TSTP Solution File: MSC010+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : MSC010+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n010.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 09:21:03 EDT 2023

% Result   : Theorem 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   50
% Syntax   : Number of formulae    :   69 (  13 unt;  47 typ;   0 def)
%            Number of atoms       :  260 (  63 equ)
%            Maximal formula atoms :   68 (  11 avg)
%            Number of connectives :  272 (  34   ~;  20   |; 166   &)
%                                         (   1 <=>;  51  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :   40 (  40 usr;  38 con; 0-3 aty)
%            Number of variables   :   73 (   0 sgn;  70   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    pv63: $i ).

tff(decl_23,type,
    pv64: $i ).

tff(decl_24,type,
    n0: $i ).

tff(decl_25,type,
    pv5: $i ).

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

tff(decl_27,type,
    n998: $i ).

tff(decl_28,type,
    n5: $i ).

tff(decl_29,type,
    n2: $i ).

tff(decl_30,type,
    h_ds1_filter_init: $i ).

tff(decl_31,type,
    a_select3: ( $i * $i * $i ) > $i ).

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

tff(decl_33,type,
    phi_ds1_filter_init: $i ).

tff(decl_34,type,
    dv_ds1_filter_init: $i ).

tff(decl_35,type,
    q_ds1_filter_init: $i ).

tff(decl_36,type,
    r_ds1_filter_init: $i ).

tff(decl_37,type,
    xhatmin_ds1_filter_init: $i ).

tff(decl_38,type,
    pminus_ds1_filter_init: $i ).

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

tff(decl_40,type,
    id_ds1_filter_init: $i ).

tff(decl_41,type,
    pred: $i > $i ).

tff(decl_42,type,
    epred1_0: $o ).

tff(decl_43,type,
    epred2_0: $o ).

tff(decl_44,type,
    epred3_0: $o ).

tff(decl_45,type,
    epred4_0: $o ).

tff(decl_46,type,
    epred5_0: $o ).

tff(decl_47,type,
    esk1_0: $i ).

tff(decl_48,type,
    esk2_0: $i ).

tff(decl_49,type,
    esk3_0: $i ).

tff(decl_50,type,
    esk4_0: $i ).

tff(decl_51,type,
    esk5_0: $i ).

tff(decl_52,type,
    esk6_0: $i ).

tff(decl_53,type,
    esk7_0: $i ).

tff(decl_54,type,
    esk8_0: $i ).

tff(decl_55,type,
    esk9_0: $i ).

tff(decl_56,type,
    esk10_0: $i ).

tff(decl_57,type,
    esk11_0: $i ).

tff(decl_58,type,
    esk12_0: $i ).

tff(decl_59,type,
    esk13_0: $i ).

tff(decl_60,type,
    esk14_0: $i ).

tff(decl_61,type,
    esk15_0: $i ).

tff(decl_62,type,
    esk16_0: $i ).

tff(decl_63,type,
    esk17_0: $i ).

tff(decl_64,type,
    esk18_0: $i ).

tff(decl_65,type,
    esk19_0: $i ).

tff(decl_66,type,
    esk20_0: $i ).

tff(decl_67,type,
    esk21_0: $i ).

tff(decl_68,type,
    esk22_0: $i ).

fof(n91,conjecture,
    ~ ~ ( ( pv63 != pv64
          & leq(n0,pv5)
          & leq(n0,pv63)
          & leq(n0,pv64)
          & leq(pv5,n998)
          & leq(pv63,n5)
          & leq(pv64,n5)
          & ! [X1,X2] :
              ( ( leq(n0,X1)
                & leq(n0,X2)
                & leq(X1,n2)
                & leq(X2,n5) )
             => a_select3(h_ds1_filter_init,X1,X2) = init )
          & ! [X3,X4] :
              ( ( leq(n0,X3)
                & leq(n0,X4)
                & leq(X3,n5)
                & leq(X4,n5) )
             => a_select3(phi_ds1_filter_init,X3,X4) = init )
          & ! [X5,X6] :
              ( ( leq(n0,X5)
                & leq(n0,X6)
                & leq(X5,n5)
                & leq(X6,n0) )
             => a_select3(dv_ds1_filter_init,X5,X6) = init )
          & ! [X7,X8] :
              ( ( leq(n0,X7)
                & leq(n0,X8)
                & leq(X7,n5)
                & leq(X8,n5) )
             => a_select3(q_ds1_filter_init,X7,X8) = init )
          & ! [X9,X10] :
              ( ( leq(n0,X9)
                & leq(n0,X10)
                & leq(X9,n2)
                & leq(X10,n2) )
             => a_select3(r_ds1_filter_init,X9,X10) = init )
          & ! [X11,X12] :
              ( ( leq(n0,X11)
                & leq(n0,X12)
                & leq(X11,n5)
                & leq(X12,n0) )
             => a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
          & ! [X13,X14] :
              ( ( leq(n0,X13)
                & leq(n0,X14)
                & leq(X13,n5)
                & leq(X14,n5) )
             => a_select3(pminus_ds1_filter_init,X13,X14) = init )
          & ! [X15,X16] :
              ( ( leq(n0,X15)
                & leq(n0,X16)
                & leq(X15,n5)
                & leq(X16,n5) )
             => ( ( X15 = pv63
                  & gt(pv64,X16) )
               => a_select3(id_ds1_filter_init,X15,X16) = init ) )
          & ! [X17,X18] :
              ( ( leq(n0,X17)
                & leq(n0,X18)
                & leq(X17,n5)
                & leq(X18,n5) )
             => ( gt(pv63,X17)
               => a_select3(id_ds1_filter_init,X17,X18) = init ) )
          & ! [X19] :
              ( ( leq(n0,X19)
                & leq(X19,pred(pv63)) )
             => ! [X20] :
                  ( ( leq(n0,X20)
                    & leq(X20,n5) )
                 => a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
       => ! [X21,X22] :
            ( ( leq(n0,X21)
              & leq(n0,X22)
              & leq(X21,n5)
              & leq(X22,n5) )
           => ( ( pv64 != X22
                & X21 = pv63
                & leq(X22,pv64) )
             => a_select3(id_ds1_filter_init,X21,X22) = init ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',n91) ).

