TSTP Solution File: SWV925-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV925-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 15:24:59 EDT 2022

% Result   : Unsatisfiable 0.46s 0.58s
% Output   : Proof 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   49 (  21 unt;  11 typ;   0 def)
%            Number of atoms       :   77 (  73 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   74 (  38   ~;  24   |;   0   &)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :   66 (  60   !;   0   ?;  66   :)

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

tff(tc_nat_type,type,
    tc_nat: $i ).

tff(c_Nat_Osize__class_Osize_type,type,
    c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).

tff(tc_List_Olist_type,type,
    tc_List_Olist: $i > $i ).

tff(tc_Value_Oval_type,type,
    tc_Value_Oval: $i ).

tff(c_List_Olist_OCons_type,type,
    c_List_Olist_OCons: ( $i * $i * $i ) > $i ).

tff(v_ak_type,type,
    v_ak: $i ).

tff(v_aj_type,type,
    v_aj: $i ).

tff(tc_String_Ochar_type,type,
    tc_String_Ochar: $i ).

tff(c_List_Olist_ONil_type,type,
    c_List_Olist_ONil: $i > $i ).

tff(tc_Type_Oty_type,type,
    tc_Type_Oty: $i ).

tff(1,plain,
    ^ [T_a: $i] :
      refl(
        ( ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) )
      <=> ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) )
  <=> ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) )
  <=> ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).

tff(5,plain,
    ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) )
    | ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ( ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) )
  <=> ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(12,plain,
    c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))),
    inference(symmetry,[status(thm)],[12]) ).

tff(14,plain,
    ( ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) )
  <=> ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(16,plain,
    c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(transitivity,[status(thm)],[16,13,9]) ).

tff(18,plain,
    ^ [V_a_H: $i,V_list_H: $i,T_a: $i] :
      refl(
        ( ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) )
      <=> ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) )
  <=> ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) )
  <=> ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

tff(22,plain,
    ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
    inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
    ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
    inference(modus_ponens,[status(thm)],[23,19]) ).

tff(25,plain,
    ( ~ ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) )
    | ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) != c_List_Olist_ONil(tc_Value_Oval) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(26,plain,
    c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) != c_List_Olist_ONil(tc_Value_Oval),
    inference(unit_resolution,[status(thm)],[25,24]) ).

tff(27,plain,
    ^ [V_xs: $i,T_a: $i] :
      refl(
        ( ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
          | ( V_xs = c_List_Olist_ONil(T_a) ) )
      <=> ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
          | ( V_xs = c_List_Olist_ONil(T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(28,plain,
    ( ! [V_xs: $i,T_a: $i] :
        ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
        | ( V_xs = c_List_Olist_ONil(T_a) ) )
  <=> ! [V_xs: $i,T_a: $i] :
        ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
        | ( V_xs = c_List_Olist_ONil(T_a) ) ) ),
    inference(quant_intro,[status(thm)],[27]) ).

tff(29,plain,
    ( ! [V_xs: $i,T_a: $i] :
        ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
        | ( V_xs = c_List_Olist_ONil(T_a) ) )
  <=> ! [V_xs: $i,T_a: $i] :
        ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
        | ( V_xs = c_List_Olist_ONil(T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
      | ( V_xs = c_List_Olist_ONil(T_a) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).

tff(31,plain,
    ! [V_xs: $i,T_a: $i] :
      ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
      | ( V_xs = c_List_Olist_ONil(T_a) ) ),
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    ! [V_xs: $i,T_a: $i] :
      ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
      | ( V_xs = c_List_Olist_ONil(T_a) ) ),
    inference(skolemize,[status(sab)],[31]) ).

tff(33,plain,
    ! [V_xs: $i,T_a: $i] :
      ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
      | ( V_xs = c_List_Olist_ONil(T_a) ) ),
    inference(modus_ponens,[status(thm)],[32,28]) ).

tff(34,plain,
    ( ( ~ ! [V_xs: $i,T_a: $i] :
            ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
            | ( V_xs = c_List_Olist_ONil(T_a) ) )
      | ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat) )
      | ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) = c_List_Olist_ONil(tc_Value_Oval) ) )
  <=> ( ~ ! [V_xs: $i,T_a: $i] :
            ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
            | ( V_xs = c_List_Olist_ONil(T_a) ) )
      | ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat) )
      | ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) = c_List_Olist_ONil(tc_Value_Oval) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ~ ! [V_xs: $i,T_a: $i] :
          ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
          | ( V_xs = c_List_Olist_ONil(T_a) ) )
    | ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat) )
    | ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) = c_List_Olist_ONil(tc_Value_Oval) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(36,plain,
    ( ~ ! [V_xs: $i,T_a: $i] :
          ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
          | ( V_xs = c_List_Olist_ONil(T_a) ) )
    | ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat) )
    | ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) = c_List_Olist_ONil(tc_Value_Oval) ) ),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unit_resolution,[status(thm)],[36,33,26]) ).

tff(38,plain,
    $false,
    inference(unit_resolution,[status(thm)],[37,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWV925-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35  % Computer : n008.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sun Sep  4 09:59:25 EDT 2022
% 0.15/0.35  % CPUTime  : 
% 0.15/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36  Usage: tptp [options] [-file:]file
% 0.15/0.36    -h, -?       prints this message.
% 0.15/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.15/0.36    -m, -model   generate model.
% 0.15/0.36    -p, -proof   generate proof.
% 0.15/0.36    -c, -core    generate unsat core of named formulas.
% 0.15/0.36    -st, -statistics display statistics.
% 0.15/0.36    -t:timeout   set timeout (in second).
% 0.15/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.15/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36    -<param>:<value> configuration parameter and value.
% 0.15/0.36    -o:<output-file> file to place output in.
% 0.46/0.58  % SZS status Unsatisfiable
% 0.46/0.58  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------