TSTP Solution File: KRS193+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : KRS193+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 : Sat Sep 17 17:45:09 EDT 2022

% Result   : Theorem 0.13s 0.42s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   95 (  21 unt;   9 typ;   0 def)
%            Number of atoms       :  650 (   0 equ)
%            Maximal formula atoms :   12 (   7 avg)
%            Number of connectives : 1134 ( 602   ~; 442   |;  18   &)
%                                         (  66 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   32 (  32 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   7   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  321 ( 289   !;   4   ?; 321   :)

% Comments : 
%------------------------------------------------------------------------------
tff(model_type,type,
    model: ( $i * $i ) > $o ).

tff(tptp_fun_Ax_21_type,type,
    tptp_fun_Ax_21: ( $i * $i ) > $i ).

tff(cax_type,type,
    cax: $i ).

tff(thm_type,type,
    thm: $i ).

tff(status_type,type,
    status: ( $i * $i * $i ) > $o ).

tff(tptp_fun_C_20_type,type,
    tptp_fun_C_20: ( $i * $i ) > $i ).

tff(tptp_fun_I1_0_type,type,
    tptp_fun_I1_0: $i > $i ).

tff(isa_type,type,
    isa: ( $i * $i ) > $o ).

tff(tptp_fun_I1_3_type,type,
    tptp_fun_I1_3: ( $i * $i ) > $i ).

tff(1,plain,
    ^ [Ax: $i,C: $i] :
      rewrite(
        ( ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
                | status(Ax,C,cax) )
            | ~ ( ! [I1: $i] : ~ model(I1,Ax)
                | ~ status(Ax,C,cax) ) )
      <=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
                | status(Ax,C,cax) )
            | ~ ( ~ status(Ax,C,cax)
                | ! [I1: $i] : ~ model(I1,Ax) ) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [Ax: $i,C: $i] :
        ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
          | ~ ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
          | ~ ( ~ status(Ax,C,cax)
              | ! [I1: $i] : ~ model(I1,Ax) ) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [Ax: $i,C: $i] :
      refl(
        ( ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
                | status(Ax,C,cax) )
            | ~ ( ! [I1: $i] : ~ model(I1,Ax)
                | ~ status(Ax,C,cax) ) )
      <=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
                | status(Ax,C,cax) )
            | ~ ( ! [I1: $i] : ~ model(I1,Ax)
                | ~ status(Ax,C,cax) ) ) )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [Ax: $i,C: $i] :
        ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
          | ~ ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
          | ~ ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) ) ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ^ [Ax: $i,C: $i] :
      rewrite(
        ( ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
                | status(Ax,C,cax) )
            | ~ ( ! [I1: $i] : ~ model(I1,Ax)
                | ~ status(Ax,C,cax) ) )
      <=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
                | status(Ax,C,cax) )
            | ~ ( ! [I1: $i] : ~ model(I1,Ax)
                | ~ status(Ax,C,cax) ) ) )),
    inference(bind,[status(th)],]) ).

tff(6,plain,
    ( ! [Ax: $i,C: $i] :
        ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
          | ~ ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
          | ~ ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) ) ),
    inference(quant_intro,[status(thm)],[5]) ).

tff(7,plain,
    ( ! [Ax: $i,C: $i] :
        ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
          | ~ ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
          | ~ ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) ) ),
    inference(transitivity,[status(thm)],[6,4]) ).

tff(8,plain,
    ^ [Ax: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) )
          <=> ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) )),
          ( ( ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
            & ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) )
        <=> ( ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
            & ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) ) )),
        rewrite(
          ( ( ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
            & ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) )
        <=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
                  | status(Ax,C,cax) )
              | ~ ( ! [I1: $i] : ~ model(I1,Ax)
                  | ~ status(Ax,C,cax) ) ) )),
        ( ( ( model(tptp_fun_I1_0(Ax),Ax)
            | status(Ax,C,cax) )
          & ( ! [I1: $i] : ~ model(I1,Ax)
            | ~ status(Ax,C,cax) ) )
      <=> ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
                | status(Ax,C,cax) )
            | ~ ( ! [I1: $i] : ~ model(I1,Ax)
                | ~ status(Ax,C,cax) ) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [Ax: $i,C: $i] :
        ( ( model(tptp_fun_I1_0(Ax),Ax)
          | status(Ax,C,cax) )
        & ( ! [I1: $i] : ~ model(I1,Ax)
          | ~ status(Ax,C,cax) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
              | status(Ax,C,cax) )
          | ~ ( ! [I1: $i] : ~ model(I1,Ax)
              | ~ status(Ax,C,cax) ) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [Ax: $i,C: $i] :
        ( ~ ? [I1: $i] : model(I1,Ax)
      <=> status(Ax,C,cax) )
  <=> ! [Ax: $i,C: $i] :
        ( ~ ? [I1: $i] : model(I1,Ax)
      <=> status(Ax,C,cax) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ! [Ax: $i,C: $i] :
      ( ~ ? [I1: $i] : model(I1,Ax)
    <=> status(Ax,C,cax) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',cax) ).

