TSTP Solution File: SEU239+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 16:23:42 EDT 2023

% Result   : Theorem 0.21s 0.61s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   61 (  10 unt;  25 typ;   0 def)
%            Number of atoms       :  102 (   6 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  113 (  47   ~;  49   |;   6   &)
%                                         (   4 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  17   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   8 con; 0-2 aty)
%            Number of variables   :   51 (   0 sgn;  22   !;   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,
    relation: $i > $o ).

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

tff(decl_27,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_28,type,
    set_union2: ( $i * $i ) > $i ).

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

tff(decl_30,type,
    ordered_pair: ( $i * $i ) > $i ).

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

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

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

tff(decl_34,type,
    relation_rng: $i > $i ).

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

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

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

tff(decl_38,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk2_1: $i > $i ).

tff(decl_40,type,
    esk3_0: $i ).

tff(decl_41,type,
    esk4_0: $i ).

tff(decl_42,type,
    esk5_0: $i ).

tff(decl_43,type,
    esk6_0: $i ).

tff(decl_44,type,
    esk7_0: $i ).

tff(decl_45,type,
    esk8_0: $i ).

tff(decl_46,type,
    esk9_0: $i ).

fof(l1_wellord1,conjecture,
    ! [X1] :
      ( relation(X1)
     => ( reflexive(X1)
      <=> ! [X2] :
            ( in(X2,relation_field(X1))
           => in(ordered_pair(X2,X2),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).

fof(d1_relat_2,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( is_reflexive_in(X1,X2)
        <=> ! [X3] :
              ( in(X3,X2)
             => in(ordered_pair(X3,X3),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(d9_relat_2,axiom,
    ! [X1] :
      ( relation(X1)
     => ( reflexive(X1)
      <=> is_reflexive_in(X1,relation_field(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1] :
        ( relation(X1)
       => ( reflexive(X1)
        <=> ! [X2] :
              ( in(X2,relation_field(X1))
             => in(ordered_pair(X2,X2),X1) ) ) ),
    inference(assume_negation,[status(cth)],[l1_wellord1]) ).

fof(c_0_6,plain,
    ! [X12,X13,X14,X15] :
      ( ( ~ is_reflexive_in(X12,X13)
        | ~ in(X14,X13)
        | in(ordered_pair(X14,X14),X12)
        | ~ relation(X12) )
      & ( in(esk1_2(X12,X15),X15)
        | is_reflexive_in(X12,X15)
        | ~ relation(X12) )
      & ( ~ in(ordered_pair(esk1_2(X12,X15),esk1_2(X12,X15)),X12)
        | is_reflexive_in(X12,X15)
        | ~ relation(X12) ) ),
    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)],[d1_relat_2])])])])])]) ).

fof(c_0_7,plain,
    ! [X17,X18] : ordered_pair(X17,X18) = unordered_pair(unordered_pair(X17,X18),singleton(X17)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_8,negated_conjecture,
    ! [X32] :
      ( relation(esk3_0)
      & ( in(esk4_0,relation_field(esk3_0))
        | ~ reflexive(esk3_0) )
      & ( ~ in(ordered_pair(esk4_0,esk4_0),esk3_0)
        | ~ reflexive(esk3_0) )
      & ( reflexive(esk3_0)
        | ~ in(X32,relation_field(esk3_0))
        | in(ordered_pair(X32,X32),esk3_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_5])])])])]) ).

cnf(c_0_9,plain,
    ( in(ordered_pair(X3,X3),X1)
    | ~ is_reflexive_in(X1,X2)
    | ~ in(X3,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X20] :
      ( ( ~ reflexive(X20)
        | is_reflexive_in(X20,relation_field(X20))
        | ~ relation(X20) )
      & ( ~ is_reflexive_in(X20,relation_field(X20))
        | reflexive(X20)
        | ~ relation(X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).

