TSTP Solution File: GEO511+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO511+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 : Wed Aug 30 22:48:28 EDT 2023

% Result   : Theorem 178.62s 178.60s
% Output   : CNFRefutation 178.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   54
% Syntax   : Number of formulae    :   99 (  21 unt;  46 typ;   0 def)
%            Number of atoms       :  180 (  32 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  252 ( 125   ~; 121   |;   6   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  153 (  36   >; 117   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-8 aty)
%            Number of functors    :   32 (  32 usr;  10 con; 0-6 aty)
%            Number of variables   :  153 (   0 sgn;  89   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    alpha: $i ).

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

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

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

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

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

tff(decl_32,type,
    s_e3: ( $i * $i * $i * $i * $i * $i ) > $o ).

tff(decl_33,type,
    s_col: ( $i * $i * $i ) > $o ).

tff(decl_34,type,
    insert5: ( $i * $i * $i * $i * $i ) > $i ).

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

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

tff(decl_37,type,
    ins: ( $i * $i * $i * $i ) > $i ).

tff(decl_38,type,
    sameside: ( $i * $i * $i ) > $o ).

tff(decl_39,type,
    c63: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    pointOffLine: ( $i * $i ) > $i ).

tff(decl_41,type,
    s_m: ( $i * $i * $i ) > $o ).

tff(decl_42,type,
    s: ( $i * $i ) > $i ).

tff(decl_43,type,
    s_kf: ( $i * $i * $i * $i * $i * $i * $i ) > $o ).

tff(decl_44,type,
    isomidpoint: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    s_r: ( $i * $i * $i ) > $o ).

tff(decl_46,type,
    perpAt: ( $i * $i * $i * $i * $i ) > $o ).

tff(decl_47,type,
    perp: ( $i * $i * $i * $i ) > $o ).

tff(decl_48,type,
    f813: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_49,type,
    g813: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_50,type,
    il: ( $i * $i * $i * $i ) > $i ).

tff(decl_51,type,
    foot: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    erect21a: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    erectAux21a: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    erect: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    erectAux: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    midpointAux: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_57,type,
    midpoint: ( $i * $i ) > $i ).

tff(decl_58,type,
    s_afs: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).

tff(decl_59,type,
    xb: $i ).

tff(decl_60,type,
    f811: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_61,type,
    g811: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk1_0: $i ).

tff(decl_63,type,
    esk2_0: $i ).

tff(decl_64,type,
    esk3_0: $i ).

tff(decl_65,type,
    esk4_0: $i ).

tff(decl_66,type,
    esk5_0: $i ).

tff(decl_67,type,
    esk6_0: $i ).

fof(aSatz8_24a,axiom,
    ! [X13,X12,X15,X16,X36,X27,X34] :
      ( ~ perp(X13,X12,X12,X15)
      | ~ perp(X16,X15,X12,X15)
      | ~ s_col(X12,X15,X36)
      | ~ s_t(X13,X36,X16)
      | ~ s_t(X15,X27,X16)
      | ~ s_e(X12,X13,X15,X27)
      | X34 != ip(X13,X36,X16,X15,X27)
      | s_m(X12,X34,X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24a) ).

fof(aSatz8_24b,axiom,
    ! [X13,X12,X15,X16,X36,X27,X34] :
      ( ~ perp(X13,X12,X12,X15)
      | ~ perp(X16,X15,X12,X15)
      | ~ s_col(X12,X15,X36)
      | ~ s_t(X13,X36,X16)
      | ~ s_t(X15,X27,X16)
      | ~ s_e(X12,X13,X15,X27)
      | X34 != ip(X13,X36,X16,X15,X27)
      | s_m(X13,X34,X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24b) ).

fof(aSatz8_24,conjecture,
    ! [X13,X12,X15,X16,X36,X27] :
      ( ~ perp(X13,X12,X12,X15)
      | ~ perp(X16,X15,X12,X15)
      | ~ s_col(X12,X15,X36)
      | ~ s_t(X13,X36,X16)
      | ~ s_t(X15,X27,X16)
      | ~ s_e(X12,X13,X15,X27)
      | s_m(X13,midpoint(X12,X15),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24) ).

fof(aSatz7_6,axiom,
    ! [X13,X12,X16] :
      ( ~ s_m(X13,X12,X16)
      | X16 = s(X12,X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_6) ).

