TSTP Solution File: SEU056+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU056+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 16:22:17 EDT 2023

% Result   : Theorem 0.20s 0.63s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   50 (  10 unt;  27 typ;   0 def)
%            Number of atoms       :   53 (  15 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   45 (  15   ~;  12   |;  10   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  15   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  12 con; 0-2 aty)
%            Number of variables   :   28 (   0 sgn;  18   !;   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,
    set_intersection2: ( $i * $i ) > $i ).

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

tff(decl_29,type,
    empty_set: $i ).

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

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

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

tff(decl_33,type,
    subset: ( $i * $i ) > $o ).

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

tff(decl_35,type,
    esk1_1: $i > $i ).

tff(decl_36,type,
    esk2_0: $i ).

tff(decl_37,type,
    esk3_0: $i ).

tff(decl_38,type,
    esk4_1: $i > $i ).

tff(decl_39,type,
    esk5_0: $i ).

tff(decl_40,type,
    esk6_0: $i ).

tff(decl_41,type,
    esk7_0: $i ).

tff(decl_42,type,
    esk8_1: $i > $i ).

tff(decl_43,type,
    esk9_0: $i ).

tff(decl_44,type,
    esk10_0: $i ).

tff(decl_45,type,
    esk11_0: $i ).

tff(decl_46,type,
    esk12_0: $i ).

tff(decl_47,type,
    esk13_0: $i ).

tff(decl_48,type,
    esk14_0: $i ).

fof(t125_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( ( disjoint(X1,X2)
          & one_to_one(X3) )
       => disjoint(relation_image(X3,X1),relation_image(X3,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_funct_1) ).

fof(t121_funct_1,axiom,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( one_to_one(X3)
       => relation_image(X3,set_intersection2(X1,X2)) = set_intersection2(relation_image(X3,X1),relation_image(X3,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_1) ).

fof(d7_xboole_0,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_intersection2(X1,X2) = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).

fof(t149_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => relation_image(X1,empty_set) = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( ( disjoint(X1,X2)
            & one_to_one(X3) )
         => disjoint(relation_image(X3,X1),relation_image(X3,X2)) ) ),
    inference(assume_negation,[status(cth)],[t125_funct_1]) ).

fof(c_0_5,plain,
    ! [X34,X35,X36] :
      ( ~ relation(X36)
      | ~ function(X36)
      | ~ one_to_one(X36)
      | relation_image(X36,set_intersection2(X34,X35)) = set_intersection2(relation_image(X36,X34),relation_image(X36,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t121_funct_1])]) ).

fof(c_0_6,negated_conjecture,
    ( relation(esk14_0)
    & function(esk14_0)
    & disjoint(esk12_0,esk13_0)
    & one_to_one(esk14_0)
    & ~ disjoint(relation_image(esk14_0,esk12_0),relation_image(esk14_0,esk13_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_7,plain,
    ! [X11,X12] :
      ( ( ~ disjoint(X11,X12)
        | set_intersection2(X11,X12) = empty_set )
      & ( set_intersection2(X11,X12) != empty_set
        | disjoint(X11,X12) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).

fof(c_0_8,plain,
    ! [X40] :
      ( ~ relation(X40)
      | relation_image(X40,empty_set) = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t149_relat_1])]) ).

cnf(c_0_9,plain,
    ( relation_image(X1,set_intersection2(X2,X3)) = set_intersection2(relation_image(X1,X2),relation_image(X1,X3))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,negated_conjecture,
    one_to_one(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    relation(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,negated_conjecture,
    function(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,plain,
    ( set_intersection2(X1,X2) = empty_set
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_14,negated_conjecture,
    disjoint(esk12_0,esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_15,plain,
    ( relation_image(X1,empty_set) = empty_set
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,negated_conjecture,
    relation_image(esk14_0,set_intersection2(X1,X2)) = set_intersection2(relation_image(esk14_0,X1),relation_image(esk14_0,X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]) ).

cnf(c_0_17,negated_conjecture,
    set_intersection2(esk12_0,esk13_0) = empty_set,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    relation_image(esk14_0,empty_set) = empty_set,
    inference(spm,[status(thm)],[c_0_15,c_0_11]) ).

cnf(c_0_19,plain,
    ( disjoint(X1,X2)
    | set_intersection2(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_20,negated_conjecture,
    set_intersection2(relation_image(esk14_0,esk12_0),relation_image(esk14_0,esk13_0)) = empty_set,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    ~ disjoint(relation_image(esk14_0,esk12_0),relation_image(esk14_0,esk13_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU056+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 18:25:19 EDT 2023
% 0.20/0.35  % CPUTime  : 
% 0.20/0.61  start to proof: theBenchmark
% 0.20/0.63  % Version  : CSE_E---1.5
% 0.20/0.63  % Problem  : theBenchmark.p
% 0.20/0.63  % Proof found
% 0.20/0.63  % SZS status Theorem for theBenchmark.p
% 0.20/0.63  % SZS output start Proof
% See solution above
% 0.20/0.63  % Total time : 0.009000 s
% 0.20/0.63  % SZS output end Proof
% 0.20/0.63  % Total time : 0.011000 s
%------------------------------------------------------------------------------