TSTP Solution File: SWV221+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV221+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n021.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 21:37:04 EDT 2023

% Result   : Theorem 0.63s 0.74s
% Output   : CNFRefutation 0.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   75
% Syntax   : Number of formulae    :   93 (  11 unt;  72 typ;   0 def)
%            Number of atoms       :  227 (  48 equ)
%            Maximal formula atoms :   51 (  10 avg)
%            Number of connectives :  271 (  65   ~;  56   |; 113   &)
%                                         (   1 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  144 (  50   >;  94   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   3 prp; 0-4 aty)
%            Number of functors    :   65 (  65 usr;  20 con; 0-7 aty)
%            Number of variables   :   62 (   0 sgn;  54   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    succ: $i > $i ).

tff(decl_28,type,
    n0: $i ).

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

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

tff(decl_31,type,
    tptp_const_array1: ( $i * $i ) > $i ).

tff(decl_32,type,
    a_select2: ( $i * $i ) > $i ).

tff(decl_33,type,
    tptp_const_array2: ( $i * $i * $i ) > $i ).

tff(decl_34,type,
    a_select3: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    trans: $i > $i ).

tff(decl_36,type,
    inv: $i > $i ).

tff(decl_37,type,
    tptp_update3: ( $i * $i * $i * $i ) > $i ).

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

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

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

tff(decl_41,type,
    tptp_minus_1: $i ).

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

tff(decl_43,type,
    tptp_float_0_0: $i ).

tff(decl_44,type,
    n1: $i ).

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

tff(decl_46,type,
    n2: $i ).

tff(decl_47,type,
    n3: $i ).

tff(decl_48,type,
    n4: $i ).

tff(decl_49,type,
    n5: $i ).

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

tff(decl_51,type,
    tptp_update2: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    true: $o ).

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

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

tff(decl_55,type,
    pv5: $i ).

tff(decl_56,type,
    pv57: $i ).

tff(decl_57,type,
    n998: $i ).

tff(decl_58,type,
    pv58: $i ).

tff(decl_59,type,
    q_ds1_filter: $i ).

tff(decl_60,type,
    r_ds1_filter: $i ).

tff(decl_61,type,
    pminus_ds1_filter: $i ).

tff(decl_62,type,
    id_ds1_filter: $i ).

tff(decl_63,type,
    epred1_4: ( $i * $i * $i * $i ) > $o ).

tff(decl_64,type,
    epred2_0: $o ).

tff(decl_65,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_67,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk19_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk20_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk21_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk22_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk23_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk24_0: $i ).

tff(decl_89,type,
    esk25_0: $i ).

tff(decl_90,type,
    esk26_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk27_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk28_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk29_4: ( $i * $i * $i * $i ) > $i ).

fof(pred_minus_1,axiom,
    ! [X1] : minus(X1,n1) = pred(X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).

