%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU147+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:38:45 EDT 2022
% Result : Theorem 22.24s 22.42s
% Output : CNFRefutation 22.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 127
% Syntax : Number of formulae : 644 ( 297 unt; 0 def)
% Number of atoms : 1142 ( 928 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 940 ( 442 ~; 459 |; 17 &)
% ( 19 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 1122 ( 65 sgn 145 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ) ).
fof(l1_zfmisc_1,lemma,
! [A] : singleton(A) != empty_set ).
fof(l2_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A ).
fof(t1_zfmisc_1,conjecture,
powerset(empty_set) = singleton(empty_set) ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ~ ( ? [C] :
( in(C,A)
& in(C,B) )
& disjoint(A,B) ) ) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ) ).
fof(subgoal_0,plain,
powerset(empty_set) = singleton(empty_set),
inference(strip,[],[t1_zfmisc_1]) ).
fof(negate_0_0,plain,
powerset(empty_set) != singleton(empty_set),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[t48_xboole_1]) ).
fof(normalize_0_1,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[t40_xboole_1]) ).
fof(normalize_0_3,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_5,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[t39_xboole_1]) ).
fof(normalize_0_7,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_9,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(canonicalize,[],[t36_xboole_1]) ).
fof(normalize_0_11,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[t12_xboole_1]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A] : set_difference(A,empty_set) = A,
inference(canonicalize,[],[t3_boole]) ).
fof(normalize_0_15,plain,
! [A] : set_difference(A,empty_set) = A,
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(canonicalize,[],[t2_boole]) ).
fof(normalize_0_17,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A] : set_union2(A,empty_set) = A,
inference(canonicalize,[],[t1_boole]) ).
fof(normalize_0_19,plain,
! [A] : set_union2(A,empty_set) = A,
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(canonicalize,[],[t7_xboole_1]) ).
fof(normalize_0_21,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(canonicalize,[],[d1_zfmisc_1]) ).
fof(normalize_0_23,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B,C] :
( ( B != powerset(A)
| ~ in(C,B)
| subset(C,A) )
& ( B != powerset(A)
| ~ subset(C,A)
| in(C,B) )
& ( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ subset(skolemFOFtoCNF_C_1(A,B),A)
| B = powerset(A) )
& ( B = powerset(A)
| in(skolemFOFtoCNF_C_1(A,B),B)
| subset(skolemFOFtoCNF_C_1(A,B),A) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B,C] :
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(canonicalize,[],[l2_zfmisc_1]) ).
fof(normalize_0_27,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( ~ subset(singleton(A),B)
| in(A,B) ) ),
inference(clausify,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(conjunct,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_0_31,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [A] :
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(conjunct,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(canonicalize,[],[t28_xboole_1]) ).
fof(normalize_0_35,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(specialize,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [A] :
( ~ subset(A,empty_set)
| A = empty_set ),
inference(canonicalize,[],[t3_xboole_1]) ).
fof(normalize_0_37,plain,
! [A] :
( ~ subset(A,empty_set)
| A = empty_set ),
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [A,B,C] :
( B != powerset(A)
| ~ in(C,B)
| subset(C,A) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_39,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[t83_xboole_1]) ).
fof(normalize_0_40,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_difference(A,B) = A ) ),
inference(clausify,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
! [A,B] :
( ~ disjoint(A,B)
| set_difference(A,B) = A ),
inference(conjunct,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_0_44,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [A,B] :
( ( set_difference(A,B) != empty_set
| subset(A,B) )
& ( ~ subset(A,B)
| set_difference(A,B) = empty_set ) ),
inference(clausify,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(conjunct,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,A)
| ~ in(C,B) ) )
& ! [A,B] :
( disjoint(A,B)
| ? [C] :
( in(C,A)
& in(C,B) ) ) ),
inference(canonicalize,[],[t3_xboole_0]) ).
fof(normalize_0_48,plain,
! [A,B] :
( disjoint(A,B)
| ? [C] :
( in(C,A)
& in(C,B) ) ),
inference(conjunct,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
! [A,B] :
( disjoint(A,B)
| ? [C] :
( in(C,A)
& in(C,B) ) ),
inference(specialize,[],[normalize_0_48]) ).
fof(normalize_0_50,plain,
! [A,B] :
( ( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),A) )
& ( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),B) ) ),
inference(clausify,[],[normalize_0_49]) ).
fof(normalize_0_51,plain,
! [A,B] :
( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),B) ),
inference(conjunct,[],[normalize_0_50]) ).
fof(normalize_0_52,plain,
! [A,B] :
( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),A) ),
inference(conjunct,[],[normalize_0_50]) ).
fof(normalize_0_53,plain,
! [A] : singleton(A) != empty_set,
inference(canonicalize,[],[l1_zfmisc_1]) ).
fof(normalize_0_54,plain,
! [A] : singleton(A) != empty_set,
inference(specialize,[],[normalize_0_53]) ).
fof(normalize_0_55,plain,
powerset(empty_set) != singleton(empty_set),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_56,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[t4_boole]) ).
fof(normalize_0_57,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(specialize,[],[normalize_0_56]) ).
cnf(refute_0_0,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
set_difference(set_union2(X_33,B),set_difference(set_union2(X_33,B),B)) = set_intersection2(set_union2(X_33,B),B),
inference(subst,[],[refute_0_0:[bind(A,$fot(set_union2(X_33,B)))]]) ).
cnf(refute_0_2,plain,
set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
set_difference(set_union2(X_33,B),B) = set_difference(X_33,B),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_33))]]) ).
cnf(refute_0_4,plain,
( set_difference(set_union2(X_33,B),B) != set_difference(X_33,B)
| set_difference(set_union2(X_33,B),set_difference(set_union2(X_33,B),B)) != set_intersection2(set_union2(X_33,B),B)
| set_difference(set_union2(X_33,B),set_difference(X_33,B)) = set_intersection2(set_union2(X_33,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(X_33,B),set_difference(set_union2(X_33,B),B)),set_intersection2(set_union2(X_33,B),B)) ),[0,1],$fot(set_difference(X_33,B))]]) ).
cnf(refute_0_5,plain,
( set_difference(set_union2(X_33,B),set_difference(set_union2(X_33,B),B)) != set_intersection2(set_union2(X_33,B),B)
| set_difference(set_union2(X_33,B),set_difference(X_33,B)) = set_intersection2(set_union2(X_33,B),B) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_33,B),B),set_difference(X_33,B)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
set_difference(set_union2(X_33,B),set_difference(X_33,B)) = set_intersection2(set_union2(X_33,B),B),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_33,B),set_difference(set_union2(X_33,B),B)),set_intersection2(set_union2(X_33,B),B)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_12,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
set_intersection2(set_union2(X_33,B),B) = set_intersection2(B,set_union2(X_33,B)),
inference(subst,[],[refute_0_12:[bind(A,$fot(B)),bind(B,$fot(set_union2(X_33,B)))]]) ).
cnf(refute_0_14,plain,
( set_difference(set_union2(X_33,B),set_difference(X_33,B)) != set_intersection2(set_union2(X_33,B),B)
| set_intersection2(set_union2(X_33,B),B) != set_intersection2(B,set_union2(X_33,B))
| set_difference(set_union2(X_33,B),set_difference(X_33,B)) = set_intersection2(B,set_union2(X_33,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(X_33,B),set_difference(X_33,B)),set_intersection2(B,set_union2(X_33,B))) ),[0],$fot(set_intersection2(set_union2(X_33,B),B))]]) ).
cnf(refute_0_15,plain,
( set_difference(set_union2(X_33,B),set_difference(X_33,B)) != set_intersection2(set_union2(X_33,B),B)
| set_difference(set_union2(X_33,B),set_difference(X_33,B)) = set_intersection2(B,set_union2(X_33,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_union2(X_33,B),B),set_intersection2(B,set_union2(X_33,B))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
set_difference(set_union2(X_33,B),set_difference(X_33,B)) = set_intersection2(B,set_union2(X_33,B)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_33,B),set_difference(X_33,B)),set_intersection2(set_union2(X_33,B),B)) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
set_difference(set_union2(A,set_difference(X_58,A)),set_difference(X_58,A)) = set_difference(A,set_difference(X_58,A)),
inference(subst,[],[refute_0_2:[bind(B,$fot(set_difference(X_58,A)))]]) ).
cnf(refute_0_18,plain,
set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_19,plain,
set_union2(A,set_difference(X_58,A)) = set_union2(A,X_58),
inference(subst,[],[refute_0_18:[bind(B,$fot(X_58))]]) ).
cnf(refute_0_20,plain,
( set_difference(set_union2(A,set_difference(X_58,A)),set_difference(X_58,A)) != set_difference(A,set_difference(X_58,A))
| set_union2(A,set_difference(X_58,A)) != set_union2(A,X_58)
| set_difference(set_union2(A,X_58),set_difference(X_58,A)) = set_difference(A,set_difference(X_58,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,set_difference(X_58,A)),set_difference(X_58,A)),set_difference(A,set_difference(X_58,A))) ),[0,0],$fot(set_union2(A,X_58))]]) ).
cnf(refute_0_21,plain,
( set_difference(set_union2(A,set_difference(X_58,A)),set_difference(X_58,A)) != set_difference(A,set_difference(X_58,A))
| set_difference(set_union2(A,X_58),set_difference(X_58,A)) = set_difference(A,set_difference(X_58,A)) ),
inference(resolve,[$cnf( $equal(set_union2(A,set_difference(X_58,A)),set_union2(A,X_58)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
set_difference(set_union2(A,X_58),set_difference(X_58,A)) = set_difference(A,set_difference(X_58,A)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,set_difference(X_58,A)),set_difference(X_58,A)),set_difference(A,set_difference(X_58,A))) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
set_difference(set_union2(B,X_53),set_difference(set_union2(B,X_53),B)) = set_intersection2(set_union2(B,X_53),B),
inference(subst,[],[refute_0_0:[bind(A,$fot(set_union2(B,X_53)))]]) ).
cnf(refute_0_24,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_25,plain,
( set_difference(set_union2(A,B),B) != set_difference(A,B)
| set_union2(A,B) != set_union2(B,A)
| set_difference(set_union2(B,A),B) = set_difference(A,B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,B),B),set_difference(A,B)) ),[0,0],$fot(set_union2(B,A))]]) ).
cnf(refute_0_26,plain,
( set_difference(set_union2(A,B),B) != set_difference(A,B)
| set_difference(set_union2(B,A),B) = set_difference(A,B) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
set_difference(set_union2(B,A),B) = set_difference(A,B),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,B),B),set_difference(A,B)) )],[refute_0_2,refute_0_26]) ).
cnf(refute_0_28,plain,
set_difference(set_union2(B,X_53),B) = set_difference(X_53,B),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_53))]]) ).
cnf(refute_0_29,plain,
( set_difference(set_union2(B,X_53),B) != set_difference(X_53,B)
| set_difference(set_union2(B,X_53),set_difference(set_union2(B,X_53),B)) != set_intersection2(set_union2(B,X_53),B)
| set_difference(set_union2(B,X_53),set_difference(X_53,B)) = set_intersection2(set_union2(B,X_53),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(B,X_53),set_difference(set_union2(B,X_53),B)),set_intersection2(set_union2(B,X_53),B)) ),[0,1],$fot(set_difference(X_53,B))]]) ).
cnf(refute_0_30,plain,
( set_difference(set_union2(B,X_53),set_difference(set_union2(B,X_53),B)) != set_intersection2(set_union2(B,X_53),B)
| set_difference(set_union2(B,X_53),set_difference(X_53,B)) = set_intersection2(set_union2(B,X_53),B) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_53),B),set_difference(X_53,B)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
set_difference(set_union2(B,X_53),set_difference(X_53,B)) = set_intersection2(set_union2(B,X_53),B),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_53),set_difference(set_union2(B,X_53),B)),set_intersection2(set_union2(B,X_53),B)) )],[refute_0_23,refute_0_30]) ).
cnf(refute_0_32,plain,
set_intersection2(set_union2(B,X_53),B) = set_intersection2(B,set_union2(B,X_53)),
inference(subst,[],[refute_0_12:[bind(A,$fot(B)),bind(B,$fot(set_union2(B,X_53)))]]) ).
cnf(refute_0_33,plain,
( set_difference(set_union2(B,X_53),set_difference(X_53,B)) != set_intersection2(set_union2(B,X_53),B)
| set_intersection2(set_union2(B,X_53),B) != set_intersection2(B,set_union2(B,X_53))
| set_difference(set_union2(B,X_53),set_difference(X_53,B)) = set_intersection2(B,set_union2(B,X_53)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(B,X_53),set_difference(X_53,B)),set_intersection2(B,set_union2(B,X_53))) ),[0],$fot(set_intersection2(set_union2(B,X_53),B))]]) ).
cnf(refute_0_34,plain,
( set_difference(set_union2(B,X_53),set_difference(X_53,B)) != set_intersection2(set_union2(B,X_53),B)
| set_difference(set_union2(B,X_53),set_difference(X_53,B)) = set_intersection2(B,set_union2(B,X_53)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_union2(B,X_53),B),set_intersection2(B,set_union2(B,X_53))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
set_difference(set_union2(B,X_53),set_difference(X_53,B)) = set_intersection2(B,set_union2(B,X_53)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_53),set_difference(X_53,B)),set_intersection2(set_union2(B,X_53),B)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
set_difference(set_union2(A,X_58),set_difference(X_58,A)) = set_intersection2(A,set_union2(A,X_58)),
inference(subst,[],[refute_0_35:[bind(B,$fot(A)),bind(X_53,$fot(X_58))]]) ).
cnf(refute_0_37,plain,
( set_difference(set_union2(A,X_58),set_difference(X_58,A)) != set_difference(A,set_difference(X_58,A))
| set_difference(set_union2(A,X_58),set_difference(X_58,A)) != set_intersection2(A,set_union2(A,X_58))
| set_intersection2(A,set_union2(A,X_58)) = set_difference(A,set_difference(X_58,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,X_58),set_difference(X_58,A)),set_difference(A,set_difference(X_58,A))) ),[0],$fot(set_intersection2(A,set_union2(A,X_58)))]]) ).
cnf(refute_0_38,plain,
( set_difference(set_union2(A,X_58),set_difference(X_58,A)) != set_difference(A,set_difference(X_58,A))
| set_intersection2(A,set_union2(A,X_58)) = set_difference(A,set_difference(X_58,A)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_58),set_difference(X_58,A)),set_intersection2(A,set_union2(A,X_58))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
set_intersection2(A,set_union2(A,X_58)) = set_difference(A,set_difference(X_58,A)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_58),set_difference(X_58,A)),set_difference(A,set_difference(X_58,A))) )],[refute_0_22,refute_0_38]) ).
cnf(refute_0_40,plain,
set_intersection2(X_59,set_union2(X_59,X_60)) = set_difference(X_59,set_difference(X_60,X_59)),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_59)),bind(X_58,$fot(X_60))]]) ).
cnf(refute_0_41,plain,
set_union2(X_60,X_59) = set_union2(X_59,X_60),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_60)),bind(B,$fot(X_59))]]) ).
cnf(refute_0_42,plain,
( set_union2(X_60,X_59) != set_union2(X_59,X_60)
| set_union2(X_59,X_60) = set_union2(X_60,X_59) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_union2(X_60,X_59))),bind(Y,$fot(set_union2(X_59,X_60)))]]) ).
cnf(refute_0_43,plain,
set_union2(X_59,X_60) = set_union2(X_60,X_59),
inference(resolve,[$cnf( $equal(set_union2(X_60,X_59),set_union2(X_59,X_60)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( set_intersection2(X_59,set_union2(X_59,X_60)) != set_difference(X_59,set_difference(X_60,X_59))
| set_union2(X_59,X_60) != set_union2(X_60,X_59)
| set_intersection2(X_59,set_union2(X_60,X_59)) = set_difference(X_59,set_difference(X_60,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(X_59,set_union2(X_59,X_60)),set_difference(X_59,set_difference(X_60,X_59))) ),[0,1],$fot(set_union2(X_60,X_59))]]) ).
cnf(refute_0_45,plain,
( set_intersection2(X_59,set_union2(X_59,X_60)) != set_difference(X_59,set_difference(X_60,X_59))
| set_intersection2(X_59,set_union2(X_60,X_59)) = set_difference(X_59,set_difference(X_60,X_59)) ),
inference(resolve,[$cnf( $equal(set_union2(X_59,X_60),set_union2(X_60,X_59)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
set_intersection2(X_59,set_union2(X_60,X_59)) = set_difference(X_59,set_difference(X_60,X_59)),
inference(resolve,[$cnf( $equal(set_intersection2(X_59,set_union2(X_59,X_60)),set_difference(X_59,set_difference(X_60,X_59))) )],[refute_0_40,refute_0_45]) ).
cnf(refute_0_47,plain,
set_intersection2(B,set_union2(X_33,B)) = set_difference(B,set_difference(X_33,B)),
inference(subst,[],[refute_0_46:[bind(X_59,$fot(B)),bind(X_60,$fot(X_33))]]) ).
cnf(refute_0_48,plain,
( set_difference(set_union2(X_33,B),set_difference(X_33,B)) != set_intersection2(B,set_union2(X_33,B))
| set_intersection2(B,set_union2(X_33,B)) != set_difference(B,set_difference(X_33,B))
| set_difference(set_union2(X_33,B),set_difference(X_33,B)) = set_difference(B,set_difference(X_33,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(X_33,B),set_difference(X_33,B)),set_difference(B,set_difference(X_33,B))) ),[0],$fot(set_intersection2(B,set_union2(X_33,B)))]]) ).
cnf(refute_0_49,plain,
( set_difference(set_union2(X_33,B),set_difference(X_33,B)) != set_intersection2(B,set_union2(X_33,B))
| set_difference(set_union2(X_33,B),set_difference(X_33,B)) = set_difference(B,set_difference(X_33,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(B,set_union2(X_33,B)),set_difference(B,set_difference(X_33,B))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
set_difference(set_union2(X_33,B),set_difference(X_33,B)) = set_difference(B,set_difference(X_33,B)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_33,B),set_difference(X_33,B)),set_intersection2(B,set_union2(X_33,B))) )],[refute_0_16,refute_0_49]) ).
cnf(refute_0_51,plain,
set_union2(set_intersection2(X_153,B),set_difference(B,set_intersection2(X_153,B))) = set_union2(set_intersection2(X_153,B),B),
inference(subst,[],[refute_0_18:[bind(A,$fot(set_intersection2(X_153,B)))]]) ).
cnf(refute_0_52,plain,
set_difference(A,set_difference(A,set_difference(A,X_26))) = set_intersection2(A,set_difference(A,X_26)),
inference(subst,[],[refute_0_0:[bind(B,$fot(set_difference(A,X_26)))]]) ).
cnf(refute_0_53,plain,
set_difference(A,set_difference(A,X_26)) = set_intersection2(A,X_26),
inference(subst,[],[refute_0_0:[bind(B,$fot(X_26))]]) ).
