TSTP Solution File: SWV263-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV263-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n017.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 15:10:41 EDT 2022

% Result   : Unsatisfiable 0.51s 0.62s
% Output   : Proof 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   45 (  11 unt;   8 typ;   0 def)
%            Number of atoms       :  152 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  213 ( 101   ~;  96   |;   0   &)
%                                         (  16 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :  110 ( 100   !;   0   ?; 110   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_in_type,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(tc_Message_Omsg_type,type,
    tc_Message_Omsg: $i ).

tff(v_H_type,type,
    v_H: $i ).

tff(v_X_type,type,
    v_X: $i ).

tff(c_Message_Oparts_type,type,
    c_Message_Oparts: $i > $i ).

tff(v_G_type,type,
    v_G: $i ).

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

tff(tc_set_type,type,
    tc_set: $i > $i ).

tff(1,plain,
    ( ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
  <=> ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(3,plain,
    ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [V_H: $i,V_X: $i] :
      refl(
        ( ( ~ c_in(V_X,V_H,tc_Message_Omsg)
          | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
      <=> ( ~ c_in(V_X,V_H,tc_Message_Omsg)
          | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_H: $i,V_X: $i] :
        ( ~ c_in(V_X,V_H,tc_Message_Omsg)
        | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
  <=> ! [V_H: $i,V_X: $i] :
        ( ~ c_in(V_X,V_H,tc_Message_Omsg)
        | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [V_H: $i,V_X: $i] :
        ( ~ c_in(V_X,V_H,tc_Message_Omsg)
        | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
  <=> ! [V_H: $i,V_X: $i] :
        ( ~ c_in(V_X,V_H,tc_Message_Omsg)
        | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [V_H: $i,V_X: $i] :
      ( ~ c_in(V_X,V_H,tc_Message_Omsg)
      | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).

tff(8,plain,
    ! [V_H: $i,V_X: $i] :
      ( ~ c_in(V_X,V_H,tc_Message_Omsg)
      | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [V_H: $i,V_X: $i] :
      ( ~ c_in(V_X,V_H,tc_Message_Omsg)
      | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_H: $i,V_X: $i] :
      ( ~ c_in(V_X,V_H,tc_Message_Omsg)
      | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [V_H: $i,V_X: $i] :
            ( ~ c_in(V_X,V_H,tc_Message_Omsg)
            | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(v_X,v_H,tc_Message_Omsg)
      | c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) )
  <=> ( ~ ! [V_H: $i,V_X: $i] :
            ( ~ c_in(V_X,V_H,tc_Message_Omsg)
            | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(v_X,v_H,tc_Message_Omsg)
      | c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [V_H: $i,V_X: $i] :
          ( ~ c_in(V_X,V_H,tc_Message_Omsg)
          | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(v_X,v_H,tc_Message_Omsg)
    | c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [V_H: $i,V_X: $i] :
          ( ~ c_in(V_X,V_H,tc_Message_Omsg)
          | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(v_X,v_H,tc_Message_Omsg)
    | c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ~ c_in(v_X,v_H,tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,plain,
    ( c_in(v_X,v_G,tc_Message_Omsg)
  <=> c_in(v_X,v_G,tc_Message_Omsg) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    c_in(v_X,v_G,tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(17,plain,
    c_in(v_X,v_G,tc_Message_Omsg),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ( c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
  <=> c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(20,plain,
    c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
      refl(
        ( ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
          | c_in(V_c,V_B,T_a)
          | ~ c_in(V_c,V_A,T_a) )
      <=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
          | c_in(V_c,V_B,T_a)
          | ~ c_in(V_c,V_A,T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
        ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
        | c_in(V_c,V_B,T_a)
        | ~ c_in(V_c,V_A,T_a) )
  <=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
        ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
        | c_in(V_c,V_B,T_a)
        | ~ c_in(V_c,V_A,T_a) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
        ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
        | c_in(V_c,V_B,T_a)
        | ~ c_in(V_c,V_A,T_a) )
  <=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
        ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
        | c_in(V_c,V_B,T_a)
        | ~ c_in(V_c,V_A,T_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
      rewrite(
        ( ( ~ c_in(V_c,V_A,T_a)
          | ~ c_lessequals(V_A,V_B,tc_set(T_a))
          | c_in(V_c,V_B,T_a) )
      <=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
          | c_in(V_c,V_B,T_a)
          | ~ c_in(V_c,V_A,T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
        ( ~ c_in(V_c,V_A,T_a)
        | ~ c_lessequals(V_A,V_B,tc_set(T_a))
        | c_in(V_c,V_B,T_a) )
  <=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
        ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
        | c_in(V_c,V_B,T_a)
        | ~ c_in(V_c,V_A,T_a) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,axiom,
    ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
      ( ~ c_in(V_c,V_A,T_a)
      | ~ c_lessequals(V_A,V_B,tc_set(T_a))
      | c_in(V_c,V_B,T_a) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetD_0) ).

