TSTP Solution File: SEU094+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU094+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 : n022.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 16:22:24 EDT 2023

% Result   : Theorem 0.20s 0.57s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   57
% Syntax   : Number of formulae    :   86 (   8 unt;  51 typ;   0 def)
%            Number of atoms       :   92 (   0 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :   94 (  37   ~;  39   |;   9   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   29 (  26   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   19 (  18 usr;   1 prp; 0-2 aty)
%            Number of functors    :   33 (  33 usr;  25 con; 0-1 aty)
%            Number of variables   :   34 (   0 sgn;  20   !;   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,
    union: $i > $i ).

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

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

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

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

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

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

tff(decl_44,type,
    esk1_1: $i > $i ).

tff(decl_45,type,
    esk2_1: $i > $i ).

tff(decl_46,type,
    esk3_0: $i ).

tff(decl_47,type,
    esk4_0: $i ).

tff(decl_48,type,
    esk5_0: $i ).

tff(decl_49,type,
    esk6_0: $i ).

tff(decl_50,type,
    esk7_0: $i ).

tff(decl_51,type,
    esk8_0: $i ).

tff(decl_52,type,
    esk9_0: $i ).

tff(decl_53,type,
    esk10_1: $i > $i ).

tff(decl_54,type,
    esk11_0: $i ).

tff(decl_55,type,
    esk12_0: $i ).

tff(decl_56,type,
    esk13_1: $i > $i ).

tff(decl_57,type,
    esk14_0: $i ).

tff(decl_58,type,
    esk15_0: $i ).

tff(decl_59,type,
    esk16_0: $i ).

tff(decl_60,type,
    esk17_0: $i ).

tff(decl_61,type,
    esk18_1: $i > $i ).

tff(decl_62,type,
    esk19_0: $i ).

tff(decl_63,type,
    esk20_0: $i ).

tff(decl_64,type,
    esk21_1: $i > $i ).

tff(decl_65,type,
    esk22_0: $i ).

tff(decl_66,type,
    esk23_0: $i ).

tff(decl_67,type,
    esk24_0: $i ).

tff(decl_68,type,
    esk25_0: $i ).

tff(decl_69,type,
    esk26_0: $i ).

tff(decl_70,type,
    esk27_0: $i ).

tff(decl_71,type,
    esk28_0: $i ).

tff(decl_72,type,
    esk29_0: $i ).

fof(t13_finset_1,axiom,
    ! [X1,X2] :
      ( ( subset(X1,X2)
        & finite(X2) )
     => finite(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).

fof(t100_zfmisc_1,axiom,
    ! [X1] : subset(X1,powerset(union(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).

fof(t24_finset_1,axiom,
    ! [X1] :
      ( finite(X1)
    <=> finite(powerset(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).

fof(t25_finset_1,conjecture,
    ! [X1] :
      ( ( finite(X1)
        & ! [X2] :
            ( in(X2,X1)
           => finite(X2) ) )
    <=> finite(union(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).

fof(l22_finset_1,axiom,
    ! [X1] :
      ( ( finite(X1)
        & ! [X2] :
            ( in(X2,X1)
           => finite(X2) ) )
     => finite(union(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l22_finset_1) ).

fof(t92_zfmisc_1,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => subset(X1,union(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).

fof(c_0_6,plain,
    ! [X56,X57] :
      ( ~ subset(X56,X57)
      | ~ finite(X57)
      | finite(X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_finset_1])]) ).

fof(c_0_7,plain,
    ! [X55] : subset(X55,powerset(union(X55))),
    inference(variable_rename,[status(thm)],[t100_zfmisc_1]) ).

cnf(c_0_8,plain,
    ( finite(X1)
    | ~ subset(X1,X2)
    | ~ finite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    subset(X1,powerset(union(X1))),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X60] :
      ( ( ~ finite(X60)
        | finite(powerset(X60)) )
      & ( ~ finite(powerset(X60))
        | finite(X60) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t24_finset_1])]) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X1] :
        ( ( finite(X1)
          & ! [X2] :
              ( in(X2,X1)
             => finite(X2) ) )
      <=> finite(union(X1)) ),
    inference(assume_negation,[status(cth)],[t25_finset_1]) ).

cnf(c_0_12,plain,
    ( finite(X1)
    | ~ finite(powerset(union(X1))) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    ( finite(powerset(X1))
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,negated_conjecture,
    ! [X63] :
      ( ( in(esk29_0,esk28_0)
        | ~ finite(esk28_0)
        | ~ finite(union(esk28_0)) )
      & ( ~ finite(esk29_0)
        | ~ finite(esk28_0)
        | ~ finite(union(esk28_0)) )
      & ( finite(esk28_0)
        | finite(union(esk28_0)) )
      & ( ~ in(X63,esk28_0)
        | finite(X63)
        | finite(union(esk28_0)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).

fof(c_0_15,plain,
    ! [X23] :
      ( ( in(esk2_1(X23),X23)
        | ~ finite(X23)
        | finite(union(X23)) )
      & ( ~ finite(esk2_1(X23))
        | ~ finite(X23)
        | finite(union(X23)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l22_finset_1])])])]) ).

cnf(c_0_16,plain,
    ( finite(X1)
    | ~ finite(union(X1)) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    ( finite(esk28_0)
    | finite(union(esk28_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_18,plain,
    ! [X79,X80] :
      ( ~ in(X79,X80)
      | subset(X79,union(X80)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t92_zfmisc_1])]) ).

cnf(c_0_19,negated_conjecture,
    ( finite(X1)
    | finite(union(esk28_0))
    | ~ in(X1,esk28_0) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    ( in(esk2_1(X1),X1)
    | finite(union(X1))
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    finite(esk28_0),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,plain,
    ( subset(X1,union(X2))
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,plain,
    ( finite(union(X1))
    | ~ finite(esk2_1(X1))
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,negated_conjecture,
    ( finite(esk2_1(esk28_0))
    | finite(union(esk28_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_25,negated_conjecture,
    ( in(esk29_0,esk28_0)
    | ~ finite(esk28_0)
    | ~ finite(union(esk28_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ finite(esk29_0)
    | ~ finite(esk28_0)
    | ~ finite(union(esk28_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_27,plain,
    ( finite(X1)
    | ~ finite(union(X2))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_22]) ).

cnf(c_0_28,negated_conjecture,
    finite(union(esk28_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21])]) ).

cnf(c_0_29,negated_conjecture,
    ( in(esk29_0,esk28_0)
    | ~ finite(union(esk28_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_21])]) ).

cnf(c_0_30,negated_conjecture,
    ( ~ finite(union(esk28_0))
    | ~ finite(esk29_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_21])]) ).

cnf(c_0_31,negated_conjecture,
    ( finite(X1)
    | ~ in(X1,esk28_0) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    in(esk29_0,esk28_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_28])]) ).

cnf(c_0_33,negated_conjecture,
    ~ finite(esk29_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_28])]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU094+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n022.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   : Wed Aug 23 19:07:41 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.57  % Version  : CSE_E---1.5
% 0.20/0.57  % Problem  : theBenchmark.p
% 0.20/0.57  % Proof found
% 0.20/0.57  % SZS status Theorem for theBenchmark.p
% 0.20/0.57  % SZS output start Proof
% See solution above
% 0.20/0.57  % Total time : 0.016000 s
% 0.20/0.57  % SZS output end Proof
% 0.20/0.57  % Total time : 0.020000 s
%------------------------------------------------------------------------------