TSTP Solution File: SEU148+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU148+2 : 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 : n006.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 16:22:47 EDT 2023

% Result   : Theorem 0.21s 0.61s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   47 (   8 unt;  27 typ;   0 def)
%            Number of atoms       :   47 (  22 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   45 (  18   ~;  17   |;   5   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   44 (  22   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;   5 con; 0-3 aty)
%            Number of variables   :   32 (   0 sgn;  19   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_26,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

tff(decl_34,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk2_1: $i > $i ).

tff(decl_36,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk9_0: $i ).

tff(decl_43,type,
    esk10_0: $i ).

tff(decl_44,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_45,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_47,type,
    esk14_0: $i ).

tff(decl_48,type,
    esk15_0: $i ).

fof(t6_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( subset(singleton(X1),singleton(X2))
     => X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(t69_enumset1,lemma,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

fof(l2_zfmisc_1,lemma,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(singleton(X1),singleton(X2))
       => X1 = X2 ),
    inference(assume_negation,[status(cth)],[t6_zfmisc_1]) ).

fof(c_0_5,plain,
    ! [X17,X18,X19,X20,X21,X22] :
      ( ( ~ in(X19,X18)
        | X19 = X17
        | X18 != singleton(X17) )
      & ( X20 != X17
        | in(X20,X18)
        | X18 != singleton(X17) )
      & ( ~ in(esk1_2(X21,X22),X22)
        | esk1_2(X21,X22) != X21
        | X22 = singleton(X21) )
      & ( in(esk1_2(X21,X22),X22)
        | esk1_2(X21,X22) = X21
        | X22 = singleton(X21) ) ),
    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)],[d1_tarski])])])])])]) ).

fof(c_0_6,lemma,
    ! [X159] : unordered_pair(X159,X159) = singleton(X159),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_7,lemma,
    ! [X89,X90] :
      ( ( ~ subset(singleton(X89),X90)
        | in(X89,X90) )
      & ( ~ in(X89,X90)
        | subset(singleton(X89),X90) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).

fof(c_0_8,negated_conjecture,
    ( subset(singleton(esk14_0),singleton(esk15_0))
    & esk14_0 != esk15_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_9,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,lemma,
    ( in(X1,X2)
    | ~ subset(singleton(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    subset(singleton(esk14_0),singleton(esk15_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( X1 = X3
    | X2 != unordered_pair(X3,X3)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,lemma,
    ( in(X1,X2)
    | ~ subset(unordered_pair(X1,X1),X2) ),
    inference(rw,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    subset(unordered_pair(esk14_0,esk14_0),unordered_pair(esk15_0,esk15_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_10]),c_0_10]) ).

cnf(c_0_16,plain,
    ( X1 = X2
    | ~ in(X1,unordered_pair(X2,X2)) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    in(esk14_0,unordered_pair(esk15_0,esk15_0)),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    esk14_0 != esk15_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_19,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU148+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Wed Aug 23 23:52:52 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 0.21/0.61  % Version  : CSE_E---1.5
% 0.21/0.61  % Problem  : theBenchmark.p
% 0.21/0.61  % Proof found
% 0.21/0.61  % SZS status Theorem for theBenchmark.p
% 0.21/0.61  % SZS output start Proof
% See solution above
% 0.21/0.61  % Total time : 0.013000 s
% 0.21/0.61  % SZS output end Proof
% 0.21/0.61  % Total time : 0.015000 s
%------------------------------------------------------------------------------