TSTP Solution File: SEU321+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n028.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 16:24:25 EDT 2023

% Result   : Theorem 0.20s 0.62s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   57 (   8 unt;  28 typ;   0 def)
%            Number of atoms       :   89 (   7 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   98 (  38   ~;  26   |;  15   &)
%                                         (   2 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  21   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :   33 (   0 sgn;  24   !;   0   ?;   0   :)

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

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

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

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

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

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

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

tff(decl_29,type,
    v5_membered: $i > $o ).

tff(decl_30,type,
    v4_membered: $i > $o ).

tff(decl_31,type,
    v3_membered: $i > $o ).

tff(decl_32,type,
    v2_membered: $i > $o ).

tff(decl_33,type,
    v1_membered: $i > $o ).

tff(decl_34,type,
    v1_xcmplx_0: $i > $o ).

tff(decl_35,type,
    v1_xreal_0: $i > $o ).

tff(decl_36,type,
    v1_rat_1: $i > $o ).

tff(decl_37,type,
    v1_int_1: $i > $o ).

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

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

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

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

tff(decl_42,type,
    esk1_1: $i > $i ).

tff(decl_43,type,
    esk2_0: $i ).

tff(decl_44,type,
    esk3_0: $i ).

tff(decl_45,type,
    esk4_1: $i > $i ).

tff(decl_46,type,
    esk5_0: $i ).

tff(decl_47,type,
    esk6_0: $i ).

tff(decl_48,type,
    esk7_0: $i ).

tff(decl_49,type,
    esk8_0: $i ).

fof(t50_subset_1,axiom,
    ! [X1] :
      ( X1 != empty_set
     => ! [X2] :
          ( element(X2,powerset(X1))
         => ! [X3] :
              ( element(X3,X1)
             => ( ~ in(X3,X2)
               => in(X3,subset_complement(X1,X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).

fof(l40_tops_1,conjecture,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ( in(X3,subset_complement(the_carrier(X1),X2))
              <=> ~ in(X3,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).

fof(fc1_struct_0,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(the_carrier(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).

fof(t54_subset_1,axiom,
    ! [X1,X2,X3] :
      ( element(X3,powerset(X1))
     => ~ ( in(X2,subset_complement(X1,X3))
          & in(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).

fof(fc6_membered,axiom,
    ( empty(empty_set)
    & v1_membered(empty_set)
    & v2_membered(empty_set)
    & v3_membered(empty_set)
    & v4_membered(empty_set)
    & v5_membered(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).

fof(c_0_5,plain,
    ! [X1] :
      ( X1 != empty_set
     => ! [X2] :
          ( element(X2,powerset(X1))
         => ! [X3] :
              ( element(X3,X1)
             => ( ~ in(X3,X2)
               => in(X3,subset_complement(X1,X2)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[t50_subset_1]) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( element(X2,powerset(the_carrier(X1)))
           => ! [X3] :
                ( element(X3,the_carrier(X1))
               => ( in(X3,subset_complement(the_carrier(X1),X2))
                <=> ~ in(X3,X2) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l40_tops_1])]) ).

fof(c_0_7,plain,
    ! [X64,X65,X66] :
      ( X64 = empty_set
      | ~ element(X65,powerset(X64))
      | ~ element(X66,X64)
      | in(X66,X65)
      | in(X66,subset_complement(X64,X65)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,negated_conjecture,
    ( ~ empty_carrier(esk6_0)
    & one_sorted_str(esk6_0)
    & element(esk7_0,powerset(the_carrier(esk6_0)))
    & element(esk8_0,the_carrier(esk6_0))
    & ( ~ in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0))
      | in(esk8_0,esk7_0) )
    & ( in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0))
      | ~ in(esk8_0,esk7_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

cnf(c_0_9,plain,
    ( X1 = empty_set
    | in(X3,X2)
    | in(X3,subset_complement(X1,X2))
    | ~ element(X2,powerset(X1))
    | ~ element(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    element(esk8_0,the_carrier(esk6_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_11,plain,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(the_carrier(X1)) ),
    inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).

cnf(c_0_12,negated_conjecture,
    ( the_carrier(esk6_0) = empty_set
    | in(esk8_0,subset_complement(the_carrier(esk6_0),X1))
    | in(esk8_0,X1)
    | ~ element(X1,powerset(the_carrier(esk6_0))) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    element(esk7_0,powerset(the_carrier(esk6_0))),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ( in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0))
    | ~ in(esk8_0,esk7_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_15,plain,
    ! [X67,X68,X69] :
      ( ~ element(X69,powerset(X67))
      | ~ in(X68,subset_complement(X67,X69))
      | ~ in(X68,X69) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_subset_1])]) ).

fof(c_0_16,plain,
    ! [X50] :
      ( empty_carrier(X50)
      | ~ one_sorted_str(X50)
      | ~ empty(the_carrier(X50)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).

cnf(c_0_17,negated_conjecture,
    ( in(esk8_0,esk7_0)
    | ~ in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_18,negated_conjecture,
    ( the_carrier(esk6_0) = empty_set
    | in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_19,plain,
    ( ~ element(X1,powerset(X2))
    | ~ in(X3,subset_complement(X2,X1))
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,plain,
    ( empty_carrier(X1)
    | ~ one_sorted_str(X1)
    | ~ empty(the_carrier(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    ( the_carrier(esk6_0) = empty_set
    | in(esk8_0,esk7_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[fc6_membered]) ).

cnf(c_0_23,negated_conjecture,
    one_sorted_str(esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_24,negated_conjecture,
    ~ empty_carrier(esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ in(X1,subset_complement(the_carrier(esk6_0),esk7_0))
    | ~ in(X1,esk7_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_13]) ).

cnf(c_0_26,negated_conjecture,
    in(esk8_0,esk7_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).

cnf(c_0_27,negated_conjecture,
    ~ in(esk8_0,subset_complement(the_carrier(esk6_0),esk7_0)),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_26])]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n028.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 21:46:49 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 0.20/0.62  % Version  : CSE_E---1.5
% 0.20/0.62  % Problem  : theBenchmark.p
% 0.20/0.62  % Proof found
% 0.20/0.62  % SZS status Theorem for theBenchmark.p
% 0.20/0.62  % SZS output start Proof
% See solution above
% 0.20/0.63  % Total time : 0.065000 s
% 0.20/0.63  % SZS output end Proof
% 0.20/0.63  % Total time : 0.069000 s
%------------------------------------------------------------------------------