TSTP Solution File: SET146+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET146+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n023.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 14:33:18 EDT 2023

% Result   : Theorem 0.53s 0.59s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   31 (  14 unt;   9 typ;   0 def)
%            Number of atoms       :   48 (  17 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   45 (  19   ~;  17   |;   6   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   7   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   36 (   3 sgn;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    intersection: ( $i * $i ) > $i ).

tff(decl_23,type,
    member: ( $i * $i ) > $o ).

tff(decl_24,type,
    empty_set: $i ).

tff(decl_25,type,
    subset: ( $i * $i ) > $o ).

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

tff(decl_27,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk2_1: $i > $i ).

tff(decl_29,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk4_0: $i ).

fof(empty_set_defn,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(equal_member_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ! [X3] :
          ( member(X3,X1)
        <=> member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).

fof(prove_th61,conjecture,
    ! [X1] : intersection(X1,empty_set) = empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th61) ).

fof(intersection_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).

fof(commutativity_of_intersection,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(c_0_5,plain,
    ! [X1] : ~ member(X1,empty_set),
    inference(fof_simplification,[status(thm)],[empty_set_defn]) ).

fof(c_0_6,plain,
    ! [X7] : ~ member(X7,empty_set),
    inference(variable_rename,[status(thm)],[c_0_5]) ).

fof(c_0_7,plain,
    ! [X23,X24,X25,X26,X27,X28] :
      ( ( ~ member(X25,X23)
        | member(X25,X24)
        | X23 != X24 )
      & ( ~ member(X26,X24)
        | member(X26,X23)
        | X23 != X24 )
      & ( ~ member(esk3_2(X27,X28),X27)
        | ~ member(esk3_2(X27,X28),X28)
        | X27 = X28 )
      & ( member(esk3_2(X27,X28),X27)
        | member(esk3_2(X27,X28),X28)
        | X27 = X28 ) ),
    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)],[equal_member_defn])])])])])]) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1] : intersection(X1,empty_set) = empty_set,
    inference(assume_negation,[status(cth)],[prove_th61]) ).

fof(c_0_9,plain,
    ! [X4,X5,X6] :
      ( ( member(X6,X4)
        | ~ member(X6,intersection(X4,X5)) )
      & ( member(X6,X5)
        | ~ member(X6,intersection(X4,X5)) )
      & ( ~ member(X6,X4)
        | ~ member(X6,X5)
        | member(X6,intersection(X4,X5)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).

cnf(c_0_10,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( member(esk3_2(X1,X2),X1)
    | member(esk3_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_12,negated_conjecture,
    intersection(esk4_0,empty_set) != empty_set,
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_13,plain,
    ! [X10,X11] : intersection(X10,X11) = intersection(X11,X10),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_14,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( empty_set = X1
    | member(esk3_2(empty_set,X1),X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_16,negated_conjecture,
    intersection(esk4_0,empty_set) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,plain,
    ( intersection(X1,X2) = empty_set
    | member(esk3_2(empty_set,intersection(X1,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    intersection(empty_set,esk4_0) != empty_set,
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,plain,
    intersection(empty_set,X1) = empty_set,
    inference(spm,[status(thm)],[c_0_10,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET146+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n023.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   : Sat Aug 26 10:14:56 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.53/0.57  start to proof: theBenchmark
% 0.53/0.59  % Version  : CSE_E---1.5
% 0.53/0.59  % Problem  : theBenchmark.p
% 0.53/0.59  % Proof found
% 0.53/0.59  % SZS status Theorem for theBenchmark.p
% 0.53/0.59  % SZS output start Proof
% See solution above
% 0.53/0.59  % Total time : 0.009000 s
% 0.53/0.59  % SZS output end Proof
% 0.53/0.59  % Total time : 0.011000 s
%------------------------------------------------------------------------------