cnf(refute_0_54,plain,
( set_difference(A,set_difference(A,X_26)) != set_intersection2(A,X_26)
| set_difference(A,set_difference(A,set_difference(A,X_26))) != set_intersection2(A,set_difference(A,X_26))
| set_difference(A,set_intersection2(A,X_26)) = set_intersection2(A,set_difference(A,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(A,set_difference(A,set_difference(A,X_26))),set_intersection2(A,set_difference(A,X_26))) ),[0,1],$fot(set_intersection2(A,X_26))]]) ).
cnf(refute_0_55,plain,
( set_difference(A,set_difference(A,set_difference(A,X_26))) != set_intersection2(A,set_difference(A,X_26))
| set_difference(A,set_intersection2(A,X_26)) = set_intersection2(A,set_difference(A,X_26)) ),
inference(resolve,[$cnf( $equal(set_difference(A,set_difference(A,X_26)),set_intersection2(A,X_26)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
set_difference(A,set_intersection2(A,X_26)) = set_intersection2(A,set_difference(A,X_26)),
inference(resolve,[$cnf( $equal(set_difference(A,set_difference(A,set_difference(A,X_26))),set_intersection2(A,set_difference(A,X_26))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
set_difference(X_35,set_intersection2(X_35,X_36)) = set_intersection2(X_35,set_difference(X_35,X_36)),
inference(subst,[],[refute_0_56:[bind(A,$fot(X_35)),bind(X_26,$fot(X_36))]]) ).
cnf(refute_0_58,plain,
set_intersection2(X_36,X_35) = set_intersection2(X_35,X_36),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_36)),bind(B,$fot(X_35))]]) ).
cnf(refute_0_59,plain,
( set_intersection2(X_36,X_35) != set_intersection2(X_35,X_36)
| set_intersection2(X_35,X_36) = set_intersection2(X_36,X_35) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_intersection2(X_36,X_35))),bind(Y,$fot(set_intersection2(X_35,X_36)))]]) ).
cnf(refute_0_60,plain,
set_intersection2(X_35,X_36) = set_intersection2(X_36,X_35),
inference(resolve,[$cnf( $equal(set_intersection2(X_36,X_35),set_intersection2(X_35,X_36)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( set_difference(X_35,set_intersection2(X_35,X_36)) != set_intersection2(X_35,set_difference(X_35,X_36))
| set_intersection2(X_35,X_36) != set_intersection2(X_36,X_35)
| set_difference(X_35,set_intersection2(X_36,X_35)) = set_intersection2(X_35,set_difference(X_35,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_35,set_intersection2(X_35,X_36)),set_intersection2(X_35,set_difference(X_35,X_36))) ),[0,1],$fot(set_intersection2(X_36,X_35))]]) ).
cnf(refute_0_62,plain,
( set_difference(X_35,set_intersection2(X_35,X_36)) != set_intersection2(X_35,set_difference(X_35,X_36))
| set_difference(X_35,set_intersection2(X_36,X_35)) = set_intersection2(X_35,set_difference(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_35,X_36),set_intersection2(X_36,X_35)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
set_difference(X_35,set_intersection2(X_36,X_35)) = set_intersection2(X_35,set_difference(X_35,X_36)),
inference(resolve,[$cnf( $equal(set_difference(X_35,set_intersection2(X_35,X_36)),set_intersection2(X_35,set_difference(X_35,X_36))) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
( set_difference(A,set_intersection2(A,X_26)) != set_intersection2(A,set_difference(A,X_26))
| set_intersection2(A,set_difference(A,X_26)) = set_difference(A,set_intersection2(A,X_26)) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_difference(A,set_intersection2(A,X_26)))),bind(Y,$fot(set_intersection2(A,set_difference(A,X_26))))]]) ).
cnf(refute_0_65,plain,
set_intersection2(A,set_difference(A,X_26)) = set_difference(A,set_intersection2(A,X_26)),
inference(resolve,[$cnf( $equal(set_difference(A,set_intersection2(A,X_26)),set_intersection2(A,set_difference(A,X_26))) )],[refute_0_56,refute_0_64]) ).
cnf(refute_0_66,plain,
set_intersection2(X_35,set_difference(X_35,X_36)) = set_difference(X_35,set_intersection2(X_35,X_36)),
inference(subst,[],[refute_0_65:[bind(A,$fot(X_35)),bind(X_26,$fot(X_36))]]) ).
cnf(refute_0_67,plain,
( set_difference(X_35,set_intersection2(X_36,X_35)) != set_intersection2(X_35,set_difference(X_35,X_36))
| set_intersection2(X_35,set_difference(X_35,X_36)) != set_difference(X_35,set_intersection2(X_35,X_36))
| set_difference(X_35,set_intersection2(X_36,X_35)) = set_difference(X_35,set_intersection2(X_35,X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(X_35,set_intersection2(X_36,X_35)),set_difference(X_35,set_intersection2(X_35,X_36))) ),[0],$fot(set_intersection2(X_35,set_difference(X_35,X_36)))]]) ).
cnf(refute_0_68,plain,
( set_difference(X_35,set_intersection2(X_36,X_35)) != set_intersection2(X_35,set_difference(X_35,X_36))
| set_difference(X_35,set_intersection2(X_36,X_35)) = set_difference(X_35,set_intersection2(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_35,set_difference(X_35,X_36)),set_difference(X_35,set_intersection2(X_35,X_36))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
set_difference(X_35,set_intersection2(X_36,X_35)) = set_difference(X_35,set_intersection2(X_35,X_36)),
inference(resolve,[$cnf( $equal(set_difference(X_35,set_intersection2(X_36,X_35)),set_intersection2(X_35,set_difference(X_35,X_36))) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
set_difference(set_difference(B,X_113),set_difference(set_difference(B,X_113),B)) = set_intersection2(set_difference(B,X_113),B),
inference(subst,[],[refute_0_0:[bind(A,$fot(set_difference(B,X_113)))]]) ).
cnf(refute_0_71,plain,
set_difference(set_union2(B,set_difference(B,X_110)),B) = set_difference(set_difference(B,X_110),B),
inference(subst,[],[refute_0_27:[bind(A,$fot(set_difference(B,X_110)))]]) ).
cnf(refute_0_72,plain,
subset(set_difference(A,B),A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_73,plain,
subset(set_difference(X_101,B),X_101),
inference(subst,[],[refute_0_72:[bind(A,$fot(X_101))]]) ).
cnf(refute_0_74,plain,
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_75,plain,
( ~ subset(set_difference(X_101,B),X_101)
| set_union2(set_difference(X_101,B),X_101) = X_101 ),
inference(subst,[],[refute_0_74:[bind(A,$fot(set_difference(X_101,B))),bind(B,$fot(X_101))]]) ).
cnf(refute_0_76,plain,
set_union2(set_difference(X_101,B),X_101) = X_101,
inference(resolve,[$cnf( subset(set_difference(X_101,B),X_101) )],[refute_0_73,refute_0_75]) ).
cnf(refute_0_77,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_78,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_24,refute_0_77]) ).
cnf(refute_0_79,plain,
set_union2(set_difference(X_101,B),X_101) = set_union2(X_101,set_difference(X_101,B)),
inference(subst,[],[refute_0_78:[bind(A,$fot(X_101)),bind(B,$fot(set_difference(X_101,B)))]]) ).
cnf(refute_0_80,plain,
( set_union2(set_difference(X_101,B),X_101) != X_101
| set_union2(set_difference(X_101,B),X_101) != set_union2(X_101,set_difference(X_101,B))
| set_union2(X_101,set_difference(X_101,B)) = X_101 ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(X_101,B),X_101),X_101) ),[0],$fot(set_union2(X_101,set_difference(X_101,B)))]]) ).
cnf(refute_0_81,plain,
( set_union2(set_difference(X_101,B),X_101) != X_101
| set_union2(X_101,set_difference(X_101,B)) = X_101 ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_101,B),X_101),set_union2(X_101,set_difference(X_101,B))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
set_union2(X_101,set_difference(X_101,B)) = X_101,
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_101,B),X_101),X_101) )],[refute_0_76,refute_0_81]) ).
cnf(refute_0_83,plain,
set_union2(B,set_difference(B,X_110)) = B,
inference(subst,[],[refute_0_82:[bind(B,$fot(X_110)),bind(X_101,$fot(B))]]) ).
cnf(refute_0_84,plain,
( set_difference(set_union2(B,set_difference(B,X_110)),B) != set_difference(set_difference(B,X_110),B)
| set_union2(B,set_difference(B,X_110)) != B
| set_difference(B,B) = set_difference(set_difference(B,X_110),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(B,set_difference(B,X_110)),B),set_difference(set_difference(B,X_110),B)) ),[0,0],$fot(B)]]) ).
cnf(refute_0_85,plain,
( set_difference(set_union2(B,set_difference(B,X_110)),B) != set_difference(set_difference(B,X_110),B)
| set_difference(B,B) = set_difference(set_difference(B,X_110),B) ),
inference(resolve,[$cnf( $equal(set_union2(B,set_difference(B,X_110)),B) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
set_difference(B,B) = set_difference(set_difference(B,X_110),B),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,set_difference(B,X_110)),B),set_difference(set_difference(B,X_110),B)) )],[refute_0_71,refute_0_85]) ).
cnf(refute_0_87,plain,
set_difference(X_25,set_difference(X_25,empty_set)) = set_intersection2(X_25,empty_set),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_25)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_88,plain,
set_difference(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_89,plain,
set_difference(X_25,empty_set) = X_25,
inference(subst,[],[refute_0_88:[bind(A,$fot(X_25))]]) ).
cnf(refute_0_90,plain,
( set_difference(X_25,empty_set) != X_25
| set_difference(X_25,set_difference(X_25,empty_set)) != set_intersection2(X_25,empty_set)
| set_difference(X_25,X_25) = set_intersection2(X_25,empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_25,set_difference(X_25,empty_set)),set_intersection2(X_25,empty_set)) ),[0,1],$fot(X_25)]]) ).
cnf(refute_0_91,plain,
( set_difference(X_25,set_difference(X_25,empty_set)) != set_intersection2(X_25,empty_set)
| set_difference(X_25,X_25) = set_intersection2(X_25,empty_set) ),
inference(resolve,[$cnf( $equal(set_difference(X_25,empty_set),X_25) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
set_difference(X_25,X_25) = set_intersection2(X_25,empty_set),
inference(resolve,[$cnf( $equal(set_difference(X_25,set_difference(X_25,empty_set)),set_intersection2(X_25,empty_set)) )],[refute_0_87,refute_0_91]) ).
cnf(refute_0_93,plain,
set_intersection2(A,empty_set) = empty_set,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_94,plain,
set_intersection2(X_25,empty_set) = empty_set,
inference(subst,[],[refute_0_93:[bind(A,$fot(X_25))]]) ).
cnf(refute_0_95,plain,
( set_difference(X_25,X_25) != set_intersection2(X_25,empty_set)
| set_intersection2(X_25,empty_set) != empty_set
| set_difference(X_25,X_25) = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(X_25,X_25),empty_set) ),[0],$fot(set_intersection2(X_25,empty_set))]]) ).
cnf(refute_0_96,plain,
( set_difference(X_25,X_25) != set_intersection2(X_25,empty_set)
| set_difference(X_25,X_25) = empty_set ),
inference(resolve,[$cnf( $equal(set_intersection2(X_25,empty_set),empty_set) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
set_difference(X_25,X_25) = empty_set,
inference(resolve,[$cnf( $equal(set_difference(X_25,X_25),set_intersection2(X_25,empty_set)) )],[refute_0_92,refute_0_96]) ).
cnf(refute_0_98,plain,
set_difference(B,B) = empty_set,
inference(subst,[],[refute_0_97:[bind(X_25,$fot(B))]]) ).
cnf(refute_0_99,plain,
( set_difference(B,B) != empty_set
| set_difference(B,B) != set_difference(set_difference(B,X_110),B)
| empty_set = set_difference(set_difference(B,X_110),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(B,B),set_difference(set_difference(B,X_110),B)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_100,plain,
( set_difference(B,B) != set_difference(set_difference(B,X_110),B)
| empty_set = set_difference(set_difference(B,X_110),B) ),
inference(resolve,[$cnf( $equal(set_difference(B,B),empty_set) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
empty_set = set_difference(set_difference(B,X_110),B),
inference(resolve,[$cnf( $equal(set_difference(B,B),set_difference(set_difference(B,X_110),B)) )],[refute_0_86,refute_0_100]) ).
cnf(refute_0_102,plain,
empty_set = set_difference(set_difference(B,X_113),B),
inference(subst,[],[refute_0_101:[bind(X_110,$fot(X_113))]]) ).
cnf(refute_0_103,plain,
( empty_set != set_difference(set_difference(B,X_113),B)
| set_difference(set_difference(B,X_113),B) = empty_set ),
inference(subst,[],[refute_0_10:[bind(X,$fot(empty_set)),bind(Y,$fot(set_difference(set_difference(B,X_113),B)))]]) ).
cnf(refute_0_104,plain,
set_difference(set_difference(B,X_113),B) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,set_difference(set_difference(B,X_113),B)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( set_difference(set_difference(B,X_113),B) != empty_set
| set_difference(set_difference(B,X_113),set_difference(set_difference(B,X_113),B)) != set_intersection2(set_difference(B,X_113),B)
| set_difference(set_difference(B,X_113),empty_set) = set_intersection2(set_difference(B,X_113),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_difference(B,X_113),set_difference(set_difference(B,X_113),B)),set_intersection2(set_difference(B,X_113),B)) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_106,plain,
( set_difference(set_difference(B,X_113),set_difference(set_difference(B,X_113),B)) != set_intersection2(set_difference(B,X_113),B)
| set_difference(set_difference(B,X_113),empty_set) = set_intersection2(set_difference(B,X_113),B) ),
inference(resolve,[$cnf( $equal(set_difference(set_difference(B,X_113),B),empty_set) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
set_difference(set_difference(B,X_113),empty_set) = set_intersection2(set_difference(B,X_113),B),
inference(resolve,[$cnf( $equal(set_difference(set_difference(B,X_113),set_difference(set_difference(B,X_113),B)),set_intersection2(set_difference(B,X_113),B)) )],[refute_0_70,refute_0_106]) ).
cnf(refute_0_108,plain,
set_difference(set_difference(B,X_113),empty_set) = set_difference(B,X_113),
inference(subst,[],[refute_0_88:[bind(A,$fot(set_difference(B,X_113)))]]) ).
cnf(refute_0_109,plain,
( set_difference(set_difference(B,X_113),empty_set) != set_difference(B,X_113)
| set_difference(set_difference(B,X_113),empty_set) != set_intersection2(set_difference(B,X_113),B)
| set_difference(B,X_113) = set_intersection2(set_difference(B,X_113),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_difference(B,X_113),empty_set),set_intersection2(set_difference(B,X_113),B)) ),[0],$fot(set_difference(B,X_113))]]) ).
cnf(refute_0_110,plain,
( set_difference(set_difference(B,X_113),empty_set) != set_intersection2(set_difference(B,X_113),B)
| set_difference(B,X_113) = set_intersection2(set_difference(B,X_113),B) ),
inference(resolve,[$cnf( $equal(set_difference(set_difference(B,X_113),empty_set),set_difference(B,X_113)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
set_intersection2(B,set_difference(B,X_113)) = set_difference(B,set_intersection2(B,X_113)),
inference(subst,[],[refute_0_65:[bind(A,$fot(B)),bind(X_26,$fot(X_113))]]) ).
cnf(refute_0_112,plain,
set_intersection2(set_difference(B,X_113),B) = set_intersection2(B,set_difference(B,X_113)),
inference(subst,[],[refute_0_12:[bind(A,$fot(B)),bind(B,$fot(set_difference(B,X_113)))]]) ).
cnf(refute_0_113,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_114,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_10,refute_0_113]) ).
cnf(refute_0_115,plain,
( set_intersection2(B,set_difference(B,X_113)) != set_difference(B,set_intersection2(B,X_113))
| set_intersection2(set_difference(B,X_113),B) != set_intersection2(B,set_difference(B,X_113))
| set_intersection2(set_difference(B,X_113),B) = set_difference(B,set_intersection2(B,X_113)) ),
inference(subst,[],[refute_0_114:[bind(X,$fot(set_intersection2(set_difference(B,X_113),B))),bind(Y,$fot(set_intersection2(B,set_difference(B,X_113)))),bind(Z,$fot(set_difference(B,set_intersection2(B,X_113))))]]) ).
cnf(refute_0_116,plain,
( set_intersection2(B,set_difference(B,X_113)) != set_difference(B,set_intersection2(B,X_113))
| set_intersection2(set_difference(B,X_113),B) = set_difference(B,set_intersection2(B,X_113)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_difference(B,X_113),B),set_intersection2(B,set_difference(B,X_113))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
set_intersection2(set_difference(B,X_113),B) = set_difference(B,set_intersection2(B,X_113)),
inference(resolve,[$cnf( $equal(set_intersection2(B,set_difference(B,X_113)),set_difference(B,set_intersection2(B,X_113))) )],[refute_0_111,refute_0_116]) ).
cnf(refute_0_118,plain,
( set_difference(B,X_113) != set_intersection2(set_difference(B,X_113),B)
| set_intersection2(set_difference(B,X_113),B) != set_difference(B,set_intersection2(B,X_113))
| set_difference(B,X_113) = set_difference(B,set_intersection2(B,X_113)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(B,X_113),set_difference(B,set_intersection2(B,X_113))) ),[0],$fot(set_intersection2(set_difference(B,X_113),B))]]) ).
cnf(refute_0_119,plain,
( set_difference(B,X_113) != set_intersection2(set_difference(B,X_113),B)
| set_difference(B,X_113) = set_difference(B,set_intersection2(B,X_113)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_difference(B,X_113),B),set_difference(B,set_intersection2(B,X_113))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
( set_difference(set_difference(B,X_113),empty_set) != set_intersection2(set_difference(B,X_113),B)
| set_difference(B,X_113) = set_difference(B,set_intersection2(B,X_113)) ),
inference(resolve,[$cnf( $equal(set_difference(B,X_113),set_intersection2(set_difference(B,X_113),B)) )],[refute_0_110,refute_0_119]) ).
cnf(refute_0_121,plain,
set_difference(B,X_113) = set_difference(B,set_intersection2(B,X_113)),
inference(resolve,[$cnf( $equal(set_difference(set_difference(B,X_113),empty_set),set_intersection2(set_difference(B,X_113),B)) )],[refute_0_107,refute_0_120]) ).
cnf(refute_0_122,plain,
( set_difference(B,X_113) != set_difference(B,set_intersection2(B,X_113))
| set_difference(B,set_intersection2(B,X_113)) = set_difference(B,X_113) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_difference(B,X_113))),bind(Y,$fot(set_difference(B,set_intersection2(B,X_113))))]]) ).
cnf(refute_0_123,plain,
set_difference(B,set_intersection2(B,X_113)) = set_difference(B,X_113),
inference(resolve,[$cnf( $equal(set_difference(B,X_113),set_difference(B,set_intersection2(B,X_113))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
set_difference(X_35,set_intersection2(X_35,X_36)) = set_difference(X_35,X_36),
inference(subst,[],[refute_0_123:[bind(B,$fot(X_35)),bind(X_113,$fot(X_36))]]) ).