cnf(c_0_12,negated_conjecture,
    ( reflexive(esk3_0)
    | in(ordered_pair(X1,X1),esk3_0)
    | ~ in(X1,relation_field(esk3_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,plain,
    ! [X8,X9] : unordered_pair(X8,X9) = unordered_pair(X9,X8),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_14,negated_conjecture,
    ( ~ in(ordered_pair(esk4_0,esk4_0),esk3_0)
    | ~ reflexive(esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    ( in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),X1)
    | ~ relation(X1)
    | ~ in(X3,X2)
    | ~ is_reflexive_in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_16,plain,
    ( is_reflexive_in(X1,relation_field(X1))
    | ~ reflexive(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,negated_conjecture,
    ( reflexive(esk3_0)
    | in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),esk3_0)
    | ~ in(X1,relation_field(esk3_0)) ),
    inference(rw,[status(thm)],[c_0_12,c_0_10]) ).

cnf(c_0_18,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ reflexive(esk3_0)
    | ~ in(unordered_pair(unordered_pair(esk4_0,esk4_0),singleton(esk4_0)),esk3_0) ),
    inference(rw,[status(thm)],[c_0_14,c_0_10]) ).

cnf(c_0_20,plain,
    ( in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),X2)
    | ~ reflexive(X2)
    | ~ relation(X2)
    | ~ in(X1,relation_field(X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    relation(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_22,negated_conjecture,
    ( in(esk4_0,relation_field(esk3_0))
    | ~ reflexive(esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_23,plain,
    ( is_reflexive_in(X1,X2)
    | ~ in(ordered_pair(esk1_2(X1,X2),esk1_2(X1,X2)),X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_24,negated_conjecture,
    ( reflexive(esk3_0)
    | in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),esk3_0)
    | ~ in(X1,relation_field(esk3_0)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_25,negated_conjecture,
    ~ reflexive(esk3_0),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]) ).

cnf(c_0_26,plain,
    ( is_reflexive_in(X1,X2)
    | ~ relation(X1)
    | ~ in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2)),singleton(esk1_2(X1,X2))),X1) ),
    inference(rw,[status(thm)],[c_0_23,c_0_10]) ).

cnf(c_0_27,negated_conjecture,
    ( in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),esk3_0)
    | ~ in(X1,relation_field(esk3_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_18]),c_0_25]) ).

cnf(c_0_28,plain,
    ( is_reflexive_in(X1,X2)
    | ~ relation(X1)
    | ~ in(unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X1) ),
    inference(rw,[status(thm)],[c_0_26,c_0_18]) ).

cnf(c_0_29,negated_conjecture,
    ( in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),esk3_0)
    | ~ in(X1,relation_field(esk3_0)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_18]) ).

cnf(c_0_30,plain,
    ( in(esk1_2(X1,X2),X2)
    | is_reflexive_in(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_31,negated_conjecture,
    ( is_reflexive_in(esk3_0,X1)
    | ~ in(esk1_2(esk3_0,X1),relation_field(esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_21])]) ).

cnf(c_0_32,negated_conjecture,
    ( is_reflexive_in(esk3_0,X1)
    | in(esk1_2(esk3_0,X1),X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_21]) ).

cnf(c_0_33,plain,
    ( reflexive(X1)
    | ~ is_reflexive_in(X1,relation_field(X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_34,negated_conjecture,
    is_reflexive_in(esk3_0,relation_field(esk3_0)),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_21])]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 18:54:38 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.61  % Version  : CSE_E---1.5
% 0.21/0.61  % Problem  : theBenchmark.p
% 0.21/0.61  % Proof found
% 0.21/0.61  % SZS status Theorem for theBenchmark.p
% 0.21/0.61  % SZS output start Proof
% See solution above
% 0.21/0.62  % Total time : 0.029000 s
% 0.21/0.62  % SZS output end Proof
% 0.21/0.62  % Total time : 0.032000 s
%------------------------------------------------------------------------------