%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ITP010+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 Aug 31 03:10:24 EDT 2023

% Result   : Theorem 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   27 (   3 unt;  22 typ;   0 def)
%            Number of atoms       :   13 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   12 (   4   ~;   0   |;   0   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  14   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   2 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-4 aty)
%            Number of variables   :    8 (   1 sgn;   8   !;   0   ?;   0   :)

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

tff(decl_23,type,
    ne: $i > $o ).

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

tff(decl_25,type,
    arr: ( $i * $i ) > $i ).

tff(decl_26,type,
    mem: ( $i * $i ) > $o ).

tff(decl_27,type,
    ap: ( $i * $i ) > $i ).

tff(decl_28,type,
    p: $i > $o ).

tff(decl_29,type,
    k: ( $i * $i ) > $i ).

tff(decl_30,type,
    i: $i > $i ).

tff(decl_31,type,
    c_2Ebool_2ET: $i ).

tff(decl_32,type,
    c_2Ecardinal_2Ecardleq: ( $i * $i ) > $i ).

tff(decl_33,type,
    c_2Ebool_2EF: $i ).

tff(decl_34,type,
    c_2Emin_2E_3D_3D_3E: $i ).

tff(decl_35,type,
    c_2Ebool_2E_5C_2F: $i ).

tff(decl_36,type,
    c_2Ebool_2E_2F_5C: $i ).

tff(decl_37,type,
    c_2Ebool_2E_7E: $i ).

tff(decl_38,type,
    c_2Emin_2E_3D: $i > $i ).

tff(decl_39,type,
    c_2Ebool_2E_21: $i > $i ).

tff(decl_40,type,
    epred1_3: ( $i * $i * $i ) > $o ).

tff(decl_41,type,
    esk1_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_43,type,
    esk3_2: ( $i * $i ) > $i ).

fof(conj_thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
    ! [X9] :
      ( ne(X9)
     => ! [X10] :
          ( ne(X10)
         => ! [X14] :
              ( mem(X14,arr(X9,bool))
             => ! [X15] :
                  ( mem(X15,arr(X10,bool))
                 => ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X9,X10),X14),X15))
                  <=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X9,X10),X14),X15)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).

fof(c_0_1,negated_conjecture,
    ~ ! [X9] :
        ( ne(X9)
       => ! [X10] :
            ( ne(X10)
           => ! [X14] :
                ( mem(X14,arr(X9,bool))
               => ! [X15] : $true ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_thm_2Ecardinal_2ECARD__NOT__LE])]) ).

fof(c_0_2,negated_conjecture,
    ~ $true,
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

cnf(c_0_3,negated_conjecture,
    $false,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[c_0_3]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ITP010+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n011.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   : Sun Aug 27 12:55:54 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.008000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.011000 s
%------------------------------------------------------------------------------