TSTP Solution File: SEU430+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU430+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n002.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 16:26:35 EDT 2023

% Result   : Theorem 0.94s 1.03s
% Output   : CNFRefutation 0.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   85 (  14 unt;  23 typ;   0 def)
%            Number of atoms       :  154 (  60 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  149 (  57   ~;  66   |;  13   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  16   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   7 con; 0-3 aty)
%            Number of variables   :   76 (   5 sgn;  41   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    k1_zfmisc_1: $i > $i ).

tff(decl_23,type,
    m1_subset_1: ( $i * $i ) > $o ).

tff(decl_24,type,
    k5_setfam_1: ( $i * $i ) > $i ).

tff(decl_25,type,
    k1_xboole_0: $i ).

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

tff(decl_27,type,
    v1_xboole_0: $i > $o ).

tff(decl_28,type,
    v1_relat_1: $i > $o ).

tff(decl_29,type,
    k3_tarski: $i > $i ).

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

tff(decl_31,type,
    r1_tarski: ( $i * $i ) > $o ).

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

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

tff(decl_34,type,
    esk3_0: $i ).

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

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

tff(decl_37,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk8_1: $i > $i ).

tff(decl_40,type,
    esk9_0: $i ).

tff(decl_41,type,
    esk10_1: $i > $i ).

tff(decl_42,type,
    esk11_0: $i ).

tff(decl_43,type,
    esk12_1: $i > $i ).

tff(decl_44,type,
    esk13_0: $i ).

fof(t30_relset_2,conjecture,
    ! [X1,X2] :
      ( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
     => ( k5_setfam_1(X1,X2) = k1_xboole_0
      <=> ! [X3] :
            ( r2_hidden(X3,X2)
           => X3 = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_2) ).

fof(t6_boole,axiom,
    ! [X1] :
      ( v1_xboole_0(X1)
     => X1 = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(rc1_relat_1,axiom,
    ? [X1] :
      ( v1_xboole_0(X1)
      & v1_relat_1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

fof(d1_xboole_0,axiom,
    ! [X1] :
      ( X1 = k1_xboole_0
    <=> ! [X2] : ~ r2_hidden(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(redefinition_k5_setfam_1,axiom,
    ! [X1,X2] :
      ( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
     => k5_setfam_1(X1,X2) = k3_tarski(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).

fof(d4_tarski,axiom,
    ! [X1,X2] :
      ( X2 = k3_tarski(X1)
    <=> ! [X3] :
          ( r2_hidden(X3,X2)
        <=> ? [X4] :
              ( r2_hidden(X3,X4)
              & r2_hidden(X4,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).

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

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : m1_subset_1(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( r2_hidden(X1,X2)
        & v1_xboole_0(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X1,X2] :
        ( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
       => ( k5_setfam_1(X1,X2) = k1_xboole_0
        <=> ! [X3] :
              ( r2_hidden(X3,X2)
             => X3 = k1_xboole_0 ) ) ),
    inference(assume_negation,[status(cth)],[t30_relset_2]) ).

fof(c_0_10,plain,
    ! [X54] :
      ( ~ v1_xboole_0(X54)
      | X54 = k1_xboole_0 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_11,plain,
    ( v1_xboole_0(esk9_0)
    & v1_relat_1(esk9_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).

fof(c_0_12,plain,
    ! [X1] :
      ( X1 = k1_xboole_0
    <=> ! [X2] : ~ r2_hidden(X2,X1) ),
    inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).

fof(c_0_13,negated_conjecture,
    ! [X8] :
      ( m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
      & ( r2_hidden(esk3_0,esk2_0)
        | k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
      & ( esk3_0 != k1_xboole_0
        | k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
      & ( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
        | ~ r2_hidden(X8,esk2_0)
        | X8 = k1_xboole_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_9])])])])]) ).

cnf(c_0_14,plain,
    ( X1 = k1_xboole_0
    | ~ v1_xboole_0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    v1_xboole_0(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_16,plain,
    ! [X12,X13,X14] :
      ( ( X12 != k1_xboole_0
        | ~ r2_hidden(X13,X12) )
      & ( r2_hidden(esk4_1(X14),X14)
        | X14 = k1_xboole_0 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).

