TSTP Solution File: SET620+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET620+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n019.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 : Tue Jul 19 03:36:03 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   76 (  54 unt;   0 def)
%            Number of atoms       :  108 ( 107 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   69 (  37   ~;  32   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  141 (   0 sgn  45   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
    ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ).

fof(difference_into_intersection,axiom,
    ! [B,C] : difference(B,intersection(B,C)) = difference(B,C) ).

fof(difference_distributes_over_union,axiom,
    ! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)) ).

fof(commutativity_of_union,axiom,
    ! [B,C] : union(B,C) = union(C,B) ).

fof(commutativity_of_intersection,axiom,
    ! [B,C] : intersection(B,C) = intersection(C,B) ).

fof(commutativity_of_symmetric_difference,axiom,
    ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ).

fof(prove_th96,conjecture,
    ! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)) ).

fof(subgoal_0,plain,
    ! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
    inference(strip,[],[prove_th96]) ).

fof(negate_0_0,plain,
    ~ ! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [B,C] : symmetric_difference(B,C) != difference(union(B,C),intersection(B,C)),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
    inference(canonicalize,[],[commutativity_of_symmetric_difference]) ).

fof(normalize_0_3,plain,
    ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
    inference(canonicalize,[],[difference_distributes_over_union]) ).

fof(normalize_0_5,plain,
    ! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
    inference(canonicalize,[],[difference_into_intersection]) ).

fof(normalize_0_7,plain,
    ! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [B,C] : intersection(B,C) = intersection(C,B),
    inference(canonicalize,[],[commutativity_of_intersection]) ).

fof(normalize_0_9,plain,
    ! [B,C] : intersection(B,C) = intersection(C,B),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [B,C] : union(B,C) = union(C,B),
    inference(canonicalize,[],[commutativity_of_union]) ).

fof(normalize_0_11,plain,
    ! [B,C] : union(B,C) = union(C,B),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
    inference(canonicalize,[],[symmetric_difference_defn]) ).

fof(normalize_0_13,plain,
    ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
    inference(specialize,[],[normalize_0_12]) ).

cnf(refute_0_0,plain,
    symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    symmetric_difference(B,C) = symmetric_difference(C,B),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_3,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_4,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( symmetric_difference(B,C) != symmetric_difference(C,B)
    | symmetric_difference(C,B) = symmetric_difference(B,C) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(symmetric_difference(B,C))),bind(Y,$fot(symmetric_difference(C,B)))]]) ).

cnf(refute_0_6,plain,
    symmetric_difference(C,B) = symmetric_difference(B,C),
    inference(resolve,[$cnf( $equal(symmetric_difference(B,C),symmetric_difference(C,B)) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B) = symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
    inference(subst,[],[refute_0_6:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).

cnf(refute_0_8,plain,
    difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_9,plain,
    difference(union(X_15,X_16),intersection(X_8,X_16)) = union(difference(X_15,intersection(X_8,X_16)),difference(X_16,intersection(X_8,X_16))),
    inference(subst,[],[refute_0_8:[bind(B,$fot(X_15)),bind(C,$fot(X_16)),bind(D,$fot(intersection(X_8,X_16)))]]) ).

cnf(refute_0_10,plain,
    difference(B,intersection(B,C)) = difference(B,C),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_11,plain,
    difference(X_7,intersection(X_7,X_8)) = difference(X_7,X_8),
    inference(subst,[],[refute_0_10:[bind(B,$fot(X_7)),bind(C,$fot(X_8))]]) ).

cnf(refute_0_12,plain,
    intersection(B,C) = intersection(C,B),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_13,plain,
    intersection(X_8,X_7) = intersection(X_7,X_8),
    inference(subst,[],[refute_0_12:[bind(B,$fot(X_8)),bind(C,$fot(X_7))]]) ).

cnf(refute_0_14,plain,
    ( intersection(X_8,X_7) != intersection(X_7,X_8)
    | intersection(X_7,X_8) = intersection(X_8,X_7) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(intersection(X_8,X_7))),bind(Y,$fot(intersection(X_7,X_8)))]]) ).

cnf(refute_0_15,plain,
    intersection(X_7,X_8) = intersection(X_8,X_7),
    inference(resolve,[$cnf( $equal(intersection(X_8,X_7),intersection(X_7,X_8)) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( difference(X_7,intersection(X_7,X_8)) != difference(X_7,X_8)
    | intersection(X_7,X_8) != intersection(X_8,X_7)
    | difference(X_7,intersection(X_8,X_7)) = difference(X_7,X_8) ),
    introduced(tautology,[equality,[$cnf( $equal(difference(X_7,intersection(X_7,X_8)),difference(X_7,X_8)) ),[0,1],$fot(intersection(X_8,X_7))]]) ).

cnf(refute_0_17,plain,
    ( difference(X_7,intersection(X_7,X_8)) != difference(X_7,X_8)
    | difference(X_7,intersection(X_8,X_7)) = difference(X_7,X_8) ),
    inference(resolve,[$cnf( $equal(intersection(X_7,X_8),intersection(X_8,X_7)) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    difference(X_7,intersection(X_8,X_7)) = difference(X_7,X_8),
    inference(resolve,[$cnf( $equal(difference(X_7,intersection(X_7,X_8)),difference(X_7,X_8)) )],[refute_0_11,refute_0_17]) ).