fof(aSatz7_18,axiom,
    ! [X12,X13,X15] :
      ( s(X12,X13) != s(X15,X13)
      | X12 = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_18) ).

fof(aSatz7_7,axiom,
    ! [X12,X13] : s(X12,s(X12,X13)) = X13,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_7) ).

fof(aSatz8_22,axiom,
    ! [X12,X15] : s_m(X12,midpoint(X12,X15),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_22) ).

fof(aSatz7_17,axiom,
    ! [X13,X12,X16,X15] :
      ( ~ s_m(X13,X12,X16)
      | ~ s_m(X13,X15,X16)
      | X12 = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_17) ).

fof(c_0_8,plain,
    ! [X13,X12,X15,X16,X36,X27,X34] :
      ( ~ perp(X13,X12,X12,X15)
      | ~ perp(X16,X15,X12,X15)
      | ~ s_col(X12,X15,X36)
      | ~ s_t(X13,X36,X16)
      | ~ s_t(X15,X27,X16)
      | ~ s_e(X12,X13,X15,X27)
      | X34 != ip(X13,X36,X16,X15,X27)
      | s_m(X12,X34,X15) ),
    inference(fof_simplification,[status(thm)],[aSatz8_24a]) ).

fof(c_0_9,plain,
    ! [X13,X12,X15,X16,X36,X27,X34] :
      ( ~ perp(X13,X12,X12,X15)
      | ~ perp(X16,X15,X12,X15)
      | ~ s_col(X12,X15,X36)
      | ~ s_t(X13,X36,X16)
      | ~ s_t(X15,X27,X16)
      | ~ s_e(X12,X13,X15,X27)
      | X34 != ip(X13,X36,X16,X15,X27)
      | s_m(X13,X34,X27) ),
    inference(fof_simplification,[status(thm)],[aSatz8_24b]) ).

fof(c_0_10,plain,
    ! [X605,X606,X607,X608,X609,X610,X611] :
      ( ~ perp(X605,X606,X606,X607)
      | ~ perp(X608,X607,X606,X607)
      | ~ s_col(X606,X607,X609)
      | ~ s_t(X605,X609,X608)
      | ~ s_t(X607,X610,X608)
      | ~ s_e(X606,X605,X607,X610)
      | X611 != ip(X605,X609,X608,X607,X610)
      | s_m(X606,X611,X607) ),
    inference(variable_rename,[status(thm)],[c_0_8]) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X13,X12,X15,X16,X36,X27] :
        ( ~ perp(X13,X12,X12,X15)
        | ~ perp(X16,X15,X12,X15)
        | ~ s_col(X12,X15,X36)
        | ~ s_t(X13,X36,X16)
        | ~ s_t(X15,X27,X16)
        | ~ s_e(X12,X13,X15,X27)
        | s_m(X13,midpoint(X12,X15),X27) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[aSatz8_24])]) ).

fof(c_0_12,plain,
    ! [X612,X613,X614,X615,X616,X617,X618] :
      ( ~ perp(X612,X613,X613,X614)
      | ~ perp(X615,X614,X613,X614)
      | ~ s_col(X613,X614,X616)
      | ~ s_t(X612,X616,X615)
      | ~ s_t(X614,X617,X615)
      | ~ s_e(X613,X612,X614,X617)
      | X618 != ip(X612,X616,X615,X614,X617)
      | s_m(X612,X618,X617) ),
    inference(variable_rename,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( s_m(X2,X7,X3)
    | ~ perp(X1,X2,X2,X3)
    | ~ perp(X4,X3,X2,X3)
    | ~ s_col(X2,X3,X5)
    | ~ s_t(X1,X5,X4)
    | ~ s_t(X3,X6,X4)
    | ~ s_e(X2,X1,X3,X6)
    | X7 != ip(X1,X5,X4,X3,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,negated_conjecture,
    ( perp(esk1_0,esk2_0,esk2_0,esk3_0)
    & perp(esk4_0,esk3_0,esk2_0,esk3_0)
    & s_col(esk2_0,esk3_0,esk5_0)
    & s_t(esk1_0,esk5_0,esk4_0)
    & s_t(esk3_0,esk6_0,esk4_0)
    & s_e(esk2_0,esk1_0,esk3_0,esk6_0)
    & ~ s_m(esk1_0,midpoint(esk2_0,esk3_0),esk6_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_15,plain,
    ! [X13,X12,X16] :
      ( ~ s_m(X13,X12,X16)
      | X16 = s(X12,X13) ),
    inference(fof_simplification,[status(thm)],[aSatz7_6]) ).

