%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET891+1 : 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 : n013.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 14:36:10 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   21 (  12 unt;   9 typ;   0 def)
%            Number of atoms       :   12 (  11 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn;  12   !;   0   ?;   0   :)

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

tff(decl_23,type,
    set_union2: ( $i * $i ) > $i ).

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

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

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

tff(decl_27,type,
    esk1_0: $i ).

tff(decl_28,type,
    esk2_0: $i ).

tff(decl_29,type,
    esk3_0: $i ).

tff(decl_30,type,
    esk4_0: $i ).

fof(t32_zfmisc_1,conjecture,
    ! [X1,X2] : union(unordered_pair(singleton(X1),singleton(X2))) = unordered_pair(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_zfmisc_1) ).

fof(t41_enumset1,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).

fof(l52_zfmisc_1,axiom,
    ! [X1,X2] : union(unordered_pair(X1,X2)) = set_union2(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l52_zfmisc_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] : union(unordered_pair(singleton(X1),singleton(X2))) = unordered_pair(X1,X2),
    inference(assume_negation,[status(cth)],[t32_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X18,X19] : unordered_pair(X18,X19) = set_union2(singleton(X18),singleton(X19)),
    inference(variable_rename,[status(thm)],[t41_enumset1]) ).

fof(c_0_5,plain,
    ! [X12,X13] : union(unordered_pair(X12,X13)) = set_union2(X12,X13),
    inference(variable_rename,[status(thm)],[l52_zfmisc_1]) ).

fof(c_0_6,negated_conjecture,
    union(unordered_pair(singleton(esk3_0),singleton(esk4_0))) != unordered_pair(esk3_0,esk4_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_7,plain,
    unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    union(unordered_pair(X1,X2)) = set_union2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    union(unordered_pair(singleton(esk3_0),singleton(esk4_0))) != unordered_pair(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    unordered_pair(X1,X2) = union(unordered_pair(singleton(X1),singleton(X2))),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET891+1 : 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
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 12:50:47 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.006000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.008000 s
%------------------------------------------------------------------------------