fof(quaternion_ds1_symm_0401,conjecture,
    ( ( leq(n0,pv5)
      & leq(n0,pv57)
      & leq(pv5,n998)
      & leq(pv57,n5)
      & leq(pv58,n5)
      & gt(pv58,pv57)
      & ! [X14,X18] :
          ( ( leq(n0,X14)
            & leq(n0,X18)
            & leq(X14,n5)
            & leq(X18,n5) )
         => a_select3(q_ds1_filter,X14,X18) = a_select3(q_ds1_filter,X18,X14) )
      & ! [X4,X20] :
          ( ( leq(n0,X4)
            & leq(n0,X20)
            & leq(X4,n2)
            & leq(X20,n2) )
         => a_select3(r_ds1_filter,X4,X20) = a_select3(r_ds1_filter,X20,X4) )
      & ! [X21,X22] :
          ( ( leq(n0,X21)
            & leq(n0,X22)
            & leq(X21,n5)
            & leq(X22,n5) )
         => a_select3(pminus_ds1_filter,X21,X22) = a_select3(pminus_ds1_filter,X22,X21) )
      & ! [X28,X29] :
          ( ( leq(n0,X28)
            & leq(n0,X29)
            & leq(X28,n5)
            & leq(X29,n5) )
         => ( ( X28 = pv57
              & gt(pv58,X29) )
           => a_select3(id_ds1_filter,X28,X29) = a_select3(id_ds1_filter,X29,X28) ) )
      & ! [X5,X11] :
          ( ( leq(n0,X5)
            & leq(n0,X11)
            & leq(X5,n5)
            & leq(X11,n5) )
         => ( gt(pv57,X5)
           => a_select3(id_ds1_filter,X5,X11) = a_select3(id_ds1_filter,X11,X5) ) )
      & ! [X16] :
          ( ( leq(n0,X16)
            & leq(X16,pred(pv57)) )
         => ! [X6] :
              ( ( leq(n0,X6)
                & leq(X6,n5) )
             => a_select3(id_ds1_filter,X16,X6) = a_select3(id_ds1_filter,X6,X16) ) ) )
   => ! [X19] :
        ( ( leq(n0,X19)
          & leq(X19,pred(pv57)) )
       => ! [X15] :
            ( ( leq(n0,X15)
              & leq(X15,n5) )
           => ( ( ~ ( pv57 = X15
                    & X15 = X19 )
                & pv57 != X19 )
             => a_select3(id_ds1_filter,X19,X15) = a_select3(id_ds1_filter,X15,X19) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0401) ).

fof(c_0_2,plain,
    ( epred2_0
  <=> ( leq(n0,pv5)
      & leq(n0,pv57)
      & leq(pv5,n998)
      & leq(pv57,n5)
      & leq(pv58,n5)
      & gt(pv58,pv57)
      & ! [X14,X18] :
          ( ( leq(n0,X14)
            & leq(n0,X18)
            & leq(X14,n5)
            & leq(X18,n5) )
         => a_select3(q_ds1_filter,X14,X18) = a_select3(q_ds1_filter,X18,X14) )
      & ! [X4,X20] :
          ( ( leq(n0,X4)
            & leq(n0,X20)
            & leq(X4,n2)
            & leq(X20,n2) )
         => a_select3(r_ds1_filter,X4,X20) = a_select3(r_ds1_filter,X20,X4) )
      & ! [X21,X22] :
          ( ( leq(n0,X21)
            & leq(n0,X22)
            & leq(X21,n5)
            & leq(X22,n5) )
         => a_select3(pminus_ds1_filter,X21,X22) = a_select3(pminus_ds1_filter,X22,X21) )
      & ! [X28,X29] :
          ( ( leq(n0,X28)
            & leq(n0,X29)
            & leq(X28,n5)
            & leq(X29,n5) )
         => ( ( X28 = pv57
              & gt(pv58,X29) )
           => a_select3(id_ds1_filter,X28,X29) = a_select3(id_ds1_filter,X29,X28) ) )
      & ! [X5,X11] :
          ( ( leq(n0,X5)
            & leq(n0,X11)
            & leq(X5,n5)
            & leq(X11,n5) )
         => ( gt(pv57,X5)
           => a_select3(id_ds1_filter,X5,X11) = a_select3(id_ds1_filter,X11,X5) ) )
      & ! [X16] :
          ( ( leq(n0,X16)
            & leq(X16,pred(pv57)) )
         => ! [X6] :
              ( ( leq(n0,X6)
                & leq(X6,n5) )
             => a_select3(id_ds1_filter,X16,X6) = a_select3(id_ds1_filter,X6,X16) ) ) ) ),
    introduced(definition) ).

