%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUN088+3 : TPTP v8.1.2. Released v7.3.0.
% 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 12:46:00 EDT 2023

% Result   : Theorem 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   39 (   5 unt;  26 typ;   0 def)
%            Number of atoms       :   28 (   8 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   36 (  21   ~;  13   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  23   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   22 (  22 usr;   3 con; 0-2 aty)
%            Number of variables   :   18 (   2 sgn;  13   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    r1: $i > $o ).

tff(decl_23,type,
    r2: ( $i * $i ) > $o ).

tff(decl_24,type,
    r3: ( $i * $i * $i ) > $o ).

tff(decl_25,type,
    r4: ( $i * $i * $i ) > $o ).

tff(decl_26,type,
    esk1_0: $i ).

tff(decl_27,type,
    esk2_1: $i > $i ).

tff(decl_28,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_29,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_31,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_33,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk13_1: $i > $i ).

tff(decl_39,type,
    esk14_1: $i > $i ).

tff(decl_40,type,
    esk15_1: $i > $i ).

tff(decl_41,type,
    esk16_1: $i > $i ).

tff(decl_42,type,
    esk17_1: $i > $i ).

tff(decl_43,type,
    esk18_1: $i > $i ).

tff(decl_44,type,
    esk19_1: $i > $i ).

tff(decl_45,type,
    esk20_1: $i > $i ).

tff(decl_46,type,
    esk21_0: $i ).

tff(decl_47,type,
    esk22_0: $i ).

fof(axiom_7a,axiom,
    ! [X41,X42] :
      ( ! [X43] :
          ( ~ r1(X43)
          | X43 != X42 )
      | ~ r2(X41,X42) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).

fof(zerouneqone2,conjecture,
    ! [X44] :
      ( ! [X39] :
          ( X44 != X39
          | ~ r2(X44,X39) )
      | ~ r1(X44) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerouneqone2) ).

fof(c_0_2,plain,
    ! [X41,X42] :
      ( ! [X43] :
          ( ~ r1(X43)
          | X43 != X42 )
      | ~ r2(X41,X42) ),
    inference(fof_simplification,[status(thm)],[axiom_7a]) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X44] :
        ( ! [X39] :
            ( X44 != X39
            | ~ r2(X44,X39) )
        | ~ r1(X44) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[zerouneqone2])]) ).

fof(c_0_4,plain,
    ! [X85,X86,X87] :
      ( ~ r1(X87)
      | X87 != X86
      | ~ r2(X85,X86) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_2])]) ).

fof(c_0_5,negated_conjecture,
    ( esk21_0 = esk22_0
    & r2(esk21_0,esk22_0)
    & r1(esk21_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_6,plain,
    ( ~ r1(X1)
    | X1 != X2
    | ~ r2(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    r2(esk21_0,esk22_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    esk21_0 = esk22_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( ~ r2(X1,X2)
    | ~ r1(X2) ),
    inference(er,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    r2(esk21_0,esk21_0),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    r1(esk21_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUN088+3 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n011.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   : Sun Aug 27 09:50:54 EDT 2023
% 0.13/0.34  % 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 : 0.007000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.010000 s
%------------------------------------------------------------------------------