TSTP Solution File: SEU422+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU422+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n010.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 16:26:07 EDT 2023

% Result   : Theorem 119.09s 119.20s
% Output   : CNFRefutation 119.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   59 (  14 unt;  21 typ;   0 def)
%            Number of atoms       :  106 (   6 equ)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives :  112 (  44   ~;  40   |;  15   &)
%                                         (   5 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  15   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   6 con; 0-3 aty)
%            Number of variables   :   61 (   1 sgn;  37   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    v1_xboole_0: $i > $o ).

tff(decl_23,type,
    k1_zfmisc_1: $i > $i ).

tff(decl_24,type,
    m1_subset_1: ( $i * $i ) > $o ).

tff(decl_25,type,
    a_2_0_relset_2: ( $i * $i ) > $i ).

tff(decl_26,type,
    r2_hidden: ( $i * $i ) > $o ).

tff(decl_27,type,
    v1_relat_1: $i > $o ).

tff(decl_28,type,
    r1_tarski: ( $i * $i ) > $o ).

tff(decl_29,type,
    k1_xboole_0: $i ).

tff(decl_30,type,
    v3_relat_1: $i > $o ).

tff(decl_31,type,
    k1_tarski: $i > $i ).

tff(decl_32,type,
    esk1_0: $i ).

tff(decl_33,type,
    esk2_0: $i ).

tff(decl_34,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk4_1: $i > $i ).

tff(decl_36,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_37,type,
    esk6_0: $i ).

tff(decl_38,type,
    esk7_1: $i > $i ).

tff(decl_39,type,
    esk8_0: $i ).

tff(decl_40,type,
    esk9_1: $i > $i ).

tff(decl_41,type,
    esk10_0: $i ).

tff(decl_42,type,
    esk11_2: ( $i * $i ) > $i ).

fof(t16_relset_2,conjecture,
    ! [X1] :
      ( ~ v1_xboole_0(X1)
     => ! [X2] :
          ( m1_subset_1(X2,k1_zfmisc_1(X1))
         => m1_subset_1(a_2_0_relset_2(X1,X2),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_2) ).

fof(fc1_subset_1,axiom,
    ! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

fof(t3_subset,axiom,
    ! [X1,X2] :
      ( m1_subset_1(X1,k1_zfmisc_1(X2))
    <=> r1_tarski(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( m1_subset_1(X1,X2)
     => ( v1_xboole_0(X2)
        | r2_hidden(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(fraenkel_a_2_0_relset_2,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_subset_1(X3,k1_zfmisc_1(X2)) )
     => ( r2_hidden(X1,a_2_0_relset_2(X2,X3))
      <=> ? [X4] :
            ( m1_subset_1(X4,X2)
            & X1 = k1_tarski(X4)
            & r2_hidden(X4,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_relset_2) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( r1_tarski(X1,X2)
    <=> ! [X3] :
          ( r2_hidden(X3,X1)
         => r2_hidden(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(t37_zfmisc_1,axiom,
    ! [X1,X2] :
      ( r1_tarski(k1_tarski(X1),X2)
    <=> r2_hidden(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( ~ v1_xboole_0(X1)
       => ! [X2] :
            ( m1_subset_1(X2,k1_zfmisc_1(X1))
           => m1_subset_1(a_2_0_relset_2(X1,X2),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t16_relset_2])]) ).

fof(c_0_8,plain,
    ! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
    inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).

fof(c_0_9,negated_conjecture,
    ( ~ v1_xboole_0(esk1_0)
    & m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0))
    & ~ m1_subset_1(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_10,plain,
    ! [X42,X43] :
      ( ( ~ m1_subset_1(X42,k1_zfmisc_1(X43))
        | r1_tarski(X42,X43) )
      & ( ~ r1_tarski(X42,X43)
        | m1_subset_1(X42,k1_zfmisc_1(X43)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).

fof(c_0_11,plain,
    ! [X35,X36] :
      ( ~ m1_subset_1(X35,X36)
      | v1_xboole_0(X36)
      | r2_hidden(X35,X36) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

fof(c_0_12,plain,
    ! [X18] : ~ v1_xboole_0(k1_zfmisc_1(X18)),
    inference(variable_rename,[status(thm)],[c_0_8]) ).

fof(c_0_13,plain,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_subset_1(X3,k1_zfmisc_1(X2)) )
     => ( r2_hidden(X1,a_2_0_relset_2(X2,X3))
      <=> ? [X4] :
            ( m1_subset_1(X4,X2)
            & X1 = k1_tarski(X4)
            & r2_hidden(X4,X3) ) ) ),
    inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_relset_2]) ).

