TSTP Solution File: SEU039+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 16:22:13 EDT 2023

% Result   : Theorem 0.19s 0.63s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   70 (  11 unt;  34 typ;   0 def)
%            Number of atoms       :  185 (  43 equ)
%            Maximal formula atoms :   32 (   5 avg)
%            Number of connectives :  246 (  97   ~; 101   |;  31   &)
%                                         (   5 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   36 (  22   >;  14   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   26 (  26 usr;  12 con; 0-3 aty)
%            Number of variables   :   85 (   2 sgn;  54   !;   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,
    set_intersection2: ( $i * $i ) > $i ).

tff(decl_28,type,
    relation_rng: $i > $i ).

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

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

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

tff(decl_32,type,
    element: ( $i * $i ) > $o ).

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

tff(decl_34,type,
    relation_empty_yielding: $i > $o ).

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

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

tff(decl_37,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_41,type,
    esk5_1: $i > $i ).

tff(decl_42,type,
    esk6_0: $i ).

tff(decl_43,type,
    esk7_0: $i ).

tff(decl_44,type,
    esk8_1: $i > $i ).

tff(decl_45,type,
    esk9_0: $i ).

tff(decl_46,type,
    esk10_0: $i ).

tff(decl_47,type,
    esk11_0: $i ).

tff(decl_48,type,
    esk12_1: $i > $i ).

tff(decl_49,type,
    esk13_0: $i ).

tff(decl_50,type,
    esk14_0: $i ).

tff(decl_51,type,
    esk15_0: $i ).

tff(decl_52,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk17_0: $i ).

tff(decl_54,type,
    esk18_0: $i ).

tff(decl_55,type,
    esk19_0: $i ).

fof(d5_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( X2 = relation_rng(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,relation_dom(X1))
                  & X3 = apply(X1,X4) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).

fof(t73_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( ( in(X2,relation_dom(X3))
          & in(X2,X1) )
       => in(apply(X3,X2),relation_rng(relation_dom_restriction(X3,X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).

fof(t72_funct_1,axiom,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(X2,X1)
       => apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_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/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(dt_k7_relat_1,axiom,
    ! [X1,X2] :
      ( relation(X1)
     => relation(relation_dom_restriction(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_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/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(d3_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(c_0_8,plain,
    ! [X21,X22,X23,X25,X26,X27,X29] :
      ( ( in(esk2_3(X21,X22,X23),relation_dom(X21))
        | ~ in(X23,X22)
        | X22 != relation_rng(X21)
        | ~ relation(X21)
        | ~ function(X21) )
      & ( X23 = apply(X21,esk2_3(X21,X22,X23))
        | ~ in(X23,X22)
        | X22 != relation_rng(X21)
        | ~ relation(X21)
        | ~ function(X21) )
      & ( ~ in(X26,relation_dom(X21))
        | X25 != apply(X21,X26)
        | in(X25,X22)
        | X22 != relation_rng(X21)
        | ~ relation(X21)
        | ~ function(X21) )
      & ( ~ in(esk3_2(X21,X27),X27)
        | ~ in(X29,relation_dom(X21))
        | esk3_2(X21,X27) != apply(X21,X29)
        | X27 = relation_rng(X21)
        | ~ relation(X21)
        | ~ function(X21) )
      & ( in(esk4_2(X21,X27),relation_dom(X21))
        | in(esk3_2(X21,X27),X27)
        | X27 = relation_rng(X21)
        | ~ relation(X21)
        | ~ function(X21) )
      & ( esk3_2(X21,X27) = apply(X21,esk4_2(X21,X27))
        | in(esk3_2(X21,X27),X27)
        | X27 = relation_rng(X21)
        | ~ relation(X21)
        | ~ function(X21) ) ),
    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)],[d5_funct_1])])])])])]) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( ( in(X2,relation_dom(X3))
            & in(X2,X1) )
         => in(apply(X3,X2),relation_rng(relation_dom_restriction(X3,X1))) ) ),
    inference(assume_negation,[status(cth)],[t73_funct_1]) ).

cnf(c_0_10,plain,
    ( in(X3,X4)
    | ~ in(X1,relation_dom(X2))
    | X3 != apply(X2,X1)
    | X4 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_11,plain,
    ! [X79,X80,X81] :
      ( ~ relation(X81)
      | ~ function(X81)
      | ~ in(X80,X79)
      | apply(relation_dom_restriction(X81,X79),X80) = apply(X81,X80) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t72_funct_1])]) ).

fof(c_0_12,plain,
    ! [X40,X41] :
      ( ( relation(relation_dom_restriction(X40,X41))
        | ~ relation(X40)
        | ~ function(X40) )
      & ( function(relation_dom_restriction(X40,X41))
        | ~ relation(X40)
        | ~ function(X40) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).

fof(c_0_13,plain,
    ! [X31,X32] :
      ( ~ relation(X31)
      | relation(relation_dom_restriction(X31,X32)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).