cnf(refute_0_125,plain,
( set_difference(X_35,set_intersection2(X_35,X_36)) != set_difference(X_35,X_36)
| set_difference(X_35,set_intersection2(X_36,X_35)) != set_difference(X_35,set_intersection2(X_35,X_36))
| set_difference(X_35,set_intersection2(X_36,X_35)) = set_difference(X_35,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_35,set_intersection2(X_36,X_35)),set_difference(X_35,set_intersection2(X_35,X_36))) ),[1],$fot(set_difference(X_35,X_36))]]) ).
cnf(refute_0_126,plain,
( set_difference(X_35,set_intersection2(X_36,X_35)) != set_difference(X_35,set_intersection2(X_35,X_36))
| set_difference(X_35,set_intersection2(X_36,X_35)) = set_difference(X_35,X_36) ),
inference(resolve,[$cnf( $equal(set_difference(X_35,set_intersection2(X_35,X_36)),set_difference(X_35,X_36)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
set_difference(X_35,set_intersection2(X_36,X_35)) = set_difference(X_35,X_36),
inference(resolve,[$cnf( $equal(set_difference(X_35,set_intersection2(X_36,X_35)),set_difference(X_35,set_intersection2(X_35,X_36))) )],[refute_0_69,refute_0_126]) ).
cnf(refute_0_128,plain,
set_difference(B,set_intersection2(X_153,B)) = set_difference(B,X_153),
inference(subst,[],[refute_0_127:[bind(X_35,$fot(B)),bind(X_36,$fot(X_153))]]) ).
cnf(refute_0_129,plain,
( set_difference(B,set_intersection2(X_153,B)) != set_difference(B,X_153)
| set_union2(set_intersection2(X_153,B),set_difference(B,set_intersection2(X_153,B))) != set_union2(set_intersection2(X_153,B),B)
| set_union2(set_intersection2(X_153,B),set_difference(B,X_153)) = set_union2(set_intersection2(X_153,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_intersection2(X_153,B),set_difference(B,set_intersection2(X_153,B))),set_union2(set_intersection2(X_153,B),B)) ),[0,1],$fot(set_difference(B,X_153))]]) ).
cnf(refute_0_130,plain,
( set_union2(set_intersection2(X_153,B),set_difference(B,set_intersection2(X_153,B))) != set_union2(set_intersection2(X_153,B),B)
| set_union2(set_intersection2(X_153,B),set_difference(B,X_153)) = set_union2(set_intersection2(X_153,B),B) ),
inference(resolve,[$cnf( $equal(set_difference(B,set_intersection2(X_153,B)),set_difference(B,X_153)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
set_union2(set_intersection2(X_153,B),set_difference(B,X_153)) = set_union2(set_intersection2(X_153,B),B),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_153,B),set_difference(B,set_intersection2(X_153,B))),set_union2(set_intersection2(X_153,B),B)) )],[refute_0_51,refute_0_130]) ).
cnf(refute_0_132,plain,
set_union2(set_intersection2(X_153,B),set_difference(B,X_153)) = set_union2(set_difference(B,X_153),set_intersection2(X_153,B)),
inference(subst,[],[refute_0_78:[bind(A,$fot(set_difference(B,X_153))),bind(B,$fot(set_intersection2(X_153,B)))]]) ).
cnf(refute_0_133,plain,
( set_union2(set_intersection2(X_153,B),set_difference(B,X_153)) != set_union2(set_difference(B,X_153),set_intersection2(X_153,B))
| set_union2(set_intersection2(X_153,B),set_difference(B,X_153)) != set_union2(set_intersection2(X_153,B),B)
| set_union2(set_difference(B,X_153),set_intersection2(X_153,B)) = set_union2(set_intersection2(X_153,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_intersection2(X_153,B),set_difference(B,X_153)),set_union2(set_intersection2(X_153,B),B)) ),[0],$fot(set_union2(set_difference(B,X_153),set_intersection2(X_153,B)))]]) ).
cnf(refute_0_134,plain,
( set_union2(set_intersection2(X_153,B),set_difference(B,X_153)) != set_union2(set_intersection2(X_153,B),B)
| set_union2(set_difference(B,X_153),set_intersection2(X_153,B)) = set_union2(set_intersection2(X_153,B),B) ),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_153,B),set_difference(B,X_153)),set_union2(set_difference(B,X_153),set_intersection2(X_153,B))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
subset(set_difference(A,set_difference(A,X_26)),A),
inference(subst,[],[refute_0_72:[bind(B,$fot(set_difference(A,X_26)))]]) ).
cnf(refute_0_136,plain,
( set_difference(A,set_difference(A,X_26)) != set_intersection2(A,X_26)
| ~ subset(set_difference(A,set_difference(A,X_26)),A)
| subset(set_intersection2(A,X_26),A) ),
introduced(tautology,[equality,[$cnf( subset(set_difference(A,set_difference(A,X_26)),A) ),[0],$fot(set_intersection2(A,X_26))]]) ).
cnf(refute_0_137,plain,
( ~ subset(set_difference(A,set_difference(A,X_26)),A)
| subset(set_intersection2(A,X_26),A) ),
inference(resolve,[$cnf( $equal(set_difference(A,set_difference(A,X_26)),set_intersection2(A,X_26)) )],[refute_0_53,refute_0_136]) ).
cnf(refute_0_138,plain,
subset(set_intersection2(A,X_26),A),
inference(resolve,[$cnf( subset(set_difference(A,set_difference(A,X_26)),A) )],[refute_0_135,refute_0_137]) ).
cnf(refute_0_139,plain,
subset(set_intersection2(X_28,X_29),X_28),
inference(subst,[],[refute_0_138:[bind(A,$fot(X_28)),bind(X_26,$fot(X_29))]]) ).
cnf(refute_0_140,plain,
set_intersection2(X_29,X_28) = set_intersection2(X_28,X_29),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_29)),bind(B,$fot(X_28))]]) ).
cnf(refute_0_141,plain,
( set_intersection2(X_29,X_28) != set_intersection2(X_28,X_29)
| set_intersection2(X_28,X_29) = set_intersection2(X_29,X_28) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_intersection2(X_29,X_28))),bind(Y,$fot(set_intersection2(X_28,X_29)))]]) ).
cnf(refute_0_142,plain,
set_intersection2(X_28,X_29) = set_intersection2(X_29,X_28),
inference(resolve,[$cnf( $equal(set_intersection2(X_29,X_28),set_intersection2(X_28,X_29)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
( set_intersection2(X_28,X_29) != set_intersection2(X_29,X_28)
| ~ subset(set_intersection2(X_28,X_29),X_28)
| subset(set_intersection2(X_29,X_28),X_28) ),
introduced(tautology,[equality,[$cnf( subset(set_intersection2(X_28,X_29),X_28) ),[0],$fot(set_intersection2(X_29,X_28))]]) ).
cnf(refute_0_144,plain,
( ~ subset(set_intersection2(X_28,X_29),X_28)
| subset(set_intersection2(X_29,X_28),X_28) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_28,X_29),set_intersection2(X_29,X_28)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
subset(set_intersection2(X_29,X_28),X_28),
inference(resolve,[$cnf( subset(set_intersection2(X_28,X_29),X_28) )],[refute_0_139,refute_0_144]) ).
cnf(refute_0_146,plain,
subset(set_intersection2(X_29,X_101),X_101),
inference(subst,[],[refute_0_145:[bind(X_28,$fot(X_101))]]) ).
cnf(refute_0_147,plain,
( ~ subset(set_intersection2(X_29,X_101),X_101)
| set_union2(set_intersection2(X_29,X_101),X_101) = X_101 ),
inference(subst,[],[refute_0_74:[bind(A,$fot(set_intersection2(X_29,X_101))),bind(B,$fot(X_101))]]) ).
cnf(refute_0_148,plain,
set_union2(set_intersection2(X_29,X_101),X_101) = X_101,
inference(resolve,[$cnf( subset(set_intersection2(X_29,X_101),X_101) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
set_union2(set_intersection2(X_29,X_101),X_101) = set_union2(X_101,set_intersection2(X_29,X_101)),
inference(subst,[],[refute_0_78:[bind(A,$fot(X_101)),bind(B,$fot(set_intersection2(X_29,X_101)))]]) ).
cnf(refute_0_150,plain,
( set_union2(set_intersection2(X_29,X_101),X_101) != X_101
| set_union2(set_intersection2(X_29,X_101),X_101) != set_union2(X_101,set_intersection2(X_29,X_101))
| set_union2(X_101,set_intersection2(X_29,X_101)) = X_101 ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_intersection2(X_29,X_101),X_101),X_101) ),[0],$fot(set_union2(X_101,set_intersection2(X_29,X_101)))]]) ).
cnf(refute_0_151,plain,
( set_union2(set_intersection2(X_29,X_101),X_101) != X_101
| set_union2(X_101,set_intersection2(X_29,X_101)) = X_101 ),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_29,X_101),X_101),set_union2(X_101,set_intersection2(X_29,X_101))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
set_union2(X_101,set_intersection2(X_29,X_101)) = X_101,
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_29,X_101),X_101),X_101) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
set_union2(B,set_intersection2(X_153,B)) = B,
inference(subst,[],[refute_0_152:[bind(X_101,$fot(B)),bind(X_29,$fot(X_153))]]) ).
cnf(refute_0_154,plain,
set_union2(set_intersection2(X_153,B),B) = set_union2(B,set_intersection2(X_153,B)),
inference(subst,[],[refute_0_78:[bind(A,$fot(B)),bind(B,$fot(set_intersection2(X_153,B)))]]) ).
cnf(refute_0_155,plain,
( set_union2(B,set_intersection2(X_153,B)) != B
| set_union2(set_intersection2(X_153,B),B) != set_union2(B,set_intersection2(X_153,B))
| set_union2(set_intersection2(X_153,B),B) = B ),
inference(subst,[],[refute_0_114:[bind(X,$fot(set_union2(set_intersection2(X_153,B),B))),bind(Y,$fot(set_union2(B,set_intersection2(X_153,B)))),bind(Z,$fot(B))]]) ).
cnf(refute_0_156,plain,
( set_union2(B,set_intersection2(X_153,B)) != B
| set_union2(set_intersection2(X_153,B),B) = B ),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_153,B),B),set_union2(B,set_intersection2(X_153,B))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
set_union2(set_intersection2(X_153,B),B) = B,
inference(resolve,[$cnf( $equal(set_union2(B,set_intersection2(X_153,B)),B) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( set_union2(set_difference(B,X_153),set_intersection2(X_153,B)) != set_union2(set_intersection2(X_153,B),B)
| set_union2(set_intersection2(X_153,B),B) != B
| set_union2(set_difference(B,X_153),set_intersection2(X_153,B)) = B ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_union2(set_difference(B,X_153),set_intersection2(X_153,B)),B) ),[0],$fot(set_union2(set_intersection2(X_153,B),B))]]) ).
cnf(refute_0_159,plain,
( set_union2(set_difference(B,X_153),set_intersection2(X_153,B)) != set_union2(set_intersection2(X_153,B),B)
| set_union2(set_difference(B,X_153),set_intersection2(X_153,B)) = B ),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_153,B),B),B) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( set_union2(set_intersection2(X_153,B),set_difference(B,X_153)) != set_union2(set_intersection2(X_153,B),B)
| set_union2(set_difference(B,X_153),set_intersection2(X_153,B)) = B ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(B,X_153),set_intersection2(X_153,B)),set_union2(set_intersection2(X_153,B),B)) )],[refute_0_134,refute_0_159]) ).
cnf(refute_0_161,plain,
set_union2(set_difference(B,X_153),set_intersection2(X_153,B)) = B,
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_153,B),set_difference(B,X_153)),set_union2(set_intersection2(X_153,B),B)) )],[refute_0_131,refute_0_160]) ).
cnf(refute_0_162,plain,
set_union2(set_difference(B,set_union2(B,X_171)),set_intersection2(set_union2(B,X_171),B)) = B,
inference(subst,[],[refute_0_161:[bind(X_153,$fot(set_union2(B,X_171)))]]) ).
cnf(refute_0_163,plain,
set_difference(set_union2(A,set_union2(A,X_168)),set_union2(A,X_168)) = set_difference(A,set_union2(A,X_168)),
inference(subst,[],[refute_0_2:[bind(B,$fot(set_union2(A,X_168)))]]) ).
cnf(refute_0_164,plain,
set_union2(X_57,set_difference(set_union2(X_57,A),X_57)) = set_union2(X_57,set_union2(X_57,A)),
inference(subst,[],[refute_0_18:[bind(A,$fot(X_57)),bind(B,$fot(set_union2(X_57,A)))]]) ).
cnf(refute_0_165,plain,
set_difference(set_union2(X_57,A),X_57) = set_difference(A,X_57),
inference(subst,[],[refute_0_27:[bind(B,$fot(X_57))]]) ).
cnf(refute_0_166,plain,
( set_difference(set_union2(X_57,A),X_57) != set_difference(A,X_57)
| set_union2(X_57,set_difference(set_union2(X_57,A),X_57)) != set_union2(X_57,set_union2(X_57,A))
| set_union2(X_57,set_difference(A,X_57)) = set_union2(X_57,set_union2(X_57,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(X_57,set_difference(set_union2(X_57,A),X_57)),set_union2(X_57,set_union2(X_57,A))) ),[0,1],$fot(set_difference(A,X_57))]]) ).
cnf(refute_0_167,plain,
( set_union2(X_57,set_difference(set_union2(X_57,A),X_57)) != set_union2(X_57,set_union2(X_57,A))
| set_union2(X_57,set_difference(A,X_57)) = set_union2(X_57,set_union2(X_57,A)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_57,A),X_57),set_difference(A,X_57)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
set_union2(X_57,set_difference(A,X_57)) = set_union2(X_57,set_union2(X_57,A)),
inference(resolve,[$cnf( $equal(set_union2(X_57,set_difference(set_union2(X_57,A),X_57)),set_union2(X_57,set_union2(X_57,A))) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
set_union2(X_57,set_difference(A,X_57)) = set_union2(X_57,A),
inference(subst,[],[refute_0_18:[bind(A,$fot(X_57)),bind(B,$fot(A))]]) ).
cnf(refute_0_170,plain,
( set_union2(X_57,set_difference(A,X_57)) != set_union2(X_57,A)
| set_union2(X_57,set_difference(A,X_57)) != set_union2(X_57,set_union2(X_57,A))
| set_union2(X_57,A) = set_union2(X_57,set_union2(X_57,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(X_57,set_difference(A,X_57)),set_union2(X_57,set_union2(X_57,A))) ),[0],$fot(set_union2(X_57,A))]]) ).
cnf(refute_0_171,plain,
( set_union2(X_57,set_difference(A,X_57)) != set_union2(X_57,set_union2(X_57,A))
| set_union2(X_57,A) = set_union2(X_57,set_union2(X_57,A)) ),
inference(resolve,[$cnf( $equal(set_union2(X_57,set_difference(A,X_57)),set_union2(X_57,A)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
set_union2(X_57,A) = set_union2(X_57,set_union2(X_57,A)),
inference(resolve,[$cnf( $equal(set_union2(X_57,set_difference(A,X_57)),set_union2(X_57,set_union2(X_57,A))) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
set_union2(A,X_168) = set_union2(A,set_union2(A,X_168)),
inference(subst,[],[refute_0_172:[bind(A,$fot(X_168)),bind(X_57,$fot(A))]]) ).
cnf(refute_0_174,plain,
( set_union2(A,X_168) != set_union2(A,set_union2(A,X_168))
| set_union2(A,set_union2(A,X_168)) = set_union2(A,X_168) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_union2(A,X_168))),bind(Y,$fot(set_union2(A,set_union2(A,X_168))))]]) ).
cnf(refute_0_175,plain,
set_union2(A,set_union2(A,X_168)) = set_union2(A,X_168),
inference(resolve,[$cnf( $equal(set_union2(A,X_168),set_union2(A,set_union2(A,X_168))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
( set_difference(set_union2(A,set_union2(A,X_168)),set_union2(A,X_168)) != set_difference(A,set_union2(A,X_168))
| set_union2(A,set_union2(A,X_168)) != set_union2(A,X_168)
| set_difference(set_union2(A,X_168),set_union2(A,X_168)) = set_difference(A,set_union2(A,X_168)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,set_union2(A,X_168)),set_union2(A,X_168)),set_difference(A,set_union2(A,X_168))) ),[0,0],$fot(set_union2(A,X_168))]]) ).
cnf(refute_0_177,plain,
( set_difference(set_union2(A,set_union2(A,X_168)),set_union2(A,X_168)) != set_difference(A,set_union2(A,X_168))
| set_difference(set_union2(A,X_168),set_union2(A,X_168)) = set_difference(A,set_union2(A,X_168)) ),
inference(resolve,[$cnf( $equal(set_union2(A,set_union2(A,X_168)),set_union2(A,X_168)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
set_difference(set_union2(A,X_168),set_union2(A,X_168)) = set_difference(A,set_union2(A,X_168)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,set_union2(A,X_168)),set_union2(A,X_168)),set_difference(A,set_union2(A,X_168))) )],[refute_0_163,refute_0_177]) ).
cnf(refute_0_179,plain,
set_difference(set_union2(A,X_168),set_union2(A,X_168)) = empty_set,
inference(subst,[],[refute_0_97:[bind(X_25,$fot(set_union2(A,X_168)))]]) ).
cnf(refute_0_180,plain,
( set_difference(set_union2(A,X_168),set_union2(A,X_168)) != empty_set
| set_difference(set_union2(A,X_168),set_union2(A,X_168)) != set_difference(A,set_union2(A,X_168))
| empty_set = set_difference(A,set_union2(A,X_168)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,X_168),set_union2(A,X_168)),set_difference(A,set_union2(A,X_168))) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_181,plain,
( set_difference(set_union2(A,X_168),set_union2(A,X_168)) != set_difference(A,set_union2(A,X_168))
| empty_set = set_difference(A,set_union2(A,X_168)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_168),set_union2(A,X_168)),empty_set) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
empty_set = set_difference(A,set_union2(A,X_168)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_168),set_union2(A,X_168)),set_difference(A,set_union2(A,X_168))) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
empty_set = set_difference(B,set_union2(B,X_171)),
inference(subst,[],[refute_0_182:[bind(A,$fot(B)),bind(X_168,$fot(X_171))]]) ).
cnf(refute_0_184,plain,
( empty_set != set_difference(B,set_union2(B,X_171))
| set_difference(B,set_union2(B,X_171)) = empty_set ),
inference(subst,[],[refute_0_10:[bind(X,$fot(empty_set)),bind(Y,$fot(set_difference(B,set_union2(B,X_171))))]]) ).
cnf(refute_0_185,plain,
set_difference(B,set_union2(B,X_171)) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,set_difference(B,set_union2(B,X_171))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
( set_difference(B,set_union2(B,X_171)) != empty_set
| set_union2(set_difference(B,set_union2(B,X_171)),set_intersection2(set_union2(B,X_171),B)) != B
| set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(B,set_union2(B,X_171)),set_intersection2(set_union2(B,X_171),B)),B) ),[0,0],$fot(empty_set)]]) ).