cnf(c_0_14,negated_conjecture,
    ~ m1_subset_1(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( m1_subset_1(X1,k1_zfmisc_1(X2))
    | ~ r1_tarski(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_16,plain,
    ! [X10,X11,X12,X13,X14] :
      ( ( ~ r1_tarski(X10,X11)
        | ~ r2_hidden(X12,X10)
        | r2_hidden(X12,X11) )
      & ( r2_hidden(esk3_2(X13,X14),X13)
        | r1_tarski(X13,X14) )
      & ( ~ r2_hidden(esk3_2(X13,X14),X14)
        | r1_tarski(X13,X14) ) ),
    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)],[d3_tarski])])])])])]) ).

cnf(c_0_17,plain,
    ( v1_xboole_0(X2)
    | r2_hidden(X1,X2)
    | ~ m1_subset_1(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ~ v1_xboole_0(k1_zfmisc_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_19,plain,
    ! [X40,X41] :
      ( ( ~ r1_tarski(k1_tarski(X40),X41)
        | r2_hidden(X40,X41) )
      & ( ~ r2_hidden(X40,X41)
        | r1_tarski(k1_tarski(X40),X41) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])]) ).

fof(c_0_20,plain,
    ! [X20,X21,X22,X24] :
      ( ( m1_subset_1(esk5_3(X20,X21,X22),X21)
        | ~ r2_hidden(X20,a_2_0_relset_2(X21,X22))
        | v1_xboole_0(X21)
        | ~ m1_subset_1(X22,k1_zfmisc_1(X21)) )
      & ( X20 = k1_tarski(esk5_3(X20,X21,X22))
        | ~ r2_hidden(X20,a_2_0_relset_2(X21,X22))
        | v1_xboole_0(X21)
        | ~ m1_subset_1(X22,k1_zfmisc_1(X21)) )
      & ( r2_hidden(esk5_3(X20,X21,X22),X22)
        | ~ r2_hidden(X20,a_2_0_relset_2(X21,X22))
        | v1_xboole_0(X21)
        | ~ m1_subset_1(X22,k1_zfmisc_1(X21)) )
      & ( ~ m1_subset_1(X24,X21)
        | X20 != k1_tarski(X24)
        | ~ r2_hidden(X24,X22)
        | r2_hidden(X20,a_2_0_relset_2(X21,X22))
        | v1_xboole_0(X21)
        | ~ m1_subset_1(X22,k1_zfmisc_1(X21)) ) ),
    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_13])])])])]) ).

cnf(c_0_21,negated_conjecture,
    ~ r1_tarski(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_22,plain,
    ( r2_hidden(esk3_2(X1,X2),X1)
    | r1_tarski(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ( r2_hidden(X1,k1_zfmisc_1(X2))
    | ~ r1_tarski(X1,X2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18]) ).

cnf(c_0_24,plain,
    ( r1_tarski(k1_tarski(X1),X2)
    | ~ r2_hidden(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    ( X1 = k1_tarski(esk5_3(X1,X2,X3))
    | v1_xboole_0(X2)
    | ~ r2_hidden(X1,a_2_0_relset_2(X2,X3))
    | ~ m1_subset_1(X3,k1_zfmisc_1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    r2_hidden(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),a_2_0_relset_2(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_28,negated_conjecture,
    ~ v1_xboole_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_29,plain,
    ( m1_subset_1(esk5_3(X1,X2,X3),X2)
    | v1_xboole_0(X2)
    | ~ r2_hidden(X1,a_2_0_relset_2(X2,X3))
    | ~ m1_subset_1(X3,k1_zfmisc_1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,plain,
    ( r2_hidden(k1_tarski(X1),k1_zfmisc_1(X2))
    | ~ r2_hidden(X1,X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    k1_tarski(esk5_3(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),esk1_0,esk2_0)) = esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    m1_subset_1(esk5_3(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),esk1_0,esk2_0),esk1_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_27])]),c_0_28]) ).

cnf(c_0_33,plain,
    ( r1_tarski(X1,X2)
    | ~ r2_hidden(esk3_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_34,negated_conjecture,
    ( r2_hidden(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),k1_zfmisc_1(X1))
    | ~ r2_hidden(esk5_3(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),esk1_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    r2_hidden(esk5_3(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),esk1_0,esk2_0),esk1_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_32]),c_0_28]) ).

cnf(c_0_36,negated_conjecture,
    ~ r2_hidden(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),k1_zfmisc_1(esk1_0)),
    inference(spm,[status(thm)],[c_0_21,c_0_33]) ).

cnf(c_0_37,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU422+1 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33  % Computer : n010.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Wed Aug 23 19:52:36 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.17/0.57  start to proof: theBenchmark
% 119.09/119.20  % Version  : CSE_E---1.5
% 119.09/119.20  % Problem  : theBenchmark.p
% 119.09/119.20  % Proof found
% 119.09/119.20  % SZS status Theorem for theBenchmark.p
% 119.09/119.20  % SZS output start Proof
% See solution above
% 119.18/119.21  % Total time : 118.578000 s
% 119.18/119.21  % SZS output end Proof
% 119.18/119.21  % Total time : 118.586000 s
%------------------------------------------------------------------------------