fof(n1,axiom,
    ( ( pv63 != pv64
      & leq(n0,pv5)
      & leq(n0,pv63)
      & leq(n0,pv64)
      & leq(pv5,n998)
      & leq(pv63,n5)
      & leq(pv64,n5)
      & ! [X1,X2] :
          ( ( leq(n0,X1)
            & leq(n0,X2)
            & leq(X1,n2)
            & leq(X2,n5) )
         => a_select3(h_ds1_filter_init,X1,X2) = init )
      & ! [X3,X4] :
          ( ( leq(n0,X3)
            & leq(n0,X4)
            & leq(X3,n5)
            & leq(X4,n5) )
         => a_select3(phi_ds1_filter_init,X3,X4) = init )
      & ! [X5,X6] :
          ( ( leq(n0,X5)
            & leq(n0,X6)
            & leq(X5,n5)
            & leq(X6,n0) )
         => a_select3(dv_ds1_filter_init,X5,X6) = init )
      & ! [X7,X8] :
          ( ( leq(n0,X7)
            & leq(n0,X8)
            & leq(X7,n5)
            & leq(X8,n5) )
         => a_select3(q_ds1_filter_init,X7,X8) = init )
      & ! [X9,X10] :
          ( ( leq(n0,X9)
            & leq(n0,X10)
            & leq(X9,n2)
            & leq(X10,n2) )
         => a_select3(r_ds1_filter_init,X9,X10) = init )
      & ! [X11,X12] :
          ( ( leq(n0,X11)
            & leq(n0,X12)
            & leq(X11,n5)
            & leq(X12,n0) )
         => a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
      & ! [X13,X14] :
          ( ( leq(n0,X13)
            & leq(n0,X14)
            & leq(X13,n5)
            & leq(X14,n5) )
         => a_select3(pminus_ds1_filter_init,X13,X14) = init )
      & ! [X15,X16] :
          ( ( leq(n0,X15)
            & leq(n0,X16)
            & leq(X15,n5)
            & leq(X16,n5) )
         => ( ( X15 = pv63
              & gt(pv64,X16) )
           => a_select3(id_ds1_filter_init,X15,X16) = init ) )
      & ! [X17,X18] :
          ( ( leq(n0,X17)
            & leq(n0,X18)
            & leq(X17,n5)
            & leq(X18,n5) )
         => ( gt(pv63,X17)
           => a_select3(id_ds1_filter_init,X17,X18) = init ) )
      & ! [X19] :
          ( ( leq(n0,X19)
            & leq(X19,pred(pv63)) )
         => ! [X20] :
              ( ( leq(n0,X20)
                & leq(X20,n5) )
             => a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
   => ! [X21,X22] :
        ( ( leq(n0,X21)
          & leq(n0,X22)
          & leq(X21,n5)
          & leq(X22,n5) )
       => ( ( pv64 != X22
            & X21 = pv63
            & leq(X22,pv64) )
         => a_select3(id_ds1_filter_init,X21,X22) = init ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',n1) ).

