%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 14:32:08 EDT 2023

% Result   : Theorem 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   48 (   8 unt;  19 typ;   0 def)
%            Number of atoms       :   72 (  23 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   67 (  24   ~;  27   |;   9   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  14   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-2 aty)
%            Number of variables   :   50 (   2 sgn;  30   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    power_set: $i > $i ).

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

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

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

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

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

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

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

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

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

tff(decl_35,type,
    esk2_2: ( $i * $i ) > $i ).

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

tff(decl_37,type,
    esk4_0: $i ).

tff(decl_38,type,
    esk5_0: $i ).

tff(decl_39,type,
    esk6_0: $i ).

tff(decl_40,type,
    esk7_0: $i ).

fof(thI50a,conjecture,
    ! [X1,X2,X6,X7] :
      ( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
     => X1 = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI50a) ).

fof(equal_set,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).

fof(subset,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).

fof(unordered_pair,axiom,
    ! [X3,X1,X2] :
      ( member(X3,unordered_pair(X1,X2))
    <=> ( X3 = X1
        | X3 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',unordered_pair) ).

fof(singleton,axiom,
    ! [X3,X1] :
      ( member(X3,singleton(X1))
    <=> X3 = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X6,X7] :
        ( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
       => X1 = X6 ),
    inference(assume_negation,[status(cth)],[thI50a]) ).

fof(c_0_6,plain,
    ! [X14,X15] :
      ( ( subset(X14,X15)
        | ~ equal_set(X14,X15) )
      & ( subset(X15,X14)
        | ~ equal_set(X14,X15) )
      & ( ~ subset(X14,X15)
        | ~ subset(X15,X14)
        | equal_set(X14,X15) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).

fof(c_0_7,negated_conjecture,
    ( equal_set(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0)))
    & esk4_0 != esk6_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( ~ subset(X8,X9)
        | ~ member(X10,X8)
        | member(X10,X9) )
      & ( member(esk1_2(X11,X12),X11)
        | subset(X11,X12) )
      & ( ~ member(esk1_2(X11,X12),X12)
        | subset(X11,X12) ) ),
    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)],[subset])])])])])]) ).

cnf(c_0_9,plain,
    ( subset(X1,X2)
    | ~ equal_set(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    equal_set(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0))),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X30,X31,X32] :
      ( ( ~ member(X30,unordered_pair(X31,X32))
        | X30 = X31
        | X30 = X32 )
      & ( X30 != X31
        | member(X30,unordered_pair(X31,X32)) )
      & ( X30 != X32
        | member(X30,unordered_pair(X31,X32)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])]) ).

cnf(c_0_12,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    subset(unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0)),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    ( member(X1,unordered_pair(X2,X3))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    ( member(X1,unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)))
    | ~ member(X1,unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0))) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,plain,
    member(X1,unordered_pair(X1,X2)),
    inference(er,[status(thm)],[c_0_14]) ).

cnf(c_0_17,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    member(singleton(esk6_0),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

fof(c_0_19,plain,
    ! [X28,X29] :
      ( ( ~ member(X28,singleton(X29))
        | X28 = X29 )
      & ( X28 != X29
        | member(X28,singleton(X29)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).

cnf(c_0_20,negated_conjecture,
    ( unordered_pair(esk4_0,esk5_0) = singleton(esk6_0)
    | singleton(esk6_0) = singleton(esk4_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    ( singleton(esk6_0) = singleton(esk4_0)
    | member(esk4_0,singleton(esk6_0)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    esk4_0 != esk6_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_24,negated_conjecture,
    singleton(esk6_0) = singleton(esk4_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_25,plain,
    ( member(X1,singleton(X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,negated_conjecture,
    ( X1 = esk6_0
    | ~ member(X1,singleton(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_24]) ).

cnf(c_0_27,plain,
    member(X1,singleton(X1)),
    inference(er,[status(thm)],[c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n004.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   : Sat Aug 26 11:06:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.009000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.012000 s
%------------------------------------------------------------------------------