cnf(c_0_16,plain,
    ( s_m(X1,X7,X6)
    | ~ perp(X1,X2,X2,X3)
    | ~ perp(X4,X3,X2,X3)
    | ~ s_col(X2,X3,X5)
    | ~ s_t(X1,X5,X4)
    | ~ s_t(X3,X6,X4)
    | ~ s_e(X2,X1,X3,X6)
    | X7 != ip(X1,X5,X4,X3,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( s_m(X1,ip(X2,X3,X4,X5,X6),X5)
    | ~ perp(X4,X5,X1,X5)
    | ~ perp(X2,X1,X1,X5)
    | ~ s_col(X1,X5,X3)
    | ~ s_t(X5,X6,X4)
    | ~ s_t(X2,X3,X4)
    | ~ s_e(X1,X2,X5,X6) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    perp(esk4_0,esk3_0,esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_19,plain,
    ! [X450,X451,X452] :
      ( s(X450,X451) != s(X452,X451)
      | X450 = X452 ),
    inference(variable_rename,[status(thm)],[aSatz7_18]) ).

fof(c_0_20,plain,
    ! [X412,X413] : s(X412,s(X412,X413)) = X413,
    inference(variable_rename,[status(thm)],[aSatz7_7]) ).

fof(c_0_21,plain,
    ! [X409,X410,X411] :
      ( ~ s_m(X409,X410,X411)
      | X411 = s(X410,X409) ),
    inference(variable_rename,[status(thm)],[c_0_15]) ).

fof(c_0_22,plain,
    ! [X603,X604] : s_m(X603,midpoint(X603,X604),X604),
    inference(variable_rename,[status(thm)],[aSatz8_22]) ).

cnf(c_0_23,plain,
    ( s_m(X1,ip(X1,X2,X3,X4,X5),X5)
    | ~ perp(X3,X4,X6,X4)
    | ~ perp(X1,X6,X6,X4)
    | ~ s_col(X6,X4,X2)
    | ~ s_t(X4,X5,X3)
    | ~ s_t(X1,X2,X3)
    | ~ s_e(X6,X1,X4,X5) ),
    inference(er,[status(thm)],[c_0_16]) ).

fof(c_0_24,plain,
    ! [X13,X12,X16,X15] :
      ( ~ s_m(X13,X12,X16)
      | ~ s_m(X13,X15,X16)
      | X12 = X15 ),
    inference(fof_simplification,[status(thm)],[aSatz7_17]) ).

cnf(c_0_25,negated_conjecture,
    ( s_m(esk2_0,ip(X1,X2,esk4_0,esk3_0,X3),esk3_0)
    | ~ perp(X1,esk2_0,esk2_0,esk3_0)
    | ~ s_col(esk2_0,esk3_0,X2)
    | ~ s_t(esk3_0,X3,esk4_0)
    | ~ s_t(X1,X2,esk4_0)
    | ~ s_e(esk2_0,X1,esk3_0,X3) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_26,negated_conjecture,
    s_col(esk2_0,esk3_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_27,plain,
    ( X1 = X3
    | s(X1,X2) != s(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_28,plain,
    s(X1,s(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_29,plain,
    ( X3 = s(X2,X1)
    | ~ s_m(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    s_m(X1,midpoint(X1,X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_31,negated_conjecture,
    ( s_m(X1,ip(X1,X2,esk4_0,esk3_0,X3),X3)
    | ~ perp(X1,esk2_0,esk2_0,esk3_0)
    | ~ s_col(esk2_0,esk3_0,X2)
    | ~ s_t(esk3_0,X3,esk4_0)
    | ~ s_t(X1,X2,esk4_0)
    | ~ s_e(esk2_0,X1,esk3_0,X3) ),
    inference(spm,[status(thm)],[c_0_23,c_0_18]) ).

fof(c_0_32,plain,
    ! [X446,X447,X448,X449] :
      ( ~ s_m(X446,X447,X448)
      | ~ s_m(X446,X449,X448)
      | X447 = X449 ),
    inference(variable_rename,[status(thm)],[c_0_24]) ).