cnf(c_0_17,negated_conjecture,
    ( r2_hidden(esk3_0,esk2_0)
    | k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,plain,
    k1_xboole_0 = esk9_0,
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

fof(c_0_19,plain,
    ! [X39,X40] :
      ( ~ m1_subset_1(X40,k1_zfmisc_1(k1_zfmisc_1(X39)))
      | k5_setfam_1(X39,X40) = k3_tarski(X40) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).

cnf(c_0_20,plain,
    ( X1 != k1_xboole_0
    | ~ r2_hidden(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    ( esk3_0 != k1_xboole_0
    | k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,negated_conjecture,
    ( r2_hidden(esk3_0,esk2_0)
    | k5_setfam_1(esk1_0,esk2_0) != esk9_0 ),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,plain,
    ( k5_setfam_1(X2,X1) = k3_tarski(X1)
    | ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_25,plain,
    ! [X16,X17,X18,X20,X21,X22,X23,X25] :
      ( ( r2_hidden(X18,esk5_3(X16,X17,X18))
        | ~ r2_hidden(X18,X17)
        | X17 != k3_tarski(X16) )
      & ( r2_hidden(esk5_3(X16,X17,X18),X16)
        | ~ r2_hidden(X18,X17)
        | X17 != k3_tarski(X16) )
      & ( ~ r2_hidden(X20,X21)
        | ~ r2_hidden(X21,X16)
        | r2_hidden(X20,X17)
        | X17 != k3_tarski(X16) )
      & ( ~ r2_hidden(esk6_2(X22,X23),X23)
        | ~ r2_hidden(esk6_2(X22,X23),X25)
        | ~ r2_hidden(X25,X22)
        | X23 = k3_tarski(X22) )
      & ( r2_hidden(esk6_2(X22,X23),esk7_2(X22,X23))
        | r2_hidden(esk6_2(X22,X23),X23)
        | X23 = k3_tarski(X22) )
      & ( r2_hidden(esk7_2(X22,X23),X22)
        | r2_hidden(esk6_2(X22,X23),X23)
        | X23 = k3_tarski(X22) ) ),
    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)],[d4_tarski])])])])])]) ).

cnf(c_0_26,plain,
    ~ r2_hidden(X1,k1_xboole_0),
    inference(er,[status(thm)],[c_0_20]) ).

cnf(c_0_27,negated_conjecture,
    ( k5_setfam_1(esk1_0,esk2_0) != esk9_0
    | esk3_0 != esk9_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_18]),c_0_18]) ).

cnf(c_0_28,negated_conjecture,
    ( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
    | X1 = k1_xboole_0
    | ~ r2_hidden(X1,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_29,negated_conjecture,
    ( r2_hidden(esk3_0,esk2_0)
    | k3_tarski(esk2_0) != esk9_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_30,plain,
    ( r2_hidden(esk7_2(X1,X2),X1)
    | r2_hidden(esk6_2(X1,X2),X2)
    | X2 = k3_tarski(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_31,plain,
    ~ r2_hidden(X1,esk9_0),
    inference(rw,[status(thm)],[c_0_26,c_0_18]) ).

fof(c_0_32,plain,
    ! [X44,X45] :
      ( ~ m1_subset_1(X44,X45)
      | v1_xboole_0(X45)
      | r2_hidden(X44,X45) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

fof(c_0_33,plain,
    ! [X29] : m1_subset_1(esk8_1(X29),X29),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

fof(c_0_34,plain,
    ! [X55,X56] :
      ( ~ r2_hidden(X55,X56)
      | ~ v1_xboole_0(X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

cnf(c_0_35,negated_conjecture,
    ( k3_tarski(esk2_0) != esk9_0
    | esk3_0 != esk9_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_24])]) ).

cnf(c_0_36,plain,
    ( r2_hidden(X1,X4)
    | ~ r2_hidden(X1,X2)
    | ~ r2_hidden(X2,X3)
    | X4 != k3_tarski(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_37,negated_conjecture,
    ( k5_setfam_1(esk1_0,esk2_0) = esk9_0
    | X1 = esk9_0
    | ~ r2_hidden(X1,esk2_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_18]),c_0_18]) ).

cnf(c_0_38,negated_conjecture,
    ( r2_hidden(esk7_2(esk2_0,esk9_0),esk2_0)
    | r2_hidden(esk3_0,esk2_0) ),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30])]),c_0_31]) ).

