%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU186+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 : n023.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 16:23:09 EDT 2023

% Result   : Theorem 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   50 (  16 unt;  17 typ;   0 def)
%            Number of atoms       :   67 (  19 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   63 (  29   ~;  22   |;   5   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  11   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :   58 (   4 sgn;  33   !;   1   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    singleton: $i > $i ).

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

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

tff(decl_30,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_31,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    esk3_1: $i > $i ).

tff(decl_33,type,
    esk4_1: $i > $i ).

tff(decl_34,type,
    esk5_0: $i ).

tff(decl_35,type,
    esk6_0: $i ).

tff(decl_36,type,
    esk7_0: $i ).

tff(decl_37,type,
    esk8_0: $i ).

tff(decl_38,type,
    esk9_0: $i ).

fof(t56_relat_1,conjecture,
    ! [X1] :
      ( relation(X1)
     => ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
       => X1 = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(d1_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
    <=> ! [X2] :
          ~ ( in(X2,X1)
            & ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).

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(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( relation(X1)
       => ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
         => X1 = empty_set ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t56_relat_1])]) ).

fof(c_0_8,negated_conjecture,
    ! [X36,X37] :
      ( relation(esk9_0)
      & ~ in(ordered_pair(X36,X37),esk9_0)
      & esk9_0 != empty_set ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).

fof(c_0_9,plain,
    ! [X18,X19] : ordered_pair(X18,X19) = unordered_pair(unordered_pair(X18,X19),singleton(X18)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_10,plain,
    ! [X10,X11,X14,X16,X17] :
      ( ( ~ relation(X10)
        | ~ in(X11,X10)
        | X11 = ordered_pair(esk1_2(X10,X11),esk2_2(X10,X11)) )
      & ( in(esk3_1(X14),X14)
        | relation(X14) )
      & ( esk3_1(X14) != ordered_pair(X16,X17)
        | relation(X14) ) ),
    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_relat_1])])])])])]) ).

cnf(c_0_11,negated_conjecture,
    ~ in(ordered_pair(X1,X2),esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_13,plain,
    ! [X8,X9] : unordered_pair(X8,X9) = unordered_pair(X9,X8),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_14,plain,
    ( X2 = ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))
    | ~ relation(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk9_0),
    inference(rw,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    ( X2 = unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2)))
    | ~ relation(X1)
    | ~ in(X2,X1) ),
    inference(rw,[status(thm)],[c_0_14,c_0_12]) ).

fof(c_0_18,plain,
    ! [X33,X34] :
      ( ~ element(X33,X34)
      | empty(X34)
      | in(X33,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

fof(c_0_19,plain,
    ! [X20] : element(esk4_1(X20),X20),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

cnf(c_0_20,negated_conjecture,
    ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk9_0),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,plain,
    ( unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))) = X2
    | ~ relation(X1)
    | ~ in(X2,X1) ),
    inference(rw,[status(thm)],[c_0_17,c_0_16]) ).

cnf(c_0_22,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,plain,
    element(esk4_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ relation(X1)
    | ~ in(X2,esk9_0)
    | ~ in(X2,X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,plain,
    ( empty(X1)
    | in(esk4_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_26,plain,
    ! [X38] :
      ( ~ empty(X38)
      | X38 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

cnf(c_0_27,negated_conjecture,
    ( empty(esk9_0)
    | ~ relation(X1)
    | ~ in(esk4_1(esk9_0),X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    relation(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_29,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_30,negated_conjecture,
    empty(esk9_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_28])]) ).

cnf(c_0_31,negated_conjecture,
    esk9_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU186+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n023.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 17:32:28 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.009000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.012000 s
%------------------------------------------------------------------------------