TSTP Solution File: SWV366+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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 : Wed Jul 20 20:31:23 EDT 2022

% Result   : Theorem 0.60s 0.84s
% Output   : CNFRefutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   30 (  18 unt;   0 def)
%            Number of atoms       :   45 (  44 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   34 (  19   ~;  10   |;   2   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-3 aty)
%            Number of variables   :  100 (  11 sgn  64   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ax55,axiom,
    ! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X) ).

fof(l2_co,conjecture,
    ! [U] :
      ( ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y))
     => ! [Z,X1,X2,X3,X4,X5] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) ) ).

fof(subgoal_0,plain,
    ! [U] :
      ( ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y))
     => ! [Z,X1,X2,X3,X4,X5] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) ),
    inference(strip,[],[l2_co]) ).

fof(negate_0_0,plain,
    ~ ! [U] :
        ( ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y))
       => ! [Z,X1,X2,X3,X4,X5] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [U] :
      ( ? [X1,X2,X3,X4,X5,Z] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) != i(triple(X1,insert_slb(U,pair(X4,X5)),X3))
      & ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y)) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ? [X1,X2,X3,X4,X5,Z] : i(triple(Z,insert_slb(skolemFOFtoCNF_U,pair(X4,X5)),X2)) != i(triple(X1,insert_slb(skolemFOFtoCNF_U,pair(X4,X5)),X3))
    & ! [V,W,X,Y] : i(triple(V,skolemFOFtoCNF_U,X)) = i(triple(W,skolemFOFtoCNF_U,Y)) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ? [X1,X2,X3,X4,X5,Z] : i(triple(Z,insert_slb(skolemFOFtoCNF_U,pair(X4,X5)),X2)) != i(triple(X1,insert_slb(skolemFOFtoCNF_U,pair(X4,X5)),X3)),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) != i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
    inference(canonicalize,[],[ax55]) ).

fof(normalize_0_5,plain,
    ! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [V,W,X,Y] : i(triple(V,skolemFOFtoCNF_U,X)) = i(triple(W,skolemFOFtoCNF_U,Y)),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_7,plain,
    ! [V,W,X,Y] : i(triple(V,skolemFOFtoCNF_U,X)) = i(triple(W,skolemFOFtoCNF_U,Y)),
    inference(specialize,[],[normalize_0_6]) ).

cnf(refute_0_0,plain,
    i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) != i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) = insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),
    inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_Z)),bind(V,$fot(skolemFOFtoCNF_U)),bind(W,$fot(skolemFOFtoCNF_X2)),bind(X,$fot(skolemFOFtoCNF_X4)),bind(Y,$fot(skolemFOFtoCNF_X5))]]) ).

cnf(refute_0_3,plain,
    ( i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) != insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4)
    | insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))
    | i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)),i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))) ),[0],$fot(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4))]]) ).

cnf(refute_0_4,plain,
    ( insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))
    | i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
    inference(resolve,[$cnf( $equal(i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)),insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4)) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) = insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4),
    inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_X1)),bind(V,$fot(skolemFOFtoCNF_U)),bind(W,$fot(skolemFOFtoCNF_X3)),bind(X,$fot(skolemFOFtoCNF_X4)),bind(Y,$fot(skolemFOFtoCNF_X5))]]) ).

cnf(refute_0_6,plain,
    ( i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)
    | insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)
    | insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))) ),[1],$fot(insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4))]]) ).

cnf(refute_0_7,plain,
    ( insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)
    | insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
    inference(resolve,[$cnf( $equal(i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)),insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)
    | i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
    inference(resolve,[$cnf( $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))) )],[refute_0_7,refute_0_4]) ).

cnf(refute_0_9,plain,
    insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4),
    inference(resolve,[$cnf( $equal(i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)),i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))) )],[refute_0_8,refute_0_0]) ).

cnf(refute_0_10,plain,
    i(triple(V,skolemFOFtoCNF_U,X)) = i(triple(W,skolemFOFtoCNF_U,Y)),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_11,plain,
    i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)) = i(triple(X_665,skolemFOFtoCNF_U,X_667)),
    inference(subst,[],[refute_0_10:[bind(V,$fot(skolemFOFtoCNF_X1)),bind(W,$fot(X_665)),bind(X,$fot(skolemFOFtoCNF_X3)),bind(Y,$fot(X_667))]]) ).

cnf(refute_0_12,plain,
    ( i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)) != i(triple(X_665,skolemFOFtoCNF_U,X_667))
    | insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(X_665,skolemFOFtoCNF_U,X_667)),skolemFOFtoCNF_X4)
    | insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)) ),[1,0],$fot(i(triple(X_665,skolemFOFtoCNF_U,X_667)))]]) ).

cnf(refute_0_13,plain,
    ( insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(X_665,skolemFOFtoCNF_U,X_667)),skolemFOFtoCNF_X4)
    | insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4) ),
    inference(resolve,[$cnf( $equal(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),i(triple(X_665,skolemFOFtoCNF_U,X_667))) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(X_665,skolemFOFtoCNF_U,X_667)),skolemFOFtoCNF_X4),
    inference(resolve,[$cnf( $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)) )],[refute_0_13,refute_0_9]) ).

cnf(refute_0_15,plain,
    insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),
    inference(subst,[],[refute_0_14:[bind(X_665,$fot(skolemFOFtoCNF_Z)),bind(X_667,$fot(skolemFOFtoCNF_X2))]]) ).

cnf(refute_0_16,plain,
    insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),
    introduced(tautology,[refl,[$fot(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4))]]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4)) )],[refute_0_16,refute_0_15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n017.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  : 600
% 0.12/0.34  % DateTime : Wed Jun 15 04:50:39 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.19/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.84  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.84  
% 0.60/0.84  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.60/0.85  
%------------------------------------------------------------------------------