TSTP Solution File: SWV200+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV200+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 : 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 : Thu Aug 31 21:36:58 EDT 2023

% Result   : Theorem 0.19s 0.74s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   76
% Syntax   : Number of formulae    :   94 (  11 unt;  73 typ;   0 def)
%            Number of atoms       :  260 ( 145 equ)
%            Maximal formula atoms :   72 (  12 avg)
%            Number of connectives :  310 (  71   ~;  59   |; 166   &)
%                                         (   1 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   42 (  10 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    :   66 (  66 usr;  21 con; 0-7 aty)
%            Number of variables   :   30 (   0 sgn;  22   !;   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,
    rho_defuse: $i ).

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

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

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

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

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

tff(decl_61,type,
    pv5: $i ).

tff(decl_62,type,
    n998: $i ).

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

tff(decl_64,type,
    epred1_4: ( $i * $i * $i * $i ) > $o ).

tff(decl_65,type,
    epred2_0: $o ).

tff(decl_66,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_67,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk19_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk20_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk21_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk22_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk23_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk24_0: $i ).

tff(decl_90,type,
    esk25_0: $i ).

tff(decl_91,type,
    esk26_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk27_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk28_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_94,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_inuse_0011,conjecture,
    ( ( a_select2(rho_defuse,n0) = use
      & a_select2(rho_defuse,n1) = use
      & a_select2(rho_defuse,n2) = use
      & a_select2(sigma_defuse,n0) = use
      & a_select2(sigma_defuse,n1) = use
      & a_select2(sigma_defuse,n2) = use
      & a_select2(sigma_defuse,n3) = use
      & a_select2(sigma_defuse,n4) = use
      & a_select2(sigma_defuse,n5) = use
      & a_select3(u_defuse,n0,n0) = use
      & a_select3(u_defuse,n1,n0) = use
      & a_select3(u_defuse,n2,n0) = use
      & a_select2(xinit_defuse,n3) = use
      & a_select2(xinit_defuse,n4) = use
      & a_select2(xinit_defuse,n5) = use
      & a_select2(xinit_mean_defuse,n0) = use
      & a_select2(xinit_mean_defuse,n1) = use
      & a_select2(xinit_mean_defuse,n2) = use
      & a_select2(xinit_mean_defuse,n3) = use
      & a_select2(xinit_mean_defuse,n4) = use
      & a_select2(xinit_mean_defuse,n5) = use
      & a_select2(xinit_noise_defuse,n0) = use
      & a_select2(xinit_noise_defuse,n1) = use
      & a_select2(xinit_noise_defuse,n2) = use
      & a_select2(xinit_noise_defuse,n3) = use
      & a_select2(xinit_noise_defuse,n4) = use
      & a_select2(xinit_noise_defuse,n5) = use
      & leq(n0,pv5)
      & leq(pv5,n998)
      & gt(pv5,n0)
      & ! [X14,X18] :
          ( ( leq(n0,X14)
            & leq(n0,X18)
            & leq(X14,n2)
            & leq(X18,pred(pv5)) )
         => a_select3(u_defuse,X14,X18) = use )
      & ! [X4,X20] :
          ( ( leq(n0,X4)
            & leq(n0,X20)
            & leq(X4,n2)
            & leq(X20,pred(pv5)) )
         => a_select3(z_defuse,X4,X20) = use ) )
   => ! [X21,X22] :
        ( ( leq(n0,X21)
          & leq(n0,X22)
          & leq(X21,n2)
          & leq(X22,pred(pv5)) )
       => ( ( ~ ( n0 = X21
                & pv5 = X22 )
            & ~ ( n1 = X21
                & pv5 = X22 )
            & ~ ( n2 = X21
                & pv5 = X22 ) )
         => a_select3(u_defuse,X21,X22) = use ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_inuse_0011) ).