cnf(refute_0_187,plain,
( set_union2(set_difference(B,set_union2(B,X_171)),set_intersection2(set_union2(B,X_171),B)) != B
| set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) = B ),
inference(resolve,[$cnf( $equal(set_difference(B,set_union2(B,X_171)),empty_set) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) = B,
inference(resolve,[$cnf( $equal(set_union2(set_difference(B,set_union2(B,X_171)),set_intersection2(set_union2(B,X_171),B)),B) )],[refute_0_162,refute_0_187]) ).
cnf(refute_0_189,plain,
set_intersection2(B,set_union2(B,X_171)) = set_difference(B,set_difference(X_171,B)),
inference(subst,[],[refute_0_39:[bind(A,$fot(B)),bind(X_58,$fot(X_171))]]) ).
cnf(refute_0_190,plain,
set_intersection2(set_intersection2(X_155,X_154),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),
inference(subst,[],[refute_0_46:[bind(X_59,$fot(set_intersection2(X_155,X_154))),bind(X_60,$fot(set_difference(X_154,X_155)))]]) ).
cnf(refute_0_191,plain,
set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) = X_154,
inference(subst,[],[refute_0_161:[bind(B,$fot(X_154)),bind(X_153,$fot(X_155))]]) ).
cnf(refute_0_192,plain,
( set_intersection2(set_intersection2(X_155,X_154),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) != X_154
| set_intersection2(set_intersection2(X_155,X_154),X_154) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(set_intersection2(X_155,X_154),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) ),[0,1],$fot(X_154)]]) ).
cnf(refute_0_193,plain,
( set_intersection2(set_intersection2(X_155,X_154),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_intersection2(set_intersection2(X_155,X_154),X_154) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),X_154) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
set_intersection2(set_intersection2(X_155,X_154),X_154) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),
inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(X_155,X_154),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
set_difference(set_intersection2(X_105,B),set_difference(set_intersection2(X_105,B),B)) = set_intersection2(set_intersection2(X_105,B),B),
inference(subst,[],[refute_0_0:[bind(A,$fot(set_intersection2(X_105,B)))]]) ).
cnf(refute_0_196,plain,
set_difference(set_union2(B,set_intersection2(X_103,B)),B) = set_difference(set_intersection2(X_103,B),B),
inference(subst,[],[refute_0_27:[bind(A,$fot(set_intersection2(X_103,B)))]]) ).
cnf(refute_0_197,plain,
set_union2(B,set_intersection2(X_103,B)) = B,
inference(subst,[],[refute_0_152:[bind(X_101,$fot(B)),bind(X_29,$fot(X_103))]]) ).
cnf(refute_0_198,plain,
( set_difference(set_union2(B,set_intersection2(X_103,B)),B) != set_difference(set_intersection2(X_103,B),B)
| set_union2(B,set_intersection2(X_103,B)) != B
| set_difference(B,B) = set_difference(set_intersection2(X_103,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(B,set_intersection2(X_103,B)),B),set_difference(set_intersection2(X_103,B),B)) ),[0,0],$fot(B)]]) ).
cnf(refute_0_199,plain,
( set_difference(set_union2(B,set_intersection2(X_103,B)),B) != set_difference(set_intersection2(X_103,B),B)
| set_difference(B,B) = set_difference(set_intersection2(X_103,B),B) ),
inference(resolve,[$cnf( $equal(set_union2(B,set_intersection2(X_103,B)),B) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
set_difference(B,B) = set_difference(set_intersection2(X_103,B),B),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,set_intersection2(X_103,B)),B),set_difference(set_intersection2(X_103,B),B)) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
( set_difference(B,B) != empty_set
| set_difference(B,B) != set_difference(set_intersection2(X_103,B),B)
| empty_set = set_difference(set_intersection2(X_103,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(B,B),set_difference(set_intersection2(X_103,B),B)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_202,plain,
( set_difference(B,B) != set_difference(set_intersection2(X_103,B),B)
| empty_set = set_difference(set_intersection2(X_103,B),B) ),
inference(resolve,[$cnf( $equal(set_difference(B,B),empty_set) )],[refute_0_98,refute_0_201]) ).
cnf(refute_0_203,plain,
empty_set = set_difference(set_intersection2(X_103,B),B),
inference(resolve,[$cnf( $equal(set_difference(B,B),set_difference(set_intersection2(X_103,B),B)) )],[refute_0_200,refute_0_202]) ).
cnf(refute_0_204,plain,
empty_set = set_difference(set_intersection2(X_105,B),B),
inference(subst,[],[refute_0_203:[bind(X_103,$fot(X_105))]]) ).
cnf(refute_0_205,plain,
( empty_set != set_difference(set_intersection2(X_105,B),B)
| set_difference(set_intersection2(X_105,B),B) = empty_set ),
inference(subst,[],[refute_0_10:[bind(X,$fot(empty_set)),bind(Y,$fot(set_difference(set_intersection2(X_105,B),B)))]]) ).
cnf(refute_0_206,plain,
set_difference(set_intersection2(X_105,B),B) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,set_difference(set_intersection2(X_105,B),B)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
( set_difference(set_intersection2(X_105,B),B) != empty_set
| set_difference(set_intersection2(X_105,B),set_difference(set_intersection2(X_105,B),B)) != set_intersection2(set_intersection2(X_105,B),B)
| set_difference(set_intersection2(X_105,B),empty_set) = set_intersection2(set_intersection2(X_105,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_intersection2(X_105,B),set_difference(set_intersection2(X_105,B),B)),set_intersection2(set_intersection2(X_105,B),B)) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_208,plain,
( set_difference(set_intersection2(X_105,B),set_difference(set_intersection2(X_105,B),B)) != set_intersection2(set_intersection2(X_105,B),B)
| set_difference(set_intersection2(X_105,B),empty_set) = set_intersection2(set_intersection2(X_105,B),B) ),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_105,B),B),empty_set) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
set_difference(set_intersection2(X_105,B),empty_set) = set_intersection2(set_intersection2(X_105,B),B),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_105,B),set_difference(set_intersection2(X_105,B),B)),set_intersection2(set_intersection2(X_105,B),B)) )],[refute_0_195,refute_0_208]) ).
cnf(refute_0_210,plain,
set_difference(set_intersection2(X_105,B),empty_set) = set_intersection2(X_105,B),
inference(subst,[],[refute_0_88:[bind(A,$fot(set_intersection2(X_105,B)))]]) ).
cnf(refute_0_211,plain,
( set_difference(set_intersection2(X_105,B),empty_set) != set_intersection2(X_105,B)
| set_difference(set_intersection2(X_105,B),empty_set) != set_intersection2(set_intersection2(X_105,B),B)
| set_intersection2(X_105,B) = set_intersection2(set_intersection2(X_105,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_intersection2(X_105,B),empty_set),set_intersection2(set_intersection2(X_105,B),B)) ),[0],$fot(set_intersection2(X_105,B))]]) ).
cnf(refute_0_212,plain,
( set_difference(set_intersection2(X_105,B),empty_set) != set_intersection2(set_intersection2(X_105,B),B)
| set_intersection2(X_105,B) = set_intersection2(set_intersection2(X_105,B),B) ),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_105,B),empty_set),set_intersection2(X_105,B)) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
set_intersection2(set_intersection2(X_105,B),B) = set_intersection2(B,set_intersection2(X_105,B)),
inference(subst,[],[refute_0_12:[bind(A,$fot(B)),bind(B,$fot(set_intersection2(X_105,B)))]]) ).
cnf(refute_0_214,plain,
( set_intersection2(X_105,B) != set_intersection2(set_intersection2(X_105,B),B)
| set_intersection2(set_intersection2(X_105,B),B) != set_intersection2(B,set_intersection2(X_105,B))
| set_intersection2(X_105,B) = set_intersection2(B,set_intersection2(X_105,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_intersection2(X_105,B),set_intersection2(B,set_intersection2(X_105,B))) ),[0],$fot(set_intersection2(set_intersection2(X_105,B),B))]]) ).
cnf(refute_0_215,plain,
( set_intersection2(X_105,B) != set_intersection2(set_intersection2(X_105,B),B)
| set_intersection2(X_105,B) = set_intersection2(B,set_intersection2(X_105,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(X_105,B),B),set_intersection2(B,set_intersection2(X_105,B))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
( set_difference(set_intersection2(X_105,B),empty_set) != set_intersection2(set_intersection2(X_105,B),B)
| set_intersection2(X_105,B) = set_intersection2(B,set_intersection2(X_105,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_105,B),set_intersection2(set_intersection2(X_105,B),B)) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
set_intersection2(X_105,B) = set_intersection2(B,set_intersection2(X_105,B)),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_105,B),empty_set),set_intersection2(set_intersection2(X_105,B),B)) )],[refute_0_209,refute_0_216]) ).
cnf(refute_0_218,plain,
( set_intersection2(X_105,B) != set_intersection2(B,set_intersection2(X_105,B))
| set_intersection2(B,set_intersection2(X_105,B)) = set_intersection2(X_105,B) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_intersection2(X_105,B))),bind(Y,$fot(set_intersection2(B,set_intersection2(X_105,B))))]]) ).
cnf(refute_0_219,plain,
set_intersection2(B,set_intersection2(X_105,B)) = set_intersection2(X_105,B),
inference(resolve,[$cnf( $equal(set_intersection2(X_105,B),set_intersection2(B,set_intersection2(X_105,B))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
set_intersection2(X_154,set_intersection2(X_155,X_154)) = set_intersection2(X_155,X_154),
inference(subst,[],[refute_0_219:[bind(B,$fot(X_154)),bind(X_105,$fot(X_155))]]) ).
cnf(refute_0_221,plain,
set_intersection2(set_intersection2(X_155,X_154),X_154) = set_intersection2(X_154,set_intersection2(X_155,X_154)),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_154)),bind(B,$fot(set_intersection2(X_155,X_154)))]]) ).
cnf(refute_0_222,plain,
( set_intersection2(X_154,set_intersection2(X_155,X_154)) != set_intersection2(X_155,X_154)
| set_intersection2(set_intersection2(X_155,X_154),X_154) != set_intersection2(X_154,set_intersection2(X_155,X_154))
| set_intersection2(set_intersection2(X_155,X_154),X_154) = set_intersection2(X_155,X_154) ),
inference(subst,[],[refute_0_114:[bind(X,$fot(set_intersection2(set_intersection2(X_155,X_154),X_154))),bind(Y,$fot(set_intersection2(X_154,set_intersection2(X_155,X_154)))),bind(Z,$fot(set_intersection2(X_155,X_154)))]]) ).
cnf(refute_0_223,plain,
( set_intersection2(X_154,set_intersection2(X_155,X_154)) != set_intersection2(X_155,X_154)
| set_intersection2(set_intersection2(X_155,X_154),X_154) = set_intersection2(X_155,X_154) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(X_155,X_154),X_154),set_intersection2(X_154,set_intersection2(X_155,X_154))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
set_intersection2(set_intersection2(X_155,X_154),X_154) = set_intersection2(X_155,X_154),
inference(resolve,[$cnf( $equal(set_intersection2(X_154,set_intersection2(X_155,X_154)),set_intersection2(X_155,X_154)) )],[refute_0_220,refute_0_223]) ).
cnf(refute_0_225,plain,
( set_intersection2(set_intersection2(X_155,X_154),X_154) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_intersection2(set_intersection2(X_155,X_154),X_154) != set_intersection2(X_155,X_154)
| set_intersection2(X_155,X_154) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(set_intersection2(X_155,X_154),X_154),set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) ),[0],$fot(set_intersection2(X_155,X_154))]]) ).
cnf(refute_0_226,plain,
( set_intersection2(set_intersection2(X_155,X_154),X_154) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_intersection2(X_155,X_154) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(X_155,X_154),X_154),set_intersection2(X_155,X_154)) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
set_difference(set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),
inference(subst,[],[refute_0_50:[bind(B,$fot(set_intersection2(X_155,X_154))),bind(X_33,$fot(set_difference(X_154,X_155)))]]) ).
cnf(refute_0_228,plain,
( set_difference(set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) != X_154
| set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) ),[0,0],$fot(X_154)]]) ).
cnf(refute_0_229,plain,
( set_difference(set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),X_154) )],[refute_0_191,refute_0_228]) ).
cnf(refute_0_230,plain,
set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),
inference(resolve,[$cnf( $equal(set_difference(set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) )],[refute_0_227,refute_0_229]) ).
cnf(refute_0_231,plain,
( set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))))),bind(Y,$fot(set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))))]]) ).
cnf(refute_0_232,plain,
set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),
inference(resolve,[$cnf( $equal(set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
( set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_intersection2(X_155,X_154) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_intersection2(X_155,X_154) = set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(X_155,X_154),set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) ),[1],$fot(set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))))]]) ).
cnf(refute_0_234,plain,
( set_intersection2(X_155,X_154) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_intersection2(X_155,X_154) = set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
( set_intersection2(set_intersection2(X_155,X_154),X_154) != set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_intersection2(X_155,X_154) = set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_155,X_154),set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) )],[refute_0_226,refute_0_234]) ).
cnf(refute_0_236,plain,
set_intersection2(X_155,X_154) = set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),
inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(X_155,X_154),X_154),set_difference(set_intersection2(X_155,X_154),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) )],[refute_0_194,refute_0_235]) ).
cnf(refute_0_237,plain,
set_difference(X_154,set_difference(X_154,X_155)) = set_intersection2(X_154,X_155),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_154)),bind(B,$fot(X_155))]]) ).
cnf(refute_0_238,plain,
set_intersection2(set_difference(X_154,X_155),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))),
inference(subst,[],[refute_0_39:[bind(A,$fot(set_difference(X_154,X_155))),bind(X_58,$fot(set_intersection2(X_155,X_154)))]]) ).
cnf(refute_0_239,plain,
( set_intersection2(set_difference(X_154,X_155),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))
| set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) != X_154
| set_intersection2(set_difference(X_154,X_155),X_154) = set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(set_difference(X_154,X_155),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))) ),[0,1],$fot(X_154)]]) ).
cnf(refute_0_240,plain,
( set_intersection2(set_difference(X_154,X_155),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))
| set_intersection2(set_difference(X_154,X_155),X_154) = set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),X_154) )],[refute_0_191,refute_0_239]) ).
cnf(refute_0_241,plain,
set_intersection2(set_difference(X_154,X_155),X_154) = set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))),
inference(resolve,[$cnf( $equal(set_intersection2(set_difference(X_154,X_155),set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))) )],[refute_0_238,refute_0_240]) ).
cnf(refute_0_242,plain,
set_difference(A,set_intersection2(A,X_26)) = set_difference(A,X_26),
inference(subst,[],[refute_0_123:[bind(B,$fot(A)),bind(X_113,$fot(X_26))]]) ).
cnf(refute_0_243,plain,
( set_difference(A,set_intersection2(A,X_26)) != set_difference(A,X_26)
| set_difference(A,set_intersection2(A,X_26)) != set_intersection2(A,set_difference(A,X_26))
| set_difference(A,X_26) = set_intersection2(A,set_difference(A,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(A,set_intersection2(A,X_26)),set_intersection2(A,set_difference(A,X_26))) ),[0],$fot(set_difference(A,X_26))]]) ).
cnf(refute_0_244,plain,
( set_difference(A,set_intersection2(A,X_26)) != set_intersection2(A,set_difference(A,X_26))
| set_difference(A,X_26) = set_intersection2(A,set_difference(A,X_26)) ),
inference(resolve,[$cnf( $equal(set_difference(A,set_intersection2(A,X_26)),set_difference(A,X_26)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
set_difference(A,X_26) = set_intersection2(A,set_difference(A,X_26)),
inference(resolve,[$cnf( $equal(set_difference(A,set_intersection2(A,X_26)),set_intersection2(A,set_difference(A,X_26))) )],[refute_0_56,refute_0_244]) ).
cnf(refute_0_246,plain,
( set_difference(A,X_26) != set_intersection2(A,set_difference(A,X_26))
| set_intersection2(A,set_difference(A,X_26)) = set_difference(A,X_26) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_difference(A,X_26))),bind(Y,$fot(set_intersection2(A,set_difference(A,X_26))))]]) ).
cnf(refute_0_247,plain,
set_intersection2(A,set_difference(A,X_26)) = set_difference(A,X_26),
inference(resolve,[$cnf( $equal(set_difference(A,X_26),set_intersection2(A,set_difference(A,X_26))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
set_intersection2(X_154,set_difference(X_154,X_155)) = set_difference(X_154,X_155),
inference(subst,[],[refute_0_247:[bind(A,$fot(X_154)),bind(X_26,$fot(X_155))]]) ).
cnf(refute_0_249,plain,
set_intersection2(set_difference(X_154,X_155),X_154) = set_intersection2(X_154,set_difference(X_154,X_155)),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_154)),bind(B,$fot(set_difference(X_154,X_155)))]]) ).
cnf(refute_0_250,plain,
( set_intersection2(X_154,set_difference(X_154,X_155)) != set_difference(X_154,X_155)
| set_intersection2(set_difference(X_154,X_155),X_154) != set_intersection2(X_154,set_difference(X_154,X_155))
| set_intersection2(set_difference(X_154,X_155),X_154) = set_difference(X_154,X_155) ),
inference(subst,[],[refute_0_114:[bind(X,$fot(set_intersection2(set_difference(X_154,X_155),X_154))),bind(Y,$fot(set_intersection2(X_154,set_difference(X_154,X_155)))),bind(Z,$fot(set_difference(X_154,X_155)))]]) ).
cnf(refute_0_251,plain,
( set_intersection2(X_154,set_difference(X_154,X_155)) != set_difference(X_154,X_155)
| set_intersection2(set_difference(X_154,X_155),X_154) = set_difference(X_154,X_155) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_difference(X_154,X_155),X_154),set_intersection2(X_154,set_difference(X_154,X_155))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
set_intersection2(set_difference(X_154,X_155),X_154) = set_difference(X_154,X_155),
inference(resolve,[$cnf( $equal(set_intersection2(X_154,set_difference(X_154,X_155)),set_difference(X_154,X_155)) )],[refute_0_248,refute_0_251]) ).
cnf(refute_0_253,plain,
( set_intersection2(set_difference(X_154,X_155),X_154) != set_difference(X_154,X_155)
| set_intersection2(set_difference(X_154,X_155),X_154) != set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))
| set_difference(X_154,X_155) = set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(set_difference(X_154,X_155),X_154),set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))) ),[0],$fot(set_difference(X_154,X_155))]]) ).
cnf(refute_0_254,plain,
( set_intersection2(set_difference(X_154,X_155),X_154) != set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))
| set_difference(X_154,X_155) = set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_difference(X_154,X_155),X_154),set_difference(X_154,X_155)) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
set_difference(set_union2(X_33,set_intersection2(X_103,X_33)),set_difference(X_33,set_intersection2(X_103,X_33))) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))),
inference(subst,[],[refute_0_50:[bind(B,$fot(set_intersection2(X_103,X_33)))]]) ).
