TSTP Solution File: SET653+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET653+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 : n009.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 14:35:04 EDT 2023

% Result   : Theorem 0.44s 0.61s
% Output   : CNFRefutation 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   53 (   8 unt;  28 typ;   0 def)
%            Number of atoms       :   91 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  105 (  39   ~;  36   |;   8   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  22   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;   6 con; 0-2 aty)
%            Number of variables   :   53 (   3 sgn;  30   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    set_type: $i ).

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

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

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

tff(decl_26,type,
    domain_of: $i > $i ).

tff(decl_27,type,
    range_of: $i > $i ).

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

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

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

tff(decl_31,type,
    binary_relation_type: $i ).

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

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

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

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

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

tff(decl_37,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk3_1: $i > $i ).

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

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

tff(decl_42,type,
    esk6_1: $i > $i ).

tff(decl_43,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_44,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_45,type,
    esk9_1: $i > $i ).

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

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

tff(decl_48,type,
    esk12_0: $i ).

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

fof(p3,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,relation_type(X1,X3))
                 => ( subset(domain_of(X4),X2)
                   => ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

fof(p22,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).

fof(prove_relset_1_15,conjecture,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,relation_type(X1,X3))
                 => ( subset(X1,X2)
                   => ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_15) ).

fof(p1,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ( ( subset(X1,X2)
                  & subset(X2,X3) )
               => subset(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

fof(p2,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,relation_type(X1,X2))
             => ( subset(domain_of(X3),X1)
                & subset(range_of(X3),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(c_0_5,plain,
    ! [X11,X12,X13,X14] :
      ( ~ ilf_type(X11,set_type)
      | ~ ilf_type(X12,set_type)
      | ~ ilf_type(X13,set_type)
      | ~ ilf_type(X14,relation_type(X11,X13))
      | ~ subset(domain_of(X14),X12)
      | ilf_type(X14,relation_type(X12,X13)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])]) ).

fof(c_0_6,plain,
    ! [X60] : ilf_type(X60,set_type),
    inference(variable_rename,[status(thm)],[p22]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( ilf_type(X1,set_type)
       => ! [X2] :
            ( ilf_type(X2,set_type)
           => ! [X3] :
                ( ilf_type(X3,set_type)
               => ! [X4] :
                    ( ilf_type(X4,relation_type(X1,X3))
                   => ( subset(X1,X2)
                     => ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[prove_relset_1_15]) ).

fof(c_0_8,plain,
    ! [X5,X6,X7] :
      ( ~ ilf_type(X5,set_type)
      | ~ ilf_type(X6,set_type)
      | ~ ilf_type(X7,set_type)
      | ~ subset(X5,X6)
      | ~ subset(X6,X7)
      | subset(X5,X7) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).

fof(c_0_9,plain,
    ! [X8,X9,X10] :
      ( ( subset(domain_of(X10),X8)
        | ~ ilf_type(X10,relation_type(X8,X9))
        | ~ ilf_type(X9,set_type)
        | ~ ilf_type(X8,set_type) )
      & ( subset(range_of(X10),X9)
        | ~ ilf_type(X10,relation_type(X8,X9))
        | ~ ilf_type(X9,set_type)
        | ~ ilf_type(X8,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).

cnf(c_0_10,plain,
    ( ilf_type(X4,relation_type(X2,X3))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,relation_type(X1,X3))
    | ~ subset(domain_of(X4),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_12,negated_conjecture,
    ( ilf_type(esk10_0,set_type)
    & ilf_type(esk11_0,set_type)
    & ilf_type(esk12_0,set_type)
    & ilf_type(esk13_0,relation_type(esk10_0,esk12_0))
    & subset(esk10_0,esk11_0)
    & ~ ilf_type(esk13_0,relation_type(esk11_0,esk12_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_13,plain,
    ( subset(X1,X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( subset(domain_of(X1),X2)
    | ~ ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( ilf_type(X1,relation_type(X2,X3))
    | ~ subset(domain_of(X1),X2)
    | ~ ilf_type(X1,relation_type(X4,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]),c_0_11])]) ).

cnf(c_0_16,negated_conjecture,
    ilf_type(esk13_0,relation_type(esk10_0,esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( subset(X1,X2)
    | ~ subset(X3,X2)
    | ~ subset(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_11]),c_0_11])]) ).

cnf(c_0_18,negated_conjecture,
    subset(esk10_0,esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( subset(domain_of(X1),X2)
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_11]),c_0_11])]) ).

cnf(c_0_20,negated_conjecture,
    ( ilf_type(esk13_0,relation_type(X1,esk12_0))
    | ~ subset(domain_of(esk13_0),X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    ( subset(X1,esk11_0)
    | ~ subset(X1,esk10_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    subset(domain_of(esk13_0),esk10_0),
    inference(spm,[status(thm)],[c_0_19,c_0_16]) ).

cnf(c_0_23,negated_conjecture,
    ~ ilf_type(esk13_0,relation_type(esk11_0,esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET653+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 14:15:50 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.44/0.59  start to proof: theBenchmark
% 0.44/0.61  % Version  : CSE_E---1.5
% 0.44/0.61  % Problem  : theBenchmark.p
% 0.44/0.61  % Proof found
% 0.44/0.61  % SZS status Theorem for theBenchmark.p
% 0.44/0.61  % SZS output start Proof
% See solution above
% 0.44/0.62  % Total time : 0.014000 s
% 0.44/0.62  % SZS output end Proof
% 0.44/0.62  % Total time : 0.017000 s
%------------------------------------------------------------------------------