TSTP Solution File: GRP003-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GRP003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n016.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 : Fri Sep 16 22:25:22 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   63 (  22 unt;   4 typ;   0 def)
%            Number of atoms       :  352 (   0 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  527 ( 252   ~; 244   |;   0   &)
%                                         (  31 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   18 (  18 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :  274 ( 248   !;   0   ?; 274   :)

% Comments : 
%------------------------------------------------------------------------------
tff(product_type,type,
    product: ( $i * $i * $i ) > $o ).

tff(a_type,type,
    a: $i ).

tff(identity_type,type,
    identity: $i ).

tff(inverse_type,type,
    inverse: $i > $i ).

tff(1,plain,
    ^ [X: $i] :
      refl(
        ( product(inverse(X),X,identity)
      <=> product(inverse(X),X,identity) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i] : product(inverse(X),X,identity)
  <=> ! [X: $i] : product(inverse(X),X,identity) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X: $i] : product(inverse(X),X,identity)
  <=> ! [X: $i] : product(inverse(X),X,identity) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X: $i] : product(inverse(X),X,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

tff(5,plain,
    ! [X: $i] : product(inverse(X),X,identity),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X: $i] : product(inverse(X),X,identity),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X: $i] : product(inverse(X),X,identity),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X: $i] : product(inverse(X),X,identity)
    | product(inverse(inverse(a)),inverse(a),identity) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    product(inverse(inverse(a)),inverse(a),identity),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ( ~ ! [X: $i] : product(inverse(X),X,identity)
    | product(inverse(a),a,identity) ),
    inference(quant_inst,[status(thm)],]) ).

tff(11,plain,
    product(inverse(a),a,identity),
    inference(unit_resolution,[status(thm)],[10,7]) ).

tff(12,plain,
    ^ [X: $i] :
      refl(
        ( product(identity,X,X)
      <=> product(identity,X,X) )),
    inference(bind,[status(th)],]) ).

tff(13,plain,
    ( ! [X: $i] : product(identity,X,X)
  <=> ! [X: $i] : product(identity,X,X) ),
    inference(quant_intro,[status(thm)],[12]) ).

tff(14,plain,
    ( ! [X: $i] : product(identity,X,X)
  <=> ! [X: $i] : product(identity,X,X) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    ! [X: $i] : product(identity,X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

tff(16,plain,
    ! [X: $i] : product(identity,X,X),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [X: $i] : product(identity,X,X),
    inference(skolemize,[status(sab)],[16]) ).

tff(18,plain,
    ! [X: $i] : product(identity,X,X),
    inference(modus_ponens,[status(thm)],[17,13]) ).

tff(19,plain,
    ( ~ ! [X: $i] : product(identity,X,X)
    | product(identity,a,a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(20,plain,
    product(identity,a,a),
    inference(unit_resolution,[status(thm)],[19,18]) ).

tff(21,plain,
    ^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      refl(
        ( ( product(X,V,W)
          | ~ product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U) )
      <=> ( product(X,V,W)
          | ~ product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(X,V,W)
        | ~ product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U) )
  <=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(X,V,W)
        | ~ product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(X,V,W)
        | ~ product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U) )
  <=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(X,V,W)
        | ~ product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ product(X,Y,U)
              | ~ product(Y,Z,V)
              | ~ product(U,Z,W) )
          <=> ( ~ product(U,Z,W)
              | ~ product(Y,Z,V)
              | ~ product(X,Y,U) ) )),
          ( ( ~ product(X,Y,U)
            | ~ product(Y,Z,V)
            | ~ product(U,Z,W)
            | product(X,V,W) )
        <=> ( ~ product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | product(X,V,W) ) )),
        rewrite(
          ( ( ~ product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | product(X,V,W) )
        <=> ( product(X,V,W)
            | ~ product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U) ) )),
        ( ( ~ product(X,Y,U)
          | ~ product(Y,Z,V)
          | ~ product(U,Z,W)
          | product(X,V,W) )
      <=> ( product(X,V,W)
          | ~ product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U) ) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( ~ product(X,Y,U)
        | ~ product(Y,Z,V)
        | ~ product(U,Z,W)
        | product(X,V,W) )
  <=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(X,V,W)
        | ~ product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,axiom,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(U,Z,W)
      | product(X,V,W) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).

tff(27,plain,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( product(X,V,W)
      | ~ product(U,Z,W)
      | ~ product(Y,Z,V)
      | ~ product(X,Y,U) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( product(X,V,W)
      | ~ product(U,Z,W)
      | ~ product(Y,Z,V)
      | ~ product(X,Y,U) ),
    inference(modus_ponens,[status(thm)],[27,23]) ).

tff(29,plain,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( product(X,V,W)
      | ~ product(U,Z,W)
      | ~ product(Y,Z,V)
      | ~ product(X,Y,U) ),
    inference(skolemize,[status(sab)],[28]) ).

