%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : RNG102+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.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 : Tue Sep 20 03:18:25 EDT 2022

% Result   : Theorem 0.13s 0.39s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   16 (   1 unt;   8 typ;   0 def)
%            Number of atoms       :   29 (  11 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   25 (   4   ~;   0   |;  20   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   11 (   0   !;  11   ?;  11   :)

% Comments : 
%------------------------------------------------------------------------------
tff(xy_type,type,
    xy: $i ).

tff(sdtasdt0_type,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(xc_type,type,
    xc: $i ).

tff(aElement0_type,type,
    aElement0: $i > $o ).

tff(aElementOf0_type,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(slsdtgt0_type,type,
    slsdtgt0: $i > $i ).

tff(xx_type,type,
    xx: $i ).

tff(xz_type,type,
    xz: $i ).

tff(1,plain,
    ( ~ ? [W0: $i] :
          ( aElement0(W0)
          & ( sdtasdt0(xc,W0) = xy ) )
  <=> ~ ? [W0: $i] :
          ( aElement0(W0)
          & ( sdtasdt0(xc,W0) = xy ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xc,W0) = xy ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(3,plain,
    ~ ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xc,W0) = xy ) ),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,axiom,
    ( ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xc,W0) = xx ) )
    & aElementOf0(xx,slsdtgt0(xc))
    & ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xc,W0) = xy ) )
    & aElementOf0(xy,slsdtgt0(xc))
    & aElement0(xz) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).

tff(5,plain,
    ( ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xc,W0) = xx ) )
    & aElementOf0(xx,slsdtgt0(xc))
    & ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xc,W0) = xy ) )
    & aElementOf0(xy,slsdtgt0(xc)) ),
    inference(and_elim,[status(thm)],[4]) ).

tff(6,plain,
    ( ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xc,W0) = xx ) )
    & aElementOf0(xx,slsdtgt0(xc))
    & ? [W0: $i] :
        ( aElement0(W0)
        & ( sdtasdt0(xc,W0) = xy ) ) ),
    inference(and_elim,[status(thm)],[5]) ).

tff(7,plain,
    ? [W0: $i] :
      ( aElement0(W0)
      & ( sdtasdt0(xc,W0) = xy ) ),
    inference(and_elim,[status(thm)],[6]) ).

tff(8,plain,
    $false,
    inference(unit_resolution,[status(thm)],[7,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : RNG102+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n003.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 : Fri Sep  2 22:32:55 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.
% 0.13/0.39  % SZS status Theorem
% 0.13/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------