tff(12,plain,
    ! [Ax: $i,C: $i] :
      ( ~ ? [I1: $i] : model(I1,Ax)
    <=> status(Ax,C,cax) ),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ! [Ax: $i,C: $i] :
      ( ( model(tptp_fun_I1_0(Ax),Ax)
        | status(Ax,C,cax) )
      & ( ! [I1: $i] : ~ model(I1,Ax)
        | ~ status(Ax,C,cax) ) ),
    inference(skolemize,[status(sab)],[12]) ).

tff(14,plain,
    ! [Ax: $i,C: $i] :
      ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
            | status(Ax,C,cax) )
        | ~ ( ! [I1: $i] : ~ model(I1,Ax)
            | ~ status(Ax,C,cax) ) ),
    inference(modus_ponens,[status(thm)],[13,9]) ).

tff(15,plain,
    ! [Ax: $i,C: $i] :
      ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
            | status(Ax,C,cax) )
        | ~ ( ! [I1: $i] : ~ model(I1,Ax)
            | ~ status(Ax,C,cax) ) ),
    inference(modus_ponens,[status(thm)],[14,7]) ).

tff(16,plain,
    ! [Ax: $i,C: $i] :
      ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
            | status(Ax,C,cax) )
        | ~ ( ~ status(Ax,C,cax)
            | ! [I1: $i] : ~ model(I1,Ax) ) ),
    inference(modus_ponens,[status(thm)],[15,2]) ).

tff(17,plain,
    ( ~ ! [Ax: $i,C: $i] :
          ~ ( ~ ( model(tptp_fun_I1_0(Ax),Ax)
                | status(Ax,C,cax) )
            | ~ ( ~ status(Ax,C,cax)
                | ! [I1: $i] : ~ model(I1,Ax) ) )
    | ~ ( ~ ( model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
            | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax) )
        | ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
            | ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    ~ ( ~ ( model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
          | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax) )
      | ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
          | ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ) ),
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    ( ~ ( model(tptp_fun_I1_0(tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
        | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax) )
    | ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
        | ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) )
    | ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
    | ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ),
    inference(tautology,[status(thm)],]) ).

tff(20,plain,
    ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
    | ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ),
    inference(unit_resolution,[status(thm)],[19,18]) ).

tff(21,plain,
    ^ [S1: $i,S2: $i] :
      rewrite(
        ( ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                    | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
                | isa(S1,S2) )
            | ~ ( ! [Ax: $i,C: $i] :
                    ( ~ status(Ax,C,S1)
                    | status(Ax,C,S2) )
                | ~ isa(S1,S2) ) )
      <=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                    | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
                | isa(S1,S2) )
            | ~ ( ~ isa(S1,S2)
                | ! [Ax: $i,C: $i] :
                    ( ~ status(Ax,C,S1)
                    | status(Ax,C,S2) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [S1: $i,S2: $i] :
        ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
          | ~ ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) )
  <=> ! [S1: $i,S2: $i] :
        ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
          | ~ ( ~ isa(S1,S2)
              | ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) ) ) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ^ [S1: $i,S2: $i] :
      refl(
        ( ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                    | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
                | isa(S1,S2) )
            | ~ ( ! [Ax: $i,C: $i] :
                    ( ~ status(Ax,C,S1)
                    | status(Ax,C,S2) )
                | ~ isa(S1,S2) ) )
      <=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                    | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
                | isa(S1,S2) )
            | ~ ( ! [Ax: $i,C: $i] :
                    ( ~ status(Ax,C,S1)
                    | status(Ax,C,S2) )
                | ~ isa(S1,S2) ) ) )),
    inference(bind,[status(th)],]) ).