tff(30,plain,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( product(X,V,W)
      | ~ product(U,Z,W)
      | ~ product(Y,Z,V)
      | ~ product(X,Y,U) ),
    inference(modus_ponens,[status(thm)],[29,22]) ).

tff(31,plain,
    ( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(X,V,W)
            | ~ product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U) )
      | ~ product(inverse(inverse(a)),inverse(a),identity)
      | ~ product(identity,a,a)
      | ~ product(inverse(a),a,identity)
      | product(inverse(inverse(a)),identity,a) )
  <=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(X,V,W)
            | ~ product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U) )
      | ~ product(inverse(inverse(a)),inverse(a),identity)
      | ~ product(identity,a,a)
      | ~ product(inverse(a),a,identity)
      | product(inverse(inverse(a)),identity,a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ( product(inverse(inverse(a)),identity,a)
      | ~ product(identity,a,a)
      | ~ product(inverse(a),a,identity)
      | ~ product(inverse(inverse(a)),inverse(a),identity) )
  <=> ( ~ product(inverse(inverse(a)),inverse(a),identity)
      | ~ product(identity,a,a)
      | ~ product(inverse(a),a,identity)
      | product(inverse(inverse(a)),identity,a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(X,V,W)
            | ~ product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U) )
      | product(inverse(inverse(a)),identity,a)
      | ~ product(identity,a,a)
      | ~ product(inverse(a),a,identity)
      | ~ product(inverse(inverse(a)),inverse(a),identity) )
  <=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(X,V,W)
            | ~ product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U) )
      | ~ product(inverse(inverse(a)),inverse(a),identity)
      | ~ product(identity,a,a)
      | ~ product(inverse(a),a,identity)
      | product(inverse(inverse(a)),identity,a) ) ),
    inference(monotonicity,[status(thm)],[32]) ).

tff(34,plain,
    ( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(X,V,W)
            | ~ product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U) )
      | product(inverse(inverse(a)),identity,a)
      | ~ product(identity,a,a)
      | ~ product(inverse(a),a,identity)
      | ~ product(inverse(inverse(a)),inverse(a),identity) )
  <=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(X,V,W)
            | ~ product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U) )
      | ~ product(inverse(inverse(a)),inverse(a),identity)
      | ~ product(identity,a,a)
      | ~ product(inverse(a),a,identity)
      | product(inverse(inverse(a)),identity,a) ) ),
    inference(transitivity,[status(thm)],[33,31]) ).

tff(35,plain,
    ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
          ( product(X,V,W)
          | ~ product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U) )
    | product(inverse(inverse(a)),identity,a)
    | ~ product(identity,a,a)
    | ~ product(inverse(a),a,identity)
    | ~ product(inverse(inverse(a)),inverse(a),identity) ),
    inference(quant_inst,[status(thm)],]) ).

tff(36,plain,
    ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
          ( product(X,V,W)
          | ~ product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U) )
    | ~ product(inverse(inverse(a)),inverse(a),identity)
    | ~ product(identity,a,a)
    | ~ product(inverse(a),a,identity)
    | product(inverse(inverse(a)),identity,a) ),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    product(inverse(inverse(a)),identity,a),
    inference(unit_resolution,[status(thm)],[36,30,20,11,9]) ).

tff(38,plain,
    ( ~ ! [X: $i] : product(identity,X,X)
    | product(identity,identity,identity) ),
    inference(quant_inst,[status(thm)],]) ).

tff(39,plain,
    product(identity,identity,identity),
    inference(unit_resolution,[status(thm)],[38,18]) ).

tff(40,plain,
    ( ~ product(a,identity,a)
  <=> ~ product(a,identity,a) ),
    inference(rewrite,[status(thm)],]) ).

tff(41,axiom,
    ~ product(a,identity,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).

tff(42,plain,
    ~ product(a,identity,a),
    inference(modus_ponens,[status(thm)],[41,40]) ).

tff(43,plain,
    ^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      refl(
        ( ( product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U)
          | ~ product(X,V,W) )
      <=> ( product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U)
          | ~ product(X,V,W) ) )),
    inference(bind,[status(th)],]) ).

tff(44,plain,
    ( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U)
        | ~ product(X,V,W) )
  <=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U)
        | ~ product(X,V,W) ) ),
    inference(quant_intro,[status(thm)],[43]) ).

tff(45,plain,
    ( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U)
        | ~ product(X,V,W) )
  <=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U)
        | ~ product(X,V,W) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,plain,
    ^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ product(X,Y,U)
              | ~ product(Y,Z,V)
              | ~ product(X,V,W) )
          <=> ( ~ product(Y,Z,V)
              | ~ product(X,Y,U)
              | ~ product(X,V,W) ) )),
          ( ( ~ product(X,Y,U)
            | ~ product(Y,Z,V)
            | ~ product(X,V,W)
            | product(U,Z,W) )
        <=> ( ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | ~ product(X,V,W)
            | product(U,Z,W) ) )),
        rewrite(
          ( ( ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | ~ product(X,V,W)
            | product(U,Z,W) )
        <=> ( product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | ~ product(X,V,W) ) )),
        ( ( ~ product(X,Y,U)
          | ~ product(Y,Z,V)
          | ~ product(X,V,W)
          | product(U,Z,W) )
      <=> ( product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U)
          | ~ product(X,V,W) ) )),
    inference(bind,[status(th)],]) ).