cnf(refute_0_256,plain,
set_union2(X_33,set_intersection2(X_103,X_33)) = X_33,
inference(subst,[],[refute_0_152:[bind(X_101,$fot(X_33)),bind(X_29,$fot(X_103))]]) ).
cnf(refute_0_257,plain,
( set_difference(set_union2(X_33,set_intersection2(X_103,X_33)),set_difference(X_33,set_intersection2(X_103,X_33))) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))
| set_union2(X_33,set_intersection2(X_103,X_33)) != X_33
| set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(X_33,set_intersection2(X_103,X_33)),set_difference(X_33,set_intersection2(X_103,X_33))),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) ),[0,0],$fot(X_33)]]) ).
cnf(refute_0_258,plain,
( set_difference(set_union2(X_33,set_intersection2(X_103,X_33)),set_difference(X_33,set_intersection2(X_103,X_33))) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))
| set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) ),
inference(resolve,[$cnf( $equal(set_union2(X_33,set_intersection2(X_103,X_33)),X_33) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_33,set_intersection2(X_103,X_33)),set_difference(X_33,set_intersection2(X_103,X_33))),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) )],[refute_0_255,refute_0_258]) ).
cnf(refute_0_260,plain,
set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))) = set_intersection2(X_33,set_intersection2(X_103,X_33)),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_33)),bind(B,$fot(set_intersection2(X_103,X_33)))]]) ).
cnf(refute_0_261,plain,
( set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))
| set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))) != set_intersection2(X_33,set_intersection2(X_103,X_33))
| set_intersection2(X_33,set_intersection2(X_103,X_33)) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) ),[0],$fot(set_intersection2(X_33,set_intersection2(X_103,X_33)))]]) ).
cnf(refute_0_262,plain,
( set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))
| set_intersection2(X_33,set_intersection2(X_103,X_33)) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) ),
inference(resolve,[$cnf( $equal(set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))),set_intersection2(X_33,set_intersection2(X_103,X_33))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
set_intersection2(X_33,set_intersection2(X_103,X_33)) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))),
inference(resolve,[$cnf( $equal(set_difference(X_33,set_difference(X_33,set_intersection2(X_103,X_33))),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) )],[refute_0_259,refute_0_262]) ).
cnf(refute_0_264,plain,
set_intersection2(X_33,set_intersection2(X_103,X_33)) = set_intersection2(X_103,X_33),
inference(subst,[],[refute_0_219:[bind(B,$fot(X_33)),bind(X_105,$fot(X_103))]]) ).
cnf(refute_0_265,plain,
( set_intersection2(X_33,set_intersection2(X_103,X_33)) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))
| set_intersection2(X_33,set_intersection2(X_103,X_33)) != set_intersection2(X_103,X_33)
| set_intersection2(X_103,X_33) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(X_33,set_intersection2(X_103,X_33)),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) ),[0],$fot(set_intersection2(X_103,X_33))]]) ).
cnf(refute_0_266,plain,
( set_intersection2(X_33,set_intersection2(X_103,X_33)) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))
| set_intersection2(X_103,X_33) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_33,set_intersection2(X_103,X_33)),set_intersection2(X_103,X_33)) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
set_intersection2(X_103,X_33) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))),
inference(resolve,[$cnf( $equal(set_intersection2(X_33,set_intersection2(X_103,X_33)),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) )],[refute_0_263,refute_0_266]) ).
cnf(refute_0_268,plain,
set_difference(X_33,set_intersection2(X_103,X_33)) = set_difference(X_33,X_103),
inference(subst,[],[refute_0_127:[bind(X_35,$fot(X_33)),bind(X_36,$fot(X_103))]]) ).
cnf(refute_0_269,plain,
set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))),
introduced(tautology,[refl,[$fot(set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))))]]) ).
cnf(refute_0_270,plain,
( set_difference(X_33,set_intersection2(X_103,X_33)) != set_difference(X_33,X_103)
| set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))
| set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) ),[1,1],$fot(set_difference(X_33,X_103))]]) ).
cnf(refute_0_271,plain,
( set_difference(X_33,set_intersection2(X_103,X_33)) != set_difference(X_33,X_103)
| set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103)) ),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103)),
inference(resolve,[$cnf( $equal(set_difference(X_33,set_intersection2(X_103,X_33)),set_difference(X_33,X_103)) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
( set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103))
| set_intersection2(X_103,X_33) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))
| set_intersection2(X_103,X_33) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103)) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(X_103,X_33),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) ),[1],$fot(set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103)))]]) ).
cnf(refute_0_274,plain,
( set_intersection2(X_103,X_33) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))
| set_intersection2(X_103,X_33) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103)) ),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33))),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
set_intersection2(X_103,X_33) = set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103)),
inference(resolve,[$cnf( $equal(set_intersection2(X_103,X_33),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,set_intersection2(X_103,X_33)))) )],[refute_0_267,refute_0_274]) ).
cnf(refute_0_276,plain,
( set_intersection2(X_103,X_33) != set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103))
| set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103)) = set_intersection2(X_103,X_33) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_intersection2(X_103,X_33))),bind(Y,$fot(set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103))))]]) ).
cnf(refute_0_277,plain,
set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103)) = set_intersection2(X_103,X_33),
inference(resolve,[$cnf( $equal(set_intersection2(X_103,X_33),set_difference(set_intersection2(X_103,X_33),set_difference(X_33,X_103))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)) = set_intersection2(X_155,X_154),
inference(subst,[],[refute_0_277:[bind(X_103,$fot(X_155)),bind(X_33,$fot(X_154))]]) ).
cnf(refute_0_279,plain,
set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) = set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))),
introduced(tautology,[refl,[$fot(set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))))]]) ).
cnf(refute_0_280,plain,
( set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) != set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))
| set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)) != set_intersection2(X_155,X_154)
| set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) = set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))),set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))) ),[1,1],$fot(set_intersection2(X_155,X_154))]]) ).
cnf(refute_0_281,plain,
( set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)) != set_intersection2(X_155,X_154)
| set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) = set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) ),
inference(resolve,[$cnf( $equal(set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))),set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) = set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)),set_intersection2(X_155,X_154)) )],[refute_0_278,refute_0_281]) ).
cnf(refute_0_283,plain,
( set_difference(X_154,X_155) != set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))
| set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))) != set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))
| set_difference(X_154,X_155) = set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(X_154,X_155),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) ),[0],$fot(set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))))]]) ).
cnf(refute_0_284,plain,
( set_difference(X_154,X_155) != set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))
| set_difference(X_154,X_155) = set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) ),
inference(resolve,[$cnf( $equal(set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155))),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
( set_intersection2(set_difference(X_154,X_155),X_154) != set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))
| set_difference(X_154,X_155) = set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) ),
inference(resolve,[$cnf( $equal(set_difference(X_154,X_155),set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))) )],[refute_0_254,refute_0_284]) ).
cnf(refute_0_286,plain,
set_difference(X_154,X_155) = set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),
inference(resolve,[$cnf( $equal(set_intersection2(set_difference(X_154,X_155),X_154),set_difference(set_difference(X_154,X_155),set_difference(set_intersection2(X_155,X_154),set_difference(X_154,X_155)))) )],[refute_0_241,refute_0_285]) ).
cnf(refute_0_287,plain,
( set_difference(X_154,X_155) != set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))
| set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) = set_difference(X_154,X_155) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_difference(X_154,X_155))),bind(Y,$fot(set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))))]]) ).
cnf(refute_0_288,plain,
set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) = set_difference(X_154,X_155),
inference(resolve,[$cnf( $equal(set_difference(X_154,X_155),set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),
introduced(tautology,[refl,[$fot(set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))))]]) ).
cnf(refute_0_290,plain,
( set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) != set_difference(X_154,X_155)
| set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(X_154,set_difference(X_154,X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) ),[1,1],$fot(set_difference(X_154,X_155))]]) ).
cnf(refute_0_291,plain,
( set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) != set_difference(X_154,X_155)
| set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(X_154,set_difference(X_154,X_155)) ),
inference(resolve,[$cnf( $equal(set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_difference(X_154,set_difference(X_154,X_155)),
inference(resolve,[$cnf( $equal(set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)),set_difference(X_154,X_155)) )],[refute_0_288,refute_0_291]) ).
cnf(refute_0_293,plain,
( set_difference(X_154,set_difference(X_154,X_155)) != set_intersection2(X_154,X_155)
| set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_difference(X_154,set_difference(X_154,X_155))
| set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_intersection2(X_154,X_155) ),
inference(subst,[],[refute_0_114:[bind(X,$fot(set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))))),bind(Y,$fot(set_difference(X_154,set_difference(X_154,X_155)))),bind(Z,$fot(set_intersection2(X_154,X_155)))]]) ).
cnf(refute_0_294,plain,
( set_difference(X_154,set_difference(X_154,X_155)) != set_intersection2(X_154,X_155)
| set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_intersection2(X_154,X_155) ),
inference(resolve,[$cnf( $equal(set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_difference(X_154,set_difference(X_154,X_155))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) = set_intersection2(X_154,X_155),
inference(resolve,[$cnf( $equal(set_difference(X_154,set_difference(X_154,X_155)),set_intersection2(X_154,X_155)) )],[refute_0_237,refute_0_294]) ).
cnf(refute_0_296,plain,
( set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))) != set_intersection2(X_154,X_155)
| set_intersection2(X_155,X_154) != set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_intersection2(X_155,X_154) = set_intersection2(X_154,X_155) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(X_155,X_154),set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) ),[1],$fot(set_intersection2(X_154,X_155))]]) ).
cnf(refute_0_297,plain,
( set_intersection2(X_155,X_154) != set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))
| set_intersection2(X_155,X_154) = set_intersection2(X_154,X_155) ),
inference(resolve,[$cnf( $equal(set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154))),set_intersection2(X_154,X_155)) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
set_intersection2(X_155,X_154) = set_intersection2(X_154,X_155),
inference(resolve,[$cnf( $equal(set_intersection2(X_155,X_154),set_difference(X_154,set_difference(set_difference(X_154,X_155),set_intersection2(X_155,X_154)))) )],[refute_0_236,refute_0_297]) ).
cnf(refute_0_299,plain,
( set_intersection2(X_155,X_154) != set_intersection2(X_154,X_155)
| set_intersection2(X_154,X_155) = set_intersection2(X_155,X_154) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_intersection2(X_155,X_154))),bind(Y,$fot(set_intersection2(X_154,X_155)))]]) ).
cnf(refute_0_300,plain,
set_intersection2(X_154,X_155) = set_intersection2(X_155,X_154),
inference(resolve,[$cnf( $equal(set_intersection2(X_155,X_154),set_intersection2(X_154,X_155)) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
set_intersection2(set_union2(B,X_171),B) = set_intersection2(B,set_union2(B,X_171)),
inference(subst,[],[refute_0_300:[bind(X_154,$fot(set_union2(B,X_171))),bind(X_155,$fot(B))]]) ).
cnf(refute_0_302,plain,
( set_intersection2(B,set_union2(B,X_171)) != set_difference(B,set_difference(X_171,B))
| set_intersection2(set_union2(B,X_171),B) != set_intersection2(B,set_union2(B,X_171))
| set_intersection2(set_union2(B,X_171),B) = set_difference(B,set_difference(X_171,B)) ),
inference(subst,[],[refute_0_114:[bind(X,$fot(set_intersection2(set_union2(B,X_171),B))),bind(Y,$fot(set_intersection2(B,set_union2(B,X_171)))),bind(Z,$fot(set_difference(B,set_difference(X_171,B))))]]) ).
cnf(refute_0_303,plain,
( set_intersection2(B,set_union2(B,X_171)) != set_difference(B,set_difference(X_171,B))
| set_intersection2(set_union2(B,X_171),B) = set_difference(B,set_difference(X_171,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_union2(B,X_171),B),set_intersection2(B,set_union2(B,X_171))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
set_intersection2(set_union2(B,X_171),B) = set_difference(B,set_difference(X_171,B)),
inference(resolve,[$cnf( $equal(set_intersection2(B,set_union2(B,X_171)),set_difference(B,set_difference(X_171,B))) )],[refute_0_189,refute_0_303]) ).
cnf(refute_0_305,plain,
set_union2(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_306,plain,
set_union2(A,empty_set) = set_union2(empty_set,A),
inference(subst,[],[refute_0_24:[bind(B,$fot(empty_set))]]) ).
cnf(refute_0_307,plain,
( set_union2(A,empty_set) != A
| set_union2(A,empty_set) != set_union2(empty_set,A)
| set_union2(empty_set,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(A,empty_set),A) ),[0],$fot(set_union2(empty_set,A))]]) ).
cnf(refute_0_308,plain,
( set_union2(A,empty_set) != A
| set_union2(empty_set,A) = A ),
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),set_union2(empty_set,A)) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
set_union2(empty_set,A) = A,
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),A) )],[refute_0_305,refute_0_308]) ).
cnf(refute_0_310,plain,
set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) = set_intersection2(set_union2(B,X_171),B),
inference(subst,[],[refute_0_309:[bind(A,$fot(set_intersection2(set_union2(B,X_171),B)))]]) ).
cnf(refute_0_311,plain,
( set_intersection2(set_union2(B,X_171),B) != set_difference(B,set_difference(X_171,B))
| set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) != set_intersection2(set_union2(B,X_171),B)
| set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) = set_difference(B,set_difference(X_171,B)) ),
inference(subst,[],[refute_0_114:[bind(X,$fot(set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)))),bind(Y,$fot(set_intersection2(set_union2(B,X_171),B))),bind(Z,$fot(set_difference(B,set_difference(X_171,B))))]]) ).
cnf(refute_0_312,plain,
( set_intersection2(set_union2(B,X_171),B) != set_difference(B,set_difference(X_171,B))
| set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) = set_difference(B,set_difference(X_171,B)) ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)),set_intersection2(set_union2(B,X_171),B)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) = set_difference(B,set_difference(X_171,B)),
inference(resolve,[$cnf( $equal(set_intersection2(set_union2(B,X_171),B),set_difference(B,set_difference(X_171,B))) )],[refute_0_304,refute_0_312]) ).
cnf(refute_0_314,plain,
( set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) != B
| set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) != set_difference(B,set_difference(X_171,B))
| set_difference(B,set_difference(X_171,B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)),B) ),[0],$fot(set_difference(B,set_difference(X_171,B)))]]) ).
cnf(refute_0_315,plain,
( set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)) != B
| set_difference(B,set_difference(X_171,B)) = B ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)),set_difference(B,set_difference(X_171,B))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
set_difference(B,set_difference(X_171,B)) = B,
inference(resolve,[$cnf( $equal(set_union2(empty_set,set_intersection2(set_union2(B,X_171),B)),B) )],[refute_0_188,refute_0_315]) ).
cnf(refute_0_317,plain,
set_difference(B,set_difference(X_33,B)) = B,
inference(subst,[],[refute_0_316:[bind(X_171,$fot(X_33))]]) ).
cnf(refute_0_318,plain,
( set_difference(B,set_difference(X_33,B)) != B
| set_difference(set_union2(X_33,B),set_difference(X_33,B)) != set_difference(B,set_difference(X_33,B))
| set_difference(set_union2(X_33,B),set_difference(X_33,B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(X_33,B),set_difference(X_33,B)),set_difference(B,set_difference(X_33,B))) ),[1],$fot(B)]]) ).
cnf(refute_0_319,plain,
( set_difference(set_union2(X_33,B),set_difference(X_33,B)) != set_difference(B,set_difference(X_33,B))
| set_difference(set_union2(X_33,B),set_difference(X_33,B)) = B ),
inference(resolve,[$cnf( $equal(set_difference(B,set_difference(X_33,B)),B) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
set_difference(set_union2(X_33,B),set_difference(X_33,B)) = B,
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_33,B),set_difference(X_33,B)),set_difference(B,set_difference(X_33,B))) )],[refute_0_50,refute_0_319]) ).
cnf(refute_0_321,plain,
set_difference(set_union2(powerset(X_458),singleton(set_difference(X_458,X_457))),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) = singleton(set_difference(X_458,X_457)),
inference(subst,[],[refute_0_320:[bind(B,$fot(singleton(set_difference(X_458,X_457)))),bind(X_33,$fot(powerset(X_458)))]]) ).
cnf(refute_0_322,plain,
( ~ subset(singleton(set_difference(X_244,X_243)),powerset(X_244))
| set_union2(singleton(set_difference(X_244,X_243)),powerset(X_244)) = powerset(X_244) ),
inference(subst,[],[refute_0_74:[bind(A,$fot(singleton(set_difference(X_244,X_243)))),bind(B,$fot(powerset(X_244)))]]) ).
cnf(refute_0_323,plain,
subset(A,set_union2(A,B)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_324,plain,
( set_union2(A,B) != set_union2(B,A)
| ~ subset(A,set_union2(A,B))
| subset(A,set_union2(B,A)) ),
introduced(tautology,[equality,[$cnf( subset(A,set_union2(A,B)) ),[1],$fot(set_union2(B,A))]]) ).
cnf(refute_0_325,plain,
( ~ subset(A,set_union2(A,B))
| subset(A,set_union2(B,A)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_24,refute_0_324]) ).
cnf(refute_0_326,plain,
subset(A,set_union2(B,A)),
inference(resolve,[$cnf( subset(A,set_union2(A,B)) )],[refute_0_323,refute_0_325]) ).
cnf(refute_0_327,plain,
subset(X_200,set_union2(B,X_200)),
inference(subst,[],[refute_0_326:[bind(A,$fot(X_200))]]) ).
cnf(refute_0_328,plain,
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_329,plain,
( powerset(A) != powerset(A)
| ~ subset(C,A)
| in(C,powerset(A)) ),
inference(subst,[],[refute_0_328:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_330,plain,
powerset(A) = powerset(A),
introduced(tautology,[refl,[$fot(powerset(A))]]) ).
cnf(refute_0_331,plain,
( ~ subset(C,A)
| in(C,powerset(A)) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_330,refute_0_329]) ).
cnf(refute_0_332,plain,
( ~ subset(X_200,set_union2(B,X_200))
| in(X_200,powerset(set_union2(B,X_200))) ),
inference(subst,[],[refute_0_331:[bind(A,$fot(set_union2(B,X_200))),bind(C,$fot(X_200))]]) ).
cnf(refute_0_333,plain,
in(X_200,powerset(set_union2(B,X_200))),
inference(resolve,[$cnf( subset(X_200,set_union2(B,X_200)) )],[refute_0_327,refute_0_332]) ).
cnf(refute_0_334,plain,
in(set_difference(X_211,B),powerset(set_union2(X_211,set_difference(X_211,B)))),
inference(subst,[],[refute_0_333:[bind(B,$fot(X_211)),bind(X_200,$fot(set_difference(X_211,B)))]]) ).
cnf(refute_0_335,plain,
set_union2(X_211,set_difference(X_211,B)) = X_211,
inference(subst,[],[refute_0_82:[bind(X_101,$fot(X_211))]]) ).