tff(24,plain,
    ( ! [S1: $i,S2: $i] :
        ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
          | ~ ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) )
  <=> ! [S1: $i,S2: $i] :
        ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
          | ~ ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) ) ),
    inference(quant_intro,[status(thm)],[23]) ).

tff(25,plain,
    ^ [S1: $i,S2: $i] :
      rewrite(
        ( ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                    | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
                | isa(S1,S2) )
            | ~ ( ! [Ax: $i,C: $i] :
                    ( ~ status(Ax,C,S1)
                    | status(Ax,C,S2) )
                | ~ isa(S1,S2) ) )
      <=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                    | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
                | isa(S1,S2) )
            | ~ ( ! [Ax: $i,C: $i] :
                    ( ~ status(Ax,C,S1)
                    | status(Ax,C,S2) )
                | ~ isa(S1,S2) ) ) )),
    inference(bind,[status(th)],]) ).

tff(26,plain,
    ( ! [S1: $i,S2: $i] :
        ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
          | ~ ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) )
  <=> ! [S1: $i,S2: $i] :
        ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
          | ~ ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) ) ),
    inference(quant_intro,[status(thm)],[25]) ).

tff(27,plain,
    ( ! [S1: $i,S2: $i] :
        ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
          | ~ ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) )
  <=> ! [S1: $i,S2: $i] :
        ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
          | ~ ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) ) ),
    inference(transitivity,[status(thm)],[26,24]) ).

tff(28,plain,
    ^ [S1: $i,S2: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) )
          <=> ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) )),
          ( ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
            & ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) )
        <=> ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
            & ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) ) )),
        rewrite(
          ( ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
            & ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) )
        <=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                      | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
                  | isa(S1,S2) )
              | ~ ( ! [Ax: $i,C: $i] :
                      ( ~ status(Ax,C,S1)
                      | status(Ax,C,S2) )
                  | ~ isa(S1,S2) ) ) )),
        ( ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
            | isa(S1,S2) )
          & ( ! [Ax: $i,C: $i] :
                ( ~ status(Ax,C,S1)
                | status(Ax,C,S2) )
            | ~ isa(S1,S2) ) )
      <=> ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                    | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
                | isa(S1,S2) )
            | ~ ( ! [Ax: $i,C: $i] :
                    ( ~ status(Ax,C,S1)
                    | status(Ax,C,S2) )
                | ~ isa(S1,S2) ) ) )),
    inference(bind,[status(th)],]) ).

tff(29,plain,
    ( ! [S1: $i,S2: $i] :
        ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
              | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
          | isa(S1,S2) )
        & ( ! [Ax: $i,C: $i] :
              ( ~ status(Ax,C,S1)
              | status(Ax,C,S2) )
          | ~ isa(S1,S2) ) )
  <=> ! [S1: $i,S2: $i] :
        ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                  | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
              | isa(S1,S2) )
          | ~ ( ! [Ax: $i,C: $i] :
                  ( ~ status(Ax,C,S1)
                  | status(Ax,C,S2) )
              | ~ isa(S1,S2) ) ) ),
    inference(quant_intro,[status(thm)],[28]) ).

tff(30,plain,
    ( ! [S1: $i,S2: $i] :
        ( ! [Ax: $i,C: $i] :
            ( ~ status(Ax,C,S1)
            | status(Ax,C,S2) )
      <=> isa(S1,S2) )
  <=> ! [S1: $i,S2: $i] :
        ( ! [Ax: $i,C: $i] :
            ( ~ status(Ax,C,S1)
            | status(Ax,C,S2) )
      <=> isa(S1,S2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ^ [S1: $i,S2: $i] :
      rewrite(
        ( ( ! [Ax: $i,C: $i] :
              ( status(Ax,C,S1)
             => status(Ax,C,S2) )
        <=> isa(S1,S2) )
      <=> ( ! [Ax: $i,C: $i] :
              ( ~ status(Ax,C,S1)
              | status(Ax,C,S2) )
        <=> isa(S1,S2) ) )),
    inference(bind,[status(th)],]) ).

