%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : CAT019-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n002.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  6 17:29:50 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   22 (   3 unt;   2 typ;   0 def)
%            Number of atoms       :   60 (  52 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   74 (  34   ~;  28   |;   0   &)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   0 usr;   2 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   13 (  13   !;   0   ?;  13   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c1_type,type,
    c1: $i ).

tff(c2_type,type,
    c2: $i ).

tff(1,plain,
    ( ( c2 != c1 )
  <=> ( c2 != c1 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    c2 != c1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c1_equals_c2) ).

tff(3,plain,
    c2 != c1,
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ( ! [Z: $i] :
        ( ( c2 = Z )
        | ( c1 != Z ) )
  <=> ! [Z: $i] :
        ( ( c2 = Z )
        | ( c1 != Z ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    ! [Z: $i] :
      ( ( c2 = Z )
      | ( c1 != Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_to_c1_and_c2_2) ).

tff(6,plain,
    ! [Z: $i] :
      ( ( c2 = Z )
      | ( c1 != Z ) ),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    ! [Z: $i] :
      ( ( c2 = Z )
      | ( c1 != Z ) ),
    inference(skolemize,[status(sab)],[6]) ).

tff(8,plain,
    ( ( ~ ! [Z: $i] :
            ( ( c2 = Z )
            | ( c1 != Z ) )
      | ( c2 = c1 ) )
  <=> ( ~ ! [Z: $i] :
            ( ( c2 = Z )
            | ( c1 != Z ) )
      | ( c2 = c1 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,plain,
    ( ( ( c2 = c1 )
      | $false )
  <=> ( c2 = c1 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(10,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(11,plain,
    ( ( c1 = c1 )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ( c1 != c1 )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[11]) ).

tff(13,plain,
    ( ( c1 != c1 )
  <=> $false ),
    inference(transitivity,[status(thm)],[12,10]) ).

tff(14,plain,
    ( ( ( c2 = c1 )
      | ( c1 != c1 ) )
  <=> ( ( c2 = c1 )
      | $false ) ),
    inference(monotonicity,[status(thm)],[13]) ).

tff(15,plain,
    ( ( ( c2 = c1 )
      | ( c1 != c1 ) )
  <=> ( c2 = c1 ) ),
    inference(transitivity,[status(thm)],[14,9]) ).

tff(16,plain,
    ( ( ~ ! [Z: $i] :
            ( ( c2 = Z )
            | ( c1 != Z ) )
      | ( c2 = c1 )
      | ( c1 != c1 ) )
  <=> ( ~ ! [Z: $i] :
            ( ( c2 = Z )
            | ( c1 != Z ) )
      | ( c2 = c1 ) ) ),
    inference(monotonicity,[status(thm)],[15]) ).

tff(17,plain,
    ( ( ~ ! [Z: $i] :
            ( ( c2 = Z )
            | ( c1 != Z ) )
      | ( c2 = c1 )
      | ( c1 != c1 ) )
  <=> ( ~ ! [Z: $i] :
            ( ( c2 = Z )
            | ( c1 != Z ) )
      | ( c2 = c1 ) ) ),
    inference(transitivity,[status(thm)],[16,8]) ).

tff(18,plain,
    ( ~ ! [Z: $i] :
          ( ( c2 = Z )
          | ( c1 != Z ) )
    | ( c2 = c1 )
    | ( c1 != c1 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [Z: $i] :
          ( ( c2 = Z )
          | ( c1 != Z ) )
    | ( c2 = c1 ) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    $false,
    inference(unit_resolution,[status(thm)],[19,7,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : CAT019-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n002.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 : Tue Aug 30 06:46:13 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35  Usage: tptp [options] [-file:]file
% 0.19/0.35    -h, -?       prints this message.
% 0.19/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.19/0.35    -m, -model   generate model.
% 0.19/0.35    -p, -proof   generate proof.
% 0.19/0.35    -c, -core    generate unsat core of named formulas.
% 0.19/0.35    -st, -statistics display statistics.
% 0.19/0.35    -t:timeout   set timeout (in second).
% 0.19/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.19/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35    -<param>:<value> configuration parameter and value.
% 0.19/0.35    -o:<output-file> file to place output in.
% 0.19/0.42  % SZS status Unsatisfiable
% 0.19/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------