TSTP Solution File: SEU096+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 16:22:25 EDT 2023

% Result   : Theorem 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   56
% Syntax   : Number of formulae    :   70 (   7 unt;  53 typ;   0 def)
%            Number of atoms       :   48 (   4 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   47 (  16   ~;  13   |;  11   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  28   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   34 (  34 usr;  25 con; 0-2 aty)
%            Number of variables   :   17 (   0 sgn;  12   !;   0   ?;   0   :)

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

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

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

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

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

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

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

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

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

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

tff(decl_32,type,
    powerset: $i > $i ).

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

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

tff(decl_35,type,
    empty_set: $i ).

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

tff(decl_37,type,
    relation_image: ( $i * $i ) > $i ).

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

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

tff(decl_40,type,
    with_non_empty_elements: $i > $o ).

tff(decl_41,type,
    function_yielding: $i > $o ).

tff(decl_42,type,
    being_limit_ordinal: $i > $o ).

tff(decl_43,type,
    transfinite_sequence: $i > $o ).

tff(decl_44,type,
    ordinal_yielding: $i > $o ).

tff(decl_45,type,
    subset: ( $i * $i ) > $o ).

tff(decl_46,type,
    relation_inverse_image: ( $i * $i ) > $i ).

tff(decl_47,type,
    esk1_1: $i > $i ).

tff(decl_48,type,
    esk2_0: $i ).

tff(decl_49,type,
    esk3_0: $i ).

tff(decl_50,type,
    esk4_0: $i ).

tff(decl_51,type,
    esk5_0: $i ).

tff(decl_52,type,
    esk6_0: $i ).

tff(decl_53,type,
    esk7_0: $i ).

tff(decl_54,type,
    esk8_0: $i ).

tff(decl_55,type,
    esk9_1: $i > $i ).

tff(decl_56,type,
    esk10_0: $i ).

tff(decl_57,type,
    esk11_0: $i ).

tff(decl_58,type,
    esk12_1: $i > $i ).

tff(decl_59,type,
    esk13_0: $i ).

tff(decl_60,type,
    esk14_0: $i ).

tff(decl_61,type,
    esk15_0: $i ).

tff(decl_62,type,
    esk16_0: $i ).

tff(decl_63,type,
    esk17_1: $i > $i ).

tff(decl_64,type,
    esk18_0: $i ).

tff(decl_65,type,
    esk19_0: $i ).

tff(decl_66,type,
    esk20_1: $i > $i ).

tff(decl_67,type,
    esk21_0: $i ).

tff(decl_68,type,
    esk22_0: $i ).

tff(decl_69,type,
    esk23_0: $i ).

tff(decl_70,type,
    esk24_0: $i ).

tff(decl_71,type,
    esk25_0: $i ).

tff(decl_72,type,
    esk26_0: $i ).

tff(decl_73,type,
    esk27_0: $i ).

tff(decl_74,type,
    esk28_0: $i ).

fof(t27_finset_1,conjecture,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( ( subset(X1,relation_rng(X2))
          & finite(relation_inverse_image(X2,X1)) )
       => finite(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finset_1) ).

fof(fc13_finset_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1)
        & finite(X2) )
     => finite(relation_image(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).

fof(t147_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( subset(X1,relation_rng(X2))
       => relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( relation(X2)
          & function(X2) )
       => ( ( subset(X1,relation_rng(X2))
            & finite(relation_inverse_image(X2,X1)) )
         => finite(X1) ) ),
    inference(assume_negation,[status(cth)],[t27_finset_1]) ).

fof(c_0_4,plain,
    ! [X21,X22] :
      ( ~ relation(X21)
      | ~ function(X21)
      | ~ finite(X22)
      | finite(relation_image(X21,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc13_finset_1])]) ).

fof(c_0_5,negated_conjecture,
    ( relation(esk28_0)
    & function(esk28_0)
    & subset(esk27_0,relation_rng(esk28_0))
    & finite(relation_inverse_image(esk28_0,esk27_0))
    & ~ finite(esk27_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_6,plain,
    ! [X57,X58] :
      ( ~ relation(X58)
      | ~ function(X58)
      | ~ subset(X57,relation_rng(X58))
      | relation_image(X58,relation_inverse_image(X58,X57)) = X57 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t147_funct_1])]) ).

cnf(c_0_7,plain,
    ( finite(relation_image(X1,X2))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ finite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    relation(esk28_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    function(esk28_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( relation_image(X1,relation_inverse_image(X1,X2)) = X2
    | ~ relation(X1)
    | ~ function(X1)
    | ~ subset(X2,relation_rng(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    subset(esk27_0,relation_rng(esk28_0)),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    ( finite(relation_image(esk28_0,X1))
    | ~ finite(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).

cnf(c_0_13,negated_conjecture,
    finite(relation_inverse_image(esk28_0,esk27_0)),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_14,negated_conjecture,
    relation_image(esk28_0,relation_inverse_image(esk28_0,esk27_0)) = esk27_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_8]),c_0_9])]) ).

cnf(c_0_15,negated_conjecture,
    ~ finite(esk27_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n004.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   : Wed Aug 23 17:59:23 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.55  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
% 0.19/0.58  % Total time : 0.015000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.018000 s
%------------------------------------------------------------------------------