TSTP Solution File: NUM390+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM390+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 : n007.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 10:37:10 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   65 (  10 unt;  31 typ;   0 def)
%            Number of atoms       :  100 (   6 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  105 (  39   ~;  34   |;  16   &)
%                                         (   2 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  16   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  15 con; 0-1 aty)
%            Number of variables   :   48 (   0 sgn;  31   !;   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,
    subset: ( $i * $i ) > $o ).

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

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

tff(decl_34,type,
    relation_empty_yielding: $i > $o ).

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

tff(decl_36,type,
    powerset: $i > $i ).

tff(decl_37,type,
    esk1_1: $i > $i ).

tff(decl_38,type,
    esk2_1: $i > $i ).

tff(decl_39,type,
    esk3_0: $i ).

tff(decl_40,type,
    esk4_0: $i ).

tff(decl_41,type,
    esk5_0: $i ).

tff(decl_42,type,
    esk6_0: $i ).

tff(decl_43,type,
    esk7_0: $i ).

tff(decl_44,type,
    esk8_0: $i ).

tff(decl_45,type,
    esk9_0: $i ).

tff(decl_46,type,
    esk10_0: $i ).

tff(decl_47,type,
    esk11_0: $i ).

tff(decl_48,type,
    esk12_0: $i ).

tff(decl_49,type,
    esk13_0: $i ).

tff(decl_50,type,
    esk14_0: $i ).

tff(decl_51,type,
    esk15_0: $i ).

tff(decl_52,type,
    esk16_0: $i ).

fof(t22_ordinal1,conjecture,
    ! [X1] :
      ( epsilon_transitive(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ! [X3] :
              ( ordinal(X3)
             => ( ( subset(X1,X2)
                  & in(X2,X3) )
               => in(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_ordinal1) ).

fof(cc1_ordinal1,axiom,
    ! [X1] :
      ( ordinal(X1)
     => ( epsilon_transitive(X1)
        & epsilon_connected(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).

fof(d2_ordinal1,axiom,
    ! [X1] :
      ( epsilon_transitive(X1)
    <=> ! [X2] :
          ( in(X2,X1)
         => subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).

fof(t1_xboole_1,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(t21_ordinal1,axiom,
    ! [X1] :
      ( epsilon_transitive(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ( proper_subset(X1,X2)
           => in(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_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(t7_ordinal1,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & subset(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( epsilon_transitive(X1)
       => ! [X2] :
            ( ordinal(X2)
           => ! [X3] :
                ( ordinal(X3)
               => ( ( subset(X1,X2)
                    & in(X2,X3) )
                 => in(X1,X3) ) ) ) ),
    inference(assume_negation,[status(cth)],[t22_ordinal1]) ).

fof(c_0_8,plain,
    ! [X9] :
      ( ( epsilon_transitive(X9)
        | ~ ordinal(X9) )
      & ( epsilon_connected(X9)
        | ~ ordinal(X9) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).

fof(c_0_9,negated_conjecture,
    ( epsilon_transitive(esk14_0)
    & ordinal(esk15_0)
    & ordinal(esk16_0)
    & subset(esk14_0,esk15_0)
    & in(esk15_0,esk16_0)
    & ~ in(esk14_0,esk16_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_10,plain,
    ! [X13,X14,X15] :
      ( ( ~ epsilon_transitive(X13)
        | ~ in(X14,X13)
        | subset(X14,X13) )
      & ( in(esk1_1(X15),X15)
        | epsilon_transitive(X15) )
      & ( ~ subset(esk1_1(X15),X15)
        | epsilon_transitive(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_ordinal1])])])])])]) ).

cnf(c_0_11,plain,
    ( epsilon_transitive(X1)
    | ~ ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ordinal(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_13,plain,
    ! [X36,X37,X38] :
      ( ~ subset(X36,X37)
      | ~ subset(X37,X38)
      | subset(X36,X38) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).

cnf(c_0_14,plain,
    ( subset(X2,X1)
    | ~ epsilon_transitive(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    epsilon_transitive(esk16_0),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

fof(c_0_16,plain,
    ! [X39,X40] :
      ( ~ epsilon_transitive(X39)
      | ~ ordinal(X40)
      | ~ proper_subset(X39,X40)
      | in(X39,X40) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_ordinal1])])]) ).

fof(c_0_17,plain,
    ! [X17,X18] :
      ( ( subset(X17,X18)
        | ~ proper_subset(X17,X18) )
      & ( X17 != X18
        | ~ proper_subset(X17,X18) )
      & ( ~ subset(X17,X18)
        | X17 = X18
        | proper_subset(X17,X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).

cnf(c_0_18,plain,
    ( subset(X1,X3)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ( subset(X1,esk16_0)
    | ~ in(X1,esk16_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

fof(c_0_20,plain,
    ! [X57,X58] :
      ( ~ in(X57,X58)
      | ~ subset(X58,X57) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_ordinal1])]) ).

cnf(c_0_21,plain,
    ( in(X1,X2)
    | ~ epsilon_transitive(X1)
    | ~ ordinal(X2)
    | ~ proper_subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    ( X1 = X2
    | proper_subset(X1,X2)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    ( subset(X1,esk16_0)
    | ~ subset(X1,X2)
    | ~ in(X2,esk16_0) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    subset(esk14_0,esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_25,negated_conjecture,
    in(esk15_0,esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_26,plain,
    ( ~ in(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,plain,
    ( X1 = X2
    | in(X1,X2)
    | ~ subset(X1,X2)
    | ~ epsilon_transitive(X1)
    | ~ ordinal(X2) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,negated_conjecture,
    subset(esk14_0,esk16_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_29,negated_conjecture,
    epsilon_transitive(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_30,negated_conjecture,
    ~ in(esk14_0,esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_31,negated_conjecture,
    ~ in(esk15_0,esk14_0),
    inference(spm,[status(thm)],[c_0_26,c_0_24]) ).

cnf(c_0_32,negated_conjecture,
    esk14_0 = esk16_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_12])]),c_0_30]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : NUM390+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n007.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Aug 25 11:38:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  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
% 0.19/0.59  % Total time : 0.019000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.021000 s
%------------------------------------------------------------------------------