tff(32,plain,
    ( ! [S1: $i,S2: $i] :
        ( ! [Ax: $i,C: $i] :
            ( status(Ax,C,S1)
           => status(Ax,C,S2) )
      <=> isa(S1,S2) )
  <=> ! [S1: $i,S2: $i] :
        ( ! [Ax: $i,C: $i] :
            ( ~ status(Ax,C,S1)
            | status(Ax,C,S2) )
      <=> isa(S1,S2) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,axiom,
    ! [S1: $i,S2: $i] :
      ( ! [Ax: $i,C: $i] :
          ( status(Ax,C,S1)
         => status(Ax,C,S2) )
    <=> isa(S1,S2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax',isa) ).

tff(34,plain,
    ! [S1: $i,S2: $i] :
      ( ! [Ax: $i,C: $i] :
          ( ~ status(Ax,C,S1)
          | status(Ax,C,S2) )
    <=> isa(S1,S2) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    ! [S1: $i,S2: $i] :
      ( ! [Ax: $i,C: $i] :
          ( ~ status(Ax,C,S1)
          | status(Ax,C,S2) )
    <=> isa(S1,S2) ),
    inference(modus_ponens,[status(thm)],[34,30]) ).

tff(36,plain,
    ! [S1: $i,S2: $i] :
      ( ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
            | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
        | isa(S1,S2) )
      & ( ! [Ax: $i,C: $i] :
            ( ~ status(Ax,C,S1)
            | status(Ax,C,S2) )
        | ~ isa(S1,S2) ) ),
    inference(skolemize,[status(sab)],[35]) ).

tff(37,plain,
    ! [S1: $i,S2: $i] :
      ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
            | isa(S1,S2) )
        | ~ ( ! [Ax: $i,C: $i] :
                ( ~ status(Ax,C,S1)
                | status(Ax,C,S2) )
            | ~ isa(S1,S2) ) ),
    inference(modus_ponens,[status(thm)],[36,29]) ).

tff(38,plain,
    ! [S1: $i,S2: $i] :
      ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
            | isa(S1,S2) )
        | ~ ( ! [Ax: $i,C: $i] :
                ( ~ status(Ax,C,S1)
                | status(Ax,C,S2) )
            | ~ isa(S1,S2) ) ),
    inference(modus_ponens,[status(thm)],[37,27]) ).

tff(39,plain,
    ! [S1: $i,S2: $i] :
      ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
            | isa(S1,S2) )
        | ~ ( ~ isa(S1,S2)
            | ! [Ax: $i,C: $i] :
                ( ~ status(Ax,C,S1)
                | status(Ax,C,S2) ) ) ),
    inference(modus_ponens,[status(thm)],[38,22]) ).

tff(40,plain,
    ( ~ ! [S1: $i,S2: $i] :
          ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S1)
                    | status(tptp_fun_Ax_21(S2,S1),tptp_fun_C_20(S2,S1),S2) )
                | isa(S1,S2) )
            | ~ ( ~ isa(S1,S2)
                | ! [Ax: $i,C: $i] :
                    ( ~ status(Ax,C,S1)
                    | status(Ax,C,S2) ) ) )
    | ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
                | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
            | isa(cax,thm) )
        | ~ ( ~ isa(cax,thm)
            | ! [Ax: $i,C: $i] :
                ( ~ status(Ax,C,cax)
                | status(Ax,C,thm) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(41,plain,
    ~ ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
              | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
          | isa(cax,thm) )
      | ~ ( ~ isa(cax,thm)
          | ! [Ax: $i,C: $i] :
              ( ~ status(Ax,C,cax)
              | status(Ax,C,thm) ) ) ),
    inference(unit_resolution,[status(thm)],[40,39]) ).

tff(42,plain,
    ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
            | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
        | isa(cax,thm) )
    | ~ ( ~ isa(cax,thm)
        | ! [Ax: $i,C: $i] :
            ( ~ status(Ax,C,cax)
            | status(Ax,C,thm) ) )
    | ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
        | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
    | isa(cax,thm) ),
    inference(tautology,[status(thm)],]) ).

tff(43,plain,
    ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
        | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
    | isa(cax,thm) ),
    inference(unit_resolution,[status(thm)],[42,41]) ).

