TSTP Solution File: SWV181+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n024.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 21:36:54 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   82
% Syntax   : Number of formulae    :  112 (  17 unt;  74 typ;   0 def)
%            Number of atoms       :  165 (  29 equ)
%            Maximal formula atoms :   31 (   4 avg)
%            Number of connectives :  173 (  46   ~;  38   |;  53   &)
%                                         (   2 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   4 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    :   67 (  67 usr;  22 con; 0-7 aty)
%            Number of variables   :   61 (   0 sgn;  45   !;   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,
    tptp_float_0_001: $i ).

tff(decl_56,type,
    pv76: $i ).

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

tff(decl_58,type,
    n135299: $i ).

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

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

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

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

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

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

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

tff(decl_66,type,
    epred1_4: ( $i * $i * $i * $i ) > $o ).

tff(decl_67,type,
    epred2_0: $o ).

tff(decl_68,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_73,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_74,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk19_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk20_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk21_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk22_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_90,type,
    esk23_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk24_0: $i ).

tff(decl_92,type,
    esk25_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk26_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_94,type,
    esk27_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk28_4: ( $i * $i * $i * $i ) > $i ).

fof(leq_succ_gt_equiv,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> gt(succ(X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_succ_gt_equiv) ).

fof(succ_plus_1_r,axiom,
    ! [X1] : plus(X1,n1) = succ(X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).

fof(cl5_nebula_init_0081,conjecture,
    ( ( leq(tptp_float_0_001,pv76)
      & leq(n1,loopcounter)
      & gt(n1,loopcounter)
      & ! [X14] :
          ( ( leq(n0,X14)
            & leq(X14,n135299) )
         => ! [X18] :
              ( ( leq(n0,X18)
                & leq(X18,n4) )
             => a_select3(q_init,X14,X18) = init ) )
      & ! [X4] :
          ( ( leq(n0,X4)
            & leq(X4,n4) )
         => a_select3(center_init,X4,n0) = init )
      & ( gt(loopcounter,n0)
       => ! [X20] :
            ( ( leq(n0,X20)
              & leq(X20,n4) )
           => a_select2(mu_init,X20) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X21] :
            ( ( leq(n0,X21)
              & leq(X21,n4) )
           => a_select2(rho_init,X21) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X22] :
            ( ( leq(n0,X22)
              & leq(X22,n4) )
           => a_select2(sigma_init,X22) = init ) ) )
   => ! [X28] :
        ( ( leq(n0,X28)
          & leq(X28,n4) )
       => a_select2(muold_init,X28) = init ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0081) ).

fof(successor_1,axiom,
    succ(n0) = n1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).

fof(irreflexivity_gt,axiom,
    ! [X1] : ~ gt(X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).

fof(leq_succ_gt,axiom,
    ! [X1,X2] :
      ( leq(succ(X1),X2)
     => gt(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_succ_gt) ).

fof(transitivity_leq,axiom,
    ! [X1,X2,X3] :
      ( ( leq(X1,X2)
        & leq(X2,X3) )
     => leq(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',transitivity_leq) ).

fof(c_0_7,plain,
    ( epred2_0
  <=> ( leq(tptp_float_0_001,pv76)
      & leq(n1,loopcounter)
      & gt(n1,loopcounter)
      & ! [X14] :
          ( ( leq(n0,X14)
            & leq(X14,n135299) )
         => ! [X18] :
              ( ( leq(n0,X18)
                & leq(X18,n4) )
             => a_select3(q_init,X14,X18) = init ) )
      & ! [X4] :
          ( ( leq(n0,X4)
            & leq(X4,n4) )
         => a_select3(center_init,X4,n0) = init )
      & ( gt(loopcounter,n0)
       => ! [X20] :
            ( ( leq(n0,X20)
              & leq(X20,n4) )
           => a_select2(mu_init,X20) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X21] :
            ( ( leq(n0,X21)
              & leq(X21,n4) )
           => a_select2(rho_init,X21) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X22] :
            ( ( leq(n0,X22)
              & leq(X22,n4) )
           => a_select2(sigma_init,X22) = init ) ) ) ),
    introduced(definition) ).

fof(c_0_8,plain,
    ! [X52,X53] :
      ( ( ~ leq(X52,X53)
        | gt(succ(X53),X52) )
      & ( ~ gt(succ(X53),X52)
        | leq(X52,X53) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt_equiv])]) ).

fof(c_0_9,plain,
    ! [X136] : plus(X136,n1) = succ(X136),
    inference(variable_rename,[status(thm)],[succ_plus_1_r]) ).

