TSTP Solution File: SEU225+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU225+3 : 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 : n005.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 16:23:32 EDT 2023

% Result   : Theorem 5.53s 5.79s
% Output   : CNFRefutation 5.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   73 (  10 unt;  32 typ;   0 def)
%            Number of atoms       :  183 (  44 equ)
%            Maximal formula atoms :   27 (   4 avg)
%            Number of connectives :  230 (  88   ~;  90   |;  29   &)
%                                         (   6 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  20   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  12 con; 0-3 aty)
%            Number of variables   :   71 (   3 sgn;  39   !;   1   ?;   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_intersection2: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

tff(decl_37,type,
    powerset: $i > $i ).

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

tff(decl_39,type,
    esk1_1: $i > $i ).

tff(decl_40,type,
    esk2_0: $i ).

tff(decl_41,type,
    esk3_0: $i ).

tff(decl_42,type,
    esk4_1: $i > $i ).

tff(decl_43,type,
    esk5_0: $i ).

tff(decl_44,type,
    esk6_0: $i ).

tff(decl_45,type,
    esk7_0: $i ).

tff(decl_46,type,
    esk8_1: $i > $i ).

tff(decl_47,type,
    esk9_0: $i ).

tff(decl_48,type,
    esk10_0: $i ).

tff(decl_49,type,
    esk11_0: $i ).

tff(decl_50,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk13_0: $i ).

tff(decl_52,type,
    esk14_0: $i ).

tff(decl_53,type,
    esk15_0: $i ).

fof(d4_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( ( in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> in(ordered_pair(X2,X3),X1) ) )
          & ( ~ in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> X3 = empty_set ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).

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

fof(rc2_funct_1,axiom,
    ? [X1] :
      ( relation(X1)
      & empty(X1)
      & function(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

fof(dt_k7_relat_1,axiom,
    ! [X1,X2] :
      ( relation(X1)
     => relation(relation_dom_restriction(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).

fof(fc4_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1) )
     => ( relation(relation_dom_restriction(X1,X2))
        & function(relation_dom_restriction(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(t72_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(X2,X1)
       => apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).

fof(t68_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( X2 = relation_dom_restriction(X3,X1)
          <=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
              & ! [X4] :
                  ( in(X4,relation_dom(X2))
                 => apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).

fof(l82_funct_1,axiom,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
      <=> ( in(X2,relation_dom(X3))
          & in(X2,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).

fof(c_0_8,plain,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( ( in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> in(ordered_pair(X2,X3),X1) ) )
          & ( ~ in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> X3 = empty_set ) ) ) ),
    inference(fof_simplification,[status(thm)],[d4_funct_1]) ).

fof(c_0_9,plain,
    ! [X14,X15,X16] :
      ( ( X16 != apply(X14,X15)
        | in(ordered_pair(X15,X16),X14)
        | ~ in(X15,relation_dom(X14))
        | ~ relation(X14)
        | ~ function(X14) )
      & ( ~ in(ordered_pair(X15,X16),X14)
        | X16 = apply(X14,X15)
        | ~ in(X15,relation_dom(X14))
        | ~ relation(X14)
        | ~ function(X14) )
      & ( X16 != apply(X14,X15)
        | X16 = empty_set
        | in(X15,relation_dom(X14))
        | ~ relation(X14)
        | ~ function(X14) )
      & ( X16 != empty_set
        | X16 = apply(X14,X15)
        | in(X15,relation_dom(X14))
        | ~ relation(X14)
        | ~ function(X14) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

fof(c_0_10,plain,
    ! [X72] :
      ( ~ empty(X72)
      | X72 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_11,plain,
    ( relation(esk6_0)
    & empty(esk6_0)
    & function(esk6_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).

cnf(c_0_12,plain,
    ( X1 = empty_set
    | in(X3,relation_dom(X2))
    | X1 != apply(X2,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    empty(esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    ( apply(X1,X2) = empty_set
    | in(X2,relation_dom(X1))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    empty_set = esk6_0,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

fof(c_0_17,plain,
    ! [X19,X20] :
      ( ~ relation(X19)
      | relation(relation_dom_restriction(X19,X20)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).

cnf(c_0_18,plain,
    ( apply(X1,X2) = esk6_0
    | in(X2,relation_dom(X1))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,plain,
    ( relation(relation_dom_restriction(X1,X2))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_20,plain,
    ! [X33,X34] :
      ( ( relation(relation_dom_restriction(X33,X34))
        | ~ relation(X33)
        | ~ function(X33) )
      & ( function(relation_dom_restriction(X33,X34))
        | ~ relation(X33)
        | ~ function(X33) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).

fof(c_0_21,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( in(X2,X1)
         => apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
    inference(assume_negation,[status(cth)],[t72_funct_1]) ).