fof(c_0_2,plain,
    ( epred2_0
  <=> ( a_select2(rho_defuse,n0) = use
      & a_select2(rho_defuse,n1) = use
      & a_select2(rho_defuse,n2) = use
      & a_select2(sigma_defuse,n0) = use
      & a_select2(sigma_defuse,n1) = use
      & a_select2(sigma_defuse,n2) = use
      & a_select2(sigma_defuse,n3) = use
      & a_select2(sigma_defuse,n4) = use
      & a_select2(sigma_defuse,n5) = use
      & a_select3(u_defuse,n0,n0) = use
      & a_select3(u_defuse,n1,n0) = use
      & a_select3(u_defuse,n2,n0) = use
      & a_select2(xinit_defuse,n3) = use
      & a_select2(xinit_defuse,n4) = use
      & a_select2(xinit_defuse,n5) = use
      & a_select2(xinit_mean_defuse,n0) = use
      & a_select2(xinit_mean_defuse,n1) = use
      & a_select2(xinit_mean_defuse,n2) = use
      & a_select2(xinit_mean_defuse,n3) = use
      & a_select2(xinit_mean_defuse,n4) = use
      & a_select2(xinit_mean_defuse,n5) = use
      & a_select2(xinit_noise_defuse,n0) = use
      & a_select2(xinit_noise_defuse,n1) = use
      & a_select2(xinit_noise_defuse,n2) = use
      & a_select2(xinit_noise_defuse,n3) = use
      & a_select2(xinit_noise_defuse,n4) = use
      & a_select2(xinit_noise_defuse,n5) = use
      & leq(n0,pv5)
      & leq(pv5,n998)
      & gt(pv5,n0)
      & ! [X14,X18] :
          ( ( leq(n0,X14)
            & leq(n0,X18)
            & leq(X14,n2)
            & leq(X18,pred(pv5)) )
         => a_select3(u_defuse,X14,X18) = use )
      & ! [X4,X20] :
          ( ( leq(n0,X4)
            & leq(n0,X20)
            & leq(X4,n2)
            & leq(X20,pred(pv5)) )
         => a_select3(z_defuse,X4,X20) = use ) ) ),
    introduced(definition) ).

fof(c_0_3,plain,
    ( epred2_0
   => ( a_select2(rho_defuse,n0) = use
      & a_select2(rho_defuse,n1) = use
      & a_select2(rho_defuse,n2) = use
      & a_select2(sigma_defuse,n0) = use
      & a_select2(sigma_defuse,n1) = use
      & a_select2(sigma_defuse,n2) = use
      & a_select2(sigma_defuse,n3) = use
      & a_select2(sigma_defuse,n4) = use
      & a_select2(sigma_defuse,n5) = use
      & a_select3(u_defuse,n0,n0) = use
      & a_select3(u_defuse,n1,n0) = use
      & a_select3(u_defuse,n2,n0) = use
      & a_select2(xinit_defuse,n3) = use
      & a_select2(xinit_defuse,n4) = use
      & a_select2(xinit_defuse,n5) = use
      & a_select2(xinit_mean_defuse,n0) = use
      & a_select2(xinit_mean_defuse,n1) = use
      & a_select2(xinit_mean_defuse,n2) = use
      & a_select2(xinit_mean_defuse,n3) = use
      & a_select2(xinit_mean_defuse,n4) = use
      & a_select2(xinit_mean_defuse,n5) = use
      & a_select2(xinit_noise_defuse,n0) = use
      & a_select2(xinit_noise_defuse,n1) = use
      & a_select2(xinit_noise_defuse,n2) = use
      & a_select2(xinit_noise_defuse,n3) = use
      & a_select2(xinit_noise_defuse,n4) = use
      & a_select2(xinit_noise_defuse,n5) = use
      & leq(n0,pv5)
      & leq(pv5,n998)
      & gt(pv5,n0)
      & ! [X14,X18] :
          ( ( leq(n0,X14)
            & leq(n0,X18)
            & leq(X14,n2)
            & leq(X18,pred(pv5)) )
         => a_select3(u_defuse,X14,X18) = use )
      & ! [X4,X20] :
          ( ( leq(n0,X4)
            & leq(n0,X20)
            & leq(X4,n2)
            & leq(X20,pred(pv5)) )
         => a_select3(z_defuse,X4,X20) = use ) ) ),
    inference(split_equiv,[status(thm)],[c_0_2]) ).