fof(c_0_3,plain,
    ( epred2_0
   => ( leq(n0,pv5)
      & leq(n0,pv57)
      & leq(pv5,n998)
      & leq(pv57,n5)
      & leq(pv58,n5)
      & gt(pv58,pv57)
      & ! [X14,X18] :
          ( ( leq(n0,X14)
            & leq(n0,X18)
            & leq(X14,n5)
            & leq(X18,n5) )
         => a_select3(q_ds1_filter,X14,X18) = a_select3(q_ds1_filter,X18,X14) )
      & ! [X4,X20] :
          ( ( leq(n0,X4)
            & leq(n0,X20)
            & leq(X4,n2)
            & leq(X20,n2) )
         => a_select3(r_ds1_filter,X4,X20) = a_select3(r_ds1_filter,X20,X4) )
      & ! [X21,X22] :
          ( ( leq(n0,X21)
            & leq(n0,X22)
            & leq(X21,n5)
            & leq(X22,n5) )
         => a_select3(pminus_ds1_filter,X21,X22) = a_select3(pminus_ds1_filter,X22,X21) )
      & ! [X28,X29] :
          ( ( leq(n0,X28)
            & leq(n0,X29)
            & leq(X28,n5)
            & leq(X29,n5) )
         => ( ( X28 = pv57
              & gt(pv58,X29) )
           => a_select3(id_ds1_filter,X28,X29) = a_select3(id_ds1_filter,X29,X28) ) )
      & ! [X5,X11] :
          ( ( leq(n0,X5)
            & leq(n0,X11)
            & leq(X5,n5)
            & leq(X11,n5) )
         => ( gt(pv57,X5)
           => a_select3(id_ds1_filter,X5,X11) = a_select3(id_ds1_filter,X11,X5) ) )
      & ! [X16] :
          ( ( leq(n0,X16)
            & leq(X16,pred(pv57)) )
         => ! [X6] :
              ( ( leq(n0,X6)
                & leq(X6,n5) )
             => a_select3(id_ds1_filter,X16,X6) = a_select3(id_ds1_filter,X6,X16) ) ) ) ),
    inference(split_equiv,[status(thm)],[c_0_2]) ).

fof(c_0_4,plain,
    ! [X204,X205,X206,X207,X208,X209,X210,X211,X212,X213,X214,X215] :
      ( ( leq(n0,pv5)
        | ~ epred2_0 )
      & ( leq(n0,pv57)
        | ~ epred2_0 )
      & ( leq(pv5,n998)
        | ~ epred2_0 )
      & ( leq(pv57,n5)
        | ~ epred2_0 )
      & ( leq(pv58,n5)
        | ~ epred2_0 )
      & ( gt(pv58,pv57)
        | ~ epred2_0 )
      & ( ~ leq(n0,X204)
        | ~ leq(n0,X205)
        | ~ leq(X204,n5)
        | ~ leq(X205,n5)
        | a_select3(q_ds1_filter,X204,X205) = a_select3(q_ds1_filter,X205,X204)
        | ~ epred2_0 )
      & ( ~ leq(n0,X206)
        | ~ leq(n0,X207)
        | ~ leq(X206,n2)
        | ~ leq(X207,n2)
        | a_select3(r_ds1_filter,X206,X207) = a_select3(r_ds1_filter,X207,X206)
        | ~ epred2_0 )
      & ( ~ leq(n0,X208)
        | ~ leq(n0,X209)
        | ~ leq(X208,n5)
        | ~ leq(X209,n5)
        | a_select3(pminus_ds1_filter,X208,X209) = a_select3(pminus_ds1_filter,X209,X208)
        | ~ epred2_0 )
      & ( ~ leq(n0,X210)
        | ~ leq(n0,X211)
        | ~ leq(X210,n5)
        | ~ leq(X211,n5)
        | X210 != pv57
        | ~ gt(pv58,X211)
        | a_select3(id_ds1_filter,X210,X211) = a_select3(id_ds1_filter,X211,X210)
        | ~ epred2_0 )
      & ( ~ leq(n0,X212)
        | ~ leq(n0,X213)
        | ~ leq(X212,n5)
        | ~ leq(X213,n5)
        | ~ gt(pv57,X212)
        | a_select3(id_ds1_filter,X212,X213) = a_select3(id_ds1_filter,X213,X212)
        | ~ epred2_0 )
      & ( ~ leq(n0,X214)
        | ~ leq(X214,pred(pv57))
        | ~ leq(n0,X215)
        | ~ leq(X215,n5)
        | a_select3(id_ds1_filter,X214,X215) = a_select3(id_ds1_filter,X215,X214)
        | ~ epred2_0 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