fof(c_0_22,plain,
    ! [X67,X68,X69,X70] :
      ( ( relation_dom(X68) = set_intersection2(relation_dom(X69),X67)
        | X68 != relation_dom_restriction(X69,X67)
        | ~ relation(X69)
        | ~ function(X69)
        | ~ relation(X68)
        | ~ function(X68) )
      & ( ~ in(X70,relation_dom(X68))
        | apply(X68,X70) = apply(X69,X70)
        | X68 != relation_dom_restriction(X69,X67)
        | ~ relation(X69)
        | ~ function(X69)
        | ~ relation(X68)
        | ~ function(X68) )
      & ( in(esk12_3(X67,X68,X69),relation_dom(X68))
        | relation_dom(X68) != set_intersection2(relation_dom(X69),X67)
        | X68 = relation_dom_restriction(X69,X67)
        | ~ relation(X69)
        | ~ function(X69)
        | ~ relation(X68)
        | ~ function(X68) )
      & ( apply(X68,esk12_3(X67,X68,X69)) != apply(X69,esk12_3(X67,X68,X69))
        | relation_dom(X68) != set_intersection2(relation_dom(X69),X67)
        | X68 = relation_dom_restriction(X69,X67)
        | ~ relation(X69)
        | ~ function(X69)
        | ~ relation(X68)
        | ~ function(X68) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).

cnf(c_0_23,plain,
    ( apply(relation_dom_restriction(X1,X2),X3) = esk6_0
    | in(X3,relation_dom(relation_dom_restriction(X1,X2)))
    | ~ relation(X1)
    | ~ function(relation_dom_restriction(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,plain,
    ( function(relation_dom_restriction(X1,X2))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_25,negated_conjecture,
    ( relation(esk15_0)
    & function(esk15_0)
    & in(esk14_0,esk13_0)
    & apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) != apply(esk15_0,esk14_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).

cnf(c_0_26,plain,
    ( apply(X2,X1) = apply(X3,X1)
    | ~ in(X1,relation_dom(X2))
    | X2 != relation_dom_restriction(X3,X4)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    ( apply(relation_dom_restriction(X1,X2),X3) = esk6_0
    | in(X3,relation_dom(relation_dom_restriction(X1,X2)))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    relation(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    function(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) != apply(esk15_0,esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_31,plain,
    ( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X3,relation_dom(relation_dom_restriction(X1,X2))) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_24]),c_0_19]) ).

fof(c_0_32,plain,
    ! [X38,X39,X40] :
      ( ( in(X39,relation_dom(X40))
        | ~ in(X39,relation_dom(relation_dom_restriction(X40,X38)))
        | ~ relation(X40)
        | ~ function(X40) )
      & ( in(X39,X38)
        | ~ in(X39,relation_dom(relation_dom_restriction(X40,X38)))
        | ~ relation(X40)
        | ~ function(X40) )
      & ( ~ in(X39,relation_dom(X40))
        | ~ in(X39,X38)
        | in(X39,relation_dom(relation_dom_restriction(X40,X38)))
        | ~ relation(X40)
        | ~ function(X40) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l82_funct_1])])]) ).

cnf(c_0_33,negated_conjecture,
    ( apply(relation_dom_restriction(esk15_0,X1),X2) = esk6_0
    | in(X2,relation_dom(relation_dom_restriction(esk15_0,X1))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).

cnf(c_0_34,negated_conjecture,
    ~ in(esk14_0,relation_dom(relation_dom_restriction(esk15_0,esk13_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28]),c_0_29])]) ).

cnf(c_0_35,plain,
    ( in(X1,relation_dom(relation_dom_restriction(X2,X3)))
    | ~ in(X1,relation_dom(X2))
    | ~ in(X1,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    in(esk14_0,esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_37,negated_conjecture,
    apply(esk15_0,esk14_0) != esk6_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    ( apply(esk15_0,X1) = esk6_0
    | in(X1,relation_dom(esk15_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_29])]) ).

cnf(c_0_39,negated_conjecture,
    ~ in(esk14_0,relation_dom(esk15_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_28]),c_0_29]),c_0_36])]) ).

cnf(c_0_40,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU225+3 : 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 : n005.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 21:32:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 5.53/5.79  % Version  : CSE_E---1.5
% 5.53/5.79  % Problem  : theBenchmark.p
% 5.53/5.79  % Proof found
% 5.53/5.79  % SZS status Theorem for theBenchmark.p
% 5.53/5.79  % SZS output start Proof
% See solution above
% 5.53/5.79  % Total time : 5.202000 s
% 5.53/5.79  % SZS output end Proof
% 5.53/5.79  % Total time : 5.206000 s
%------------------------------------------------------------------------------