TSTP Solution File: SET881+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET881+1 : 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 : n007.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 14:36:07 EDT 2023

% Result   : Theorem 0.21s 0.59s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   24 (   7 unt;  11 typ;   0 def)
%            Number of atoms       :   42 (  28 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :   47 (  18   ~;  20   |;   6   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   30 (   3 sgn;  20   !;   0   ?;   0   :)

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

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

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

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

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

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

tff(decl_28,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_29,type,
    esk2_0: $i ).

tff(decl_30,type,
    esk3_0: $i ).

tff(decl_31,type,
    esk4_0: $i ).

tff(decl_32,type,
    esk5_0: $i ).

fof(d2_tarski,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(t22_zfmisc_1,conjecture,
    ! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).

fof(l36_zfmisc_1,axiom,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = empty_set
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).

fof(c_0_3,plain,
    ! [X9,X10,X11,X12,X13,X14,X15,X16] :
      ( ( ~ in(X12,X11)
        | X12 = X9
        | X12 = X10
        | X11 != unordered_pair(X9,X10) )
      & ( X13 != X9
        | in(X13,X11)
        | X11 != unordered_pair(X9,X10) )
      & ( X13 != X10
        | in(X13,X11)
        | X11 != unordered_pair(X9,X10) )
      & ( esk1_3(X14,X15,X16) != X14
        | ~ in(esk1_3(X14,X15,X16),X16)
        | X16 = unordered_pair(X14,X15) )
      & ( esk1_3(X14,X15,X16) != X15
        | ~ in(esk1_3(X14,X15,X16),X16)
        | X16 = unordered_pair(X14,X15) )
      & ( in(esk1_3(X14,X15,X16),X16)
        | esk1_3(X14,X15,X16) = X14
        | esk1_3(X14,X15,X16) = X15
        | X16 = unordered_pair(X14,X15) ) ),
    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)],[d2_tarski])])])])])]) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
    inference(assume_negation,[status(cth)],[t22_zfmisc_1]) ).

fof(c_0_5,plain,
    ! [X18,X19] :
      ( ( set_difference(singleton(X18),X19) != empty_set
        | in(X18,X19) )
      & ( ~ in(X18,X19)
        | set_difference(singleton(X18),X19) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l36_zfmisc_1])]) ).

cnf(c_0_6,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != unordered_pair(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

fof(c_0_7,negated_conjecture,
    set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != empty_set,
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_8,plain,
    ( set_difference(singleton(X1),X2) = empty_set
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    in(X1,unordered_pair(X1,X2)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6])]) ).

cnf(c_0_10,negated_conjecture,
    set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat Aug 26 11:57:11 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.59  % Version  : CSE_E---1.5
% 0.21/0.59  % Problem  : theBenchmark.p
% 0.21/0.59  % Proof found
% 0.21/0.59  % SZS status Theorem for theBenchmark.p
% 0.21/0.59  % SZS output start Proof
% See solution above
% 0.21/0.59  % Total time : 0.004000 s
% 0.21/0.59  % SZS output end Proof
% 0.21/0.59  % Total time : 0.006000 s
%------------------------------------------------------------------------------