cnf(refute_0_19,plain,
    difference(X_16,intersection(X_8,X_16)) = difference(X_16,X_8),
    inference(subst,[],[refute_0_18:[bind(X_7,$fot(X_16))]]) ).

cnf(refute_0_20,plain,
    ( difference(X_16,intersection(X_8,X_16)) != difference(X_16,X_8)
    | difference(union(X_15,X_16),intersection(X_8,X_16)) != union(difference(X_15,intersection(X_8,X_16)),difference(X_16,intersection(X_8,X_16)))
    | difference(union(X_15,X_16),intersection(X_8,X_16)) = union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8)) ),
    introduced(tautology,[equality,[$cnf( $equal(difference(union(X_15,X_16),intersection(X_8,X_16)),union(difference(X_15,intersection(X_8,X_16)),difference(X_16,intersection(X_8,X_16)))) ),[1,1],$fot(difference(X_16,X_8))]]) ).

cnf(refute_0_21,plain,
    ( difference(union(X_15,X_16),intersection(X_8,X_16)) != union(difference(X_15,intersection(X_8,X_16)),difference(X_16,intersection(X_8,X_16)))
    | difference(union(X_15,X_16),intersection(X_8,X_16)) = union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8)) ),
    inference(resolve,[$cnf( $equal(difference(X_16,intersection(X_8,X_16)),difference(X_16,X_8)) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    difference(union(X_15,X_16),intersection(X_8,X_16)) = union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8)),
    inference(resolve,[$cnf( $equal(difference(union(X_15,X_16),intersection(X_8,X_16)),union(difference(X_15,intersection(X_8,X_16)),difference(X_16,intersection(X_8,X_16)))) )],[refute_0_9,refute_0_21]) ).

cnf(refute_0_23,plain,
    union(B,C) = union(C,B),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_24,plain,
    ( union(B,C) != union(C,B)
    | union(C,B) = union(B,C) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(union(B,C))),bind(Y,$fot(union(C,B)))]]) ).

cnf(refute_0_25,plain,
    union(C,B) = union(B,C),
    inference(resolve,[$cnf( $equal(union(B,C),union(C,B)) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8)) = union(difference(X_16,X_8),difference(X_15,intersection(X_8,X_16))),
    inference(subst,[],[refute_0_25:[bind(B,$fot(difference(X_16,X_8))),bind(C,$fot(difference(X_15,intersection(X_8,X_16))))]]) ).

cnf(refute_0_27,plain,
    ( difference(union(X_15,X_16),intersection(X_8,X_16)) != union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8))
    | union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8)) != union(difference(X_16,X_8),difference(X_15,intersection(X_8,X_16)))
    | difference(union(X_15,X_16),intersection(X_8,X_16)) = union(difference(X_16,X_8),difference(X_15,intersection(X_8,X_16))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(difference(union(X_15,X_16),intersection(X_8,X_16)),union(difference(X_16,X_8),difference(X_15,intersection(X_8,X_16)))) ),[0],$fot(union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8)))]]) ).

cnf(refute_0_28,plain,
    ( difference(union(X_15,X_16),intersection(X_8,X_16)) != union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8))
    | difference(union(X_15,X_16),intersection(X_8,X_16)) = union(difference(X_16,X_8),difference(X_15,intersection(X_8,X_16))) ),
    inference(resolve,[$cnf( $equal(union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8)),union(difference(X_16,X_8),difference(X_15,intersection(X_8,X_16)))) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    difference(union(X_15,X_16),intersection(X_8,X_16)) = union(difference(X_16,X_8),difference(X_15,intersection(X_8,X_16))),
    inference(resolve,[$cnf( $equal(difference(union(X_15,X_16),intersection(X_8,X_16)),union(difference(X_15,intersection(X_8,X_16)),difference(X_16,X_8))) )],[refute_0_22,refute_0_28]) ).

cnf(refute_0_30,plain,
    difference(union(X_90,X_89),intersection(X_90,X_89)) = union(difference(X_89,X_90),difference(X_90,intersection(X_90,X_89))),
    inference(subst,[],[refute_0_29:[bind(X_15,$fot(X_90)),bind(X_16,$fot(X_89)),bind(X_8,$fot(X_90))]]) ).

cnf(refute_0_31,plain,
    difference(X_90,intersection(X_90,X_89)) = difference(X_90,X_89),
    inference(subst,[],[refute_0_10:[bind(B,$fot(X_90)),bind(C,$fot(X_89))]]) ).

cnf(refute_0_32,plain,
    ( difference(X_90,intersection(X_90,X_89)) != difference(X_90,X_89)
    | difference(union(X_90,X_89),intersection(X_90,X_89)) != union(difference(X_89,X_90),difference(X_90,intersection(X_90,X_89)))
    | difference(union(X_90,X_89),intersection(X_90,X_89)) = union(difference(X_89,X_90),difference(X_90,X_89)) ),
    introduced(tautology,[equality,[$cnf( $equal(difference(union(X_90,X_89),intersection(X_90,X_89)),union(difference(X_89,X_90),difference(X_90,intersection(X_90,X_89)))) ),[1,1],$fot(difference(X_90,X_89))]]) ).

