TSTP Solution File: NUM410+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM410+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 : 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 10:37:14 EDT 2023

% Result   : Theorem 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   55 (   9 unt;  36 typ;   0 def)
%            Number of atoms       :   61 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   69 (  27   ~;  24   |;  10   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  20   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  15 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  16 con; 0-1 aty)
%            Number of variables   :   16 (   1 sgn;  11   !;   0   ?;   0   :)

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

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

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

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

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

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

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

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

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

tff(decl_31,type,
    relation_dom: $i > $i ).

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

tff(decl_33,type,
    relation_rng: $i > $i ).

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

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

tff(decl_36,type,
    empty_set: $i ).

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

tff(decl_38,type,
    relation_non_empty: $i > $o ).

tff(decl_39,type,
    with_non_empty_elements: $i > $o ).

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

tff(decl_41,type,
    esk1_1: $i > $i ).

tff(decl_42,type,
    esk2_1: $i > $i ).

tff(decl_43,type,
    esk3_0: $i ).

tff(decl_44,type,
    esk4_0: $i ).

tff(decl_45,type,
    esk5_0: $i ).

tff(decl_46,type,
    esk6_0: $i ).

tff(decl_47,type,
    esk7_0: $i ).

tff(decl_48,type,
    esk8_0: $i ).

tff(decl_49,type,
    esk9_0: $i ).

tff(decl_50,type,
    esk10_0: $i ).

tff(decl_51,type,
    esk11_0: $i ).

tff(decl_52,type,
    esk12_0: $i ).

tff(decl_53,type,
    esk13_0: $i ).

tff(decl_54,type,
    esk14_0: $i ).

tff(decl_55,type,
    esk15_0: $i ).

tff(decl_56,type,
    esk16_0: $i ).

tff(decl_57,type,
    esk17_0: $i ).

fof(t46_ordinal1,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( ordinal(relation_dom(X1))
       => transfinite_sequence_of(X1,relation_rng(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_ordinal1) ).

fof(d8_ordinal1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2)
        & transfinite_sequence(X2) )
     => ( transfinite_sequence_of(X2,X1)
      <=> subset(relation_rng(X2),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(d7_ordinal1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( transfinite_sequence(X1)
      <=> ordinal(relation_dom(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ( ordinal(relation_dom(X1))
         => transfinite_sequence_of(X1,relation_rng(X1)) ) ),
    inference(assume_negation,[status(cth)],[t46_ordinal1]) ).

fof(c_0_5,plain,
    ! [X13,X14] :
      ( ( ~ transfinite_sequence_of(X14,X13)
        | subset(relation_rng(X14),X13)
        | ~ relation(X14)
        | ~ function(X14)
        | ~ transfinite_sequence(X14) )
      & ( ~ subset(relation_rng(X14),X13)
        | transfinite_sequence_of(X14,X13)
        | ~ relation(X14)
        | ~ function(X14)
        | ~ transfinite_sequence(X14) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])]) ).

fof(c_0_6,plain,
    ! [X40] : subset(X40,X40),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

fof(c_0_7,plain,
    ! [X12] :
      ( ( ~ transfinite_sequence(X12)
        | ordinal(relation_dom(X12))
        | ~ relation(X12)
        | ~ function(X12) )
      & ( ~ ordinal(relation_dom(X12))
        | transfinite_sequence(X12)
        | ~ relation(X12)
        | ~ function(X12) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_ordinal1])])]) ).

fof(c_0_8,negated_conjecture,
    ( relation(esk17_0)
    & function(esk17_0)
    & ordinal(relation_dom(esk17_0))
    & ~ transfinite_sequence_of(esk17_0,relation_rng(esk17_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_9,plain,
    ( transfinite_sequence_of(X1,X2)
    | ~ subset(relation_rng(X1),X2)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ transfinite_sequence(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( transfinite_sequence(X1)
    | ~ ordinal(relation_dom(X1))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    ordinal(relation_dom(esk17_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    relation(esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    function(esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    ~ transfinite_sequence_of(esk17_0,relation_rng(esk17_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,plain,
    ( transfinite_sequence_of(X1,relation_rng(X1))
    | ~ transfinite_sequence(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_17,negated_conjecture,
    transfinite_sequence(esk17_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_13]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/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   : Fri Aug 25 09:32:23 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
% 0.19/0.59  % Total time : 0.017000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.020000 s
%------------------------------------------------------------------------------