%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN105-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n028.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 23:53:46 EDT 2022

% Result   : Unsatisfiable 0.21s 0.51s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   21 (   6 unt;   4 typ;   0 def)
%            Number of atoms       :   46 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   54 (  26   ~;  22   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   26 (  24   !;   0   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
tff(k1_type,type,
    k1: $i > $o ).

tff(b_type,type,
    b: $i ).

tff(n0_type,type,
    n0: ( $i * $i ) > $o ).

tff(d_type,type,
    d: $i ).

tff(1,plain,
    ( ~ k1(b)
  <=> ~ k1(b) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ k1(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

tff(3,plain,
    ~ k1(b),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [I: $i,J: $i] :
      refl(
        ( ( k1(I)
          | ~ n0(J,I) )
      <=> ( k1(I)
          | ~ n0(J,I) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) )
  <=> ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) )
  <=> ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).

tff(8,plain,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( n0(d,b)
  <=> n0(d,b) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    n0(d,b),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_7) ).

tff(13,plain,
    n0(d,b),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ( ~ ! [I: $i,J: $i] :
            ( k1(I)
            | ~ n0(J,I) )
      | k1(b)
      | ~ n0(d,b) )
  <=> ( ~ ! [I: $i,J: $i] :
            ( k1(I)
            | ~ n0(J,I) )
      | k1(b)
      | ~ n0(d,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ~ ! [I: $i,J: $i] :
          ( k1(I)
          | ~ n0(J,I) )
    | k1(b)
    | ~ n0(d,b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(16,plain,
    ( ~ ! [I: $i,J: $i] :
          ( k1(I)
          | ~ n0(J,I) )
    | k1(b)
    | ~ n0(d,b) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    $false,
    inference(unit_resolution,[status(thm)],[16,13,10,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN105-1 : TPTP v8.1.0. Released v1.1.0.
% 0.06/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n028.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Sep  5 01:57:25 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34  Usage: tptp [options] [-file:]file
% 0.14/0.34    -h, -?       prints this message.
% 0.14/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.34    -m, -model   generate model.
% 0.14/0.34    -p, -proof   generate proof.
% 0.14/0.34    -c, -core    generate unsat core of named formulas.
% 0.14/0.34    -st, -statistics display statistics.
% 0.14/0.34    -t:timeout   set timeout (in second).
% 0.14/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34    -<param>:<value> configuration parameter and value.
% 0.14/0.34    -o:<output-file> file to place output in.
% 0.21/0.51  % SZS status Unsatisfiable
% 0.21/0.51  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------