fof(c_0_10,plain,
    ( epred2_0
   => ( leq(tptp_float_0_001,pv76)
      & leq(n1,loopcounter)
      & gt(n1,loopcounter)
      & ! [X14] :
          ( ( leq(n0,X14)
            & leq(X14,n135299) )
         => ! [X18] :
              ( ( leq(n0,X18)
                & leq(X18,n4) )
             => a_select3(q_init,X14,X18) = init ) )
      & ! [X4] :
          ( ( leq(n0,X4)
            & leq(X4,n4) )
         => a_select3(center_init,X4,n0) = init )
      & ( gt(loopcounter,n0)
       => ! [X20] :
            ( ( leq(n0,X20)
              & leq(X20,n4) )
           => a_select2(mu_init,X20) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X21] :
            ( ( leq(n0,X21)
              & leq(X21,n4) )
           => a_select2(rho_init,X21) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X22] :
            ( ( leq(n0,X22)
              & leq(X22,n4) )
           => a_select2(sigma_init,X22) = init ) ) ) ),
    inference(split_equiv,[status(thm)],[c_0_7]) ).

fof(c_0_11,negated_conjecture,
    ~ ( epred2_0
     => ! [X28] :
          ( ( leq(n0,X28)
            & leq(X28,n4) )
         => a_select2(muold_init,X28) = init ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cl5_nebula_init_0081]),c_0_7]) ).

cnf(c_0_12,plain,
    ( leq(X2,X1)
    | ~ gt(succ(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    plus(X1,n1) = succ(X1),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    succ(n0) = n1,
    inference(split_conjunct,[status(thm)],[successor_1]) ).

fof(c_0_15,plain,
    ! [X202,X203,X204,X205,X206,X207] :
      ( ( leq(tptp_float_0_001,pv76)
        | ~ epred2_0 )
      & ( leq(n1,loopcounter)
        | ~ epred2_0 )
      & ( gt(n1,loopcounter)
        | ~ epred2_0 )
      & ( ~ leq(n0,X202)
        | ~ leq(X202,n135299)
        | ~ leq(n0,X203)
        | ~ leq(X203,n4)
        | a_select3(q_init,X202,X203) = init
        | ~ epred2_0 )
      & ( ~ leq(n0,X204)
        | ~ leq(X204,n4)
        | a_select3(center_init,X204,n0) = init
        | ~ epred2_0 )
      & ( ~ gt(loopcounter,n0)
        | ~ leq(n0,X205)
        | ~ leq(X205,n4)
        | a_select2(mu_init,X205) = init
        | ~ epred2_0 )
      & ( ~ gt(loopcounter,n0)
        | ~ leq(n0,X206)
        | ~ leq(X206,n4)
        | a_select2(rho_init,X206) = init
        | ~ epred2_0 )
      & ( ~ gt(loopcounter,n0)
        | ~ leq(n0,X207)
        | ~ leq(X207,n4)
        | a_select2(sigma_init,X207) = init
        | ~ epred2_0 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).

fof(c_0_16,negated_conjecture,
    ( epred2_0
    & leq(n0,esk24_0)
    & leq(esk24_0,n4)
    & a_select2(muold_init,esk24_0) != init ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_17,plain,
    ! [X1] : ~ gt(X1,X1),
    inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).

fof(c_0_18,plain,
    ! [X151,X152] :
      ( ~ leq(succ(X151),X152)
      | gt(X152,X151) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt])]) ).

cnf(c_0_19,plain,
    ( leq(X2,X1)
    | ~ gt(plus(X1,n1),X2) ),
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_20,plain,
    plus(n0,n1) = n1,
    inference(rw,[status(thm)],[c_0_14,c_0_13]) ).

cnf(c_0_21,plain,
    ( gt(n1,loopcounter)
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,negated_conjecture,
    epred2_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_23,plain,
    ! [X34] : ~ gt(X34,X34),
    inference(variable_rename,[status(thm)],[c_0_17]) ).

cnf(c_0_24,plain,
    ( gt(X2,X1)
    | ~ leq(succ(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_25,plain,
    ! [X36,X37,X38] :
      ( ~ leq(X36,X37)
      | ~ leq(X37,X38)
      | leq(X36,X38) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_leq])]) ).

cnf(c_0_26,plain,
    ( leq(X1,n0)
    | ~ gt(n1,X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_27,plain,
    gt(n1,loopcounter),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).

cnf(c_0_28,plain,
    ~ gt(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,plain,
    ( gt(X2,X1)
    | ~ leq(plus(X1,n1),X2) ),
    inference(rw,[status(thm)],[c_0_24,c_0_13]) ).

cnf(c_0_30,plain,
    ( leq(X1,X3)
    | ~ leq(X1,X2)
    | ~ leq(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_31,plain,
    leq(loopcounter,n0),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_32,plain,
    ( leq(n1,loopcounter)
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_33,plain,
    ~ leq(plus(X1,n1),X1),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    ( leq(X1,n0)
    | ~ leq(X1,loopcounter) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,plain,
    leq(n1,loopcounter),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_22])]) ).

cnf(c_0_36,plain,
    ~ leq(n1,n0),
    inference(spm,[status(thm)],[c_0_33,c_0_20]) ).

cnf(c_0_37,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.11/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 29 06:16:23 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.61  % Total time : 0.048000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.052000 s
%------------------------------------------------------------------------------