cnf(c_0_39,plain,
    ( v1_xboole_0(X2)
    | r2_hidden(X1,X2)
    | ~ m1_subset_1(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_40,plain,
    m1_subset_1(esk8_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_41,plain,
    ( ~ r2_hidden(X1,X2)
    | ~ v1_xboole_0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_42,plain,
    ( r2_hidden(esk6_2(X1,X2),esk7_2(X1,X2))
    | r2_hidden(esk6_2(X1,X2),X2)
    | X2 = k3_tarski(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_43,negated_conjecture,
    ( r2_hidden(esk7_2(esk2_0,esk9_0),esk2_0)
    | esk3_0 != esk9_0 ),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30])]),c_0_31]) ).

cnf(c_0_44,plain,
    ( r2_hidden(X1,k3_tarski(X2))
    | ~ r2_hidden(X3,X2)
    | ~ r2_hidden(X1,X3) ),
    inference(er,[status(thm)],[c_0_36]) ).

cnf(c_0_45,negated_conjecture,
    ( esk7_2(esk2_0,esk9_0) = esk9_0
    | r2_hidden(esk3_0,esk2_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_22]) ).

cnf(c_0_46,plain,
    ( X1 = esk9_0
    | ~ v1_xboole_0(X1) ),
    inference(rw,[status(thm)],[c_0_14,c_0_18]) ).

cnf(c_0_47,plain,
    ( v1_xboole_0(X1)
    | r2_hidden(esk8_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_48,plain,
    ( X1 = k3_tarski(X2)
    | r2_hidden(esk6_2(X2,X1),X1)
    | ~ v1_xboole_0(esk7_2(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_49,negated_conjecture,
    ( esk7_2(esk2_0,esk9_0) = esk9_0
    | esk3_0 != esk9_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_43]),c_0_27]) ).

cnf(c_0_50,negated_conjecture,
    ( esk7_2(esk2_0,esk9_0) = esk9_0
    | r2_hidden(X1,k3_tarski(esk2_0))
    | ~ r2_hidden(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_51,plain,
    ( X1 = esk9_0
    | r2_hidden(esk8_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_52,negated_conjecture,
    esk3_0 != esk9_0,
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_15])]),c_0_31]),c_0_35]) ).

cnf(c_0_53,negated_conjecture,
    ( esk7_2(esk2_0,esk9_0) = esk9_0
    | k5_setfam_1(esk1_0,esk2_0) = esk9_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_45]),c_0_49]) ).

cnf(c_0_54,negated_conjecture,
    ( esk7_2(esk2_0,esk9_0) = esk9_0
    | r2_hidden(esk8_1(esk3_0),k3_tarski(esk2_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).

cnf(c_0_55,negated_conjecture,
    ( esk7_2(esk2_0,esk9_0) = esk9_0
    | k3_tarski(esk2_0) = esk9_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_53]),c_0_24])]) ).

cnf(c_0_56,negated_conjecture,
    ( r2_hidden(esk6_2(esk2_0,esk9_0),esk7_2(esk2_0,esk9_0))
    | r2_hidden(esk3_0,esk2_0) ),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_42])]),c_0_31]) ).

cnf(c_0_57,negated_conjecture,
    esk7_2(esk2_0,esk9_0) = esk9_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_31]) ).

cnf(c_0_58,negated_conjecture,
    r2_hidden(esk3_0,esk2_0),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57]),c_0_31]) ).

cnf(c_0_59,negated_conjecture,
    k3_tarski(esk2_0) = esk9_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_57]),c_0_15])]),c_0_31]) ).

cnf(c_0_60,negated_conjecture,
    ~ r2_hidden(X1,esk3_0),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_58]),c_0_59]),c_0_31]) ).

cnf(c_0_61,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_51]),c_0_52]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU430+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n002.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   : Thu Aug 24 01:41:16 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.94/1.03  % Version  : CSE_E---1.5
% 0.94/1.03  % Problem  : theBenchmark.p
% 0.94/1.03  % Proof found
% 0.94/1.03  % SZS status Theorem for theBenchmark.p
% 0.94/1.03  % SZS output start Proof
% See solution above
% 0.94/1.03  % Total time : 0.445000 s
% 0.94/1.03  % SZS output end Proof
% 0.94/1.03  % Total time : 0.448000 s
%------------------------------------------------------------------------------