tff(47,plain,
    ( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( ~ product(X,Y,U)
        | ~ product(Y,Z,V)
        | ~ product(X,V,W)
        | product(U,Z,W) )
  <=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
        ( product(U,Z,W)
        | ~ product(Y,Z,V)
        | ~ product(X,Y,U)
        | ~ product(X,V,W) ) ),
    inference(quant_intro,[status(thm)],[46]) ).

tff(48,axiom,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(X,V,W)
      | product(U,Z,W) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).

tff(49,plain,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( product(U,Z,W)
      | ~ product(Y,Z,V)
      | ~ product(X,Y,U)
      | ~ product(X,V,W) ),
    inference(modus_ponens,[status(thm)],[48,47]) ).

tff(50,plain,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( product(U,Z,W)
      | ~ product(Y,Z,V)
      | ~ product(X,Y,U)
      | ~ product(X,V,W) ),
    inference(modus_ponens,[status(thm)],[49,45]) ).

tff(51,plain,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( product(U,Z,W)
      | ~ product(Y,Z,V)
      | ~ product(X,Y,U)
      | ~ product(X,V,W) ),
    inference(skolemize,[status(sab)],[50]) ).

tff(52,plain,
    ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
      ( product(U,Z,W)
      | ~ product(Y,Z,V)
      | ~ product(X,Y,U)
      | ~ product(X,V,W) ),
    inference(modus_ponens,[status(thm)],[51,44]) ).

tff(53,plain,
    ( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | ~ product(X,V,W) )
      | product(a,identity,a)
      | ~ product(identity,identity,identity)
      | ~ product(inverse(inverse(a)),identity,a) )
  <=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | ~ product(X,V,W) )
      | product(a,identity,a)
      | ~ product(identity,identity,identity)
      | ~ product(inverse(inverse(a)),identity,a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ( ( product(a,identity,a)
      | ~ product(identity,identity,identity)
      | ~ product(inverse(inverse(a)),identity,a)
      | ~ product(inverse(inverse(a)),identity,a) )
  <=> ( product(a,identity,a)
      | ~ product(identity,identity,identity)
      | ~ product(inverse(inverse(a)),identity,a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | ~ product(X,V,W) )
      | product(a,identity,a)
      | ~ product(identity,identity,identity)
      | ~ product(inverse(inverse(a)),identity,a)
      | ~ product(inverse(inverse(a)),identity,a) )
  <=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | ~ product(X,V,W) )
      | product(a,identity,a)
      | ~ product(identity,identity,identity)
      | ~ product(inverse(inverse(a)),identity,a) ) ),
    inference(monotonicity,[status(thm)],[54]) ).

tff(56,plain,
    ( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | ~ product(X,V,W) )
      | product(a,identity,a)
      | ~ product(identity,identity,identity)
      | ~ product(inverse(inverse(a)),identity,a)
      | ~ product(inverse(inverse(a)),identity,a) )
  <=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
            ( product(U,Z,W)
            | ~ product(Y,Z,V)
            | ~ product(X,Y,U)
            | ~ product(X,V,W) )
      | product(a,identity,a)
      | ~ product(identity,identity,identity)
      | ~ product(inverse(inverse(a)),identity,a) ) ),
    inference(transitivity,[status(thm)],[55,53]) ).

tff(57,plain,
    ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
          ( product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U)
          | ~ product(X,V,W) )
    | product(a,identity,a)
    | ~ product(identity,identity,identity)
    | ~ product(inverse(inverse(a)),identity,a)
    | ~ product(inverse(inverse(a)),identity,a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(58,plain,
    ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
          ( product(U,Z,W)
          | ~ product(Y,Z,V)
          | ~ product(X,Y,U)
          | ~ product(X,V,W) )
    | product(a,identity,a)
    | ~ product(identity,identity,identity)
    | ~ product(inverse(inverse(a)),identity,a) ),
    inference(modus_ponens,[status(thm)],[57,56]) ).

tff(59,plain,
    $false,
    inference(unit_resolution,[status(thm)],[58,52,42,39,37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n016.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Aug 31 14:25:02 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33  Usage: tptp [options] [-file:]file
% 0.13/0.33    -h, -?       prints this message.
% 0.13/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.33    -m, -model   generate model.
% 0.13/0.33    -p, -proof   generate proof.
% 0.13/0.33    -c, -core    generate unsat core of named formulas.
% 0.13/0.33    -st, -statistics display statistics.
% 0.13/0.33    -t:timeout   set timeout (in second).
% 0.13/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33    -<param>:<value> configuration parameter and value.
% 0.13/0.33    -o:<output-file> file to place output in.
% 0.19/0.48  % SZS status Unsatisfiable
% 0.19/0.48  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------