%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM430+3 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Sep 18 13:09:39 EDT 2022

% Result   : Theorem 0.14s 0.40s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   18 (   1 unt;  10 typ;   0 def)
%            Number of atoms       :   32 (  11 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :   28 (   4   ~;   0   |;  23   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   11 (   0   !;  11   ?;  11   :)

% Comments : 
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(smndt0_type,type,
    smndt0: $i > $i ).

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

tff(xb_type,type,
    xb: $i ).

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

tff(xq_type,type,
    xq: $i ).

tff(aInteger0_type,type,
    aInteger0: $i > $o ).

tff(sdteqdtlpzmzozddtrp0_type,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

tff(xa_type,type,
    xa: $i ).

tff(aDivisorOf0_type,type,
    aDivisorOf0: ( $i * $i ) > $o ).

tff(1,plain,
    ( ~ ? [W0: $i] :
          ( aInteger0(W0)
          & ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) )
  <=> ~ ? [W0: $i] :
          ( aInteger0(W0)
          & ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(3,plain,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) ),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,axiom,
    ( ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) )
    & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    & sdteqdtlpzmzozddtrp0(xa,xb,xq)
    & ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) )
    & aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
    & sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__853) ).

tff(5,plain,
    ( ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) )
    & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    & sdteqdtlpzmzozddtrp0(xa,xb,xq)
    & ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) )
    & aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc))) ),
    inference(and_elim,[status(thm)],[4]) ).

tff(6,plain,
    ( ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) )
    & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    & sdteqdtlpzmzozddtrp0(xa,xb,xq)
    & ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) ) ),
    inference(and_elim,[status(thm)],[5]) ).

tff(7,plain,
    ? [W0: $i] :
      ( aInteger0(W0)
      & ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) ),
    inference(and_elim,[status(thm)],[6]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM430+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % 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 : Fri Sep  2 10:31:37 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35  Usage: tptp [options] [-file:]file
% 0.14/0.35    -h, -?       prints this message.
% 0.14/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.35    -m, -model   generate model.
% 0.14/0.35    -p, -proof   generate proof.
% 0.14/0.35    -c, -core    generate unsat core of named formulas.
% 0.14/0.35    -st, -statistics display statistics.
% 0.14/0.35    -t:timeout   set timeout (in second).
% 0.14/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35    -<param>:<value> configuration parameter and value.
% 0.14/0.35    -o:<output-file> file to place output in.
% 0.14/0.40  % SZS status Theorem
% 0.14/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------