%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 03:36:04 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 91 ( 56 unt; 0 def)
% Number of atoms : 141 ( 140 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 106 ( 56 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_intersection,axiom,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)) ).
fof(difference_difference_union2,axiom,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)) ).
fof(symmetric_difference_and_difference,axiom,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(prove_th98,conjecture,
! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)) ).
fof(subgoal_0,plain,
! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(strip,[],[prove_th98]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C,D] : difference(B,symmetric_difference(C,D)) != union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_0_3,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
inference(canonicalize,[],[symmetric_difference_and_difference]) ).
fof(normalize_0_5,plain,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
inference(canonicalize,[],[difference_difference_union2]) ).
fof(normalize_0_7,plain,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(canonicalize,[],[associativity_of_intersection]) ).
fof(normalize_0_9,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
intersection(B,C) = intersection(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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( intersection(B,C) != intersection(C,B)
| intersection(C,B) = intersection(B,C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(intersection(B,C))),bind(Y,$fot(intersection(C,B)))]]) ).
cnf(refute_0_6,plain,
intersection(C,B) = intersection(B,C),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2) = intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_6:[bind(B,$fot(skolemFOFtoCNF_D_2)),bind(C,$fot(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_8,plain,
union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)),
introduced(tautology,[refl,[$fot(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_9,plain,
( intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2) != intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)) != union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) ),
introduced(tautology,[equality,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2))) ),[1,1],$fot(intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_10,plain,
( intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2) != intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) ),
inference(resolve,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),
inference(resolve,[$cnf( $equal(intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)) != union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))
| difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2))) ),[1],$fot(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))))]]) ).
cnf(refute_0_13,plain,
( difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))
| difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2))) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_16,plain,
( symmetric_difference(B,C) != difference(union(B,C),intersection(B,C))
| difference(union(B,C),intersection(B,C)) = symmetric_difference(B,C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(symmetric_difference(B,C))),bind(Y,$fot(difference(union(B,C),intersection(B,C))))]]) ).
cnf(refute_0_17,plain,
difference(union(B,C),intersection(B,C)) = symmetric_difference(B,C),
inference(resolve,[$cnf( $equal(symmetric_difference(B,C),difference(union(B,C),intersection(B,C))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) = symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),
inference(subst,[],[refute_0_17:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_19,plain,
difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) = difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),
introduced(tautology,[refl,[$fot(difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))]]) ).
cnf(refute_0_20,plain,
( difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) != difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))
| difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)
| difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))) ),[1,1],$fot(symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_21,plain,
( difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)
| difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( $equal(difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_24,plain,
( difference(B,difference(C,D)) != union(difference(B,C),intersection(B,D))
| union(difference(B,C),intersection(B,D)) = difference(B,difference(C,D)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(difference(B,difference(C,D)))),bind(Y,$fot(union(difference(B,C),intersection(B,D))))]]) ).
cnf(refute_0_25,plain,
union(difference(B,C),intersection(B,D)) = difference(B,difference(C,D)),
inference(resolve,[$cnf( $equal(difference(B,difference(C,D)),union(difference(B,C),intersection(B,D))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) = difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),
inference(subst,[],[refute_0_25:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),bind(D,$fot(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_27,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_28,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_27]) ).
cnf(refute_0_29,plain,
( difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) != difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) != difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))),bind(Y,$fot(difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))),bind(Z,$fot(difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))]]) ).
cnf(refute_0_30,plain,
( difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) != difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,difference(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) )],[refute_0_22,refute_0_30]) ).
cnf(refute_0_32,plain,
intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_33,plain,
intersection(intersection(X_13,X_14),X_15) = intersection(X_13,intersection(X_14,X_15)),
inference(subst,[],[refute_0_32:[bind(B,$fot(X_13)),bind(C,$fot(X_14)),bind(D,$fot(X_15))]]) ).
cnf(refute_0_34,plain,
intersection(X_15,X_14) = intersection(X_14,X_15),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_15)),bind(C,$fot(X_14))]]) ).
cnf(refute_0_35,plain,
( intersection(X_15,X_14) != intersection(X_14,X_15)
| intersection(X_14,X_15) = intersection(X_15,X_14) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(intersection(X_15,X_14))),bind(Y,$fot(intersection(X_14,X_15)))]]) ).