cnf(refute_0_336,plain,
( set_union2(X_211,set_difference(X_211,B)) != X_211
| ~ in(set_difference(X_211,B),powerset(set_union2(X_211,set_difference(X_211,B))))
| in(set_difference(X_211,B),powerset(X_211)) ),
introduced(tautology,[equality,[$cnf( in(set_difference(X_211,B),powerset(set_union2(X_211,set_difference(X_211,B)))) ),[1,0],$fot(X_211)]]) ).
cnf(refute_0_337,plain,
( ~ in(set_difference(X_211,B),powerset(set_union2(X_211,set_difference(X_211,B))))
| in(set_difference(X_211,B),powerset(X_211)) ),
inference(resolve,[$cnf( $equal(set_union2(X_211,set_difference(X_211,B)),X_211) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
in(set_difference(X_211,B),powerset(X_211)),
inference(resolve,[$cnf( in(set_difference(X_211,B),powerset(set_union2(X_211,set_difference(X_211,B)))) )],[refute_0_334,refute_0_337]) ).
cnf(refute_0_339,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_340,plain,
( ~ in(set_difference(X_211,B),powerset(X_211))
| subset(singleton(set_difference(X_211,B)),powerset(X_211)) ),
inference(subst,[],[refute_0_339:[bind(A,$fot(set_difference(X_211,B))),bind(B,$fot(powerset(X_211)))]]) ).
cnf(refute_0_341,plain,
subset(singleton(set_difference(X_211,B)),powerset(X_211)),
inference(resolve,[$cnf( in(set_difference(X_211,B),powerset(X_211)) )],[refute_0_338,refute_0_340]) ).
cnf(refute_0_342,plain,
subset(singleton(set_difference(X_244,X_243)),powerset(X_244)),
inference(subst,[],[refute_0_341:[bind(B,$fot(X_243)),bind(X_211,$fot(X_244))]]) ).
cnf(refute_0_343,plain,
set_union2(singleton(set_difference(X_244,X_243)),powerset(X_244)) = powerset(X_244),
inference(resolve,[$cnf( subset(singleton(set_difference(X_244,X_243)),powerset(X_244)) )],[refute_0_342,refute_0_322]) ).
cnf(refute_0_344,plain,
set_union2(X_67,X_66) = set_union2(X_66,X_67),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_67)),bind(B,$fot(X_66))]]) ).
cnf(refute_0_345,plain,
set_union2(singleton(set_difference(X_244,X_243)),powerset(X_244)) = set_union2(powerset(X_244),singleton(set_difference(X_244,X_243))),
inference(subst,[],[refute_0_344:[bind(X_66,$fot(powerset(X_244))),bind(X_67,$fot(singleton(set_difference(X_244,X_243))))]]) ).
cnf(refute_0_346,plain,
( set_union2(singleton(set_difference(X_244,X_243)),powerset(X_244)) != powerset(X_244)
| set_union2(singleton(set_difference(X_244,X_243)),powerset(X_244)) != set_union2(powerset(X_244),singleton(set_difference(X_244,X_243)))
| set_union2(powerset(X_244),singleton(set_difference(X_244,X_243))) = powerset(X_244) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(singleton(set_difference(X_244,X_243)),powerset(X_244)),powerset(X_244)) ),[0],$fot(set_union2(powerset(X_244),singleton(set_difference(X_244,X_243))))]]) ).
cnf(refute_0_347,plain,
( set_union2(singleton(set_difference(X_244,X_243)),powerset(X_244)) != powerset(X_244)
| set_union2(powerset(X_244),singleton(set_difference(X_244,X_243))) = powerset(X_244) ),
inference(resolve,[$cnf( $equal(set_union2(singleton(set_difference(X_244,X_243)),powerset(X_244)),set_union2(powerset(X_244),singleton(set_difference(X_244,X_243)))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
set_union2(powerset(X_244),singleton(set_difference(X_244,X_243))) = powerset(X_244),
inference(resolve,[$cnf( $equal(set_union2(singleton(set_difference(X_244,X_243)),powerset(X_244)),powerset(X_244)) )],[refute_0_343,refute_0_347]) ).
cnf(refute_0_349,plain,
set_union2(powerset(X_458),singleton(set_difference(X_458,X_457))) = powerset(X_458),
inference(subst,[],[refute_0_348:[bind(X_243,$fot(X_457)),bind(X_244,$fot(X_458))]]) ).
cnf(refute_0_350,plain,
( set_difference(set_union2(powerset(X_458),singleton(set_difference(X_458,X_457))),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) != singleton(set_difference(X_458,X_457))
| set_union2(powerset(X_458),singleton(set_difference(X_458,X_457))) != powerset(X_458)
| set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) = singleton(set_difference(X_458,X_457)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(powerset(X_458),singleton(set_difference(X_458,X_457))),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))),singleton(set_difference(X_458,X_457))) ),[0,0],$fot(powerset(X_458))]]) ).
cnf(refute_0_351,plain,
( set_difference(set_union2(powerset(X_458),singleton(set_difference(X_458,X_457))),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) != singleton(set_difference(X_458,X_457))
| set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) = singleton(set_difference(X_458,X_457)) ),
inference(resolve,[$cnf( $equal(set_union2(powerset(X_458),singleton(set_difference(X_458,X_457))),powerset(X_458)) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) = singleton(set_difference(X_458,X_457)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(powerset(X_458),singleton(set_difference(X_458,X_457))),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))),singleton(set_difference(X_458,X_457))) )],[refute_0_321,refute_0_351]) ).
cnf(refute_0_353,plain,
set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) = set_intersection2(powerset(X_458),singleton(set_difference(X_458,X_457))),
inference(subst,[],[refute_0_0:[bind(A,$fot(powerset(X_458))),bind(B,$fot(singleton(set_difference(X_458,X_457))))]]) ).
cnf(refute_0_354,plain,
( set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) != set_intersection2(powerset(X_458),singleton(set_difference(X_458,X_457)))
| set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) != singleton(set_difference(X_458,X_457))
| set_intersection2(powerset(X_458),singleton(set_difference(X_458,X_457))) = singleton(set_difference(X_458,X_457)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))),singleton(set_difference(X_458,X_457))) ),[0],$fot(set_intersection2(powerset(X_458),singleton(set_difference(X_458,X_457))))]]) ).
cnf(refute_0_355,plain,
( set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))) != singleton(set_difference(X_458,X_457))
| set_intersection2(powerset(X_458),singleton(set_difference(X_458,X_457))) = singleton(set_difference(X_458,X_457)) ),
inference(resolve,[$cnf( $equal(set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))),set_intersection2(powerset(X_458),singleton(set_difference(X_458,X_457)))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
set_intersection2(powerset(X_458),singleton(set_difference(X_458,X_457))) = singleton(set_difference(X_458,X_457)),
inference(resolve,[$cnf( $equal(set_difference(powerset(X_458),set_difference(powerset(X_458),singleton(set_difference(X_458,X_457)))),singleton(set_difference(X_458,X_457))) )],[refute_0_352,refute_0_355]) ).
cnf(refute_0_357,plain,
set_intersection2(powerset(empty_set),singleton(set_difference(empty_set,X_457))) = singleton(set_difference(empty_set,X_457)),
inference(subst,[],[refute_0_356:[bind(X_458,$fot(empty_set))]]) ).
cnf(refute_0_358,plain,
set_intersection2(B,set_union2(B,X_53)) = set_difference(B,set_difference(X_53,B)),
inference(subst,[],[refute_0_39:[bind(A,$fot(B)),bind(X_58,$fot(X_53))]]) ).
cnf(refute_0_359,plain,
( set_difference(set_union2(B,X_53),set_difference(X_53,B)) != set_intersection2(B,set_union2(B,X_53))
| set_intersection2(B,set_union2(B,X_53)) != set_difference(B,set_difference(X_53,B))
| set_difference(set_union2(B,X_53),set_difference(X_53,B)) = set_difference(B,set_difference(X_53,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(B,X_53),set_difference(X_53,B)),set_difference(B,set_difference(X_53,B))) ),[0],$fot(set_intersection2(B,set_union2(B,X_53)))]]) ).
cnf(refute_0_360,plain,
( set_difference(set_union2(B,X_53),set_difference(X_53,B)) != set_intersection2(B,set_union2(B,X_53))
| set_difference(set_union2(B,X_53),set_difference(X_53,B)) = set_difference(B,set_difference(X_53,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(B,set_union2(B,X_53)),set_difference(B,set_difference(X_53,B))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
set_difference(set_union2(B,X_53),set_difference(X_53,B)) = set_difference(B,set_difference(X_53,B)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_53),set_difference(X_53,B)),set_intersection2(B,set_union2(B,X_53))) )],[refute_0_35,refute_0_360]) ).
cnf(refute_0_362,plain,
set_difference(B,set_difference(X_53,B)) = B,
inference(subst,[],[refute_0_316:[bind(X_171,$fot(X_53))]]) ).
cnf(refute_0_363,plain,
( set_difference(B,set_difference(X_53,B)) != B
| set_difference(set_union2(B,X_53),set_difference(X_53,B)) != set_difference(B,set_difference(X_53,B))
| set_difference(set_union2(B,X_53),set_difference(X_53,B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(B,X_53),set_difference(X_53,B)),set_difference(B,set_difference(X_53,B))) ),[1],$fot(B)]]) ).
cnf(refute_0_364,plain,
( set_difference(set_union2(B,X_53),set_difference(X_53,B)) != set_difference(B,set_difference(X_53,B))
| set_difference(set_union2(B,X_53),set_difference(X_53,B)) = B ),
inference(resolve,[$cnf( $equal(set_difference(B,set_difference(X_53,B)),B) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
set_difference(set_union2(B,X_53),set_difference(X_53,B)) = B,
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_53),set_difference(X_53,B)),set_difference(B,set_difference(X_53,B))) )],[refute_0_361,refute_0_364]) ).
cnf(refute_0_366,plain,
set_difference(set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) = singleton(empty_set),
inference(subst,[],[refute_0_365:[bind(B,$fot(singleton(empty_set))),bind(X_53,$fot(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))))]]) ).
cnf(refute_0_367,plain,
set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))) = set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)),
inference(subst,[],[refute_0_18:[bind(A,$fot(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))),bind(B,$fot(singleton(empty_set)))]]) ).
cnf(refute_0_368,plain,
set_difference(set_union2(X_33,set_intersection2(X_33,X_116)),set_difference(X_33,set_intersection2(X_33,X_116))) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))),
inference(subst,[],[refute_0_50:[bind(B,$fot(set_intersection2(X_33,X_116)))]]) ).
cnf(refute_0_369,plain,
subset(set_difference(set_union2(X_33,B),B),set_union2(X_33,B)),
inference(subst,[],[refute_0_72:[bind(A,$fot(set_union2(X_33,B)))]]) ).
cnf(refute_0_370,plain,
( set_difference(set_union2(X_33,B),B) != set_difference(X_33,B)
| ~ subset(set_difference(set_union2(X_33,B),B),set_union2(X_33,B))
| subset(set_difference(X_33,B),set_union2(X_33,B)) ),
introduced(tautology,[equality,[$cnf( subset(set_difference(set_union2(X_33,B),B),set_union2(X_33,B)) ),[0],$fot(set_difference(X_33,B))]]) ).
cnf(refute_0_371,plain,
( ~ subset(set_difference(set_union2(X_33,B),B),set_union2(X_33,B))
| subset(set_difference(X_33,B),set_union2(X_33,B)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_33,B),B),set_difference(X_33,B)) )],[refute_0_3,refute_0_370]) ).
cnf(refute_0_372,plain,
subset(set_difference(X_33,B),set_union2(X_33,B)),
inference(resolve,[$cnf( subset(set_difference(set_union2(X_33,B),B),set_union2(X_33,B)) )],[refute_0_369,refute_0_371]) ).
cnf(refute_0_373,plain,
subset(set_difference(X_46,set_difference(X_46,B)),set_union2(X_46,set_difference(X_46,B))),
inference(subst,[],[refute_0_372:[bind(B,$fot(set_difference(X_46,B))),bind(X_33,$fot(X_46))]]) ).
cnf(refute_0_374,plain,
set_difference(X_46,set_difference(X_46,B)) = set_intersection2(X_46,B),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_46))]]) ).
cnf(refute_0_375,plain,
( set_difference(X_46,set_difference(X_46,B)) != set_intersection2(X_46,B)
| ~ subset(set_difference(X_46,set_difference(X_46,B)),set_union2(X_46,set_difference(X_46,B)))
| subset(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) ),
introduced(tautology,[equality,[$cnf( subset(set_difference(X_46,set_difference(X_46,B)),set_union2(X_46,set_difference(X_46,B))) ),[0],$fot(set_intersection2(X_46,B))]]) ).
cnf(refute_0_376,plain,
( ~ subset(set_difference(X_46,set_difference(X_46,B)),set_union2(X_46,set_difference(X_46,B)))
| subset(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) ),
inference(resolve,[$cnf( $equal(set_difference(X_46,set_difference(X_46,B)),set_intersection2(X_46,B)) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
subset(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))),
inference(resolve,[$cnf( subset(set_difference(X_46,set_difference(X_46,B)),set_union2(X_46,set_difference(X_46,B))) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
( ~ subset(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B)))
| set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) = set_union2(X_46,set_difference(X_46,B)) ),
inference(subst,[],[refute_0_74:[bind(A,$fot(set_intersection2(X_46,B))),bind(B,$fot(set_union2(X_46,set_difference(X_46,B))))]]) ).
cnf(refute_0_379,plain,
set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) = set_union2(X_46,set_difference(X_46,B)),
inference(resolve,[$cnf( subset(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
set_union2(set_intersection2(X_46,B),X_46) = set_union2(X_46,set_intersection2(X_46,B)),
inference(subst,[],[refute_0_78:[bind(A,$fot(X_46)),bind(B,$fot(set_intersection2(X_46,B)))]]) ).
cnf(refute_0_381,plain,
set_union2(X_46,set_difference(X_46,B)) = X_46,
inference(subst,[],[refute_0_82:[bind(X_101,$fot(X_46))]]) ).
cnf(refute_0_382,plain,
set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) = set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))),
introduced(tautology,[refl,[$fot(set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))))]]) ).
cnf(refute_0_383,plain,
( set_union2(X_46,set_difference(X_46,B)) != X_46
| set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) != set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B)))
| set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) = set_union2(set_intersection2(X_46,B),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))),set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B)))) ),[1,1],$fot(X_46)]]) ).
cnf(refute_0_384,plain,
( set_union2(X_46,set_difference(X_46,B)) != X_46
| set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) = set_union2(set_intersection2(X_46,B),X_46) ),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))),set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B)))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) = set_union2(set_intersection2(X_46,B),X_46),
inference(resolve,[$cnf( $equal(set_union2(X_46,set_difference(X_46,B)),X_46) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
( set_union2(set_intersection2(X_46,B),X_46) != set_union2(X_46,set_intersection2(X_46,B))
| set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) != set_union2(set_intersection2(X_46,B),X_46)
| set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) = set_union2(X_46,set_intersection2(X_46,B)) ),
inference(subst,[],[refute_0_114:[bind(X,$fot(set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))))),bind(Y,$fot(set_union2(set_intersection2(X_46,B),X_46))),bind(Z,$fot(set_union2(X_46,set_intersection2(X_46,B))))]]) ).
cnf(refute_0_387,plain,
( set_union2(set_intersection2(X_46,B),X_46) != set_union2(X_46,set_intersection2(X_46,B))
| set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) = set_union2(X_46,set_intersection2(X_46,B)) ),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))),set_union2(set_intersection2(X_46,B),X_46)) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) = set_union2(X_46,set_intersection2(X_46,B)),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_46,B),X_46),set_union2(X_46,set_intersection2(X_46,B))) )],[refute_0_380,refute_0_387]) ).
cnf(refute_0_389,plain,
( set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) != set_union2(X_46,set_difference(X_46,B))
| set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) != set_union2(X_46,set_intersection2(X_46,B))
| set_union2(X_46,set_intersection2(X_46,B)) = set_union2(X_46,set_difference(X_46,B)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))),set_union2(X_46,set_difference(X_46,B))) ),[0],$fot(set_union2(X_46,set_intersection2(X_46,B)))]]) ).
cnf(refute_0_390,plain,
( set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) != set_union2(X_46,set_difference(X_46,B))
| set_union2(X_46,set_intersection2(X_46,B)) = set_union2(X_46,set_difference(X_46,B)) ),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))),set_union2(X_46,set_intersection2(X_46,B))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
( set_union2(X_46,set_difference(X_46,B)) != X_46
| set_union2(X_46,set_intersection2(X_46,B)) != set_union2(X_46,set_difference(X_46,B))
| set_union2(X_46,set_intersection2(X_46,B)) = X_46 ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(X_46,set_intersection2(X_46,B)),set_union2(X_46,set_difference(X_46,B))) ),[1],$fot(X_46)]]) ).
cnf(refute_0_392,plain,
( set_union2(X_46,set_intersection2(X_46,B)) != set_union2(X_46,set_difference(X_46,B))
| set_union2(X_46,set_intersection2(X_46,B)) = X_46 ),
inference(resolve,[$cnf( $equal(set_union2(X_46,set_difference(X_46,B)),X_46) )],[refute_0_381,refute_0_391]) ).
cnf(refute_0_393,plain,
( set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))) != set_union2(X_46,set_difference(X_46,B))
| set_union2(X_46,set_intersection2(X_46,B)) = X_46 ),
inference(resolve,[$cnf( $equal(set_union2(X_46,set_intersection2(X_46,B)),set_union2(X_46,set_difference(X_46,B))) )],[refute_0_390,refute_0_392]) ).
cnf(refute_0_394,plain,
set_union2(X_46,set_intersection2(X_46,B)) = X_46,
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_46,B),set_union2(X_46,set_difference(X_46,B))),set_union2(X_46,set_difference(X_46,B))) )],[refute_0_379,refute_0_393]) ).
cnf(refute_0_395,plain,
set_union2(X_33,set_intersection2(X_33,X_116)) = X_33,
inference(subst,[],[refute_0_394:[bind(B,$fot(X_116)),bind(X_46,$fot(X_33))]]) ).
cnf(refute_0_396,plain,
( set_difference(set_union2(X_33,set_intersection2(X_33,X_116)),set_difference(X_33,set_intersection2(X_33,X_116))) != set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))
| set_union2(X_33,set_intersection2(X_33,X_116)) != X_33
| set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(X_33,set_intersection2(X_33,X_116)),set_difference(X_33,set_intersection2(X_33,X_116))),set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))) ),[0,0],$fot(X_33)]]) ).
cnf(refute_0_397,plain,
( set_difference(set_union2(X_33,set_intersection2(X_33,X_116)),set_difference(X_33,set_intersection2(X_33,X_116))) != set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))
| set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) ),
inference(resolve,[$cnf( $equal(set_union2(X_33,set_intersection2(X_33,X_116)),X_33) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_33,set_intersection2(X_33,X_116)),set_difference(X_33,set_intersection2(X_33,X_116))),set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))) )],[refute_0_368,refute_0_397]) ).
cnf(refute_0_399,plain,
set_difference(set_intersection2(B,X_107),set_difference(set_intersection2(B,X_107),B)) = set_intersection2(set_intersection2(B,X_107),B),
inference(subst,[],[refute_0_0:[bind(A,$fot(set_intersection2(B,X_107)))]]) ).