tff(44,plain,
    ( ~ isa(cax,thm)
  <=> ~ isa(cax,thm) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,axiom,
    ~ isa(cax,thm),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa_cax_thm) ).

tff(46,plain,
    ~ isa(cax,thm),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
            | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
        | isa(cax,thm) )
    | ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
        | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
    | isa(cax,thm) ),
    inference(tautology,[status(thm)],]) ).

tff(48,plain,
    ( ~ ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
            | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
        | isa(cax,thm) )
    | ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
        | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ) ),
    inference(unit_resolution,[status(thm)],[47,46]) ).

tff(49,plain,
    ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
      | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
    inference(unit_resolution,[status(thm)],[48,43]) ).

tff(50,plain,
    ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
    | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
    | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax) ),
    inference(tautology,[status(thm)],]) ).

tff(51,plain,
    status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax),
    inference(unit_resolution,[status(thm)],[50,49]) ).

tff(52,plain,
    ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
        | ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) )
    | ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
    | ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ),
    inference(tautology,[status(thm)],]) ).

tff(53,plain,
    ( ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
        | ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) )
    | ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)) ),
    inference(unit_resolution,[status(thm)],[52,51]) ).

tff(54,plain,
    ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax)),
    inference(unit_resolution,[status(thm)],[53,20]) ).

tff(55,plain,
    ^ [Ax: $i,C: $i] :
      rewrite(
        ( ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                    | model(tptp_fun_I1_3(C,Ax),C) )
                | status(Ax,C,thm) )
            | ~ ( ! [I1: $i] :
                    ( ~ model(I1,Ax)
                    | model(I1,C) )
                | ~ status(Ax,C,thm) ) )
      <=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                    | model(tptp_fun_I1_3(C,Ax),C) )
                | status(Ax,C,thm) )
            | ~ ( ~ status(Ax,C,thm)
                | ! [I1: $i] :
                    ( ~ model(I1,Ax)
                    | model(I1,C) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(56,plain,
    ( ! [Ax: $i,C: $i] :
        ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
          | ~ ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
          | ~ ( ~ status(Ax,C,thm)
              | ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) ) ) ) ),
    inference(quant_intro,[status(thm)],[55]) ).

tff(57,plain,
    ^ [Ax: $i,C: $i] :
      refl(
        ( ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                    | model(tptp_fun_I1_3(C,Ax),C) )
                | status(Ax,C,thm) )
            | ~ ( ! [I1: $i] :
                    ( ~ model(I1,Ax)
                    | model(I1,C) )
                | ~ status(Ax,C,thm) ) )
      <=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                    | model(tptp_fun_I1_3(C,Ax),C) )
                | status(Ax,C,thm) )
            | ~ ( ! [I1: $i] :
                    ( ~ model(I1,Ax)
                    | model(I1,C) )
                | ~ status(Ax,C,thm) ) ) )),
    inference(bind,[status(th)],]) ).

tff(58,plain,
    ( ! [Ax: $i,C: $i] :
        ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
          | ~ ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
          | ~ ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) ) ),
    inference(quant_intro,[status(thm)],[57]) ).

tff(59,plain,
    ^ [Ax: $i,C: $i] :
      rewrite(
        ( ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                    | model(tptp_fun_I1_3(C,Ax),C) )
                | status(Ax,C,thm) )
            | ~ ( ! [I1: $i] :
                    ( ~ model(I1,Ax)
                    | model(I1,C) )
                | ~ status(Ax,C,thm) ) )
      <=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                    | model(tptp_fun_I1_3(C,Ax),C) )
                | status(Ax,C,thm) )
            | ~ ( ! [I1: $i] :
                    ( ~ model(I1,Ax)
                    | model(I1,C) )
                | ~ status(Ax,C,thm) ) ) )),
    inference(bind,[status(th)],]) ).

tff(60,plain,
    ( ! [Ax: $i,C: $i] :
        ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
          | ~ ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
          | ~ ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) ) ),
    inference(quant_intro,[status(thm)],[59]) ).

tff(61,plain,
    ( ! [Ax: $i,C: $i] :
        ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
          | ~ ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
          | ~ ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) ) ),
    inference(transitivity,[status(thm)],[60,58]) ).