cnf(refute_0_36,plain,
intersection(X_14,X_15) = intersection(X_15,X_14),
inference(resolve,[$cnf( $equal(intersection(X_15,X_14),intersection(X_14,X_15)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( intersection(X_14,X_15) != intersection(X_15,X_14)
| intersection(intersection(X_13,X_14),X_15) != intersection(X_13,intersection(X_14,X_15))
| intersection(intersection(X_13,X_14),X_15) = intersection(X_13,intersection(X_15,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(intersection(X_13,X_14),X_15),intersection(X_13,intersection(X_14,X_15))) ),[1,1],$fot(intersection(X_15,X_14))]]) ).
cnf(refute_0_38,plain,
( intersection(intersection(X_13,X_14),X_15) != intersection(X_13,intersection(X_14,X_15))
| intersection(intersection(X_13,X_14),X_15) = intersection(X_13,intersection(X_15,X_14)) ),
inference(resolve,[$cnf( $equal(intersection(X_14,X_15),intersection(X_15,X_14)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
intersection(intersection(X_13,X_14),X_15) = intersection(X_13,intersection(X_15,X_14)),
inference(resolve,[$cnf( $equal(intersection(intersection(X_13,X_14),X_15),intersection(X_13,intersection(X_14,X_15))) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
( intersection(intersection(X_13,X_14),X_15) != intersection(X_13,intersection(X_14,X_15))
| intersection(intersection(X_13,X_14),X_15) != intersection(X_13,intersection(X_15,X_14))
| intersection(X_13,intersection(X_14,X_15)) = intersection(X_13,intersection(X_15,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(intersection(X_13,X_14),X_15),intersection(X_13,intersection(X_15,X_14))) ),[0],$fot(intersection(X_13,intersection(X_14,X_15)))]]) ).
cnf(refute_0_41,plain,
( intersection(intersection(X_13,X_14),X_15) != intersection(X_13,intersection(X_15,X_14))
| intersection(X_13,intersection(X_14,X_15)) = intersection(X_13,intersection(X_15,X_14)) ),
inference(resolve,[$cnf( $equal(intersection(intersection(X_13,X_14),X_15),intersection(X_13,intersection(X_14,X_15))) )],[refute_0_33,refute_0_40]) ).
cnf(refute_0_42,plain,
intersection(X_13,intersection(X_14,X_15)) = intersection(X_13,intersection(X_15,X_14)),
inference(resolve,[$cnf( $equal(intersection(intersection(X_13,X_14),X_15),intersection(X_13,intersection(X_15,X_14))) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
( intersection(X_13,intersection(X_14,X_15)) != intersection(X_13,intersection(X_15,X_14))
| intersection(X_13,intersection(X_15,X_14)) = intersection(X_13,intersection(X_14,X_15)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(intersection(X_13,intersection(X_14,X_15)))),bind(Y,$fot(intersection(X_13,intersection(X_15,X_14))))]]) ).
cnf(refute_0_44,plain,
intersection(X_13,intersection(X_15,X_14)) = intersection(X_13,intersection(X_14,X_15)),
inference(resolve,[$cnf( $equal(intersection(X_13,intersection(X_14,X_15)),intersection(X_13,intersection(X_15,X_14))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)) = intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(subst,[],[refute_0_44:[bind(X_13,$fot(skolemFOFtoCNF_B)),bind(X_14,$fot(skolemFOFtoCNF_C)),bind(X_15,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_46,plain,
intersection(X_14,X_13) = intersection(X_13,X_14),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_14)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_47,plain,
( intersection(X_14,X_13) != intersection(X_13,X_14)
| intersection(X_13,X_14) = intersection(X_14,X_13) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(intersection(X_14,X_13))),bind(Y,$fot(intersection(X_13,X_14)))]]) ).
cnf(refute_0_48,plain,
intersection(X_13,X_14) = intersection(X_14,X_13),
inference(resolve,[$cnf( $equal(intersection(X_14,X_13),intersection(X_13,X_14)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( intersection(X_13,X_14) != intersection(X_14,X_13)
| intersection(intersection(X_13,X_14),X_15) != intersection(X_13,intersection(X_14,X_15))
| intersection(intersection(X_14,X_13),X_15) = intersection(X_13,intersection(X_14,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(intersection(X_13,X_14),X_15),intersection(X_13,intersection(X_14,X_15))) ),[0,0],$fot(intersection(X_14,X_13))]]) ).