cnf(c_0_33,negated_conjecture,
    ( s_m(esk2_0,ip(X1,esk5_0,esk4_0,esk3_0,X2),esk3_0)
    | ~ perp(X1,esk2_0,esk2_0,esk3_0)
    | ~ s_t(esk3_0,X2,esk4_0)
    | ~ s_t(X1,esk5_0,esk4_0)
    | ~ s_e(esk2_0,X1,esk3_0,X2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,negated_conjecture,
    s_t(esk3_0,esk6_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_35,plain,
    ( X1 = X2
    | s(X1,s(X2,X3)) != X3 ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_36,plain,
    s(midpoint(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_37,negated_conjecture,
    ( s_m(X1,ip(X1,esk5_0,esk4_0,esk3_0,X2),X2)
    | ~ perp(X1,esk2_0,esk2_0,esk3_0)
    | ~ s_t(esk3_0,X2,esk4_0)
    | ~ s_t(X1,esk5_0,esk4_0)
    | ~ s_e(esk2_0,X1,esk3_0,X2) ),
    inference(spm,[status(thm)],[c_0_31,c_0_26]) ).

cnf(c_0_38,plain,
    ( X2 = X4
    | ~ s_m(X1,X2,X3)
    | ~ s_m(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_39,negated_conjecture,
    ( s_m(esk2_0,ip(X1,esk5_0,esk4_0,esk3_0,esk6_0),esk3_0)
    | ~ perp(X1,esk2_0,esk2_0,esk3_0)
    | ~ s_t(X1,esk5_0,esk4_0)
    | ~ s_e(esk2_0,X1,esk3_0,esk6_0) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    s_t(esk1_0,esk5_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_41,negated_conjecture,
    perp(esk1_0,esk2_0,esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_42,negated_conjecture,
    s_e(esk2_0,esk1_0,esk3_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_43,plain,
    midpoint(s(X1,X2),X2) = X1,
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36])]) ).

cnf(c_0_44,negated_conjecture,
    ( s_m(X1,ip(X1,esk5_0,esk4_0,esk3_0,esk6_0),esk6_0)
    | ~ perp(X1,esk2_0,esk2_0,esk3_0)
    | ~ s_t(X1,esk5_0,esk4_0)
    | ~ s_e(esk2_0,X1,esk3_0,esk6_0) ),
    inference(spm,[status(thm)],[c_0_37,c_0_34]) ).

cnf(c_0_45,plain,
    ( X1 = midpoint(X2,X3)
    | ~ s_m(X2,X1,X3) ),
    inference(spm,[status(thm)],[c_0_38,c_0_30]) ).

cnf(c_0_46,negated_conjecture,
    s_m(esk2_0,ip(esk1_0,esk5_0,esk4_0,esk3_0,esk6_0),esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]) ).

cnf(c_0_47,plain,
    midpoint(X1,X2) = midpoint(X2,X1),
    inference(spm,[status(thm)],[c_0_43,c_0_36]) ).

cnf(c_0_48,negated_conjecture,
    ~ s_m(esk1_0,midpoint(esk2_0,esk3_0),esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_49,negated_conjecture,
    s_m(esk1_0,ip(esk1_0,esk5_0,esk4_0,esk3_0,esk6_0),esk6_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_40]),c_0_41]),c_0_42])]) ).

cnf(c_0_50,negated_conjecture,
    ip(esk1_0,esk5_0,esk4_0,esk3_0,esk6_0) = midpoint(esk3_0,esk2_0),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).

cnf(c_0_51,negated_conjecture,
    ~ s_m(esk1_0,midpoint(esk3_0,esk2_0),esk6_0),
    inference(rw,[status(thm)],[c_0_48,c_0_47]) ).

cnf(c_0_52,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : GEO511+1 : TPTP v8.1.2. Released v7.0.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n027.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   : Tue Aug 29 23:46:08 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.59  start to proof: theBenchmark
% 178.62/178.60  % Version  : CSE_E---1.5
% 178.62/178.60  % Problem  : theBenchmark.p
% 178.62/178.60  % Proof found
% 178.62/178.60  % SZS status Theorem for theBenchmark.p
% 178.62/178.60  % SZS output start Proof
% See solution above
% 178.69/178.61  % Total time : 178.020000 s
% 178.69/178.61  % SZS output end Proof
% 178.69/178.61  % Total time : 178.034000 s
%------------------------------------------------------------------------------