],[4]) ).

tff(15,plain,
    ! [J: $i] :
      ( ~ ( leq(n0,J)
          & leq(J,n4) )
      | ( a_select2(muold_init,J) = init ) ),
    inference(and_elim,[status(thm)],[14]) ).

tff(16,plain,
    ! [J: $i] :
      ( ~ ( leq(n0,J)
          & leq(J,n4) )
      | ( a_select2(muold_init,J) = init ) ),
    inference(modus_ponens,[status(thm)],[15,13]) ).

tff(17,plain,
    ! [J: $i] :
      ( ~ ( leq(succ(tptp_minus_1),J)
          & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
      | ( a_select2(muold_init,J) = init ) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [J: $i] :
      ( ~ ( leq(succ(tptp_minus_1),J)
          & leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
      | ( a_select2(muold_init,J) = init ) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [J: $i] :
      ( ( a_select2(muold_init,J) = init )
      | ~ leq(succ(tptp_minus_1),J)
      | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
    inference(modus_ponens,[status(thm)],[18,10]) ).

tff(20,plain,
    ! [J: $i] :
      ( ( a_select2(muold_init,J) = init )
      | ~ leq(succ(tptp_minus_1),J)
      | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
    inference(modus_ponens,[status(thm)],[19,8]) ).

tff(21,plain,
    ( leq(pv86,n4)
  <=> leq(pv86,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ( leq(pv86,n4)
  <=> leq(pv86,n4) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,plain,
    leq(pv86,n4),
    inference(and_elim,[status(thm)],[14]) ).

tff(24,plain,
    leq(pv86,n4),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    leq(pv86,succ(succ(succ(succ(succ(tptp_minus_1)))))),
    inference(modus_ponens,[status(thm)],[24,21]) ).

tff(26,plain,
    ( leq(n0,pv86)
  <=> leq(succ(tptp_minus_1),pv86) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ( leq(n0,pv86)
  <=> leq(n0,pv86) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,plain,
    leq(n0,pv86),
    inference(and_elim,[status(thm)],[14]) ).

tff(29,plain,
    leq(n0,pv86),
    inference(modus_ponens,[status(thm)],[28,27]) ).

tff(30,plain,
    leq(succ(tptp_minus_1),pv86),
    inference(modus_ponens,[status(thm)],[29,26]) ).

tff(31,plain,
    ( ( ~ ! [J: $i] :
            ( ( a_select2(muold_init,J) = init )
            | ~ leq(succ(tptp_minus_1),J)
            | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
      | ( a_select2(muold_init,pv86) = init )
      | ~ leq(succ(tptp_minus_1),pv86)
      | ~ leq(pv86,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
  <=> ( ~ ! [J: $i] :
            ( ( a_select2(muold_init,J) = init )
            | ~ leq(succ(tptp_minus_1),J)
            | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
      | ( a_select2(muold_init,pv86) = init )
      | ~ leq(succ(tptp_minus_1),pv86)
      | ~ leq(pv86,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ~ ! [J: $i] :
          ( ( a_select2(muold_init,J) = init )
          | ~ leq(succ(tptp_minus_1),J)
          | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
    | ( a_select2(muold_init,pv86) = init )
    | ~ leq(succ(tptp_minus_1),pv86)
    | ~ leq(pv86,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [J: $i] :
          ( ( a_select2(muold_init,J) = init )
          | ~ leq(succ(tptp_minus_1),J)
          | ~ leq(J,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
    | ( a_select2(muold_init,pv86) = init )
    | ~ leq(succ(tptp_minus_1),pv86)
    | ~ leq(pv86,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    $false,
    inference(unit_resolution,[status(thm)],[33,30,25,20,6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWV180+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.12/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun Sep  4 01:37:36 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36  Usage: tptp [options] [-file:]file
% 0.14/0.36    -h, -?       prints this message.
% 0.14/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.36    -m, -model   generate model.
% 0.14/0.36    -p, -proof   generate proof.
% 0.14/0.36    -c, -core    generate unsat core of named formulas.
% 0.14/0.36    -st, -statistics display statistics.
% 0.14/0.36    -t:timeout   set timeout (in second).
% 0.14/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36    -<param>:<value> configuration parameter and value.
% 0.14/0.36    -o:<output-file> file to place output in.
% 0.21/0.45  % SZS status Theorem
% 0.21/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------