cnf(refute_0_50,plain,
( intersection(intersection(X_13,X_14),X_15) != intersection(X_13,intersection(X_14,X_15))
| intersection(intersection(X_14,X_13),X_15) = intersection(X_13,intersection(X_14,X_15)) ),
inference(resolve,[$cnf( $equal(intersection(X_13,X_14),intersection(X_14,X_13)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
intersection(intersection(X_14,X_13),X_15) = intersection(X_13,intersection(X_14,X_15)),
inference(resolve,[$cnf( $equal(intersection(intersection(X_13,X_14),X_15),intersection(X_13,intersection(X_14,X_15))) )],[refute_0_33,refute_0_50]) ).
cnf(refute_0_52,plain,
intersection(intersection(X_14,X_13),X_15) = intersection(X_14,intersection(X_13,X_15)),
inference(subst,[],[refute_0_32:[bind(B,$fot(X_14)),bind(C,$fot(X_13)),bind(D,$fot(X_15))]]) ).
cnf(refute_0_53,plain,
( intersection(intersection(X_14,X_13),X_15) != intersection(X_13,intersection(X_14,X_15))
| intersection(intersection(X_14,X_13),X_15) != intersection(X_14,intersection(X_13,X_15))
| intersection(X_14,intersection(X_13,X_15)) = intersection(X_13,intersection(X_14,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(intersection(X_14,X_13),X_15),intersection(X_13,intersection(X_14,X_15))) ),[0],$fot(intersection(X_14,intersection(X_13,X_15)))]]) ).
cnf(refute_0_54,plain,
( intersection(intersection(X_14,X_13),X_15) != intersection(X_13,intersection(X_14,X_15))
| intersection(X_14,intersection(X_13,X_15)) = intersection(X_13,intersection(X_14,X_15)) ),
inference(resolve,[$cnf( $equal(intersection(intersection(X_14,X_13),X_15),intersection(X_14,intersection(X_13,X_15))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
intersection(X_14,intersection(X_13,X_15)) = intersection(X_13,intersection(X_14,X_15)),
inference(resolve,[$cnf( $equal(intersection(intersection(X_14,X_13),X_15),intersection(X_13,intersection(X_14,X_15))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( intersection(X_14,intersection(X_13,X_15)) != intersection(X_13,intersection(X_14,X_15))
| intersection(X_13,intersection(X_14,X_15)) = intersection(X_14,intersection(X_13,X_15)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(intersection(X_14,intersection(X_13,X_15)))),bind(Y,$fot(intersection(X_13,intersection(X_14,X_15))))]]) ).
cnf(refute_0_57,plain,
intersection(X_13,intersection(X_14,X_15)) = intersection(X_14,intersection(X_13,X_15)),
inference(resolve,[$cnf( $equal(intersection(X_14,intersection(X_13,X_15)),intersection(X_13,intersection(X_14,X_15))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_57:[bind(X_13,$fot(skolemFOFtoCNF_D_2)),bind(X_14,$fot(skolemFOFtoCNF_B)),bind(X_15,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_59,plain,
( intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)) != intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C))
| intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))),bind(Y,$fot(intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)))),bind(Z,$fot(intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))]]) ).
cnf(refute_0_60,plain,
( intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)) != intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) )],[refute_0_45,refute_0_60]) ).
cnf(refute_0_62,plain,
union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),
introduced(tautology,[refl,[$fot(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))))]]) ).
cnf(refute_0_63,plain,
( intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) != union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) ),
introduced(tautology,[equality,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))) ),[1,1],$fot(intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_64,plain,
( intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) ),
inference(resolve,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
( union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) != difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) != union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))))),bind(Y,$fot(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))),bind(Z,$fot(difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))]]) ).
cnf(refute_0_67,plain,
( union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) != difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) )],[refute_0_31,refute_0_67]) ).
cnf(refute_0_69,plain,
( difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) != difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))) ),[1],$fot(difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_70,plain,
( difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) = union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) ),
inference(resolve,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) != difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_D_2,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))) )],[refute_0_70,refute_0_14]) ).
cnf(refute_0_72,plain,
difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) = difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
introduced(tautology,[refl,[$fot(difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_73,plain,
$false,
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),difference(skolemFOFtoCNF_B,symmetric_difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))) )],[refute_0_72,refute_0_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n027.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 : Sun Jul 10 00:41:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.39
% 0.19/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.40
%------------------------------------------------------------------------------