TSTP Solution File: SCT002-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SCT002-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n005.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 : Tue Sep 20 03:41:18 EDT 2022

% Result   : Unsatisfiable 0.44s 0.63s
% Output   : Proof 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   41 (  15 unt;   9 typ;   0 def)
%            Number of atoms       :  146 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  207 ( 102   ~;  90   |;   0   &)
%                                         (  15 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    9 (   9 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   5   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-4 aty)
%            Number of variables   :   95 (  84   !;   0   ?;  95   :)

% Comments : 
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
    hBOOL: $i > $o ).

tff(c_in_type,type,
    c_in: ( $i * $i * $i ) > $i ).

tff(tc_prod_type,type,
    tc_prod: ( $i * $i ) > $i ).

tff(tc_Arrow__Order__Mirabelle_Oalt_type,type,
    tc_Arrow__Order__Mirabelle_Oalt: $i ).

tff(v_L_type,type,
    v_L: $i ).

tff(c_Pair_type,type,
    c_Pair: ( $i * $i * $i * $i ) > $i ).

tff(v_x_type,type,
    v_x: $i ).

tff(v_y_type,type,
    v_y: $i ).

tff(c_Relation_Otrans_type,type,
    c_Relation_Otrans: ( $i * $i ) > $o ).

tff(1,plain,
    ( hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
  <=> hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

tff(3,plain,
    hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ( hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
  <=> hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

tff(6,plain,
    hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    ( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
  <=> c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,axiom,
    c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(9,plain,
    c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
    inference(modus_ponens,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
      refl(
        ( ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ c_Relation_Otrans(V_r,T_a)
          | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
      <=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ c_Relation_Otrans(V_r,T_a)
          | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ c_Relation_Otrans(V_r,T_a)
        | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
  <=> ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ c_Relation_Otrans(V_r,T_a)
        | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ c_Relation_Otrans(V_r,T_a)
        | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
  <=> ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ c_Relation_Otrans(V_r,T_a)
        | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ^ [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
              | ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
              | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
          <=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
              | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
              | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) )),
          ( ( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ c_Relation_Otrans(V_r,T_a) )
        <=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ c_Relation_Otrans(V_r,T_a) ) )),
        rewrite(
          ( ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ c_Relation_Otrans(V_r,T_a) )
        <=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ c_Relation_Otrans(V_r,T_a)
            | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) )),
        ( ( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ c_Relation_Otrans(V_r,T_a) )
      <=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ c_Relation_Otrans(V_r,T_a)
          | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ c_Relation_Otrans(V_r,T_a) )
  <=> ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
        | ~ c_Relation_Otrans(V_r,T_a)
        | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,axiom,
    ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ c_Relation_Otrans(V_r,T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).

tff(16,plain,
    ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ c_Relation_Otrans(V_r,T_a)
      | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ c_Relation_Otrans(V_r,T_a)
      | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ c_Relation_Otrans(V_r,T_a)
      | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ c_Relation_Otrans(V_r,T_a)
      | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
    inference(modus_ponens,[status(thm)],[18,11]) ).

tff(20,plain,
    ( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
            ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ c_Relation_Otrans(V_r,T_a)
            | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
      | ~ hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
      | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
  <=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
            ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
            | ~ c_Relation_Otrans(V_r,T_a)
            | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
      | ~ hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
      | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
          ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ c_Relation_Otrans(V_r,T_a)
          | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
    | ~ hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(22,plain,
    ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
          ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
          | ~ c_Relation_Otrans(V_r,T_a)
          | hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
    | ~ hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).

tff(24,plain,
    ^ [V_x: $i] :
      refl(
        ( ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      <=> ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
  <=> ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,plain,
    ( ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
  <=> ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,axiom,
    ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(28,plain,
    ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(skolemize,[status(sab)],[28]) ).

tff(30,plain,
    ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(modus_ponens,[status(thm)],[29,25]) ).

tff(31,plain,
    ( ~ ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(32,plain,
    $false,
    inference(unit_resolution,[status(thm)],[31,30,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SCT002-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n005.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 : Fri Sep  2 23:14:18 EDT 2022
% 0.13/0.34  % 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.
% 0.44/0.63  % SZS status Unsatisfiable
% 0.44/0.63  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------