fof(c_0_14,negated_conjecture,
    ( relation(esk19_0)
    & function(esk19_0)
    & in(esk18_0,relation_dom(esk19_0))
    & in(esk18_0,esk17_0)
    & ~ in(apply(esk19_0,esk18_0),relation_rng(relation_dom_restriction(esk19_0,esk17_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_15,plain,
    ( in(apply(X1,X2),relation_rng(X1))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_dom(X1)) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).

cnf(c_0_16,plain,
    ( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( function(relation_dom_restriction(X1,X2))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( relation(relation_dom_restriction(X1,X2))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_19,plain,
    ! [X73,X74,X75,X76] :
      ( ( relation_dom(X74) = set_intersection2(relation_dom(X75),X73)
        | X74 != relation_dom_restriction(X75,X73)
        | ~ relation(X75)
        | ~ function(X75)
        | ~ relation(X74)
        | ~ function(X74) )
      & ( ~ in(X76,relation_dom(X74))
        | apply(X74,X76) = apply(X75,X76)
        | X74 != relation_dom_restriction(X75,X73)
        | ~ relation(X75)
        | ~ function(X75)
        | ~ relation(X74)
        | ~ function(X74) )
      & ( in(esk16_3(X73,X74,X75),relation_dom(X74))
        | relation_dom(X74) != set_intersection2(relation_dom(X75),X73)
        | X74 = relation_dom_restriction(X75,X73)
        | ~ relation(X75)
        | ~ function(X75)
        | ~ relation(X74)
        | ~ function(X74) )
      & ( apply(X74,esk16_3(X73,X74,X75)) != apply(X75,esk16_3(X73,X74,X75))
        | relation_dom(X74) != set_intersection2(relation_dom(X75),X73)
        | X74 = relation_dom_restriction(X75,X73)
        | ~ relation(X75)
        | ~ function(X75)
        | ~ relation(X74)
        | ~ function(X74) ) ),
    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_20,negated_conjecture,
    ~ in(apply(esk19_0,esk18_0),relation_rng(relation_dom_restriction(esk19_0,esk17_0))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    ( in(apply(X1,X2),relation_rng(relation_dom_restriction(X1,X3)))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_dom(relation_dom_restriction(X1,X3)))
    | ~ in(X2,X3) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    relation(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    function(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_24,negated_conjecture,
    in(esk18_0,esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_25,plain,
    ( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
    | X1 != relation_dom_restriction(X2,X3)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_26,plain,
    ! [X10,X11] : set_intersection2(X10,X11) = set_intersection2(X11,X10),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

fof(c_0_27,plain,
    ! [X12,X13,X14,X15,X16,X17,X18,X19] :
      ( ( in(X15,X12)
        | ~ in(X15,X14)
        | X14 != set_intersection2(X12,X13) )
      & ( in(X15,X13)
        | ~ in(X15,X14)
        | X14 != set_intersection2(X12,X13) )
      & ( ~ in(X16,X12)
        | ~ in(X16,X13)
        | in(X16,X14)
        | X14 != set_intersection2(X12,X13) )
      & ( ~ in(esk1_3(X17,X18,X19),X19)
        | ~ in(esk1_3(X17,X18,X19),X17)
        | ~ in(esk1_3(X17,X18,X19),X18)
        | X19 = set_intersection2(X17,X18) )
      & ( in(esk1_3(X17,X18,X19),X17)
        | in(esk1_3(X17,X18,X19),X19)
        | X19 = set_intersection2(X17,X18) )
      & ( in(esk1_3(X17,X18,X19),X18)
        | in(esk1_3(X17,X18,X19),X19)
        | X19 = set_intersection2(X17,X18) ) ),
    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_xboole_0])])])])])]) ).

cnf(c_0_28,negated_conjecture,
    ~ in(esk18_0,relation_dom(relation_dom_restriction(esk19_0,esk17_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).

cnf(c_0_29,plain,
    ( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_17]),c_0_18]) ).

cnf(c_0_30,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,plain,
    ( in(X1,X4)
    | ~ in(X1,X2)
    | ~ in(X1,X3)
    | X4 != set_intersection2(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    ~ in(esk18_0,set_intersection2(esk17_0,relation_dom(esk19_0))),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22]),c_0_23])]),c_0_30]) ).

cnf(c_0_33,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    in(esk18_0,relation_dom(esk19_0)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n011.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 01:34:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.19/0.63  % Version  : CSE_E---1.5
% 0.19/0.63  % Problem  : theBenchmark.p
% 0.19/0.63  % Proof found
% 0.19/0.63  % SZS status Theorem for theBenchmark.p
% 0.19/0.63  % SZS output start Proof
% See solution above
% 0.19/0.63  % Total time : 0.040000 s
% 0.19/0.63  % SZS output end Proof
% 0.19/0.63  % Total time : 0.044000 s
%------------------------------------------------------------------------------