TSTP Solution File: NUM414+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 10:37:14 EDT 2023

% Result   : Theorem 0.17s 0.57s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   57 (   7 unt;  34 typ;   0 def)
%            Number of atoms       :   72 (   8 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   84 (  35   ~;  27   |;  14   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  17   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  17 con; 0-1 aty)
%            Number of variables   :   23 (   0 sgn;  16   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    epsilon_transitive: $i > $o ).

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

tff(decl_29,type,
    relation: $i > $o ).

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

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

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

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

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

tff(decl_35,type,
    relation_empty_yielding: $i > $o ).

tff(decl_36,type,
    transfinite_sequence: $i > $o ).

tff(decl_37,type,
    relation_non_empty: $i > $o ).

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

tff(decl_39,type,
    esk1_1: $i > $i ).

tff(decl_40,type,
    esk2_0: $i ).

tff(decl_41,type,
    esk3_0: $i ).

tff(decl_42,type,
    esk4_0: $i ).

tff(decl_43,type,
    esk5_0: $i ).

tff(decl_44,type,
    esk6_0: $i ).

tff(decl_45,type,
    esk7_0: $i ).

tff(decl_46,type,
    esk8_0: $i ).

tff(decl_47,type,
    esk9_0: $i ).

tff(decl_48,type,
    esk10_0: $i ).

tff(decl_49,type,
    esk11_0: $i ).

tff(decl_50,type,
    esk12_0: $i ).

tff(decl_51,type,
    esk13_0: $i ).

tff(decl_52,type,
    esk14_0: $i ).

tff(decl_53,type,
    esk15_0: $i ).

tff(decl_54,type,
    esk16_0: $i ).

tff(decl_55,type,
    esk17_0: $i ).

fof(t50_ordinal1,conjecture,
    ! [X1] :
      ( ordinal(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ~ ( ~ proper_subset(X1,X2)
              & X1 != X2
              & ~ proper_subset(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_ordinal1) ).

fof(connectedness_r1_ordinal1,axiom,
    ! [X1,X2] :
      ( ( ordinal(X1)
        & ordinal(X2) )
     => ( ordinal_subset(X1,X2)
        | ordinal_subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).

fof(redefinition_r1_ordinal1,axiom,
    ! [X1,X2] :
      ( ( ordinal(X1)
        & ordinal(X2) )
     => ( ordinal_subset(X1,X2)
      <=> subset(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).

fof(d8_xboole_0,axiom,
    ! [X1,X2] :
      ( proper_subset(X1,X2)
    <=> ( subset(X1,X2)
        & X1 != X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1] :
        ( ordinal(X1)
       => ! [X2] :
            ( ordinal(X2)
           => ~ ( ~ proper_subset(X1,X2)
                & X1 != X2
                & ~ proper_subset(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t50_ordinal1])]) ).

fof(c_0_5,plain,
    ! [X14,X15] :
      ( ~ ordinal(X14)
      | ~ ordinal(X15)
      | ordinal_subset(X14,X15)
      | ordinal_subset(X15,X14) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).

fof(c_0_6,negated_conjecture,
    ( ordinal(esk16_0)
    & ordinal(esk17_0)
    & ~ proper_subset(esk16_0,esk17_0)
    & esk16_0 != esk17_0
    & ~ proper_subset(esk17_0,esk16_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_7,plain,
    ( ordinal_subset(X1,X2)
    | ordinal_subset(X2,X1)
    | ~ ordinal(X1)
    | ~ ordinal(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ordinal(esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X35,X36] :
      ( ( ~ ordinal_subset(X35,X36)
        | subset(X35,X36)
        | ~ ordinal(X35)
        | ~ ordinal(X36) )
      & ( ~ subset(X35,X36)
        | ordinal_subset(X35,X36)
        | ~ ordinal(X35)
        | ~ ordinal(X36) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).

cnf(c_0_10,negated_conjecture,
    ( ordinal_subset(X1,esk17_0)
    | ordinal_subset(esk17_0,X1)
    | ~ ordinal(X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    ordinal(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( subset(X1,X2)
    | ~ ordinal_subset(X1,X2)
    | ~ ordinal(X1)
    | ~ ordinal(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    ( ordinal_subset(esk17_0,esk16_0)
    | ordinal_subset(esk16_0,esk17_0) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

fof(c_0_14,plain,
    ! [X16,X17] :
      ( ( subset(X16,X17)
        | ~ proper_subset(X16,X17) )
      & ( X16 != X17
        | ~ proper_subset(X16,X17) )
      & ( ~ subset(X16,X17)
        | X16 = X17
        | proper_subset(X16,X17) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).

cnf(c_0_15,negated_conjecture,
    ( subset(esk17_0,esk16_0)
    | ordinal_subset(esk16_0,esk17_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11]),c_0_8])]) ).

cnf(c_0_16,plain,
    ( X1 = X2
    | proper_subset(X1,X2)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    ( subset(esk17_0,esk16_0)
    | subset(esk16_0,esk17_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_15]),c_0_8]),c_0_11])]) ).

cnf(c_0_18,negated_conjecture,
    esk16_0 != esk17_0,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_19,negated_conjecture,
    ~ proper_subset(esk17_0,esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_20,negated_conjecture,
    subset(esk16_0,esk17_0),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]) ).

cnf(c_0_21,negated_conjecture,
    ~ proper_subset(esk16_0,esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_20]),c_0_18]),c_0_21]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n017.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri Aug 25 09:33:25 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.17/0.55  start to proof: theBenchmark
% 0.17/0.57  % Version  : CSE_E---1.5
% 0.17/0.57  % Problem  : theBenchmark.p
% 0.17/0.57  % Proof found
% 0.17/0.57  % SZS status Theorem for theBenchmark.p
% 0.17/0.57  % SZS output start Proof
% See solution above
% 0.17/0.58  % Total time : 0.011000 s
% 0.17/0.58  % SZS output end Proof
% 0.17/0.58  % Total time : 0.014000 s
%------------------------------------------------------------------------------