TSTP Solution File: SWV860-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV860-1 : 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 15:24:45 EDT 2022

% Result   : Unsatisfiable 0.20s 0.54s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   34 (  11 unt;   9 typ;   0 def)
%            Number of atoms       :   57 (  20 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   57 (  26   ~;  22   |;   0   &)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   39 (  36   !;   0   ?;  39   :)

% Comments : 
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
    hBOOL: $i > $o ).

tff(hAPP_type,type,
    hAPP: ( $i * $i ) > $i ).

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

tff(v_x_type,type,
    v_x: $i ).

tff(v_P_type,type,
    v_P: $i ).

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

tff(c_Natural_Oevaln_type,type,
    c_Natural_Oevaln: ( $i * $i * $i * $i ) > $o ).

tff(v_n_type,type,
    v_n: $i ).

tff(c_Com_Ocom_OSKIP_type,type,
    c_Com_Ocom_OSKIP: $i ).

tff(1,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb)
  <=> c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(3,plain,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [V_n: $i,V_t: $i,V_s: $i] :
      refl(
        ( ( ( V_t = V_s )
          | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
      <=> ( ( V_t = V_s )
          | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_n: $i,V_t: $i,V_s: $i] :
        ( ( V_t = V_s )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
  <=> ! [V_n: $i,V_t: $i,V_s: $i] :
        ( ( V_t = V_s )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [V_n: $i,V_t: $i,V_s: $i] :
        ( ( V_t = V_s )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
  <=> ! [V_n: $i,V_t: $i,V_s: $i] :
        ( ( V_t = V_s )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [V_n: $i,V_t: $i,V_s: $i] :
      ( ( V_t = V_s )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).

tff(8,plain,
    ! [V_n: $i,V_t: $i,V_s: $i] :
      ( ( V_t = V_s )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [V_n: $i,V_t: $i,V_s: $i] :
      ( ( V_t = V_s )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_n: $i,V_t: $i,V_s: $i] :
      ( ( V_t = V_s )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [V_n: $i,V_t: $i,V_s: $i] :
            ( ( V_t = V_s )
            | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
      | ( v_xb = v_xa )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) )
  <=> ( ~ ! [V_n: $i,V_t: $i,V_s: $i] :
            ( ( V_t = V_s )
            | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
      | ( v_xb = v_xa )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [V_n: $i,V_t: $i,V_s: $i] :
          ( ( V_t = V_s )
          | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
    | ( v_xb = v_xa )
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [V_n: $i,V_t: $i,V_s: $i] :
          ( ( V_t = V_s )
          | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) )
    | ( v_xb = v_xa )
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    v_xb = v_xa,
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,plain,
    hAPP(hAPP(v_P,v_x),v_xb) = hAPP(hAPP(v_P,v_x),v_xa),
    inference(monotonicity,[status(thm)],[14]) ).

tff(16,plain,
    ( hBOOL(hAPP(hAPP(v_P,v_x),v_xb))
  <=> hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
    inference(monotonicity,[status(thm)],[15]) ).

tff(17,plain,
    ( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
  <=> hBOOL(hAPP(hAPP(v_P,v_x),v_xb)) ),
    inference(symmetry,[status(thm)],[16]) ).

tff(18,plain,
    ( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
  <=> hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(20,plain,
    hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    hBOOL(hAPP(hAPP(v_P,v_x),v_xb)),
    inference(modus_ponens,[status(thm)],[20,17]) ).

tff(22,plain,
    ( ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb))
  <=> ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,axiom,
    ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(24,plain,
    ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    $false,
    inference(unit_resolution,[status(thm)],[24,21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV860-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n008.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Sep  4 08:54:40 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.
% 0.20/0.54  % SZS status Unsatisfiable
% 0.20/0.54  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------