TSTP Solution File: NUN067+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUN067+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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  : 600s
% DateTime : Mon Jul 18 16:34:54 EDT 2022

% Result   : Theorem 0.19s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   73 (  22 unt;   0 def)
%            Number of atoms       :  171 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  180 (  82   ~;  58   |;  40   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :  121 (  19 sgn  63   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
    ? [Y24] :
    ! [X19] :
      ( ( id(X19,Y24)
        & r1(X19) )
      | ( ~ r1(X19)
        & ~ id(X19,Y24) ) ) ).

fof(axiom_2,axiom,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( id(X12,Y21)
        & r2(X11,X12) )
      | ( ~ r2(X11,X12)
        & ~ id(X12,Y21) ) ) ).

fof(axiom_6,axiom,
    ! [X21,X22] :
      ( ~ id(X21,X22)
      | id(X22,X21) ) ).

fof(axiom_8,axiom,
    ! [X26,X27] :
      ( ~ id(X26,X27)
      | ( ~ r1(X26)
        & ~ r1(X27) )
      | ( r1(X26)
        & r1(X27) ) ) ).

fof(axiom_4a,axiom,
    ! [X4] :
    ? [Y9] :
      ( id(Y9,X4)
      & ? [Y16] :
          ( r1(Y16)
          & r3(X4,Y16,Y9) ) ) ).

fof(axiom_7a,axiom,
    ! [X7,Y10] :
      ( ! [Y20] :
          ( ~ id(Y20,Y10)
          | ~ r1(Y20) )
      | ~ r2(X7,Y10) ) ).

fof(nonzerosexistid,conjecture,
    ? [Y1] :
    ! [Y2] :
      ( ~ id(Y1,Y2)
      | ~ r1(Y2) ) ).

fof(subgoal_0,plain,
    ? [Y1] :
    ! [Y2] :
      ( ~ id(Y1,Y2)
      | ~ r1(Y2) ),
    inference(strip,[],[nonzerosexistid]) ).

fof(negate_0_0,plain,
    ~ ? [Y1] :
      ! [Y2] :
        ( ~ id(Y1,Y2)
        | ~ r1(Y2) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [X4] :
    ? [Y9] :
      ( id(Y9,X4)
      & ? [Y16] :
          ( r1(Y16)
          & r3(X4,Y16,Y9) ) ),
    inference(canonicalize,[],[axiom_4a]) ).

fof(normalize_0_1,plain,
    ! [X4] :
    ? [Y9] :
      ( id(Y9,X4)
      & ? [Y16] :
          ( r1(Y16)
          & r3(X4,Y16,Y9) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X4] :
      ( id(skolemFOFtoCNF_Y9(X4),X4)
      & ? [Y16] :
          ( r1(Y16)
          & r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ) ),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X4] :
    ? [Y16] :
      ( r1(Y16)
      & r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X4] :
      ( r1(skolemFOFtoCNF_Y16(X4))
      & r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) ),
    inference(skolemize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X4] : r1(skolemFOFtoCNF_Y16(X4)),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ? [Y24] :
    ! [X19] :
      ( ( ~ id(X19,Y24)
        & ~ r1(X19) )
      | ( id(X19,Y24)
        & r1(X19) ) ),
    inference(canonicalize,[],[axiom_1]) ).

fof(normalize_0_7,plain,
    ! [X19] :
      ( ( ~ id(X19,skolemFOFtoCNF_Y24)
        & ~ r1(X19) )
      | ( id(X19,skolemFOFtoCNF_Y24)
        & r1(X19) ) ),
    inference(skolemize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X19] :
      ( ( ~ id(X19,skolemFOFtoCNF_Y24)
        & ~ r1(X19) )
      | ( id(X19,skolemFOFtoCNF_Y24)
        & r1(X19) ) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X19] :
      ( ( ~ id(X19,skolemFOFtoCNF_Y24)
        | r1(X19) )
      & ( ~ r1(X19)
        | id(X19,skolemFOFtoCNF_Y24) ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X19] :
      ( ~ r1(X19)
      | id(X19,skolemFOFtoCNF_Y24) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X7,Y10] :
      ( ~ r2(X7,Y10)
      | ! [Y20] :
          ( ~ id(Y20,Y10)
          | ~ r1(Y20) ) ),
    inference(canonicalize,[],[axiom_7a]) ).