tff(27,plain,
    ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
      ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
      | c_in(V_c,V_B,T_a)
      | ~ c_in(V_c,V_A,T_a) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
      ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
      | c_in(V_c,V_B,T_a)
      | ~ c_in(V_c,V_A,T_a) ),
    inference(modus_ponens,[status(thm)],[27,23]) ).

tff(29,plain,
    ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
      ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
      | c_in(V_c,V_B,T_a)
      | ~ c_in(V_c,V_A,T_a) ),
    inference(skolemize,[status(sab)],[28]) ).

tff(30,plain,
    ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
      ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
      | c_in(V_c,V_B,T_a)
      | ~ c_in(V_c,V_A,T_a) ),
    inference(modus_ponens,[status(thm)],[29,22]) ).

tff(31,plain,
    ( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
            ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
            | c_in(V_c,V_B,T_a)
            | ~ c_in(V_c,V_A,T_a) )
      | ~ c_in(v_X,v_G,tc_Message_Omsg)
      | c_in(v_X,v_H,tc_Message_Omsg)
      | ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) )
  <=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
            ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
            | c_in(V_c,V_B,T_a)
            | ~ c_in(V_c,V_A,T_a) )
      | ~ c_in(v_X,v_G,tc_Message_Omsg)
      | c_in(v_X,v_H,tc_Message_Omsg)
      | ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ( ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
      | c_in(v_X,v_H,tc_Message_Omsg)
      | ~ c_in(v_X,v_G,tc_Message_Omsg) )
  <=> ( ~ c_in(v_X,v_G,tc_Message_Omsg)
      | c_in(v_X,v_H,tc_Message_Omsg)
      | ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
            ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
            | c_in(V_c,V_B,T_a)
            | ~ c_in(V_c,V_A,T_a) )
      | ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
      | c_in(v_X,v_H,tc_Message_Omsg)
      | ~ c_in(v_X,v_G,tc_Message_Omsg) )
  <=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
            ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
            | c_in(V_c,V_B,T_a)
            | ~ c_in(V_c,V_A,T_a) )
      | ~ c_in(v_X,v_G,tc_Message_Omsg)
      | c_in(v_X,v_H,tc_Message_Omsg)
      | ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ) ),
    inference(monotonicity,[status(thm)],[32]) ).

tff(34,plain,
    ( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
            ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
            | c_in(V_c,V_B,T_a)
            | ~ c_in(V_c,V_A,T_a) )
      | ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
      | c_in(v_X,v_H,tc_Message_Omsg)
      | ~ c_in(v_X,v_G,tc_Message_Omsg) )
  <=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
            ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
            | c_in(V_c,V_B,T_a)
            | ~ c_in(V_c,V_A,T_a) )
      | ~ c_in(v_X,v_G,tc_Message_Omsg)
      | c_in(v_X,v_H,tc_Message_Omsg)
      | ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ) ),
    inference(transitivity,[status(thm)],[33,31]) ).

tff(35,plain,
    ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
          ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
          | c_in(V_c,V_B,T_a)
          | ~ c_in(V_c,V_A,T_a) )
    | ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
    | c_in(v_X,v_H,tc_Message_Omsg)
    | ~ c_in(v_X,v_G,tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],]) ).

tff(36,plain,
    ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
          ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
          | c_in(V_c,V_B,T_a)
          | ~ c_in(V_c,V_A,T_a) )
    | ~ c_in(v_X,v_G,tc_Message_Omsg)
    | c_in(v_X,v_H,tc_Message_Omsg)
    | ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    $false,
    inference(unit_resolution,[status(thm)],[36,30,20,17,14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SWV263-1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n017.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 : Sun Sep  4 01:25:09 EDT 2022
% 0.13/0.35  % 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.
% 0.51/0.62  % SZS status Unsatisfiable
% 0.51/0.62  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------