TSTP Solution File: ANA041-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ANA041-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.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 16:23:38 EDT 2022

% Result   : Unsatisfiable 1.02s 1.04s
% Output   : Proof 1.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   26 (  11 unt;   9 typ;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   16 (   8   ~;   1   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   28 (  24   !;   0   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(t_c_type,type,
    t_c: $i ).

tff(v_h_type,type,
    v_h: ( $i * $i ) > $i ).

tff(v_xb_type,type,
    v_xb: $i ).

tff(v_xa_type,type,
    v_xa: $i ).

tff(c_Nat_Osize_type,type,
    c_Nat_Osize: ( $i * $i ) > $i ).

tff(tc_Product__Type_Ounit_type,type,
    tc_Product__Type_Ounit: $i ).

tff(c_Product__Type_OUnity_type,type,
    c_Product__Type_OUnity: $i ).

tff(c_0_type,type,
    c_0: $i ).

tff(1,plain,
    ( ~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c)
  <=> ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_xa,v_xb),t_c) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c)
  <=> ~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    ~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

tff(4,plain,
    ~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_xa,v_xb),t_c),
    inference(modus_ponens,[status(thm)],[4,1]) ).

tff(6,plain,
    ^ [V_V: $i,V_U: $i] :
      refl(
        ( c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c)
      <=> c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c) )),
    inference(bind,[status(th)],]) ).

tff(7,plain,
    ( ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c)
  <=> ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c) ),
    inference(quant_intro,[status(thm)],[6]) ).

tff(8,plain,
    ^ [V_V: $i,V_U: $i] :
      rewrite(
        ( c_lessequals(c_0,v_h(V_U,V_V),t_c)
      <=> c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c)
  <=> ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c)
  <=> ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(12,plain,
    ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c),
    inference(modus_ponens,[status(thm)],[12,9]) ).

tff(14,plain,
    ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c),
    inference(skolemize,[status(sab)],[13]) ).

tff(15,plain,
    ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c),
    inference(modus_ponens,[status(thm)],[14,7]) ).

tff(16,plain,
    ( ~ ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c)
    | c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_xa,v_xb),t_c) ),
    inference(quant_inst,[status(thm)],]) ).

tff(17,plain,
    $false,
    inference(unit_resolution,[status(thm)],[16,15,5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : ANA041-1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n007.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 : Mon Aug 29 19:30:30 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 1.02/1.04  % SZS status Unsatisfiable
% 1.02/1.04  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------