fof(normalize_0_12,plain,
    ! [X7,Y10] :
      ( ~ r2(X7,Y10)
      | ! [Y20] :
          ( ~ id(Y20,Y10)
          | ~ r1(Y20) ) ),
    inference(specialize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [X7,Y10,Y20] :
      ( ~ id(Y20,Y10)
      | ~ r1(Y20)
      | ~ r2(X7,Y10) ),
    inference(clausify,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [Y1] :
    ? [Y2] :
      ( id(Y1,Y2)
      & r1(Y2) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_15,plain,
    ! [Y1] :
    ? [Y2] :
      ( id(Y1,Y2)
      & r1(Y2) ),
    inference(specialize,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    ! [Y1] :
      ( id(Y1,skolemFOFtoCNF_Y2_1(Y1))
      & r1(skolemFOFtoCNF_Y2_1(Y1)) ),
    inference(skolemize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [Y1] : id(Y1,skolemFOFtoCNF_Y2_1(Y1)),
    inference(conjunct,[],[normalize_0_16]) ).

fof(normalize_0_18,plain,
    ! [X21,X22] :
      ( ~ id(X21,X22)
      | id(X22,X21) ),
    inference(canonicalize,[],[axiom_6]) ).

fof(normalize_0_19,plain,
    ! [X21,X22] :
      ( ~ id(X21,X22)
      | id(X22,X21) ),
    inference(specialize,[],[normalize_0_18]) ).

fof(normalize_0_20,plain,
    ! [X26,X27] :
      ( ~ id(X26,X27)
      | ( ~ r1(X26)
        & ~ r1(X27) )
      | ( r1(X26)
        & r1(X27) ) ),
    inference(canonicalize,[],[axiom_8]) ).

fof(normalize_0_21,plain,
    ! [X26,X27] :
      ( ~ id(X26,X27)
      | ( ~ r1(X26)
        & ~ r1(X27) )
      | ( r1(X26)
        & r1(X27) ) ),
    inference(specialize,[],[normalize_0_20]) ).

fof(normalize_0_22,plain,
    ! [X26,X27] :
      ( ( ~ id(X26,X27)
        | ~ r1(X26)
        | r1(X27) )
      & ( ~ id(X26,X27)
        | ~ r1(X27)
        | r1(X26) ) ),
    inference(clausify,[],[normalize_0_21]) ).

fof(normalize_0_23,plain,
    ! [X26,X27] :
      ( ~ id(X26,X27)
      | ~ r1(X26)
      | r1(X27) ),
    inference(conjunct,[],[normalize_0_22]) ).

fof(normalize_0_24,plain,
    ! [Y1] : r1(skolemFOFtoCNF_Y2_1(Y1)),
    inference(conjunct,[],[normalize_0_16]) ).

fof(normalize_0_25,plain,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( ~ id(X12,Y21)
        & ~ r2(X11,X12) )
      | ( id(X12,Y21)
        & r2(X11,X12) ) ),
    inference(canonicalize,[],[axiom_2]) ).

fof(normalize_0_26,plain,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( ~ id(X12,Y21)
        & ~ r2(X11,X12) )
      | ( id(X12,Y21)
        & r2(X11,X12) ) ),
    inference(specialize,[],[normalize_0_25]) ).

fof(normalize_0_27,plain,
    ! [X11,X12] :
      ( ( ~ id(X12,skolemFOFtoCNF_Y21(X11))
        & ~ r2(X11,X12) )
      | ( id(X12,skolemFOFtoCNF_Y21(X11))
        & r2(X11,X12) ) ),
    inference(skolemize,[],[normalize_0_26]) ).