cnf(refute_0_400,plain,
empty_set = set_difference(set_intersection2(X_105,X_104),X_104),
inference(subst,[],[refute_0_203:[bind(B,$fot(X_104)),bind(X_103,$fot(X_105))]]) ).
cnf(refute_0_401,plain,
set_intersection2(X_104,X_105) = set_intersection2(X_105,X_104),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_104)),bind(B,$fot(X_105))]]) ).
cnf(refute_0_402,plain,
( set_intersection2(X_104,X_105) != set_intersection2(X_105,X_104)
| set_intersection2(X_105,X_104) = set_intersection2(X_104,X_105) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_intersection2(X_104,X_105))),bind(Y,$fot(set_intersection2(X_105,X_104)))]]) ).
cnf(refute_0_403,plain,
set_intersection2(X_105,X_104) = set_intersection2(X_104,X_105),
inference(resolve,[$cnf( $equal(set_intersection2(X_104,X_105),set_intersection2(X_105,X_104)) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
( empty_set != set_difference(set_intersection2(X_105,X_104),X_104)
| set_intersection2(X_105,X_104) != set_intersection2(X_104,X_105)
| empty_set = set_difference(set_intersection2(X_104,X_105),X_104) ),
introduced(tautology,[equality,[$cnf( $equal(empty_set,set_difference(set_intersection2(X_105,X_104),X_104)) ),[1,0],$fot(set_intersection2(X_104,X_105))]]) ).
cnf(refute_0_405,plain,
( empty_set != set_difference(set_intersection2(X_105,X_104),X_104)
| empty_set = set_difference(set_intersection2(X_104,X_105),X_104) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_105,X_104),set_intersection2(X_104,X_105)) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
empty_set = set_difference(set_intersection2(X_104,X_105),X_104),
inference(resolve,[$cnf( $equal(empty_set,set_difference(set_intersection2(X_105,X_104),X_104)) )],[refute_0_400,refute_0_405]) ).
cnf(refute_0_407,plain,
empty_set = set_difference(set_intersection2(B,X_107),B),
inference(subst,[],[refute_0_406:[bind(X_104,$fot(B)),bind(X_105,$fot(X_107))]]) ).
cnf(refute_0_408,plain,
( empty_set != set_difference(set_intersection2(B,X_107),B)
| set_difference(set_intersection2(B,X_107),B) = empty_set ),
inference(subst,[],[refute_0_10:[bind(X,$fot(empty_set)),bind(Y,$fot(set_difference(set_intersection2(B,X_107),B)))]]) ).
cnf(refute_0_409,plain,
set_difference(set_intersection2(B,X_107),B) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,set_difference(set_intersection2(B,X_107),B)) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
( set_difference(set_intersection2(B,X_107),B) != empty_set
| set_difference(set_intersection2(B,X_107),set_difference(set_intersection2(B,X_107),B)) != set_intersection2(set_intersection2(B,X_107),B)
| set_difference(set_intersection2(B,X_107),empty_set) = set_intersection2(set_intersection2(B,X_107),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_intersection2(B,X_107),set_difference(set_intersection2(B,X_107),B)),set_intersection2(set_intersection2(B,X_107),B)) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_411,plain,
( set_difference(set_intersection2(B,X_107),set_difference(set_intersection2(B,X_107),B)) != set_intersection2(set_intersection2(B,X_107),B)
| set_difference(set_intersection2(B,X_107),empty_set) = set_intersection2(set_intersection2(B,X_107),B) ),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(B,X_107),B),empty_set) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
set_difference(set_intersection2(B,X_107),empty_set) = set_intersection2(set_intersection2(B,X_107),B),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(B,X_107),set_difference(set_intersection2(B,X_107),B)),set_intersection2(set_intersection2(B,X_107),B)) )],[refute_0_399,refute_0_411]) ).
cnf(refute_0_413,plain,
set_difference(set_intersection2(B,X_107),empty_set) = set_intersection2(B,X_107),
inference(subst,[],[refute_0_88:[bind(A,$fot(set_intersection2(B,X_107)))]]) ).
cnf(refute_0_414,plain,
( set_difference(set_intersection2(B,X_107),empty_set) != set_intersection2(B,X_107)
| set_difference(set_intersection2(B,X_107),empty_set) != set_intersection2(set_intersection2(B,X_107),B)
| set_intersection2(B,X_107) = set_intersection2(set_intersection2(B,X_107),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_intersection2(B,X_107),empty_set),set_intersection2(set_intersection2(B,X_107),B)) ),[0],$fot(set_intersection2(B,X_107))]]) ).
cnf(refute_0_415,plain,
( set_difference(set_intersection2(B,X_107),empty_set) != set_intersection2(set_intersection2(B,X_107),B)
| set_intersection2(B,X_107) = set_intersection2(set_intersection2(B,X_107),B) ),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(B,X_107),empty_set),set_intersection2(B,X_107)) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
set_intersection2(set_intersection2(B,X_107),B) = set_intersection2(B,set_intersection2(B,X_107)),
inference(subst,[],[refute_0_12:[bind(A,$fot(B)),bind(B,$fot(set_intersection2(B,X_107)))]]) ).
cnf(refute_0_417,plain,
( set_intersection2(B,X_107) != set_intersection2(set_intersection2(B,X_107),B)
| set_intersection2(set_intersection2(B,X_107),B) != set_intersection2(B,set_intersection2(B,X_107))
| set_intersection2(B,X_107) = set_intersection2(B,set_intersection2(B,X_107)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_intersection2(B,X_107),set_intersection2(B,set_intersection2(B,X_107))) ),[0],$fot(set_intersection2(set_intersection2(B,X_107),B))]]) ).
cnf(refute_0_418,plain,
( set_intersection2(B,X_107) != set_intersection2(set_intersection2(B,X_107),B)
| set_intersection2(B,X_107) = set_intersection2(B,set_intersection2(B,X_107)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(B,X_107),B),set_intersection2(B,set_intersection2(B,X_107))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
( set_difference(set_intersection2(B,X_107),empty_set) != set_intersection2(set_intersection2(B,X_107),B)
| set_intersection2(B,X_107) = set_intersection2(B,set_intersection2(B,X_107)) ),
inference(resolve,[$cnf( $equal(set_intersection2(B,X_107),set_intersection2(set_intersection2(B,X_107),B)) )],[refute_0_415,refute_0_418]) ).
cnf(refute_0_420,plain,
set_intersection2(B,X_107) = set_intersection2(B,set_intersection2(B,X_107)),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(B,X_107),empty_set),set_intersection2(set_intersection2(B,X_107),B)) )],[refute_0_412,refute_0_419]) ).
cnf(refute_0_421,plain,
( set_intersection2(B,X_107) != set_intersection2(B,set_intersection2(B,X_107))
| set_intersection2(B,set_intersection2(B,X_107)) = set_intersection2(B,X_107) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_intersection2(B,X_107))),bind(Y,$fot(set_intersection2(B,set_intersection2(B,X_107))))]]) ).
cnf(refute_0_422,plain,
set_intersection2(B,set_intersection2(B,X_107)) = set_intersection2(B,X_107),
inference(resolve,[$cnf( $equal(set_intersection2(B,X_107),set_intersection2(B,set_intersection2(B,X_107))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
set_intersection2(X_33,set_intersection2(X_33,X_116)) = set_intersection2(X_33,X_116),
inference(subst,[],[refute_0_422:[bind(B,$fot(X_33)),bind(X_107,$fot(X_116))]]) ).
cnf(refute_0_424,plain,
set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) = set_intersection2(X_33,set_intersection2(X_33,X_116)),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_33)),bind(B,$fot(set_intersection2(X_33,X_116)))]]) ).
cnf(refute_0_425,plain,
( set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) != set_intersection2(X_33,set_intersection2(X_33,X_116))
| set_intersection2(X_33,set_intersection2(X_33,X_116)) != set_intersection2(X_33,X_116)
| set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) = set_intersection2(X_33,X_116) ),
inference(subst,[],[refute_0_114:[bind(X,$fot(set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))))),bind(Y,$fot(set_intersection2(X_33,set_intersection2(X_33,X_116)))),bind(Z,$fot(set_intersection2(X_33,X_116)))]]) ).
cnf(refute_0_426,plain,
( set_intersection2(X_33,set_intersection2(X_33,X_116)) != set_intersection2(X_33,X_116)
| set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) = set_intersection2(X_33,X_116) ),
inference(resolve,[$cnf( $equal(set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))),set_intersection2(X_33,set_intersection2(X_33,X_116))) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) = set_intersection2(X_33,X_116),
inference(resolve,[$cnf( $equal(set_intersection2(X_33,set_intersection2(X_33,X_116)),set_intersection2(X_33,X_116)) )],[refute_0_423,refute_0_426]) ).
cnf(refute_0_428,plain,
( set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) != set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))
| set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) != set_intersection2(X_33,X_116)
| set_intersection2(X_33,X_116) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))),set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))) ),[0],$fot(set_intersection2(X_33,X_116))]]) ).
cnf(refute_0_429,plain,
( set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) != set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))
| set_intersection2(X_33,X_116) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) ),
inference(resolve,[$cnf( $equal(set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))),set_intersection2(X_33,X_116)) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
set_difference(X_33,set_intersection2(X_33,X_116)) = set_difference(X_33,X_116),
inference(subst,[],[refute_0_123:[bind(B,$fot(X_33)),bind(X_113,$fot(X_116))]]) ).
cnf(refute_0_431,plain,
set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))),
introduced(tautology,[refl,[$fot(set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))))]]) ).
cnf(refute_0_432,plain,
( set_difference(X_33,set_intersection2(X_33,X_116)) != set_difference(X_33,X_116)
| set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) != set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))
| set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))),set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))) ),[1,1],$fot(set_difference(X_33,X_116))]]) ).
cnf(refute_0_433,plain,
( set_difference(X_33,set_intersection2(X_33,X_116)) != set_difference(X_33,X_116)
| set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116)) ),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))),set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116)),
inference(resolve,[$cnf( $equal(set_difference(X_33,set_intersection2(X_33,X_116)),set_difference(X_33,X_116)) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
( set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))) != set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116))
| set_intersection2(X_33,X_116) != set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))
| set_intersection2(X_33,X_116) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116)) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(X_33,X_116),set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))) ),[1],$fot(set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116)))]]) ).
cnf(refute_0_436,plain,
( set_intersection2(X_33,X_116) != set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))
| set_intersection2(X_33,X_116) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116)) ),
inference(resolve,[$cnf( $equal(set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116))),set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
( set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))) != set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))
| set_intersection2(X_33,X_116) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116)) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_33,X_116),set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))) )],[refute_0_429,refute_0_436]) ).
cnf(refute_0_438,plain,
set_intersection2(X_33,X_116) = set_difference(set_intersection2(X_33,X_116),set_difference(X_33,X_116)),
inference(resolve,[$cnf( $equal(set_difference(X_33,set_difference(X_33,set_intersection2(X_33,X_116))),set_difference(set_intersection2(X_33,X_116),set_difference(X_33,set_intersection2(X_33,X_116)))) )],[refute_0_398,refute_0_437]) ).
cnf(refute_0_439,plain,
set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) = set_difference(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),
inference(subst,[],[refute_0_438:[bind(X_116,$fot(singleton(skolemFOFtoCNF_B(powerset(empty_set))))),bind(X_33,$fot(powerset(empty_set)))]]) ).
cnf(refute_0_440,plain,
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_441,plain,
( X_237 = empty_set
| in(skolemFOFtoCNF_B(X_237),X_237) ),
inference(subst,[],[refute_0_440:[bind(A,$fot(X_237))]]) ).
cnf(refute_0_442,plain,
( ~ in(skolemFOFtoCNF_B(X_237),X_237)
| subset(singleton(skolemFOFtoCNF_B(X_237)),X_237) ),
inference(subst,[],[refute_0_339:[bind(A,$fot(skolemFOFtoCNF_B(X_237))),bind(B,$fot(X_237))]]) ).
cnf(refute_0_443,plain,
( X_237 = empty_set
| subset(singleton(skolemFOFtoCNF_B(X_237)),X_237) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(X_237),X_237) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
( X_622 = empty_set
| subset(singleton(skolemFOFtoCNF_B(X_622)),X_622) ),
inference(subst,[],[refute_0_443:[bind(X_237,$fot(X_622))]]) ).
cnf(refute_0_445,plain,
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_446,plain,
( ~ subset(singleton(skolemFOFtoCNF_B(X_622)),X_622)
| set_intersection2(singleton(skolemFOFtoCNF_B(X_622)),X_622) = singleton(skolemFOFtoCNF_B(X_622)) ),
inference(subst,[],[refute_0_445:[bind(A,$fot(singleton(skolemFOFtoCNF_B(X_622)))),bind(B,$fot(X_622))]]) ).
cnf(refute_0_447,plain,
( X_622 = empty_set
| set_intersection2(singleton(skolemFOFtoCNF_B(X_622)),X_622) = singleton(skolemFOFtoCNF_B(X_622)) ),
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_B(X_622)),X_622) )],[refute_0_444,refute_0_446]) ).
cnf(refute_0_448,plain,
set_intersection2(singleton(skolemFOFtoCNF_B(X_622)),X_622) = set_intersection2(X_622,singleton(skolemFOFtoCNF_B(X_622))),
inference(subst,[],[refute_0_300:[bind(X_154,$fot(singleton(skolemFOFtoCNF_B(X_622)))),bind(X_155,$fot(X_622))]]) ).
cnf(refute_0_449,plain,
( set_intersection2(singleton(skolemFOFtoCNF_B(X_622)),X_622) != set_intersection2(X_622,singleton(skolemFOFtoCNF_B(X_622)))
| set_intersection2(singleton(skolemFOFtoCNF_B(X_622)),X_622) != singleton(skolemFOFtoCNF_B(X_622))
| set_intersection2(X_622,singleton(skolemFOFtoCNF_B(X_622))) = singleton(skolemFOFtoCNF_B(X_622)) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_B(X_622)),X_622),singleton(skolemFOFtoCNF_B(X_622))) ),[0],$fot(set_intersection2(X_622,singleton(skolemFOFtoCNF_B(X_622))))]]) ).
cnf(refute_0_450,plain,
( set_intersection2(singleton(skolemFOFtoCNF_B(X_622)),X_622) != singleton(skolemFOFtoCNF_B(X_622))
| set_intersection2(X_622,singleton(skolemFOFtoCNF_B(X_622))) = singleton(skolemFOFtoCNF_B(X_622)) ),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_B(X_622)),X_622),set_intersection2(X_622,singleton(skolemFOFtoCNF_B(X_622)))) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
( X_622 = empty_set
| set_intersection2(X_622,singleton(skolemFOFtoCNF_B(X_622))) = singleton(skolemFOFtoCNF_B(X_622)) ),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_B(X_622)),X_622),singleton(skolemFOFtoCNF_B(X_622))) )],[refute_0_447,refute_0_450]) ).
cnf(refute_0_452,plain,
( powerset(empty_set) = empty_set
| set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) = singleton(skolemFOFtoCNF_B(powerset(empty_set))) ),
inference(subst,[],[refute_0_451:[bind(X_622,$fot(powerset(empty_set)))]]) ).
cnf(refute_0_453,plain,
( ~ subset(A,empty_set)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_454,plain,
( ~ subset(skolemFOFtoCNF_B(powerset(empty_set)),empty_set)
| skolemFOFtoCNF_B(powerset(empty_set)) = empty_set ),
inference(subst,[],[refute_0_453:[bind(A,$fot(skolemFOFtoCNF_B(powerset(empty_set))))]]) ).
cnf(refute_0_455,plain,
( powerset(X_196) = empty_set
| in(skolemFOFtoCNF_B(powerset(X_196)),powerset(X_196)) ),
inference(subst,[],[refute_0_440:[bind(A,$fot(powerset(X_196)))]]) ).
cnf(refute_0_456,plain,
( B != powerset(A)
| ~ in(C,B)
| subset(C,A) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_457,plain,
( powerset(A) != powerset(A)
| ~ in(C,powerset(A))
| subset(C,A) ),
inference(subst,[],[refute_0_456:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_458,plain,
( ~ in(C,powerset(A))
| subset(C,A) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_330,refute_0_457]) ).
cnf(refute_0_459,plain,
( ~ in(skolemFOFtoCNF_B(powerset(X_196)),powerset(X_196))
| subset(skolemFOFtoCNF_B(powerset(X_196)),X_196) ),
inference(subst,[],[refute_0_458:[bind(A,$fot(X_196)),bind(C,$fot(skolemFOFtoCNF_B(powerset(X_196))))]]) ).
cnf(refute_0_460,plain,
( powerset(X_196) = empty_set
| subset(skolemFOFtoCNF_B(powerset(X_196)),X_196) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(powerset(X_196)),powerset(X_196)) )],[refute_0_455,refute_0_459]) ).
cnf(refute_0_461,plain,
( powerset(empty_set) = empty_set
| subset(skolemFOFtoCNF_B(powerset(empty_set)),empty_set) ),
inference(subst,[],[refute_0_460:[bind(X_196,$fot(empty_set))]]) ).
cnf(refute_0_462,plain,
( powerset(empty_set) = empty_set
| skolemFOFtoCNF_B(powerset(empty_set)) = empty_set ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B(powerset(empty_set)),empty_set) )],[refute_0_461,refute_0_454]) ).
cnf(refute_0_463,plain,
( set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) != singleton(skolemFOFtoCNF_B(powerset(empty_set)))
| skolemFOFtoCNF_B(powerset(empty_set)) != empty_set
| set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) = singleton(empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_0_464,plain,
( set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) != singleton(skolemFOFtoCNF_B(powerset(empty_set)))
| powerset(empty_set) = empty_set
| set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B(powerset(empty_set)),empty_set) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
( powerset(empty_set) = empty_set
| set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) )],[refute_0_452,refute_0_464]) ).
cnf(refute_0_466,plain,
( set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) != set_difference(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))
| set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) != singleton(empty_set)
| set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) = set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))) ),[1,0],$fot(singleton(empty_set))]]) ).
cnf(refute_0_467,plain,
( set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) != set_difference(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))
| powerset(empty_set) = empty_set
| set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) = set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) ),
inference(resolve,[$cnf( $equal(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
( powerset(empty_set) = empty_set
| set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) = set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) ),
inference(resolve,[$cnf( $equal(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))) )],[refute_0_439,refute_0_467]) ).
cnf(refute_0_469,plain,
( set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) != set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))
| set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) = set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))),bind(Y,$fot(set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))))]]) ).
cnf(refute_0_470,plain,
( powerset(empty_set) = empty_set
| set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) = set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))) ),
inference(resolve,[$cnf( $equal(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
( set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) != set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))
| set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))) != set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))
| set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) = set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))),set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) ),[0,1],$fot(set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))]]) ).
cnf(refute_0_472,plain,
( set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))) != set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))
| powerset(empty_set) = empty_set
| set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) = set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)) ),
inference(resolve,[$cnf( $equal(set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
( powerset(empty_set) = empty_set
| set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) = set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)) ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_difference(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))),set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) )],[refute_0_367,refute_0_472]) ).
