TSTP Solution File: ALG417-1 by Z3---4.8.9.0

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%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ALG417-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n015.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  6 16:10:10 EDT 2022

% Result   : Unsatisfiable 0.19s 0.46s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   25 (   7 unt;   6 typ;   0 def)
%            Number of atoms       :   49 (  25 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   58 (  29   ~;  22   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   13 (  12   !;   0   ?;  13   :)

% Comments : 
%------------------------------------------------------------------------------
tff(class_HOL_Ozero_type,type,
    class_HOL_Ozero: $i > $o ).

tff(tc_Complex_Ocomplex_type,type,
    tc_Complex_Ocomplex: $i ).

tff(c_HOL_Ozero__class_Ozero_type,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(tc_Polynomial_Opoly_type,type,
    tc_Polynomial_Opoly: $i > $i ).

tff(c_Polynomial_OpCons_type,type,
    c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).

tff(v_s_____type,type,
    v_s____: $i ).

tff(1,plain,
    ( class_HOL_Ozero(tc_Complex_Ocomplex)
  <=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    class_HOL_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).

tff(3,plain,
    class_HOL_Ozero(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ( ( v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
  <=> ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,plain,
    ( ( v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
  <=> ( v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sne_0) ).

tff(7,plain,
    v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(modus_ponens,[status(thm)],[7,4]) ).

tff(9,plain,
    ^ [T_a: $i] :
      refl(
        ( ( ~ class_HOL_Ozero(T_a)
          | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
      <=> ( ~ class_HOL_Ozero(T_a)
          | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(10,plain,
    ( ! [T_a: $i] :
        ( ~ class_HOL_Ozero(T_a)
        | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
  <=> ! [T_a: $i] :
        ( ~ class_HOL_Ozero(T_a)
        | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
    inference(quant_intro,[status(thm)],[9]) ).

tff(11,plain,
    ( ! [T_a: $i] :
        ( ~ class_HOL_Ozero(T_a)
        | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
  <=> ! [T_a: $i] :
        ( ~ class_HOL_Ozero(T_a)
        | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    ! [T_a: $i] :
      ( ~ class_HOL_Ozero(T_a)
      | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).

tff(13,plain,
    ! [T_a: $i] :
      ( ~ class_HOL_Ozero(T_a)
      | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ! [T_a: $i] :
      ( ~ class_HOL_Ozero(T_a)
      | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    inference(skolemize,[status(sab)],[13]) ).

tff(15,plain,
    ! [T_a: $i] :
      ( ~ class_HOL_Ozero(T_a)
      | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    inference(modus_ponens,[status(thm)],[14,10]) ).

tff(16,plain,
    ( ( ~ ! [T_a: $i] :
            ( ~ class_HOL_Ozero(T_a)
            | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
      | ~ class_HOL_Ozero(tc_Complex_Ocomplex)
      | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
  <=> ( ~ ! [T_a: $i] :
            ( ~ class_HOL_Ozero(T_a)
            | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
      | ~ class_HOL_Ozero(tc_Complex_Ocomplex)
      | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(17,plain,
    ( ~ ! [T_a: $i] :
          ( ~ class_HOL_Ozero(T_a)
          | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
    | ~ class_HOL_Ozero(tc_Complex_Ocomplex)
    | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    ( ~ ! [T_a: $i] :
          ( ~ class_HOL_Ozero(T_a)
          | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
    | ~ class_HOL_Ozero(tc_Complex_Ocomplex)
    | ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(modus_ponens,[status(thm)],[17,16]) ).

tff(19,plain,
    $false,
    inference(unit_resolution,[status(thm)],[18,15,8,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : ALG417-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Aug 29 17:21:05 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.46  % SZS status Unsatisfiable
% 0.19/0.46  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------