TSTP Solution File: REL049+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : REL049+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 19:46:17 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   38 (  20 unt;   0 def)
%            Number of atoms       :   68 (  67 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   56 (  26   ~;  20   |;   7   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   41 (   0 sgn  18   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(maddux2_join_associativity,axiom,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).

fof(goals,conjecture,
    ! [X0,X1,X2] :
      ( ( join(X0,X1) = X1
        & join(X2,X1) = X1 )
     => join(join(X0,X2),X1) = X1 ) ).

fof(subgoal_0,plain,
    ! [X0,X1,X2] :
      ( ( join(X0,X1) = X1
        & join(X2,X1) = X1 )
     => join(join(X0,X2),X1) = X1 ),
    inference(strip,[],[goals]) ).

fof(negate_0_0,plain,
    ~ ! [X0,X1,X2] :
        ( ( join(X0,X1) = X1
          & join(X2,X1) = X1 )
       => join(join(X0,X2),X1) = X1 ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [X0,X1,X2] :
      ( join(join(X0,X2),X1) != X1
      & join(X0,X1) = X1
      & join(X2,X1) = X1 ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
    & join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1
    & join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1,
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_4,plain,
    join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_5,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    inference(canonicalize,[],[maddux2_join_associativity]) ).

fof(normalize_0_6,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    inference(specialize,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1,
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
    join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),
    introduced(tautology,[refl,[$fot(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)))]]) ).

cnf(refute_0_4,plain,
    ( join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) != join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))
    | join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
    | join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) ),
    introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))) ),[1,1],$fot(skolemFOFtoCNF_X1)]]) ).

cnf(refute_0_5,plain,
    ( join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
    | join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) ),
    inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),
    inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_2,refute_0_5]) ).

cnf(refute_0_7,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_8,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_9,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_11,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) != join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)
    | join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
    | join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = skolemFOFtoCNF_X1 ),
    inference(subst,[],[refute_0_11:[bind(X,$fot(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)))),bind(Y,$fot(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),bind(Z,$fot(skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_13,plain,
    ( join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
    | join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = skolemFOFtoCNF_X1 ),
    inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) )],[refute_0_6,refute_0_12]) ).

cnf(refute_0_14,plain,
    join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = skolemFOFtoCNF_X1,
    inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_1,refute_0_13]) ).

cnf(refute_0_15,plain,
    join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_16,plain,
    ( join(X0,join(X1,X2)) != join(join(X0,X1),X2)
    | join(join(X0,X1),X2) = join(X0,join(X1,X2)) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(join(X0,join(X1,X2)))),bind(Y,$fot(join(join(X0,X1),X2)))]]) ).

cnf(refute_0_17,plain,
    join(join(X0,X1),X2) = join(X0,join(X1,X2)),
    inference(resolve,[$cnf( $equal(join(X0,join(X1,X2)),join(join(X0,X1),X2)) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),
    inference(subst,[],[refute_0_17:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(skolemFOFtoCNF_X2)),bind(X2,$fot(skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_19,plain,
    ( join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))
    | join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) != skolemFOFtoCNF_X1
    | join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
    inference(subst,[],[refute_0_11:[bind(X,$fot(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1))),bind(Y,$fot(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)))),bind(Z,$fot(skolemFOFtoCNF_X1))]]) ).

cnf(refute_0_20,plain,
    ( join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) != skolemFOFtoCNF_X1
    | join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
    inference(resolve,[$cnf( $equal(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1),join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
    inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),skolemFOFtoCNF_X1) )],[refute_0_14,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
    | skolemFOFtoCNF_X1 != skolemFOFtoCNF_X1
    | join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) ),[0],$fot(skolemFOFtoCNF_X1)]]) ).

cnf(refute_0_23,plain,
    ( skolemFOFtoCNF_X1 != skolemFOFtoCNF_X1
    | join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
    inference(resolve,[$cnf( $equal(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    skolemFOFtoCNF_X1 != skolemFOFtoCNF_X1,
    inference(resolve,[$cnf( $equal(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_23,refute_0_0]) ).

cnf(refute_0_25,plain,
    skolemFOFtoCNF_X1 = skolemFOFtoCNF_X1,
    introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X1)]]) ).

cnf(refute_0_26,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1,skolemFOFtoCNF_X1) )],[refute_0_25,refute_0_24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : REL049+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Fri Jul  8 15:41:55 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37  
% 0.13/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37  
%------------------------------------------------------------------------------