TSTP Solution File: SWV866-1 by Z3---4.8.9.0

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%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV866-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n006.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 15:24:47 EDT 2022

% Result   : Unsatisfiable 0.20s 0.49s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   30 (  16 unt;   4 typ;   0 def)
%            Number of atoms       :   71 (  40 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   71 (  43   ~;  14   |;   0   &)
%                                         (  14 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   17 (  17 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   7 usr;   3 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   25 (  22   !;   0   ?;  25   :)

% Comments : 
%------------------------------------------------------------------------------
tff(v_sko__Hoare__Mirabelle__Xsingle__stateE__1_type,type,
    v_sko__Hoare__Mirabelle__Xsingle__stateE__1: $i > $i ).

tff(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1_type,type,
    v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1: $i ).

tff(v_s_H_type,type,
    v_s_H: $i ).

tff(c_Hoare__Mirabelle_Ostate__not__singleton_type,type,
    c_Hoare__Mirabelle_Ostate__not__singleton: $o ).

tff(1,plain,
    ( ! [V_Z_H: $i] : ( V_Z_H = v_s_H )
  <=> ! [V_Z_H: $i] : ( V_Z_H = v_s_H ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ! [V_Z_H: $i] : ( V_Z_H = v_s_H ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(3,plain,
    ! [V_Z_H: $i] : ( V_Z_H = v_s_H ),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ! [V_Z_H: $i] : ( V_Z_H = v_s_H ),
    inference(skolemize,[status(sab)],[3]) ).

tff(5,plain,
    ( ~ ! [V_Z_H: $i] : ( V_Z_H = v_s_H )
    | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) = v_s_H ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(6,plain,
    v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) = v_s_H,
    inference(unit_resolution,[status(thm)],[5,4]) ).

tff(7,plain,
    v_s_H = v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1),
    inference(symmetry,[status(thm)],[6]) ).

tff(8,plain,
    ( ~ ! [V_Z_H: $i] : ( V_Z_H = v_s_H )
    | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1)) = v_s_H ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1)) = v_s_H,
    inference(unit_resolution,[status(thm)],[8,4]) ).

tff(10,plain,
    v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1)) = v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1),
    inference(transitivity,[status(thm)],[9,7]) ).

tff(11,plain,
    ^ [V_t: $i] :
      refl(
        ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t )
      <=> ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t )
  <=> ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t )
  <=> ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ^ [V_t: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              iff_true(asserted(c_Hoare__Mirabelle_Ostate__not__singleton),
                ( c_Hoare__Mirabelle_Ostate__not__singleton
              <=> $true )),
              ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
            <=> ~ $true )),
            rewrite(
              ( ~ $true
            <=> $false )),
            ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
          <=> $false )),
          ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
            | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) )
        <=> ( $false
            | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) ) )),
        rewrite(
          ( ( $false
            | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) )
        <=> ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) )),
        ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
          | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) )
      <=> ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) )),
    inference(bind,[status(th)],]) ).

tff(15,plain,
    ( ! [V_t: $i] :
        ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
        | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) )
  <=> ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) ),
    inference(quant_intro,[status(thm)],[14]) ).

tff(16,plain,
    ^ [V_t: $i] :
      rewrite(
        ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t )
          | ~ c_Hoare__Mirabelle_Ostate__not__singleton )
      <=> ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
          | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) ) )),
    inference(bind,[status(th)],]) ).

tff(17,plain,
    ( ! [V_t: $i] :
        ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t )
        | ~ c_Hoare__Mirabelle_Ostate__not__singleton )
  <=> ! [V_t: $i] :
        ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
        | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) ) ),
    inference(quant_intro,[status(thm)],[16]) ).

tff(18,axiom,
    ! [V_t: $i] :
      ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t )
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__stateE_0) ).

tff(19,plain,
    ! [V_t: $i] :
      ( ~ c_Hoare__Mirabelle_Ostate__not__singleton
      | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ),
    inference(modus_ponens,[status(thm)],[19,15]) ).

tff(21,plain,
    ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ),
    inference(modus_ponens,[status(thm)],[20,13]) ).

tff(22,plain,
    ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ),
    inference(skolemize,[status(sab)],[21]) ).

tff(23,plain,
    ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ),
    inference(modus_ponens,[status(thm)],[22,12]) ).

tff(24,plain,
    ( ~ ! [V_t: $i] : ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t )
    | ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1)) != v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(25,plain,
    v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1)) != v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1),
    inference(unit_resolution,[status(thm)],[24,23]) ).

tff(26,plain,
    $false,
    inference(unit_resolution,[status(thm)],[25,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV866-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n006.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Sep  4 09:16:23 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.
% 0.20/0.49  % SZS status Unsatisfiable
% 0.20/0.49  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------