fof(c_0_2,plain,
    ( epred5_0
  <=> ( pv63 != pv64
      & leq(n0,pv5)
      & leq(n0,pv63)
      & leq(n0,pv64)
      & leq(pv5,n998)
      & leq(pv63,n5)
      & leq(pv64,n5)
      & ! [X1,X2] :
          ( ( leq(n0,X1)
            & leq(n0,X2)
            & leq(X1,n2)
            & leq(X2,n5) )
         => a_select3(h_ds1_filter_init,X1,X2) = init )
      & ! [X3,X4] :
          ( ( leq(n0,X3)
            & leq(n0,X4)
            & leq(X3,n5)
            & leq(X4,n5) )
         => a_select3(phi_ds1_filter_init,X3,X4) = init )
      & ! [X5,X6] :
          ( ( leq(n0,X5)
            & leq(n0,X6)
            & leq(X5,n5)
            & leq(X6,n0) )
         => a_select3(dv_ds1_filter_init,X5,X6) = init )
      & ! [X7,X8] :
          ( ( leq(n0,X7)
            & leq(n0,X8)
            & leq(X7,n5)
            & leq(X8,n5) )
         => a_select3(q_ds1_filter_init,X7,X8) = init )
      & ! [X9,X10] :
          ( ( leq(n0,X9)
            & leq(n0,X10)
            & leq(X9,n2)
            & leq(X10,n2) )
         => a_select3(r_ds1_filter_init,X9,X10) = init )
      & ! [X11,X12] :
          ( ( leq(n0,X11)
            & leq(n0,X12)
            & leq(X11,n5)
            & leq(X12,n0) )
         => a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
      & ! [X13,X14] :
          ( ( leq(n0,X13)
            & leq(n0,X14)
            & leq(X13,n5)
            & leq(X14,n5) )
         => a_select3(pminus_ds1_filter_init,X13,X14) = init )
      & ! [X15,X16] :
          ( ( leq(n0,X15)
            & leq(n0,X16)
            & leq(X15,n5)
            & leq(X16,n5) )
         => ( ( X15 = pv63
              & gt(pv64,X16) )
           => a_select3(id_ds1_filter_init,X15,X16) = init ) )
      & ! [X17,X18] :
          ( ( leq(n0,X17)
            & leq(n0,X18)
            & leq(X17,n5)
            & leq(X18,n5) )
         => ( gt(pv63,X17)
           => a_select3(id_ds1_filter_init,X17,X18) = init ) )
      & ! [X19] :
          ( ( leq(n0,X19)
            & leq(X19,pred(pv63)) )
         => ! [X20] :
              ( ( leq(n0,X20)
                & leq(X20,n5) )
             => a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) ),
    introduced(definition) ).

fof(c_0_3,negated_conjecture,
    ~ ~ ~ ( epred5_0
         => ! [X21,X22] :
              ( ( leq(n0,X21)
                & leq(n0,X22)
                & leq(X21,n5)
                & leq(X22,n5) )
             => ( ( pv64 != X22
                  & X21 = pv63
                  & leq(X22,pv64) )
               => a_select3(id_ds1_filter_init,X21,X22) = init ) ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[n91]),c_0_2]) ).

fof(c_0_4,axiom,
    ( epred5_0
   => ! [X21,X22] :
        ( ( leq(n0,X21)
          & leq(n0,X22)
          & leq(X21,n5)
          & leq(X22,n5) )
       => ( ( pv64 != X22
            & X21 = pv63
            & leq(X22,pv64) )
         => a_select3(id_ds1_filter_init,X21,X22) = init ) ) ),
    inference(apply_def,[status(thm)],[n1,c_0_2]) ).

fof(c_0_5,negated_conjecture,
    ( epred5_0
    & leq(n0,esk1_0)
    & leq(n0,esk2_0)
    & leq(esk1_0,n5)
    & leq(esk2_0,n5)
    & pv64 != esk2_0
    & esk1_0 = pv63
    & leq(esk2_0,pv64)
    & a_select3(id_ds1_filter_init,esk1_0,esk2_0) != init ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_6,plain,
    ! [X23,X24] :
      ( ~ epred5_0
      | ~ leq(n0,X23)
      | ~ leq(n0,X24)
      | ~ leq(X23,n5)
      | ~ leq(X24,n5)
      | pv64 = X24
      | X23 != pv63
      | ~ leq(X24,pv64)
      | a_select3(id_ds1_filter_init,X23,X24) = init ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_7,negated_conjecture,
    leq(esk1_0,n5),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    esk1_0 = pv63,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    leq(n0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( pv64 = X2
    | a_select3(id_ds1_filter_init,X1,X2) = init
    | ~ epred5_0
    | ~ leq(n0,X1)
    | ~ leq(n0,X2)
    | ~ leq(X1,n5)
    | ~ leq(X2,n5)
    | X1 != pv63
    | ~ leq(X2,pv64) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    epred5_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    leq(pv63,n5),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    leq(n0,pv63),
    inference(rw,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    a_select3(id_ds1_filter_init,esk1_0,esk2_0) != init,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_15,plain,
    ( a_select3(id_ds1_filter_init,pv63,X1) = init
    | pv64 = X1
    | ~ leq(X1,pv64)
    | ~ leq(X1,n5)
    | ~ leq(n0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])])]),c_0_12]),c_0_13])]) ).

cnf(c_0_16,negated_conjecture,
    leq(esk2_0,pv64),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_17,negated_conjecture,
    leq(esk2_0,n5),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_18,negated_conjecture,
    leq(n0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_19,negated_conjecture,
    a_select3(id_ds1_filter_init,pv63,esk2_0) != init,
    inference(rw,[status(thm)],[c_0_14,c_0_8]) ).

cnf(c_0_20,negated_conjecture,
    pv64 != esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]),c_0_19]),c_0_20]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : MSC010+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n010.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   : Thu Aug 24 13:34:50 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.015000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.018000 s
%------------------------------------------------------------------------------