tff(62,plain,
    ^ [Ax: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) )
          <=> ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) )),
          ( ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
            & ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) )
        <=> ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
            & ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) ) )),
        rewrite(
          ( ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
            & ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) )
        <=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                      | model(tptp_fun_I1_3(C,Ax),C) )
                  | status(Ax,C,thm) )
              | ~ ( ! [I1: $i] :
                      ( ~ model(I1,Ax)
                      | model(I1,C) )
                  | ~ status(Ax,C,thm) ) ) )),
        ( ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                | model(tptp_fun_I1_3(C,Ax),C) )
            | status(Ax,C,thm) )
          & ( ! [I1: $i] :
                ( ~ model(I1,Ax)
                | model(I1,C) )
            | ~ status(Ax,C,thm) ) )
      <=> ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                    | model(tptp_fun_I1_3(C,Ax),C) )
                | status(Ax,C,thm) )
            | ~ ( ! [I1: $i] :
                    ( ~ model(I1,Ax)
                    | model(I1,C) )
                | ~ status(Ax,C,thm) ) ) )),
    inference(bind,[status(th)],]) ).

tff(63,plain,
    ( ! [Ax: $i,C: $i] :
        ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
              | model(tptp_fun_I1_3(C,Ax),C) )
          | status(Ax,C,thm) )
        & ( ! [I1: $i] :
              ( ~ model(I1,Ax)
              | model(I1,C) )
          | ~ status(Ax,C,thm) ) )
  <=> ! [Ax: $i,C: $i] :
        ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                  | model(tptp_fun_I1_3(C,Ax),C) )
              | status(Ax,C,thm) )
          | ~ ( ! [I1: $i] :
                  ( ~ model(I1,Ax)
                  | model(I1,C) )
              | ~ status(Ax,C,thm) ) ) ),
    inference(quant_intro,[status(thm)],[62]) ).

tff(64,plain,
    ( ! [Ax: $i,C: $i] :
        ( ! [I1: $i] :
            ( ~ model(I1,Ax)
            | model(I1,C) )
      <=> status(Ax,C,thm) )
  <=> ! [Ax: $i,C: $i] :
        ( ! [I1: $i] :
            ( ~ model(I1,Ax)
            | model(I1,C) )
      <=> status(Ax,C,thm) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,plain,
    ^ [Ax: $i,C: $i] :
      rewrite(
        ( ( ! [I1: $i] :
              ( model(I1,Ax)
             => model(I1,C) )
        <=> status(Ax,C,thm) )
      <=> ( ! [I1: $i] :
              ( ~ model(I1,Ax)
              | model(I1,C) )
        <=> status(Ax,C,thm) ) )),
    inference(bind,[status(th)],]) ).

tff(66,plain,
    ( ! [Ax: $i,C: $i] :
        ( ! [I1: $i] :
            ( model(I1,Ax)
           => model(I1,C) )
      <=> status(Ax,C,thm) )
  <=> ! [Ax: $i,C: $i] :
        ( ! [I1: $i] :
            ( ~ model(I1,Ax)
            | model(I1,C) )
      <=> status(Ax,C,thm) ) ),
    inference(quant_intro,[status(thm)],[65]) ).

tff(67,axiom,
    ! [Ax: $i,C: $i] :
      ( ! [I1: $i] :
          ( model(I1,Ax)
         => model(I1,C) )
    <=> status(Ax,C,thm) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',thm) ).

tff(68,plain,
    ! [Ax: $i,C: $i] :
      ( ! [I1: $i] :
          ( ~ model(I1,Ax)
          | model(I1,C) )
    <=> status(Ax,C,thm) ),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    ! [Ax: $i,C: $i] :
      ( ! [I1: $i] :
          ( ~ model(I1,Ax)
          | model(I1,C) )
    <=> status(Ax,C,thm) ),
    inference(modus_ponens,[status(thm)],[68,64]) ).

tff(70,plain,
    ! [Ax: $i,C: $i] :
      ( ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
            | model(tptp_fun_I1_3(C,Ax),C) )
        | status(Ax,C,thm) )
      & ( ! [I1: $i] :
            ( ~ model(I1,Ax)
            | model(I1,C) )
        | ~ status(Ax,C,thm) ) ),
    inference(skolemize,[status(sab)],[69]) ).

