TSTP Solution File: MSC012+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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 : Sun Jul 17 22:51:31 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   63 (  22 unt;   0 def)
%            Number of atoms       :  128 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  116 (  51   ~;  56   |;   7   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-1 aty)
%            Number of variables   :   78 (   4 sgn  25   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(left_to_right,axiom,
    ! [A,B] :
      ( ( p(A)
        & less(A,B)
        & p(B) )
     => goal ) ).

fof(right_to_left,axiom,
    ! [A] :
      ( p(A)
      | ? [B] :
          ( less(A,B)
          & p(B) ) ) ).

fof(transitive_less,axiom,
    ! [A,B,C] :
      ( ( less(A,B)
        & less(B,C) )
     => less(A,C) ) ).

fof(serial_less,axiom,
    ! [A] :
    ? [B] : less(A,B) ).

fof(goal_to_be_proved,conjecture,
    goal ).

fof(subgoal_0,plain,
    goal,
    inference(strip,[],[goal_to_be_proved]) ).

fof(negate_0_0,plain,
    ~ goal,
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A,B] :
      ( ~ less(A,B)
      | ~ p(A)
      | ~ p(B)
      | goal ),
    inference(canonicalize,[],[left_to_right]) ).

fof(normalize_0_1,plain,
    ! [A,B] :
      ( ~ less(A,B)
      | ~ p(A)
      | ~ p(B)
      | goal ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ~ goal,
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_3,plain,
    ! [A] :
    ? [B] : less(A,B),
    inference(canonicalize,[],[serial_less]) ).

fof(normalize_0_4,plain,
    ! [A] :
    ? [B] : less(A,B),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [A] : less(A,skolemFOFtoCNF_B_1(A)),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [A,B,C] :
      ( ~ less(A,B)
      | ~ less(B,C)
      | less(A,C) ),
    inference(canonicalize,[],[transitive_less]) ).

fof(normalize_0_7,plain,
    ! [A,B,C] :
      ( ~ less(A,B)
      | ~ less(B,C)
      | less(A,C) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [A] :
      ( p(A)
      | ? [B] :
          ( less(A,B)
          & p(B) ) ),
    inference(canonicalize,[],[right_to_left]) ).

fof(normalize_0_9,plain,
    ! [A] :
      ( p(A)
      | ? [B] :
          ( less(A,B)
          & p(B) ) ),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [A] :
      ( ( less(A,skolemFOFtoCNF_B(A))
        | p(A) )
      & ( p(A)
        | p(skolemFOFtoCNF_B(A)) ) ),
    inference(clausify,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [A] :
      ( p(A)
      | p(skolemFOFtoCNF_B(A)) ),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [A] :
      ( less(A,skolemFOFtoCNF_B(A))
      | p(A) ),
    inference(conjunct,[],[normalize_0_10]) ).

cnf(refute_0_0,plain,
    ( ~ less(A,B)
    | ~ p(A)
    | ~ p(B)
    | goal ),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ~ goal,
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_2,plain,
    ( ~ less(A,B)
    | ~ p(A)
    | ~ p(B) ),
    inference(resolve,[$cnf( goal )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ less(X_12,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12))))
    | ~ p(X_12)
    | ~ p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(X_12)),bind(B,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))))]]) ).

cnf(refute_0_4,plain,
    less(A,skolemFOFtoCNF_B_1(A)),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_5,plain,
    less(X_6,skolemFOFtoCNF_B_1(X_6)),
    inference(subst,[],[refute_0_4:[bind(A,$fot(X_6))]]) ).

cnf(refute_0_6,plain,
    ( ~ less(A,B)
    | ~ less(B,C)
    | less(A,C) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_7,plain,
    ( ~ less(X_6,skolemFOFtoCNF_B_1(X_6))
    | ~ less(skolemFOFtoCNF_B_1(X_6),X_8)
    | less(X_6,X_8) ),
    inference(subst,[],[refute_0_6:[bind(A,$fot(X_6)),bind(B,$fot(skolemFOFtoCNF_B_1(X_6))),bind(C,$fot(X_8))]]) ).

cnf(refute_0_8,plain,
    ( ~ less(skolemFOFtoCNF_B_1(X_6),X_8)
    | less(X_6,X_8) ),
    inference(resolve,[$cnf( less(X_6,skolemFOFtoCNF_B_1(X_6)) )],[refute_0_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ less(skolemFOFtoCNF_B_1(X_6),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6))))
    | less(X_6,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))) ),
    inference(subst,[],[refute_0_8:[bind(X_8,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))))]]) ).

cnf(refute_0_10,plain,
    less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))),
    inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_1(X_9)))]]) ).

cnf(refute_0_11,plain,
    ( ~ less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9)))
    | less(X_9,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))) ),
    inference(subst,[],[refute_0_8:[bind(X_6,$fot(X_9)),bind(X_8,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))))]]) ).

cnf(refute_0_12,plain,
    less(X_9,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))),
    inference(resolve,[$cnf( less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    less(skolemFOFtoCNF_B_1(X_6),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))),
    inference(subst,[],[refute_0_12:[bind(X_9,$fot(skolemFOFtoCNF_B_1(X_6)))]]) ).

cnf(refute_0_14,plain,
    less(X_6,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))),
    inference(resolve,[$cnf( less(skolemFOFtoCNF_B_1(X_6),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))) )],[refute_0_13,refute_0_9]) ).

cnf(refute_0_15,plain,
    less(X_12,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))),
    inference(subst,[],[refute_0_14:[bind(X_6,$fot(X_12))]]) ).