fof(normalize_0_28,plain,
    ! [X11,X12] :
      ( ( ~ id(X12,skolemFOFtoCNF_Y21(X11))
        & ~ r2(X11,X12) )
      | ( id(X12,skolemFOFtoCNF_Y21(X11))
        & r2(X11,X12) ) ),
    inference(specialize,[],[normalize_0_27]) ).

fof(normalize_0_29,plain,
    ! [X11,X12] :
      ( ( ~ id(X12,skolemFOFtoCNF_Y21(X11))
        | r2(X11,X12) )
      & ( ~ r2(X11,X12)
        | id(X12,skolemFOFtoCNF_Y21(X11)) ) ),
    inference(clausify,[],[normalize_0_28]) ).

fof(normalize_0_30,plain,
    ! [X11,X12] :
      ( ~ id(X12,skolemFOFtoCNF_Y21(X11))
      | r2(X11,X12) ),
    inference(conjunct,[],[normalize_0_29]) ).

cnf(refute_0_0,plain,
    r1(skolemFOFtoCNF_Y16(X4)),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_1,plain,
    ( ~ r1(X19)
    | id(X19,skolemFOFtoCNF_Y24) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_2,plain,
    ( ~ r1(skolemFOFtoCNF_Y16(X4))
    | id(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24) ),
    inference(subst,[],[refute_0_1:[bind(X19,$fot(skolemFOFtoCNF_Y16(X4)))]]) ).

cnf(refute_0_3,plain,
    id(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24),
    inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y16(X4)) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ id(Y20,Y10)
    | ~ r1(Y20)
    | ~ r2(X7,Y10) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_5,plain,
    id(Y1,skolemFOFtoCNF_Y2_1(Y1)),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_6,plain,
    id(X_39,skolemFOFtoCNF_Y2_1(X_39)),
    inference(subst,[],[refute_0_5:[bind(Y1,$fot(X_39))]]) ).

cnf(refute_0_7,plain,
    ( ~ id(X21,X22)
    | id(X22,X21) ),
    inference(canonicalize,[],[normalize_0_19]) ).

cnf(refute_0_8,plain,
    ( ~ id(X_39,skolemFOFtoCNF_Y2_1(X_39))
    | id(skolemFOFtoCNF_Y2_1(X_39),X_39) ),
    inference(subst,[],[refute_0_7:[bind(X21,$fot(X_39)),bind(X22,$fot(skolemFOFtoCNF_Y2_1(X_39)))]]) ).

cnf(refute_0_9,plain,
    id(skolemFOFtoCNF_Y2_1(X_39),X_39),
    inference(resolve,[$cnf( id(X_39,skolemFOFtoCNF_Y2_1(X_39)) )],[refute_0_6,refute_0_8]) ).

cnf(refute_0_10,plain,
    id(skolemFOFtoCNF_Y2_1(X_80),X_80),
    inference(subst,[],[refute_0_9:[bind(X_39,$fot(X_80))]]) ).

cnf(refute_0_11,plain,
    ( ~ id(X26,X27)
    | ~ r1(X26)
    | r1(X27) ),
    inference(canonicalize,[],[normalize_0_23]) ).

cnf(refute_0_12,plain,
    ( ~ id(skolemFOFtoCNF_Y2_1(X_80),X_80)
    | ~ r1(skolemFOFtoCNF_Y2_1(X_80))
    | r1(X_80) ),
    inference(subst,[],[refute_0_11:[bind(X26,$fot(skolemFOFtoCNF_Y2_1(X_80))),bind(X27,$fot(X_80))]]) ).

cnf(refute_0_13,plain,
    ( ~ r1(skolemFOFtoCNF_Y2_1(X_80))
    | r1(X_80) ),
    inference(resolve,[$cnf( id(skolemFOFtoCNF_Y2_1(X_80),X_80) )],[refute_0_10,refute_0_12]) ).

cnf(refute_0_14,plain,
    r1(skolemFOFtoCNF_Y2_1(Y1)),
    inference(canonicalize,[],[normalize_0_24]) ).