tff(71,plain,
    ! [Ax: $i,C: $i] :
      ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                | model(tptp_fun_I1_3(C,Ax),C) )
            | status(Ax,C,thm) )
        | ~ ( ! [I1: $i] :
                ( ~ model(I1,Ax)
                | model(I1,C) )
            | ~ status(Ax,C,thm) ) ),
    inference(modus_ponens,[status(thm)],[70,63]) ).

tff(72,plain,
    ! [Ax: $i,C: $i] :
      ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                | model(tptp_fun_I1_3(C,Ax),C) )
            | status(Ax,C,thm) )
        | ~ ( ! [I1: $i] :
                ( ~ model(I1,Ax)
                | model(I1,C) )
            | ~ status(Ax,C,thm) ) ),
    inference(modus_ponens,[status(thm)],[71,61]) ).

tff(73,plain,
    ! [Ax: $i,C: $i] :
      ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                | model(tptp_fun_I1_3(C,Ax),C) )
            | status(Ax,C,thm) )
        | ~ ( ~ status(Ax,C,thm)
            | ! [I1: $i] :
                ( ~ model(I1,Ax)
                | model(I1,C) ) ) ),
    inference(modus_ponens,[status(thm)],[72,56]) ).

tff(74,plain,
    ( ~ ! [Ax: $i,C: $i] :
          ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(C,Ax),Ax)
                    | model(tptp_fun_I1_3(C,Ax),C) )
                | status(Ax,C,thm) )
            | ~ ( ~ status(Ax,C,thm)
                | ! [I1: $i] :
                    ( ~ model(I1,Ax)
                    | model(I1,C) ) ) )
    | ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
                | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
            | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
        | ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
            | ! [I1: $i] :
                ( ~ model(I1,tptp_fun_Ax_21(thm,cax))
                | model(I1,tptp_fun_C_20(thm,cax)) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(75,plain,
    ~ ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
              | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
          | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
      | ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
          | ! [I1: $i] :
              ( ~ model(I1,tptp_fun_Ax_21(thm,cax))
              | model(I1,tptp_fun_C_20(thm,cax)) ) ) ),
    inference(unit_resolution,[status(thm)],[74,73]) ).

tff(76,plain,
    ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
            | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
        | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
    | ~ ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
        | ! [I1: $i] :
            ( ~ model(I1,tptp_fun_Ax_21(thm,cax))
            | model(I1,tptp_fun_C_20(thm,cax)) ) )
    | ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
        | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
    | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
    inference(tautology,[status(thm)],]) ).

tff(77,plain,
    ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
        | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
    | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
    inference(unit_resolution,[status(thm)],[76,75]) ).

tff(78,plain,
    ( ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),cax)
    | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm)
    | ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
    inference(tautology,[status(thm)],]) ).

tff(79,plain,
    ~ status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm),
    inference(unit_resolution,[status(thm)],[78,49]) ).

tff(80,plain,
    ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
            | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
        | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
    | ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
        | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
    | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) ),
    inference(tautology,[status(thm)],]) ).

tff(81,plain,
    ( ~ ( ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
            | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) )
        | status(tptp_fun_Ax_21(thm,cax),tptp_fun_C_20(thm,cax),thm) )
    | ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
        | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) ) ),
    inference(unit_resolution,[status(thm)],[80,79]) ).

tff(82,plain,
    ~ ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
      | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax)) ),
    inference(unit_resolution,[status(thm)],[81,77]) ).

tff(83,plain,
    ( ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax))
    | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_C_20(thm,cax))
    | model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax)) ),
    inference(tautology,[status(thm)],]) ).

tff(84,plain,
    model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax)),
    inference(unit_resolution,[status(thm)],[83,82]) ).

tff(85,plain,
    ( ~ ! [I1: $i] : ~ model(I1,tptp_fun_Ax_21(thm,cax))
    | ~ model(tptp_fun_I1_3(tptp_fun_C_20(thm,cax),tptp_fun_Ax_21(thm,cax)),tptp_fun_Ax_21(thm,cax)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(86,plain,
    $false,
    inference(unit_resolution,[status(thm)],[85,84,54]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KRS193+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n009.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  : 300
% 0.13/0.34  % DateTime : Thu Sep  1 09:42:20 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.13/0.42  % SZS status Theorem
% 0.13/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------