%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ALG039+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n001.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 : Wed Aug 30 16:00:34 EDT 2023

% Result   : Theorem 0.59s 1.39s
% Output   : CNFRefutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   18 (   4 unt;   7 typ;   0 def)
%            Number of atoms       :   82 (  71 equ)
%            Maximal formula atoms :   32 (   7 avg)
%            Number of connectives :   89 (  18   ~;  18   |;  52   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   2 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    e0: $i ).

tff(decl_23,type,
    op: ( $i * $i ) > $i ).

tff(decl_24,type,
    e1: $i ).

tff(decl_25,type,
    e2: $i ).

tff(decl_26,type,
    e3: $i ).

tff(decl_27,type,
    unit: $i ).

tff(decl_28,type,
    epred1_0: $o ).

fof(co1,conjecture,
    ~ ( ( ( op(e0,e0) = e0
          & op(e1,e1) = e0
          & op(e2,e2) = e0
          & op(e3,e3) = e0 )
        | ( op(e0,e0) = e1
          & op(e1,e1) = e1
          & op(e2,e2) = e1
          & op(e3,e3) = e1 )
        | ( op(e0,e0) = e2
          & op(e1,e1) = e2
          & op(e2,e2) = e2
          & op(e3,e3) = e2 )
        | ( op(e0,e0) = e3
          & op(e1,e1) = e3
          & op(e2,e2) = e3
          & op(e3,e3) = e3 ) )
      & ~ ( ( op(e0,e0) = e0
            & op(e1,e1) = e0
            & op(e2,e2) = e0
            & op(e3,e3) = e0 )
          | ( op(e0,e0) = e1
            & op(e1,e1) = e1
            & op(e2,e2) = e1
            & op(e3,e3) = e1 )
          | ( op(e0,e0) = e2
            & op(e1,e1) = e2
            & op(e2,e2) = e2
            & op(e3,e3) = e2 )
          | ( op(e0,e0) = e3
            & op(e1,e1) = e3
            & op(e2,e2) = e3
            & op(e3,e3) = e3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax6,axiom,
    ( e0 = op(e1,e1)
    & e2 = op(e3,e1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).

fof(ax5,axiom,
    ( e0 != e1
    & e0 != e2
    & e0 != e3
    & e1 != e2
    & e1 != e3
    & e2 != e3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

fof(c_0_3,plain,
    ( epred1_0
  <=> ( ( op(e0,e0) = e0
        & op(e1,e1) = e0
        & op(e2,e2) = e0
        & op(e3,e3) = e0 )
      | ( op(e0,e0) = e1
        & op(e1,e1) = e1
        & op(e2,e2) = e1
        & op(e3,e3) = e1 )
      | ( op(e0,e0) = e2
        & op(e1,e1) = e2
        & op(e2,e2) = e2
        & op(e3,e3) = e2 ) ) ),
    introduced(definition) ).

fof(c_0_4,negated_conjecture,
    ~ ~ ( ( epred1_0
          | ( op(e0,e0) = e3
            & op(e1,e1) = e3
            & op(e2,e2) = e3
            & op(e3,e3) = e3 ) )
        & ~ ( epred1_0
            | ( op(e0,e0) = e3
              & op(e1,e1) = e3
              & op(e2,e2) = e3
              & op(e3,e3) = e3 ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[co1]),c_0_3]),c_0_3]) ).

fof(c_0_5,negated_conjecture,
    ( ( op(e0,e0) = e3
      | epred1_0 )
    & ( op(e1,e1) = e3
      | epred1_0 )
    & ( op(e2,e2) = e3
      | epred1_0 )
    & ( op(e3,e3) = e3
      | epred1_0 )
    & ~ epred1_0
    & ( op(e0,e0) != e3
      | op(e1,e1) != e3
      | op(e2,e2) != e3
      | op(e3,e3) != e3 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

cnf(c_0_6,negated_conjecture,
    ( op(e1,e1) = e3
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_7,plain,
    e0 = op(e1,e1),
    inference(split_conjunct,[status(thm)],[ax6]) ).

cnf(c_0_8,plain,
    e0 != e3,
    inference(split_conjunct,[status(thm)],[ax5]) ).

cnf(c_0_9,negated_conjecture,
    ~ epred1_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.53  % Problem    : ALG039+1 : TPTP v8.1.2. Released v2.7.0.
% 0.08/0.54  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.76  % Computer : n001.cluster.edu
% 0.14/0.76  % Model    : x86_64 x86_64
% 0.14/0.76  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.76  % Memory   : 8042.1875MB
% 0.14/0.76  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.76  % CPULimit   : 300
% 0.14/0.76  % WCLimit    : 300
% 0.14/0.76  % DateTime   : Mon Aug 28 05:35:35 EDT 2023
% 0.14/0.76  % CPUTime  : 
% 0.59/1.36  start to proof: theBenchmark
% 0.59/1.39  % Version  : CSE_E---1.5
% 0.59/1.39  % Problem  : theBenchmark.p
% 0.59/1.39  % Proof found
% 0.59/1.39  % SZS status Theorem for theBenchmark.p
% 0.59/1.39  % SZS output start Proof
% See solution above
% 0.59/1.39  % Total time : 0.010000 s
% 0.59/1.39  % SZS output end Proof
% 0.59/1.39  % Total time : 0.013000 s
%------------------------------------------------------------------------------