cnf(refute_0_15,plain,
    r1(skolemFOFtoCNF_Y2_1(X_80)),
    inference(subst,[],[refute_0_14:[bind(Y1,$fot(X_80))]]) ).

cnf(refute_0_16,plain,
    r1(X_80),
    inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y2_1(X_80)) )],[refute_0_15,refute_0_13]) ).

cnf(refute_0_17,plain,
    r1(Y20),
    inference(subst,[],[refute_0_16:[bind(X_80,$fot(Y20))]]) ).

cnf(refute_0_18,plain,
    ( ~ id(Y20,Y10)
    | ~ r2(X7,Y10) ),
    inference(resolve,[$cnf( r1(Y20) )],[refute_0_17,refute_0_4]) ).

cnf(refute_0_19,plain,
    ( ~ id(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24)
    | ~ r2(X_152,skolemFOFtoCNF_Y24) ),
    inference(subst,[],[refute_0_18:[bind(X7,$fot(X_152)),bind(Y10,$fot(skolemFOFtoCNF_Y24)),bind(Y20,$fot(skolemFOFtoCNF_Y16(X4)))]]) ).

cnf(refute_0_20,plain,
    ~ r2(X_152,skolemFOFtoCNF_Y24),
    inference(resolve,[$cnf( id(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24) )],[refute_0_3,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( ~ id(X12,skolemFOFtoCNF_Y21(X11))
    | r2(X11,X12) ),
    inference(canonicalize,[],[normalize_0_30]) ).

cnf(refute_0_22,plain,
    ( ~ id(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X11))
    | r2(X11,skolemFOFtoCNF_Y24) ),
    inference(subst,[],[refute_0_21:[bind(X12,$fot(skolemFOFtoCNF_Y24))]]) ).

cnf(refute_0_23,plain,
    ( ~ id(X_82,skolemFOFtoCNF_Y24)
    | id(skolemFOFtoCNF_Y24,X_82) ),
    inference(subst,[],[refute_0_7:[bind(X21,$fot(X_82)),bind(X22,$fot(skolemFOFtoCNF_Y24))]]) ).

cnf(refute_0_24,plain,
    ( ~ r1(X_81)
    | id(X_81,skolemFOFtoCNF_Y24) ),
    inference(subst,[],[refute_0_1:[bind(X19,$fot(X_81))]]) ).

cnf(refute_0_25,plain,
    r1(X_81),
    inference(subst,[],[refute_0_16:[bind(X_80,$fot(X_81))]]) ).

cnf(refute_0_26,plain,
    id(X_81,skolemFOFtoCNF_Y24),
    inference(resolve,[$cnf( r1(X_81) )],[refute_0_25,refute_0_24]) ).

cnf(refute_0_27,plain,
    id(X_82,skolemFOFtoCNF_Y24),
    inference(subst,[],[refute_0_26:[bind(X_81,$fot(X_82))]]) ).

cnf(refute_0_28,plain,
    id(skolemFOFtoCNF_Y24,X_82),
    inference(resolve,[$cnf( id(X_82,skolemFOFtoCNF_Y24) )],[refute_0_27,refute_0_23]) ).

cnf(refute_0_29,plain,
    id(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X11)),
    inference(subst,[],[refute_0_28:[bind(X_82,$fot(skolemFOFtoCNF_Y21(X11)))]]) ).

cnf(refute_0_30,plain,
    r2(X11,skolemFOFtoCNF_Y24),
    inference(resolve,[$cnf( id(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X11)) )],[refute_0_29,refute_0_22]) ).

cnf(refute_0_31,plain,
    r2(X_152,skolemFOFtoCNF_Y24),
    inference(subst,[],[refute_0_30:[bind(X11,$fot(X_152))]]) ).

cnf(refute_0_32,plain,
    $false,
    inference(resolve,[$cnf( r2(X_152,skolemFOFtoCNF_Y24) )],[refute_0_31,refute_0_20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUN067+1 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n028.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  : 600
% 0.13/0.33  % DateTime : Thu Jun  2 08:10:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.38  
% 0.19/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.39  
%------------------------------------------------------------------------------