fof(c_0_4,plain,
    ! [X202,X203,X204,X205] :
      ( ( a_select2(rho_defuse,n0) = use
        | ~ epred2_0 )
      & ( a_select2(rho_defuse,n1) = use
        | ~ epred2_0 )
      & ( a_select2(rho_defuse,n2) = use
        | ~ epred2_0 )
      & ( a_select2(sigma_defuse,n0) = use
        | ~ epred2_0 )
      & ( a_select2(sigma_defuse,n1) = use
        | ~ epred2_0 )
      & ( a_select2(sigma_defuse,n2) = use
        | ~ epred2_0 )
      & ( a_select2(sigma_defuse,n3) = use
        | ~ epred2_0 )
      & ( a_select2(sigma_defuse,n4) = use
        | ~ epred2_0 )
      & ( a_select2(sigma_defuse,n5) = use
        | ~ epred2_0 )
      & ( a_select3(u_defuse,n0,n0) = use
        | ~ epred2_0 )
      & ( a_select3(u_defuse,n1,n0) = use
        | ~ epred2_0 )
      & ( a_select3(u_defuse,n2,n0) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_defuse,n3) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_defuse,n4) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_defuse,n5) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_mean_defuse,n0) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_mean_defuse,n1) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_mean_defuse,n2) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_mean_defuse,n3) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_mean_defuse,n4) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_mean_defuse,n5) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_noise_defuse,n0) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_noise_defuse,n1) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_noise_defuse,n2) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_noise_defuse,n3) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_noise_defuse,n4) = use
        | ~ epred2_0 )
      & ( a_select2(xinit_noise_defuse,n5) = use
        | ~ epred2_0 )
      & ( leq(n0,pv5)
        | ~ epred2_0 )
      & ( leq(pv5,n998)
        | ~ epred2_0 )
      & ( gt(pv5,n0)
        | ~ epred2_0 )
      & ( ~ leq(n0,X202)
        | ~ leq(n0,X203)
        | ~ leq(X202,n2)
        | ~ leq(X203,pred(pv5))
        | a_select3(u_defuse,X202,X203) = use
        | ~ epred2_0 )
      & ( ~ leq(n0,X204)
        | ~ leq(n0,X205)
        | ~ leq(X204,n2)
        | ~ leq(X205,pred(pv5))
        | a_select3(z_defuse,X204,X205) = use
        | ~ 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,
    ! [X145] : minus(X145,n1) = pred(X145),
    inference(variable_rename,[status(thm)],[pred_minus_1]) ).

fof(c_0_6,negated_conjecture,
    ~ ( epred2_0
     => ! [X21,X22] :
          ( ( leq(n0,X21)
            & leq(n0,X22)
            & leq(X21,n2)
            & leq(X22,pred(pv5)) )
         => ( ( ~ ( n0 = X21
                  & pv5 = X22 )
              & ~ ( n1 = X21
                  & pv5 = X22 )
              & ~ ( n2 = X21
                  & pv5 = X22 ) )
           => a_select3(u_defuse,X21,X22) = use ) ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0011]),c_0_2]) ).

cnf(c_0_7,plain,
    ( a_select3(u_defuse,X1,X2) = use
    | ~ leq(n0,X1)
    | ~ leq(n0,X2)
    | ~ leq(X1,n2)
    | ~ leq(X2,pred(pv5))
    | ~ 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(n0,esk25_0)
    & leq(esk24_0,n2)
    & leq(esk25_0,pred(pv5))
    & ( n0 != esk24_0
      | pv5 != esk25_0 )
    & ( n1 != esk24_0
      | pv5 != esk25_0 )
    & ( n2 != esk24_0
      | pv5 != esk25_0 )
    & a_select3(u_defuse,esk24_0,esk25_0) != use ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

cnf(c_0_10,plain,
    ( a_select3(u_defuse,X1,X2) = use
    | ~ epred2_0
    | ~ leq(X1,n2)
    | ~ leq(n0,X2)
    | ~ leq(n0,X1)
    | ~ leq(X2,minus(pv5,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(esk25_0,pred(pv5)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( a_select3(u_defuse,X1,X2) = use
    | ~ leq(X2,minus(pv5,n1))
    | ~ leq(X1,n2)
    | ~ 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(esk25_0,minus(pv5,n1)),
    inference(rw,[status(thm)],[c_0_12,c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    leq(n0,esk25_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,negated_conjecture,
    ( a_select3(u_defuse,X1,esk25_0) = use
    | ~ leq(X1,n2)
    | ~ 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(esk24_0,n2),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_18,negated_conjecture,
    leq(n0,esk24_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_19,negated_conjecture,
    a_select3(u_defuse,esk24_0,esk25_0) != use,
    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
% 0.00/0.12  % Problem    : SWV200+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n027.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   : Tue Aug 29 09:53:38 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.74  % Version  : CSE_E---1.5
% 0.19/0.74  % Problem  : theBenchmark.p
% 0.19/0.74  % Proof found
% 0.19/0.74  % SZS status Theorem for theBenchmark.p
% 0.19/0.74  % SZS output start Proof
% See solution above
% 0.19/0.75  % Total time : 0.164000 s
% 0.19/0.75  % SZS output end Proof
% 0.19/0.75  % Total time : 0.169000 s
%------------------------------------------------------------------------------