TSTP Solution File: SET813+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET813+4 : 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 : 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 14:35:39 EDT 2023

% Result   : Theorem 0.16s 0.58s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   51 (   3 unt;  35 typ;   0 def)
%            Number of atoms       :   39 (   4 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   37 (  14   ~;  13   |;   5   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   60 (  31   >;  29   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   27 (  27 usr;   4 con; 0-3 aty)
%            Number of variables   :   26 (   1 sgn;  16   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    equal_set: ( $i * $i ) > $o ).

tff(decl_25,type,
    power_set: $i > $i ).

tff(decl_26,type,
    intersection: ( $i * $i ) > $i ).

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

tff(decl_28,type,
    empty_set: $i ).

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

tff(decl_30,type,
    singleton: $i > $i ).

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

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

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

tff(decl_34,type,
    on: $i ).

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

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

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

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

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

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

tff(decl_41,type,
    initial_segment: ( $i * $i * $i ) > $i ).

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

tff(decl_43,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_44,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_45,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk4_1: $i > $i ).

tff(decl_47,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk14_0: $i ).

fof(thV12,conjecture,
    ! [X1] :
      ( member(X1,on)
     => member(X1,suc(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV12) ).

fof(successor,axiom,
    ! [X1,X3] :
      ( member(X3,suc(X1))
    <=> member(X3,union(X1,singleton(X1))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',successor) ).

fof(union,axiom,
    ! [X3,X1,X2] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).

fof(singleton,axiom,
    ! [X3,X1] :
      ( member(X3,singleton(X1))
    <=> X3 = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1] :
        ( member(X1,on)
       => member(X1,suc(X1)) ),
    inference(assume_negation,[status(cth)],[thV12]) ).

fof(c_0_5,plain,
    ! [X90,X91] :
      ( ( ~ member(X91,suc(X90))
        | member(X91,union(X90,singleton(X90))) )
      & ( ~ member(X91,union(X90,singleton(X90)))
        | member(X91,suc(X90)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[successor])]) ).

fof(c_0_6,plain,
    ! [X22,X23,X24] :
      ( ( ~ member(X22,union(X23,X24))
        | member(X22,X23)
        | member(X22,X24) )
      & ( ~ member(X22,X23)
        | member(X22,union(X23,X24)) )
      & ( ~ member(X22,X24)
        | member(X22,union(X23,X24)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])]) ).

fof(c_0_7,plain,
    ! [X29,X30] :
      ( ( ~ member(X29,singleton(X30))
        | X29 = X30 )
      & ( X29 != X30
        | member(X29,singleton(X30)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).

fof(c_0_8,negated_conjecture,
    ( member(esk14_0,on)
    & ~ member(esk14_0,suc(esk14_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_9,plain,
    ( member(X1,suc(X2))
    | ~ member(X1,union(X2,singleton(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( member(X1,union(X3,X2))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

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

cnf(c_0_12,negated_conjecture,
    ~ member(esk14_0,suc(esk14_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( member(X1,suc(X2))
    | ~ member(X1,singleton(X2)) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    member(X1,singleton(X1)),
    inference(er,[status(thm)],[c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : SET813+4 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n005.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sat Aug 26 13:01:38 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.16/0.56  start to proof: theBenchmark
% 0.16/0.58  % Version  : CSE_E---1.5
% 0.16/0.58  % Problem  : theBenchmark.p
% 0.16/0.58  % Proof found
% 0.16/0.58  % SZS status Theorem for theBenchmark.p
% 0.16/0.58  % SZS output start Proof
% See solution above
% 0.16/0.59  % Total time : 0.019000 s
% 0.16/0.59  % SZS output end Proof
% 0.16/0.59  % Total time : 0.022000 s
%------------------------------------------------------------------------------