TSTP Solution File: SEU156+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU156+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 : n015.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 16:22:52 EDT 2023

% Result   : Theorem 0.22s 0.60s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   57 (  20 unt;  11 typ;   0 def)
%            Number of atoms       :   84 (  83 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   65 (  27   ~;  29   |;   5   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   78 (   9 sgn;  38   !;   0   ?;   0   :)

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

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

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

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

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

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 ).

tff(decl_31,type,
    esk5_0: $i ).

tff(decl_32,type,
    esk6_0: $i ).

fof(t33_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( ordered_pair(X1,X2) = ordered_pair(X3,X4)
     => ( X1 = X3
        & X2 = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_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(t69_enumset1,axiom,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

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(t10_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
        & X1 != X3
        & X1 != X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).

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

fof(t9_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( singleton(X1) = unordered_pair(X2,X3)
     => X2 = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ordered_pair(X1,X2) = ordered_pair(X3,X4)
       => ( X1 = X3
          & X2 = X4 ) ),
    inference(assume_negation,[status(cth)],[t33_zfmisc_1]) ).

fof(c_0_8,plain,
    ! [X7,X8] : ordered_pair(X7,X8) = unordered_pair(unordered_pair(X7,X8),singleton(X7)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_9,plain,
    ! [X22] : unordered_pair(X22,X22) = singleton(X22),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_10,negated_conjecture,
    ( ordered_pair(esk3_0,esk4_0) = ordered_pair(esk5_0,esk6_0)
    & ( esk3_0 != esk5_0
      | esk4_0 != esk6_0 ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_11,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

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

cnf(c_0_13,negated_conjecture,
    ordered_pair(esk3_0,esk4_0) = ordered_pair(esk5_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
    inference(rw,[status(thm)],[c_0_11,c_0_12]) ).

fof(c_0_15,plain,
    ! [X5,X6] : unordered_pair(X5,X6) = unordered_pair(X6,X5),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

fof(c_0_16,plain,
    ! [X14,X15,X16,X17] :
      ( unordered_pair(X14,X15) != unordered_pair(X16,X17)
      | X14 = X16
      | X14 = X17 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).

cnf(c_0_17,negated_conjecture,
    unordered_pair(unordered_pair(esk5_0,esk6_0),unordered_pair(esk5_0,esk5_0)) = unordered_pair(unordered_pair(esk3_0,esk4_0),unordered_pair(esk3_0,esk3_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).

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

fof(c_0_19,plain,
    ! [X25,X26,X27] :
      ( singleton(X25) != unordered_pair(X26,X27)
      | X25 = X26 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).

cnf(c_0_20,plain,
    ( X1 = X3
    | X1 = X4
    | unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    unordered_pair(unordered_pair(esk3_0,esk3_0),unordered_pair(esk3_0,esk4_0)) = unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).

cnf(c_0_22,plain,
    ( X1 = X2
    | singleton(X1) != unordered_pair(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    ( X1 = unordered_pair(esk3_0,esk3_0)
    | X1 = unordered_pair(esk3_0,esk4_0)
    | unordered_pair(X1,X2) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,plain,
    ( X1 = X2
    | unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
    inference(rw,[status(thm)],[c_0_22,c_0_12]) ).

cnf(c_0_25,negated_conjecture,
    ( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk5_0,esk5_0)
    | unordered_pair(esk3_0,esk3_0) = unordered_pair(esk5_0,esk5_0) ),
    inference(er,[status(thm)],[c_0_23]) ).

cnf(c_0_26,negated_conjecture,
    ( X1 = unordered_pair(esk3_0,esk4_0)
    | X1 = unordered_pair(esk3_0,esk3_0)
    | unordered_pair(X2,X1) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_18]) ).

cnf(c_0_27,negated_conjecture,
    ( unordered_pair(esk3_0,esk3_0) = unordered_pair(esk5_0,esk5_0)
    | X1 = esk3_0
    | unordered_pair(X1,X1) != unordered_pair(esk5_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,plain,
    ( X1 = X2
    | unordered_pair(X1,X1) != unordered_pair(X3,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_18]) ).

fof(c_0_29,plain,
    ! [X28,X29,X30] :
      ( singleton(X28) != unordered_pair(X29,X30)
      | X29 = X30 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).

cnf(c_0_30,negated_conjecture,
    ( unordered_pair(esk3_0,esk3_0) = unordered_pair(esk5_0,esk6_0)
    | unordered_pair(esk3_0,esk4_0) = unordered_pair(esk5_0,esk6_0) ),
    inference(er,[status(thm)],[c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    esk3_0 = esk5_0,
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_28]) ).

cnf(c_0_32,plain,
    ( X2 = X3
    | singleton(X1) != unordered_pair(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_33,plain,
    ( X1 = X2
    | X1 = X3
    | unordered_pair(X4,X1) != unordered_pair(X2,X3) ),
    inference(spm,[status(thm)],[c_0_20,c_0_18]) ).

cnf(c_0_34,negated_conjecture,
    ( unordered_pair(esk5_0,esk4_0) = unordered_pair(esk5_0,esk6_0)
    | unordered_pair(esk5_0,esk6_0) = unordered_pair(esk5_0,esk5_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    ( esk3_0 != esk5_0
    | esk4_0 != esk6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_36,plain,
    ( X2 = X3
    | unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
    inference(rw,[status(thm)],[c_0_32,c_0_12]) ).

cnf(c_0_37,negated_conjecture,
    ( unordered_pair(esk5_0,esk6_0) = unordered_pair(esk5_0,esk5_0)
    | X1 = esk4_0
    | X1 = esk5_0
    | unordered_pair(X2,X1) != unordered_pair(esk5_0,esk6_0) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    esk4_0 != esk6_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_31])]) ).

cnf(c_0_39,negated_conjecture,
    ( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk3_0,esk3_0)
    | unordered_pair(X1,X1) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_21]) ).

cnf(c_0_40,negated_conjecture,
    esk6_0 = esk5_0,
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_37]),c_0_38]),c_0_28]) ).

cnf(c_0_41,negated_conjecture,
    ( unordered_pair(esk5_0,esk4_0) = unordered_pair(esk5_0,esk5_0)
    | unordered_pair(X1,X1) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk5_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_31]),c_0_31]),c_0_31]),c_0_40]) ).

cnf(c_0_42,negated_conjecture,
    unordered_pair(esk5_0,esk4_0) = unordered_pair(esk5_0,esk5_0),
    inference(er,[status(thm)],[c_0_41]) ).

cnf(c_0_43,negated_conjecture,
    esk4_0 != esk5_0,
    inference(rw,[status(thm)],[c_0_38,c_0_40]) ).

cnf(c_0_44,negated_conjecture,
    unordered_pair(X1,X1) != unordered_pair(esk5_0,esk5_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_42]),c_0_43]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(er,[status(thm)],[c_0_44]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU156+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
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Wed Aug 23 14:03:04 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.22/0.57  start to proof: theBenchmark
% 0.22/0.60  % Version  : CSE_E---1.5
% 0.22/0.60  % Problem  : theBenchmark.p
% 0.22/0.60  % Proof found
% 0.22/0.60  % SZS status Theorem for theBenchmark.p
% 0.22/0.60  % SZS output start Proof
% See solution above
% 0.22/0.60  % Total time : 0.016000 s
% 0.22/0.60  % SZS output end Proof
% 0.22/0.60  % Total time : 0.019000 s
%------------------------------------------------------------------------------