TSTP Solution File: SEU104+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n003.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 16:22:27 EDT 2023

% Result   : Theorem 0.17s 0.61s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   59 (   7 unt;  34 typ;   0 def)
%            Number of atoms       :   79 (   3 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :   94 (  40   ~;  32   |;  11   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  28   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   6 con; 0-2 aty)
%            Number of variables   :   35 (   0 sgn;  23   !;   0   ?;   0   :)

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

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

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

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

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

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

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

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

tff(decl_30,type,
    set_union2: ( $i * $i ) > $i ).

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

tff(decl_32,type,
    set_difference: ( $i * $i ) > $i ).

tff(decl_33,type,
    empty_set: $i ).

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

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

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

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

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

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

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

tff(decl_41,type,
    natural: $i > $o ).

tff(decl_42,type,
    subset: ( $i * $i ) > $o ).

tff(decl_43,type,
    esk1_1: $i > $i ).

tff(decl_44,type,
    esk2_0: $i ).

tff(decl_45,type,
    esk3_0: $i ).

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

tff(decl_47,type,
    esk5_0: $i ).

tff(decl_48,type,
    esk6_1: $i > $i ).

tff(decl_49,type,
    esk7_1: $i > $i ).

tff(decl_50,type,
    esk8_0: $i ).

tff(decl_51,type,
    esk9_1: $i > $i ).

tff(decl_52,type,
    esk10_1: $i > $i ).

tff(decl_53,type,
    esk11_1: $i > $i ).

tff(decl_54,type,
    esk12_1: $i > $i ).

tff(decl_55,type,
    esk13_0: $i ).

fof(t10_finsub_1,axiom,
    ! [X1] :
      ( preboolean(X1)
    <=> ! [X2,X3] :
          ( ( in(X2,X1)
            & in(X3,X1) )
         => ( in(set_union2(X2,X3),X1)
            & in(set_difference(X2,X3),X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).

fof(t98_xboole_1,axiom,
    ! [X1,X2] : set_union2(X1,X2) = symmetric_difference(X1,set_difference(X2,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_xboole_1) ).

fof(t15_finsub_1,conjecture,
    ! [X1] :
      ( ~ empty(X1)
     => ( ! [X2] :
            ( element(X2,X1)
           => ! [X3] :
                ( element(X3,X1)
               => ( in(symmetric_difference(X2,X3),X1)
                  & in(set_difference(X2,X3),X1) ) ) )
       => preboolean(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finsub_1) ).

fof(t1_subset,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => element(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

fof(c_0_4,plain,
    ! [X46,X47,X48,X49] :
      ( ( in(set_union2(X47,X48),X46)
        | ~ in(X47,X46)
        | ~ in(X48,X46)
        | ~ preboolean(X46) )
      & ( in(set_difference(X47,X48),X46)
        | ~ in(X47,X46)
        | ~ in(X48,X46)
        | ~ preboolean(X46) )
      & ( in(esk11_1(X49),X49)
        | preboolean(X49) )
      & ( in(esk12_1(X49),X49)
        | preboolean(X49) )
      & ( ~ in(set_union2(esk11_1(X49),esk12_1(X49)),X49)
        | ~ in(set_difference(esk11_1(X49),esk12_1(X49)),X49)
        | preboolean(X49) ) ),
    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)],[t10_finsub_1])])])])])]) ).

fof(c_0_5,plain,
    ! [X76,X77] : set_union2(X76,X77) = symmetric_difference(X76,set_difference(X77,X76)),
    inference(variable_rename,[status(thm)],[t98_xboole_1]) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( ~ empty(X1)
       => ( ! [X2] :
              ( element(X2,X1)
             => ! [X3] :
                  ( element(X3,X1)
                 => ( in(symmetric_difference(X2,X3),X1)
                    & in(set_difference(X2,X3),X1) ) ) )
         => preboolean(X1) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t15_finsub_1])]) ).

cnf(c_0_7,plain,
    ( preboolean(X1)
    | ~ in(set_union2(esk11_1(X1),esk12_1(X1)),X1)
    | ~ in(set_difference(esk11_1(X1),esk12_1(X1)),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    set_union2(X1,X2) = symmetric_difference(X1,set_difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_9,negated_conjecture,
    ! [X53,X54] :
      ( ~ empty(esk13_0)
      & ( in(symmetric_difference(X53,X54),esk13_0)
        | ~ element(X54,esk13_0)
        | ~ element(X53,esk13_0) )
      & ( in(set_difference(X53,X54),esk13_0)
        | ~ element(X54,esk13_0)
        | ~ element(X53,esk13_0) )
      & ~ preboolean(esk13_0) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).

cnf(c_0_10,plain,
    ( preboolean(X1)
    | ~ in(set_difference(esk11_1(X1),esk12_1(X1)),X1)
    | ~ in(symmetric_difference(esk11_1(X1),set_difference(esk12_1(X1),esk11_1(X1))),X1) ),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    ( in(symmetric_difference(X1,X2),esk13_0)
    | ~ element(X2,esk13_0)
    | ~ element(X1,esk13_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    ~ preboolean(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_13,plain,
    ! [X56,X57] :
      ( ~ in(X56,X57)
      | element(X56,X57) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).

cnf(c_0_14,negated_conjecture,
    ( ~ element(set_difference(esk12_1(esk13_0),esk11_1(esk13_0)),esk13_0)
    | ~ element(esk11_1(esk13_0),esk13_0)
    | ~ in(set_difference(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).

cnf(c_0_15,plain,
    ( element(X1,X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    ( ~ element(esk11_1(esk13_0),esk13_0)
    | ~ in(set_difference(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0)
    | ~ in(set_difference(esk12_1(esk13_0),esk11_1(esk13_0)),esk13_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,negated_conjecture,
    ( in(set_difference(X1,X2),esk13_0)
    | ~ element(X2,esk13_0)
    | ~ element(X1,esk13_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_18,negated_conjecture,
    ( ~ element(esk11_1(esk13_0),esk13_0)
    | ~ element(esk12_1(esk13_0),esk13_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ element(esk11_1(esk13_0),esk13_0)
    | ~ in(esk12_1(esk13_0),esk13_0) ),
    inference(spm,[status(thm)],[c_0_18,c_0_15]) ).

cnf(c_0_20,plain,
    ( in(esk12_1(X1),X1)
    | preboolean(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_21,negated_conjecture,
    ~ element(esk11_1(esk13_0),esk13_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_12]) ).

cnf(c_0_22,negated_conjecture,
    ~ in(esk11_1(esk13_0),esk13_0),
    inference(spm,[status(thm)],[c_0_21,c_0_15]) ).

cnf(c_0_23,plain,
    ( in(esk11_1(X1),X1)
    | preboolean(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Aug 23 15:37:07 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.17/0.57  start to proof: theBenchmark
% 0.17/0.61  % Version  : CSE_E---1.5
% 0.17/0.61  % Problem  : theBenchmark.p
% 0.17/0.61  % Proof found
% 0.17/0.61  % SZS status Theorem for theBenchmark.p
% 0.17/0.61  % SZS output start Proof
% See solution above
% 0.17/0.62  % Total time : 0.026000 s
% 0.17/0.62  % SZS output end Proof
% 0.17/0.62  % Total time : 0.028000 s
%------------------------------------------------------------------------------