TSTP Solution File: SEU149+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU149+3 : 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 : 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 16:22:48 EDT 2023

% Result   : Theorem 0.20s 0.56s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   36 (  11 unt;  11 typ;   0 def)
%            Number of atoms       :   76 (  53 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :   81 (  30   ~;  36   |;   9   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    2 (   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   :   56 (   2 sgn;  31   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    singleton: $i > $i ).

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

tff(decl_26,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_28,type,
    esk3_0: $i ).

tff(decl_29,type,
    esk4_0: $i ).

tff(decl_30,type,
    esk5_0: $i ).

tff(decl_31,type,
    esk6_0: $i ).

tff(decl_32,type,
    esk7_0: $i ).

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(t8_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ( singleton(X1) = unordered_pair(X2,X3)
     => X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).

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

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(c_0_4,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( ~ in(X11,X10)
        | X11 = X9
        | X10 != singleton(X9) )
      & ( X12 != X9
        | in(X12,X10)
        | X10 != singleton(X9) )
      & ( ~ in(esk1_2(X13,X14),X14)
        | esk1_2(X13,X14) != X13
        | X14 = singleton(X13) )
      & ( in(esk1_2(X13,X14),X14)
        | esk1_2(X13,X14) = X13
        | X14 = singleton(X13) ) ),
    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_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( singleton(X1) = unordered_pair(X2,X3)
       => X1 = X2 ),
    inference(assume_negation,[status(cth)],[t8_zfmisc_1]) ).

fof(c_0_6,plain,
    ! [X16,X17,X18,X19,X20,X21,X22,X23] :
      ( ( ~ in(X19,X18)
        | X19 = X16
        | X19 = X17
        | X18 != unordered_pair(X16,X17) )
      & ( X20 != X16
        | in(X20,X18)
        | X18 != unordered_pair(X16,X17) )
      & ( X20 != X17
        | in(X20,X18)
        | X18 != unordered_pair(X16,X17) )
      & ( esk2_3(X21,X22,X23) != X21
        | ~ in(esk2_3(X21,X22,X23),X23)
        | X23 = unordered_pair(X21,X22) )
      & ( esk2_3(X21,X22,X23) != X22
        | ~ in(esk2_3(X21,X22,X23),X23)
        | X23 = unordered_pair(X21,X22) )
      & ( in(esk2_3(X21,X22,X23),X23)
        | esk2_3(X21,X22,X23) = X21
        | esk2_3(X21,X22,X23) = X22
        | X23 = unordered_pair(X21,X22) ) ),
    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])])])])])]) ).

cnf(c_0_7,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_8,negated_conjecture,
    ( singleton(esk5_0) = unordered_pair(esk6_0,esk7_0)
    & esk5_0 != esk6_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_9,plain,
    ( X1 = X3
    | X1 = X4
    | ~ in(X1,X2)
    | X2 != unordered_pair(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_7])]) ).

cnf(c_0_11,negated_conjecture,
    singleton(esk5_0) = unordered_pair(esk6_0,esk7_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | X1 = X3
    | ~ in(X1,unordered_pair(X3,X2)) ),
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    in(esk5_0,unordered_pair(esk6_0,esk7_0)),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    esk5_0 != esk6_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_15,plain,
    ! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_16,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_17,negated_conjecture,
    esk7_0 = esk5_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_18,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    ( X1 = X2
    | ~ in(X1,singleton(X2)) ),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    singleton(esk5_0) = unordered_pair(esk5_0,esk6_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_17]),c_0_18]) ).

cnf(c_0_21,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != unordered_pair(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,negated_conjecture,
    ( X1 = esk5_0
    | ~ in(X1,unordered_pair(esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,plain,
    in(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU149+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n006.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 21:55:23 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 0.20/0.56  % Version  : CSE_E---1.5
% 0.20/0.56  % Problem  : theBenchmark.p
% 0.20/0.56  % Proof found
% 0.20/0.56  % SZS status Theorem for theBenchmark.p
% 0.20/0.56  % SZS output start Proof
% See solution above
% 0.20/0.56  % Total time : 0.007000 s
% 0.20/0.56  % SZS output end Proof
% 0.20/0.56  % Total time : 0.010000 s
%------------------------------------------------------------------------------