cnf(refute_0_33,plain,
    ( difference(union(X_90,X_89),intersection(X_90,X_89)) != union(difference(X_89,X_90),difference(X_90,intersection(X_90,X_89)))
    | difference(union(X_90,X_89),intersection(X_90,X_89)) = union(difference(X_89,X_90),difference(X_90,X_89)) ),
    inference(resolve,[$cnf( $equal(difference(X_90,intersection(X_90,X_89)),difference(X_90,X_89)) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    difference(union(X_90,X_89),intersection(X_90,X_89)) = union(difference(X_89,X_90),difference(X_90,X_89)),
    inference(resolve,[$cnf( $equal(difference(union(X_90,X_89),intersection(X_90,X_89)),union(difference(X_89,X_90),difference(X_90,intersection(X_90,X_89)))) )],[refute_0_30,refute_0_33]) ).

cnf(refute_0_35,plain,
    symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_36,plain,
    ( symmetric_difference(B,C) != union(difference(B,C),difference(C,B))
    | union(difference(B,C),difference(C,B)) = symmetric_difference(B,C) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(symmetric_difference(B,C))),bind(Y,$fot(union(difference(B,C),difference(C,B))))]]) ).

cnf(refute_0_37,plain,
    union(difference(B,C),difference(C,B)) = symmetric_difference(B,C),
    inference(resolve,[$cnf( $equal(symmetric_difference(B,C),union(difference(B,C),difference(C,B))) )],[refute_0_35,refute_0_36]) ).

cnf(refute_0_38,plain,
    union(difference(X_89,X_90),difference(X_90,X_89)) = symmetric_difference(X_89,X_90),
    inference(subst,[],[refute_0_37:[bind(B,$fot(X_89)),bind(C,$fot(X_90))]]) ).

cnf(refute_0_39,plain,
    ( difference(union(X_90,X_89),intersection(X_90,X_89)) != union(difference(X_89,X_90),difference(X_90,X_89))
    | union(difference(X_89,X_90),difference(X_90,X_89)) != symmetric_difference(X_89,X_90)
    | difference(union(X_90,X_89),intersection(X_90,X_89)) = symmetric_difference(X_89,X_90) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(difference(union(X_90,X_89),intersection(X_90,X_89)),symmetric_difference(X_89,X_90)) ),[0],$fot(union(difference(X_89,X_90),difference(X_90,X_89)))]]) ).

cnf(refute_0_40,plain,
    ( difference(union(X_90,X_89),intersection(X_90,X_89)) != union(difference(X_89,X_90),difference(X_90,X_89))
    | difference(union(X_90,X_89),intersection(X_90,X_89)) = symmetric_difference(X_89,X_90) ),
    inference(resolve,[$cnf( $equal(union(difference(X_89,X_90),difference(X_90,X_89)),symmetric_difference(X_89,X_90)) )],[refute_0_38,refute_0_39]) ).

cnf(refute_0_41,plain,
    difference(union(X_90,X_89),intersection(X_90,X_89)) = symmetric_difference(X_89,X_90),
    inference(resolve,[$cnf( $equal(difference(union(X_90,X_89),intersection(X_90,X_89)),union(difference(X_89,X_90),difference(X_90,X_89))) )],[refute_0_34,refute_0_40]) ).

cnf(refute_0_42,plain,
    difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B),
    inference(subst,[],[refute_0_41:[bind(X_89,$fot(skolemFOFtoCNF_C)),bind(X_90,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_43,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_44,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_43]) ).

cnf(refute_0_45,plain,
    ( difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)
    | symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B) != symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    | difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
    inference(subst,[],[refute_0_44:[bind(X,$fot(difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))),bind(Y,$fot(symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B))),bind(Z,$fot(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).

cnf(refute_0_46,plain,
    ( symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B) != symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    | difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
    inference(resolve,[$cnf( $equal(difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)) )],[refute_0_42,refute_0_45]) ).

cnf(refute_0_47,plain,
    difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
    inference(resolve,[$cnf( $equal(symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B),symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_7,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    | symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    | symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) ),[1],$fot(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))]]) ).

cnf(refute_0_49,plain,
    ( symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    | symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),
    inference(resolve,[$cnf( $equal(difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_47,refute_0_48]) ).

cnf(refute_0_50,plain,
    symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
    inference(resolve,[$cnf( $equal(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) )],[refute_0_49,refute_0_0]) ).

cnf(refute_0_51,plain,
    symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
    introduced(tautology,[refl,[$fot(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))]]) ).

cnf(refute_0_52,plain,
    $false,
    inference(resolve,[$cnf( $equal(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_51,refute_0_50]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET620+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n019.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 : Mon Jul 11 05:53:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.51  
% 0.20/0.51  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.51  
%------------------------------------------------------------------------------