%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN131-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n026.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 23:53:52 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   15 (   8 unt;   3 typ;   0 def)
%            Number of atoms       :   18 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   18 (  13   ~;   1   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 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 (   1   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   20 (  18   !;   0   ?;  20   :)

% Comments : 
%------------------------------------------------------------------------------
tff(m0_type,type,
    m0: ( $i * $i * $i ) > $o ).

tff(e_type,type,
    e: $i ).

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

tff(1,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ~ m0(X,Y,e)
      <=> ~ m0(X,Y,e) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [Y: $i,X: $i] : ~ m0(X,Y,e)
  <=> ! [Y: $i,X: $i] : ~ m0(X,Y,e) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [Y: $i,X: $i] : ~ m0(X,Y,e)
  <=> ! [Y: $i,X: $i] : ~ m0(X,Y,e) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [Y: $i,X: $i] : ~ m0(X,Y,e),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

tff(5,plain,
    ! [Y: $i,X: $i] : ~ m0(X,Y,e),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [Y: $i,X: $i] : ~ m0(X,Y,e),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [Y: $i,X: $i] : ~ m0(X,Y,e),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( m0(e,d,e)
  <=> m0(e,d,e) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,axiom,
    m0(e,d,e),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_8) ).

tff(10,plain,
    m0(e,d,e),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ( ~ ! [Y: $i,X: $i] : ~ m0(X,Y,e)
    | ~ m0(e,d,e) ),
    inference(quant_inst,[status(thm)],]) ).

tff(12,plain,
    $false,
    inference(unit_resolution,[status(thm)],[11,10,7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYN131-1 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Sep  5 02:07:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.48  % SZS status Unsatisfiable
% 0.19/0.48  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------