fof(c_0_5,plain,
    ! [X147] : minus(X147,n1) = pred(X147),
    inference(variable_rename,[status(thm)],[pred_minus_1]) ).

fof(c_0_6,negated_conjecture,
    ~ ( epred2_0
     => ! [X19] :
          ( ( leq(n0,X19)
            & leq(X19,pred(pv57)) )
         => ! [X15] :
              ( ( leq(n0,X15)
                & leq(X15,n5) )
             => ( ( ~ ( pv57 = X15
                      & X15 = X19 )
                  & pv57 != X19 )
               => a_select3(id_ds1_filter,X19,X15) = a_select3(id_ds1_filter,X15,X19) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0401]),c_0_2]) ).

cnf(c_0_7,plain,
    ( a_select3(id_ds1_filter,X1,X2) = a_select3(id_ds1_filter,X2,X1)
    | ~ leq(n0,X1)
    | ~ leq(X1,pred(pv57))
    | ~ leq(n0,X2)
    | ~ leq(X2,n5)
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    minus(X1,n1) = pred(X1),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_9,negated_conjecture,
    ( epred2_0
    & leq(n0,esk24_0)
    & leq(esk24_0,pred(pv57))
    & leq(n0,esk25_0)
    & leq(esk25_0,n5)
    & ( pv57 != esk25_0
      | esk25_0 != esk24_0 )
    & pv57 != esk24_0
    & a_select3(id_ds1_filter,esk24_0,esk25_0) != a_select3(id_ds1_filter,esk25_0,esk24_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

cnf(c_0_10,plain,
    ( a_select3(id_ds1_filter,X1,X2) = a_select3(id_ds1_filter,X2,X1)
    | ~ epred2_0
    | ~ leq(X2,n5)
    | ~ leq(n0,X2)
    | ~ leq(n0,X1)
    | ~ leq(X1,minus(pv57,n1)) ),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    epred2_0,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    leq(esk24_0,pred(pv57)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( a_select3(id_ds1_filter,X1,X2) = a_select3(id_ds1_filter,X2,X1)
    | ~ leq(X1,minus(pv57,n1))
    | ~ leq(X2,n5)
    | ~ leq(n0,X2)
    | ~ leq(n0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).

cnf(c_0_14,negated_conjecture,
    leq(esk24_0,minus(pv57,n1)),
    inference(rw,[status(thm)],[c_0_12,c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    leq(n0,esk24_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,negated_conjecture,
    ( a_select3(id_ds1_filter,esk24_0,X1) = a_select3(id_ds1_filter,X1,esk24_0)
    | ~ leq(X1,n5)
    | ~ leq(n0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

cnf(c_0_17,negated_conjecture,
    leq(esk25_0,n5),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_18,negated_conjecture,
    leq(n0,esk25_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_19,negated_conjecture,
    a_select3(id_ds1_filter,esk24_0,esk25_0) != a_select3(id_ds1_filter,esk25_0,esk24_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWV221+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 29 08:04:14 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.63/0.74  % Version  : CSE_E---1.5
% 0.63/0.74  % Problem  : theBenchmark.p
% 0.63/0.74  % Proof found
% 0.63/0.74  % SZS status Theorem for theBenchmark.p
% 0.63/0.74  % SZS output start Proof
% See solution above
% 0.63/0.75  % Total time : 0.156000 s
% 0.63/0.75  % SZS output end Proof
% 0.63/0.75  % Total time : 0.161000 s
%------------------------------------------------------------------------------