cnf(refute_0_16,plain,
    ( ~ p(X_12)
    | ~ p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))) ),
    inference(resolve,[$cnf( less(X_12,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))) )],[refute_0_15,refute_0_3]) ).

cnf(refute_0_17,plain,
    ( p(A)
    | p(skolemFOFtoCNF_B(A)) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_18,plain,
    ( p(X_44)
    | p(skolemFOFtoCNF_B(X_44)) ),
    inference(subst,[],[refute_0_17:[bind(A,$fot(X_44))]]) ).

cnf(refute_0_19,plain,
    less(X_3,skolemFOFtoCNF_B_1(X_3)),
    inference(subst,[],[refute_0_4:[bind(A,$fot(X_3))]]) ).

cnf(refute_0_20,plain,
    ( ~ less(X_3,skolemFOFtoCNF_B_1(X_3))
    | ~ p(X_3)
    | ~ p(skolemFOFtoCNF_B_1(X_3)) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(X_3)),bind(B,$fot(skolemFOFtoCNF_B_1(X_3)))]]) ).

cnf(refute_0_21,plain,
    ( ~ p(X_3)
    | ~ p(skolemFOFtoCNF_B_1(X_3)) ),
    inference(resolve,[$cnf( less(X_3,skolemFOFtoCNF_B_1(X_3)) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( ~ p(skolemFOFtoCNF_B(X_43))
    | ~ p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(X_43))) ),
    inference(subst,[],[refute_0_21:[bind(X_3,$fot(skolemFOFtoCNF_B(X_43)))]]) ).

cnf(refute_0_23,plain,
    ( p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_41)))
    | p(skolemFOFtoCNF_B_1(X_41)) ),
    inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_B_1(X_41)))]]) ).

cnf(refute_0_24,plain,
    ( ~ less(X_15,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15)))
    | ~ p(X_15)
    | ~ p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15))) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(X_15)),bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15))))]]) ).

cnf(refute_0_25,plain,
    ( less(A,skolemFOFtoCNF_B(A))
    | p(A) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_26,plain,
    ( less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9)))
    | p(skolemFOFtoCNF_B_1(X_9)) ),
    inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_B_1(X_9)))]]) ).

cnf(refute_0_27,plain,
    ( ~ less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9)))
    | less(X_9,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9))) ),
    inference(subst,[],[refute_0_8:[bind(X_6,$fot(X_9)),bind(X_8,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9))))]]) ).

cnf(refute_0_28,plain,
    ( less(X_9,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9)))
    | p(skolemFOFtoCNF_B_1(X_9)) ),
    inference(resolve,[$cnf( less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9))) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( less(X_15,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15)))
    | p(skolemFOFtoCNF_B_1(X_15)) ),
    inference(subst,[],[refute_0_28:[bind(X_9,$fot(X_15))]]) ).

cnf(refute_0_30,plain,
    ( ~ p(X_15)
    | ~ p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15)))
    | p(skolemFOFtoCNF_B_1(X_15)) ),
    inference(resolve,[$cnf( less(X_15,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15))) )],[refute_0_29,refute_0_24]) ).

cnf(refute_0_31,plain,
    ( ~ p(X_41)
    | ~ p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_41)))
    | p(skolemFOFtoCNF_B_1(X_41)) ),
    inference(subst,[],[refute_0_30:[bind(X_15,$fot(X_41))]]) ).

cnf(refute_0_32,plain,
    ( ~ p(X_41)
    | p(skolemFOFtoCNF_B_1(X_41)) ),
    inference(resolve,[$cnf( p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_41))) )],[refute_0_23,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( ~ p(skolemFOFtoCNF_B(A))
    | p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(A))) ),
    inference(subst,[],[refute_0_32:[bind(X_41,$fot(skolemFOFtoCNF_B(A)))]]) ).

cnf(refute_0_34,plain,
    ( p(A)
    | p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(A))) ),
    inference(resolve,[$cnf( p(skolemFOFtoCNF_B(A)) )],[refute_0_17,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( p(X_43)
    | p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(X_43))) ),
    inference(subst,[],[refute_0_34:[bind(A,$fot(X_43))]]) ).

cnf(refute_0_36,plain,
    ( ~ p(skolemFOFtoCNF_B(X_43))
    | p(X_43) ),
    inference(resolve,[$cnf( p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(X_43))) )],[refute_0_35,refute_0_22]) ).

cnf(refute_0_37,plain,
    ( ~ p(skolemFOFtoCNF_B(X_44))
    | p(X_44) ),
    inference(subst,[],[refute_0_36:[bind(X_43,$fot(X_44))]]) ).

cnf(refute_0_38,plain,
    p(X_44),
    inference(resolve,[$cnf( p(skolemFOFtoCNF_B(X_44)) )],[refute_0_18,refute_0_37]) ).

cnf(refute_0_39,plain,
    p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))),
    inference(subst,[],[refute_0_38:[bind(X_44,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))))]]) ).

cnf(refute_0_40,plain,
    ~ p(X_12),
    inference(resolve,[$cnf( p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))) )],[refute_0_39,refute_0_16]) ).

cnf(refute_0_41,plain,
    p(X_12),
    inference(subst,[],[refute_0_38:[bind(X_44,$fot(X_12))]]) ).

cnf(refute_0_42,plain,
    $false,
    inference(resolve,[$cnf( p(X_12) )],[refute_0_41,refute_0_40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  1 16:56:20 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37  
% 0.13/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37  
%------------------------------------------------------------------------------