%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUN067+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n016.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 12:45:50 EDT 2023

% Result   : Theorem 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   47 (   6 unt;  25 typ;   0 def)
%            Number of atoms       :   62 (  28 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   78 (  38   ~;  25   |;  15   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   39 (  24   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   21 (  21 usr;   1 con; 0-2 aty)
%            Number of variables   :   42 (   8 sgn;  21   !;   6   ?;   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_1: $i > $i ).

fof(nonzerosexist,conjecture,
    ? [X39] :
    ! [X22] :
      ( ~ r1(X22)
      | X39 != X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerosexist) ).

fof(axiom_7a,axiom,
    ! [X41,X42] :
      ( ! [X43] :
          ( ~ r1(X43)
          | X43 != X42 )
      | ~ r2(X41,X42) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).

fof(axiom_1,axiom,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).

fof(axiom_2,axiom,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( ~ r2(X3,X5)
        & X5 != X4 )
      | ( r2(X3,X5)
        & X5 = X4 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).

fof(c_0_4,negated_conjecture,
    ~ ? [X39] :
      ! [X22] :
        ( ~ r1(X22)
        | X39 != X22 ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[nonzerosexist])]) ).

fof(c_0_5,plain,
    ! [X41,X42] :
      ( ! [X43] :
          ( ~ r1(X43)
          | X43 != X42 )
      | ~ r2(X41,X42) ),
    inference(fof_simplification,[status(thm)],[axiom_7a]) ).

fof(c_0_6,negated_conjecture,
    ! [X87] :
      ( r1(esk21_1(X87))
      & X87 = esk21_1(X87) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_7,plain,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    inference(fof_simplification,[status(thm)],[axiom_1]) ).

fof(c_0_8,plain,
    ! [X84,X85,X86] :
      ( ~ r1(X86)
      | X86 != X85
      | ~ r2(X84,X85) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).

cnf(c_0_9,negated_conjecture,
    r1(esk21_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    X1 = esk21_1(X1),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_11,plain,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( ~ r2(X3,X5)
        & X5 != X4 )
      | ( r2(X3,X5)
        & X5 = X4 ) ),
    inference(fof_simplification,[status(thm)],[axiom_2]) ).

fof(c_0_12,plain,
    ! [X45] :
      ( ( r1(X45)
        | ~ r1(X45) )
      & ( X45 = esk1_0
        | ~ r1(X45) )
      & ( r1(X45)
        | X45 != esk1_0 )
      & ( X45 = esk1_0
        | X45 != esk1_0 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).

cnf(c_0_13,plain,
    ( ~ r1(X1)
    | X1 != X2
    | ~ r2(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    r1(X1),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

fof(c_0_15,plain,
    ! [X46,X48] :
      ( ( r2(X46,X48)
        | ~ r2(X46,X48) )
      & ( X48 = esk2_1(X46)
        | ~ r2(X46,X48) )
      & ( r2(X46,X48)
        | X48 != esk2_1(X46) )
      & ( X48 = esk2_1(X46)
        | X48 != esk2_1(X46) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_11])])]) ).

cnf(c_0_16,plain,
    ( X1 = esk1_0
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    ( X1 != X2
    | ~ r2(X3,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).

cnf(c_0_18,plain,
    ( r2(X1,X2)
    | X2 != esk2_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    X1 = esk1_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14])]) ).

cnf(c_0_20,negated_conjecture,
    ~ r2(X1,X2),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]),c_0_20]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUN067+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.36  % Computer : n016.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Sun Aug 27 09:45:28 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.61  % Total time : 0.007000 s
% 0.21/0.61  % SZS output end Proof
% 0.21/0.61  % Total time : 0.010000 s
%------------------------------------------------------------------------------