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