%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUN087+2 : 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 : n020.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 12:45:59 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   46 (  10 unt;  24 typ;   0 def)
%            Number of atoms       :   57 (  19 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   57 (  22   ~;  16   |;  19   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   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    :   20 (  20 usr;   1 con; 0-2 aty)
%            Number of variables   :   34 (   6 sgn;   8   !;  11   ?;   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 ).

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

fof(axiom_5a,axiom,
    ! [X33] :
    ? [X34] :
      ( ? [X35] :
          ( r1(X35)
          & r4(X33,X35,X34) )
      & ? [X36] :
          ( r1(X36)
          & X34 = X36 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).

fof(zerotimeszeroeqzero,conjecture,
    ? [X39] :
      ( ? [X22] :
          ( r1(X22)
          & r4(X22,X22,X39) )
      & ? [X23] :
          ( r1(X23)
          & X39 = X23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerotimeszeroeqzero) ).

fof(c_0_3,plain,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    inference(fof_simplification,[status(thm)],[axiom_1]) ).

fof(c_0_4,plain,
    ! [X76] :
      ( r1(esk16_1(X76))
      & r4(X76,esk16_1(X76),esk15_1(X76))
      & r1(esk17_1(X76))
      & esk15_1(X76) = esk17_1(X76) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).

fof(c_0_5,negated_conjecture,
    ~ ? [X39] :
        ( ? [X22] :
            ( r1(X22)
            & r4(X22,X22,X39) )
        & ? [X23] :
            ( r1(X23)
            & X39 = X23 ) ),
    inference(assume_negation,[status(cth)],[zerotimeszeroeqzero]) ).

fof(c_0_6,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_3])])]) ).

cnf(c_0_7,plain,
    r1(esk17_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    esk15_1(X1) = esk17_1(X1),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_9,negated_conjecture,
    ! [X87,X88,X89] :
      ( ~ r1(X88)
      | ~ r4(X88,X88,X87)
      | ~ r1(X89)
      | X87 != X89 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_10,plain,
    ( X1 = esk1_0
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    r1(esk16_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_12,plain,
    r1(esk15_1(X1)),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    ( ~ r1(X1)
    | ~ r4(X1,X1,X2)
    | ~ r1(X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    r4(X1,esk16_1(X1),esk15_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_15,plain,
    esk16_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_16,plain,
    esk15_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_10,c_0_12]) ).

cnf(c_0_17,plain,
    ( r1(X1)
    | X1 != esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_18,negated_conjecture,
    ( ~ r4(X1,X1,X2)
    | ~ r1(X2)
    | ~ r1(X1) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    r4(X1,esk1_0,esk1_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

cnf(c_0_20,plain,
    r1(esk1_0),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUN087+2 : 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
% 0.12/0.34  % Computer : n020.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sun Aug 27 09:26:59 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.009000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.012000 s
%------------------------------------------------------------------------------