TSTP Solution File: SEU008+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU008+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 : n014.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 16:22:07 EDT 2023

% Result   : Theorem 0.20s 0.69s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   63 (  16 unt;  28 typ;   0 def)
%            Number of atoms       :  122 (  39 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  140 (  53   ~;  55   |;  20   &)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  18   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  10 con; 0-3 aty)
%            Number of variables   :   64 (   4 sgn;  38   !;   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,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

tff(decl_30,type,
    empty_set: $i ).

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

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

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

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

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

tff(decl_36,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_37,type,
    esk2_1: $i > $i ).

tff(decl_38,type,
    esk3_0: $i ).

tff(decl_39,type,
    esk4_0: $i ).

tff(decl_40,type,
    esk5_1: $i > $i ).

tff(decl_41,type,
    esk6_0: $i ).

tff(decl_42,type,
    esk7_0: $i ).

tff(decl_43,type,
    esk8_1: $i > $i ).

tff(decl_44,type,
    esk9_0: $i ).

tff(decl_45,type,
    esk10_0: $i ).

tff(decl_46,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_47,type,
    esk12_0: $i ).

tff(decl_48,type,
    esk13_0: $i ).

tff(decl_49,type,
    esk14_0: $i ).

fof(t38_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(X2,set_intersection2(relation_dom(X3),X1))
       => apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_1) ).

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(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(t34_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( X2 = identity_relation(X1)
      <=> ( relation_dom(X2) = X1
          & ! [X3] :
              ( in(X3,X1)
             => apply(X2,X3) = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).

fof(dt_k6_relat_1,axiom,
    ! [X1] : relation(identity_relation(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).

fof(fc2_funct_1,axiom,
    ! [X1] :
      ( relation(identity_relation(X1))
      & function(identity_relation(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).

fof(t23_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( in(X1,relation_dom(X2))
           => apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( in(X2,set_intersection2(relation_dom(X3),X1))
         => apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
    inference(assume_negation,[status(cth)],[t38_funct_1]) ).

fof(c_0_8,plain,
    ! [X11,X12,X13,X14,X15,X16,X17,X18] :
      ( ( in(X14,X11)
        | ~ in(X14,X13)
        | X13 != set_intersection2(X11,X12) )
      & ( in(X14,X12)
        | ~ in(X14,X13)
        | X13 != set_intersection2(X11,X12) )
      & ( ~ in(X15,X11)
        | ~ in(X15,X12)
        | in(X15,X13)
        | X13 != set_intersection2(X11,X12) )
      & ( ~ in(esk1_3(X16,X17,X18),X18)
        | ~ in(esk1_3(X16,X17,X18),X16)
        | ~ in(esk1_3(X16,X17,X18),X17)
        | X18 = set_intersection2(X16,X17) )
      & ( in(esk1_3(X16,X17,X18),X16)
        | in(esk1_3(X16,X17,X18),X18)
        | X18 = set_intersection2(X16,X17) )
      & ( in(esk1_3(X16,X17,X18),X17)
        | in(esk1_3(X16,X17,X18),X18)
        | X18 = set_intersection2(X16,X17) ) ),
    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])])])])])]) ).

fof(c_0_9,negated_conjecture,
    ( relation(esk14_0)
    & function(esk14_0)
    & in(esk13_0,set_intersection2(relation_dom(esk14_0),esk12_0))
    & apply(esk14_0,esk13_0) != apply(relation_composition(identity_relation(esk12_0),esk14_0),esk13_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_10,plain,
    ! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

fof(c_0_11,plain,
    ! [X57,X58,X59] :
      ( ( relation_dom(X58) = X57
        | X58 != identity_relation(X57)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( ~ in(X59,X57)
        | apply(X58,X59) = X59
        | X58 != identity_relation(X57)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( in(esk11_2(X57,X58),X57)
        | relation_dom(X58) != X57
        | X58 = identity_relation(X57)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( apply(X58,esk11_2(X57,X58)) != esk11_2(X57,X58)
        | relation_dom(X58) != X57
        | X58 = identity_relation(X57)
        | ~ relation(X58)
        | ~ function(X58) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).

fof(c_0_12,plain,
    ! [X22] : relation(identity_relation(X22)),
    inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).

fof(c_0_13,plain,
    ! [X32] :
      ( relation(identity_relation(X32))
      & function(identity_relation(X32)) ),
    inference(variable_rename,[status(thm)],[fc2_funct_1]) ).

cnf(c_0_14,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_intersection2(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    in(esk13_0,set_intersection2(relation_dom(esk14_0),esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_17,plain,
    ! [X51,X52,X53] :
      ( ~ relation(X52)
      | ~ function(X52)
      | ~ relation(X53)
      | ~ function(X53)
      | ~ in(X51,relation_dom(X52))
      | apply(relation_composition(X52,X53),X51) = apply(X53,apply(X52,X51)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).

cnf(c_0_18,plain,
    ( relation_dom(X1) = X2
    | X1 != identity_relation(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    relation(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    function(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ( apply(X3,X1) = X1
    | ~ in(X1,X2)
    | X3 != identity_relation(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_22,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X2,X3)) ),
    inference(er,[status(thm)],[c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    in(esk13_0,set_intersection2(esk12_0,relation_dom(esk14_0))),
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_24,plain,
    ( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X3,relation_dom(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    relation_dom(identity_relation(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]),c_0_20])]) ).

cnf(c_0_26,plain,
    ( apply(identity_relation(X1),X2) = X2
    | ~ in(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_19]),c_0_20])]) ).

cnf(c_0_27,negated_conjecture,
    in(esk13_0,esk12_0),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,plain,
    ( apply(X1,apply(identity_relation(X2),X3)) = apply(relation_composition(identity_relation(X2),X1),X3)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X3,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19]),c_0_20])]) ).

cnf(c_0_29,negated_conjecture,
    apply(identity_relation(esk12_0),esk13_0) = esk13_0,
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    apply(esk14_0,esk13_0) != apply(relation_composition(identity_relation(esk12_0),esk14_0),esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_31,negated_conjecture,
    ( apply(relation_composition(identity_relation(esk12_0),X1),esk13_0) = apply(X1,esk13_0)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_29]) ).

cnf(c_0_32,negated_conjecture,
    relation(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_33,negated_conjecture,
    function(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU008+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 : n014.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 20:18:04 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.69  % Version  : CSE_E---1.5
% 0.20/0.69  % Problem  : theBenchmark.p
% 0.20/0.69  % Proof found
% 0.20/0.69  % SZS status Theorem for theBenchmark.p
% 0.20/0.69  % SZS output start Proof
% See solution above
% 0.20/0.70  % Total time : 0.116000 s
% 0.20/0.70  % SZS output end Proof
% 0.20/0.70  % Total time : 0.120000 s
%------------------------------------------------------------------------------