cnf(refute_0_474,plain,
set_union2(set_difference(X_58,B),set_difference(X_58,set_difference(X_58,B))) = set_union2(set_difference(X_58,B),X_58),
inference(subst,[],[refute_0_18:[bind(A,$fot(set_difference(X_58,B))),bind(B,$fot(X_58))]]) ).
cnf(refute_0_475,plain,
set_difference(X_58,set_difference(X_58,B)) = set_intersection2(X_58,B),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_58))]]) ).
cnf(refute_0_476,plain,
( set_difference(X_58,set_difference(X_58,B)) != set_intersection2(X_58,B)
| set_union2(set_difference(X_58,B),set_difference(X_58,set_difference(X_58,B))) != set_union2(set_difference(X_58,B),X_58)
| set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) = set_union2(set_difference(X_58,B),X_58) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(X_58,B),set_difference(X_58,set_difference(X_58,B))),set_union2(set_difference(X_58,B),X_58)) ),[0,1],$fot(set_intersection2(X_58,B))]]) ).
cnf(refute_0_477,plain,
( set_union2(set_difference(X_58,B),set_difference(X_58,set_difference(X_58,B))) != set_union2(set_difference(X_58,B),X_58)
| set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) = set_union2(set_difference(X_58,B),X_58) ),
inference(resolve,[$cnf( $equal(set_difference(X_58,set_difference(X_58,B)),set_intersection2(X_58,B)) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) = set_union2(set_difference(X_58,B),X_58),
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_58,B),set_difference(X_58,set_difference(X_58,B))),set_union2(set_difference(X_58,B),X_58)) )],[refute_0_474,refute_0_477]) ).
cnf(refute_0_479,plain,
set_union2(set_difference(X_58,B),X_58) = set_union2(X_58,set_difference(X_58,B)),
inference(subst,[],[refute_0_78:[bind(A,$fot(X_58)),bind(B,$fot(set_difference(X_58,B)))]]) ).
cnf(refute_0_480,plain,
( set_union2(set_difference(X_58,B),X_58) != set_union2(X_58,set_difference(X_58,B))
| set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) != set_union2(set_difference(X_58,B),X_58)
| set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) = set_union2(X_58,set_difference(X_58,B)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(X_58,B),set_intersection2(X_58,B)),set_union2(set_difference(X_58,B),X_58)) ),[1],$fot(set_union2(X_58,set_difference(X_58,B)))]]) ).
cnf(refute_0_481,plain,
( set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) != set_union2(set_difference(X_58,B),X_58)
| set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) = set_union2(X_58,set_difference(X_58,B)) ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_58,B),X_58),set_union2(X_58,set_difference(X_58,B))) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) = set_union2(X_58,set_difference(X_58,B)),
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_58,B),set_intersection2(X_58,B)),set_union2(set_difference(X_58,B),X_58)) )],[refute_0_478,refute_0_481]) ).
cnf(refute_0_483,plain,
set_union2(X_58,set_difference(X_58,B)) = X_58,
inference(subst,[],[refute_0_82:[bind(X_101,$fot(X_58))]]) ).
cnf(refute_0_484,plain,
( set_union2(X_58,set_difference(X_58,B)) != X_58
| set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) != set_union2(X_58,set_difference(X_58,B))
| set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) = X_58 ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(X_58,B),set_intersection2(X_58,B)),set_union2(X_58,set_difference(X_58,B))) ),[1],$fot(X_58)]]) ).
cnf(refute_0_485,plain,
( set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) != set_union2(X_58,set_difference(X_58,B))
| set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) = X_58 ),
inference(resolve,[$cnf( $equal(set_union2(X_58,set_difference(X_58,B)),X_58) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
set_union2(set_difference(X_58,B),set_intersection2(X_58,B)) = X_58,
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_58,B),set_intersection2(X_58,B)),set_union2(X_58,set_difference(X_58,B))) )],[refute_0_482,refute_0_485]) ).
cnf(refute_0_487,plain,
set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) = powerset(empty_set),
inference(subst,[],[refute_0_486:[bind(B,$fot(singleton(skolemFOFtoCNF_B(powerset(empty_set))))),bind(X_58,$fot(powerset(empty_set)))]]) ).
cnf(refute_0_488,plain,
( set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) != powerset(empty_set)
| set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) != set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))
| powerset(empty_set) = set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) ),[0],$fot(powerset(empty_set))]]) ).
cnf(refute_0_489,plain,
( set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) != set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))
| powerset(empty_set) = set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)) ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),powerset(empty_set)) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)) = set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),
inference(subst,[],[refute_0_344:[bind(X_66,$fot(singleton(empty_set))),bind(X_67,$fot(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))))]]) ).
cnf(refute_0_491,plain,
( powerset(empty_set) != set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))
| set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)) != set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))
| powerset(empty_set) = set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(powerset(empty_set),set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))) ),[0],$fot(set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)))]]) ).
cnf(refute_0_492,plain,
( powerset(empty_set) != set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))
| powerset(empty_set) = set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set)),set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
( set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) != set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))
| powerset(empty_set) = set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) ),
inference(resolve,[$cnf( $equal(powerset(empty_set),set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) )],[refute_0_489,refute_0_492]) ).
cnf(refute_0_494,plain,
( powerset(empty_set) = empty_set
| powerset(empty_set) = set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),set_intersection2(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),set_union2(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) )],[refute_0_473,refute_0_493]) ).
cnf(refute_0_495,plain,
( powerset(empty_set) != set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))
| set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) = powerset(empty_set) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(powerset(empty_set))),bind(Y,$fot(set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))))]]) ).
cnf(refute_0_496,plain,
( powerset(empty_set) = empty_set
| set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) = powerset(empty_set) ),
inference(resolve,[$cnf( $equal(powerset(empty_set),set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))))) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
( set_difference(set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) != singleton(empty_set)
| set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))) != powerset(empty_set)
| set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) = singleton(empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))),singleton(empty_set)) ),[0,0],$fot(powerset(empty_set))]]) ).
cnf(refute_0_498,plain,
( set_difference(set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) != singleton(empty_set)
| powerset(empty_set) = empty_set
| set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),powerset(empty_set)) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
( powerset(empty_set) = empty_set
| set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(singleton(empty_set),set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))),singleton(empty_set)) )],[refute_0_366,refute_0_498]) ).
cnf(refute_0_500,plain,
( ~ disjoint(A,B)
| set_difference(A,B) = A ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_501,plain,
( ~ disjoint(powerset(empty_set),set_difference(X_1279,singleton(empty_set)))
| set_difference(powerset(empty_set),set_difference(X_1279,singleton(empty_set))) = powerset(empty_set) ),
inference(subst,[],[refute_0_500:[bind(A,$fot(powerset(empty_set))),bind(B,$fot(set_difference(X_1279,singleton(empty_set))))]]) ).
cnf(refute_0_502,plain,
set_difference(singleton(empty_set),set_difference(X_171,singleton(empty_set))) = singleton(empty_set),
inference(subst,[],[refute_0_316:[bind(B,$fot(singleton(empty_set)))]]) ).
cnf(refute_0_503,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_504,plain,
( ~ subset(singleton(empty_set),X_1268)
| set_difference(singleton(empty_set),X_1268) = empty_set ),
inference(subst,[],[refute_0_503:[bind(A,$fot(singleton(empty_set))),bind(B,$fot(X_1268))]]) ).
cnf(refute_0_505,plain,
( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),B) ),
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_506,plain,
( disjoint(A,X_237)
| in(skolemFOFtoCNF_C_4(A,X_237),X_237) ),
inference(subst,[],[refute_0_505:[bind(B,$fot(X_237))]]) ).
cnf(refute_0_507,plain,
( ~ in(skolemFOFtoCNF_C_4(A,X_237),X_237)
| subset(singleton(skolemFOFtoCNF_C_4(A,X_237)),X_237) ),
inference(subst,[],[refute_0_339:[bind(A,$fot(skolemFOFtoCNF_C_4(A,X_237))),bind(B,$fot(X_237))]]) ).
cnf(refute_0_508,plain,
( disjoint(A,X_237)
| subset(singleton(skolemFOFtoCNF_C_4(A,X_237)),X_237) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_4(A,X_237),X_237) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
( disjoint(powerset(empty_set),X_1267)
| subset(singleton(skolemFOFtoCNF_C_4(powerset(empty_set),X_1267)),X_1267) ),
inference(subst,[],[refute_0_508:[bind(A,$fot(powerset(empty_set))),bind(X_237,$fot(X_1267))]]) ).
cnf(refute_0_510,plain,
( ~ subset(skolemFOFtoCNF_C_4(powerset(empty_set),X_649),empty_set)
| skolemFOFtoCNF_C_4(powerset(empty_set),X_649) = empty_set ),
inference(subst,[],[refute_0_453:[bind(A,$fot(skolemFOFtoCNF_C_4(powerset(empty_set),X_649)))]]) ).
cnf(refute_0_511,plain,
( ~ in(skolemFOFtoCNF_C_4(powerset(A),X_647),powerset(A))
| subset(skolemFOFtoCNF_C_4(powerset(A),X_647),A) ),
inference(subst,[],[refute_0_458:[bind(C,$fot(skolemFOFtoCNF_C_4(powerset(A),X_647)))]]) ).
cnf(refute_0_512,plain,
( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),A) ),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_513,plain,
( disjoint(powerset(A),X_647)
| in(skolemFOFtoCNF_C_4(powerset(A),X_647),powerset(A)) ),
inference(subst,[],[refute_0_512:[bind(A,$fot(powerset(A))),bind(B,$fot(X_647))]]) ).
cnf(refute_0_514,plain,
( disjoint(powerset(A),X_647)
| subset(skolemFOFtoCNF_C_4(powerset(A),X_647),A) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_4(powerset(A),X_647),powerset(A)) )],[refute_0_513,refute_0_511]) ).
cnf(refute_0_515,plain,
( disjoint(powerset(empty_set),X_649)
| subset(skolemFOFtoCNF_C_4(powerset(empty_set),X_649),empty_set) ),
inference(subst,[],[refute_0_514:[bind(A,$fot(empty_set)),bind(X_647,$fot(X_649))]]) ).
cnf(refute_0_516,plain,
( skolemFOFtoCNF_C_4(powerset(empty_set),X_649) = empty_set
| disjoint(powerset(empty_set),X_649) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_4(powerset(empty_set),X_649),empty_set) )],[refute_0_515,refute_0_510]) ).
cnf(refute_0_517,plain,
( skolemFOFtoCNF_C_4(powerset(empty_set),X_1267) = empty_set
| disjoint(powerset(empty_set),X_1267) ),
inference(subst,[],[refute_0_516:[bind(X_649,$fot(X_1267))]]) ).
cnf(refute_0_518,plain,
( skolemFOFtoCNF_C_4(powerset(empty_set),X_1267) != empty_set
| ~ subset(singleton(skolemFOFtoCNF_C_4(powerset(empty_set),X_1267)),X_1267)
| subset(singleton(empty_set),X_1267) ),
introduced(tautology,[equality,[$cnf( subset(singleton(skolemFOFtoCNF_C_4(powerset(empty_set),X_1267)),X_1267) ),[0,0],$fot(empty_set)]]) ).
cnf(refute_0_519,plain,
( ~ subset(singleton(skolemFOFtoCNF_C_4(powerset(empty_set),X_1267)),X_1267)
| disjoint(powerset(empty_set),X_1267)
| subset(singleton(empty_set),X_1267) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_4(powerset(empty_set),X_1267),empty_set) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
( disjoint(powerset(empty_set),X_1267)
| subset(singleton(empty_set),X_1267) ),
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_C_4(powerset(empty_set),X_1267)),X_1267) )],[refute_0_509,refute_0_519]) ).
cnf(refute_0_521,plain,
( disjoint(powerset(empty_set),X_1268)
| subset(singleton(empty_set),X_1268) ),
inference(subst,[],[refute_0_520:[bind(X_1267,$fot(X_1268))]]) ).
cnf(refute_0_522,plain,
( set_difference(singleton(empty_set),X_1268) = empty_set
| disjoint(powerset(empty_set),X_1268) ),
inference(resolve,[$cnf( subset(singleton(empty_set),X_1268) )],[refute_0_521,refute_0_504]) ).
cnf(refute_0_523,plain,
( set_difference(singleton(empty_set),set_difference(X_171,singleton(empty_set))) = empty_set
| disjoint(powerset(empty_set),set_difference(X_171,singleton(empty_set))) ),
inference(subst,[],[refute_0_522:[bind(X_1268,$fot(set_difference(X_171,singleton(empty_set))))]]) ).
cnf(refute_0_524,plain,
( set_difference(singleton(empty_set),set_difference(X_171,singleton(empty_set))) != empty_set
| set_difference(singleton(empty_set),set_difference(X_171,singleton(empty_set))) != singleton(empty_set)
| empty_set = singleton(empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(singleton(empty_set),set_difference(X_171,singleton(empty_set))),singleton(empty_set)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_525,plain,
( set_difference(singleton(empty_set),set_difference(X_171,singleton(empty_set))) != singleton(empty_set)
| empty_set = singleton(empty_set)
| disjoint(powerset(empty_set),set_difference(X_171,singleton(empty_set))) ),
inference(resolve,[$cnf( $equal(set_difference(singleton(empty_set),set_difference(X_171,singleton(empty_set))),empty_set) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
( empty_set = singleton(empty_set)
| disjoint(powerset(empty_set),set_difference(X_171,singleton(empty_set))) ),
inference(resolve,[$cnf( $equal(set_difference(singleton(empty_set),set_difference(X_171,singleton(empty_set))),singleton(empty_set)) )],[refute_0_502,refute_0_525]) ).
cnf(refute_0_527,plain,
singleton(A) != empty_set,
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_528,plain,
( empty_set != singleton(A)
| singleton(A) = empty_set ),
inference(subst,[],[refute_0_10:[bind(X,$fot(empty_set)),bind(Y,$fot(singleton(A)))]]) ).
cnf(refute_0_529,plain,
empty_set != singleton(A),
inference(resolve,[$cnf( $equal(singleton(A),empty_set) )],[refute_0_528,refute_0_527]) ).
cnf(refute_0_530,plain,
empty_set != singleton(empty_set),
inference(subst,[],[refute_0_529:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_531,plain,
disjoint(powerset(empty_set),set_difference(X_171,singleton(empty_set))),
inference(resolve,[$cnf( $equal(empty_set,singleton(empty_set)) )],[refute_0_526,refute_0_530]) ).
cnf(refute_0_532,plain,
disjoint(powerset(empty_set),set_difference(X_1279,singleton(empty_set))),
inference(subst,[],[refute_0_531:[bind(X_171,$fot(X_1279))]]) ).
cnf(refute_0_533,plain,
set_difference(powerset(empty_set),set_difference(X_1279,singleton(empty_set))) = powerset(empty_set),
inference(resolve,[$cnf( disjoint(powerset(empty_set),set_difference(X_1279,singleton(empty_set))) )],[refute_0_532,refute_0_501]) ).
cnf(refute_0_534,plain,
set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) = powerset(empty_set),
inference(subst,[],[refute_0_533:[bind(X_1279,$fot(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set))))))]]) ).
cnf(refute_0_535,plain,
( set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) != powerset(empty_set)
| set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) != singleton(empty_set)
| powerset(empty_set) = singleton(empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))),singleton(empty_set)) ),[0],$fot(powerset(empty_set))]]) ).
cnf(refute_0_536,plain,
( set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))) != singleton(empty_set)
| powerset(empty_set) = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))),powerset(empty_set)) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
( powerset(empty_set) = empty_set
| powerset(empty_set) = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(set_difference(powerset(empty_set),set_difference(set_difference(powerset(empty_set),singleton(skolemFOFtoCNF_B(powerset(empty_set)))),singleton(empty_set))),singleton(empty_set)) )],[refute_0_499,refute_0_536]) ).
cnf(refute_0_538,plain,
powerset(empty_set) != singleton(empty_set),
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_539,plain,
powerset(empty_set) = empty_set,
inference(resolve,[$cnf( $equal(powerset(empty_set),singleton(empty_set)) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
( powerset(empty_set) != empty_set
| set_intersection2(powerset(empty_set),singleton(set_difference(empty_set,X_457))) != singleton(set_difference(empty_set,X_457))
| set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))) = singleton(set_difference(empty_set,X_457)) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(powerset(empty_set),singleton(set_difference(empty_set,X_457))),singleton(set_difference(empty_set,X_457))) ),[0,0],$fot(empty_set)]]) ).
cnf(refute_0_541,plain,
( set_intersection2(powerset(empty_set),singleton(set_difference(empty_set,X_457))) != singleton(set_difference(empty_set,X_457))
| set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))) = singleton(set_difference(empty_set,X_457)) ),
inference(resolve,[$cnf( $equal(powerset(empty_set),empty_set) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))) = singleton(set_difference(empty_set,X_457)),
inference(resolve,[$cnf( $equal(set_intersection2(powerset(empty_set),singleton(set_difference(empty_set,X_457))),singleton(set_difference(empty_set,X_457))) )],[refute_0_357,refute_0_541]) ).
cnf(refute_0_543,plain,
set_intersection2(A,empty_set) = set_intersection2(empty_set,A),
inference(subst,[],[refute_0_7:[bind(B,$fot(empty_set))]]) ).
cnf(refute_0_544,plain,
( set_intersection2(A,empty_set) != empty_set
| set_intersection2(A,empty_set) != set_intersection2(empty_set,A)
| set_intersection2(empty_set,A) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(A,empty_set),empty_set) ),[0],$fot(set_intersection2(empty_set,A))]]) ).
cnf(refute_0_545,plain,
( set_intersection2(A,empty_set) != empty_set
| set_intersection2(empty_set,A) = empty_set ),
inference(resolve,[$cnf( $equal(set_intersection2(A,empty_set),set_intersection2(empty_set,A)) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
set_intersection2(empty_set,A) = empty_set,
inference(resolve,[$cnf( $equal(set_intersection2(A,empty_set),empty_set) )],[refute_0_93,refute_0_545]) ).
cnf(refute_0_547,plain,
set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))) = empty_set,
inference(subst,[],[refute_0_546:[bind(A,$fot(singleton(set_difference(empty_set,X_457))))]]) ).
cnf(refute_0_548,plain,
( set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))) != empty_set
| set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))) != singleton(set_difference(empty_set,X_457))
| empty_set = singleton(set_difference(empty_set,X_457)) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))),singleton(set_difference(empty_set,X_457))) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_549,plain,
( set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))) != singleton(set_difference(empty_set,X_457))
| empty_set = singleton(set_difference(empty_set,X_457)) ),
inference(resolve,[$cnf( $equal(set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))),empty_set) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_551,plain,
set_difference(empty_set,X_457) = empty_set,
inference(subst,[],[refute_0_550:[bind(A,$fot(X_457))]]) ).
cnf(refute_0_552,plain,
singleton(set_difference(empty_set,X_457)) = singleton(set_difference(empty_set,X_457)),
introduced(tautology,[refl,[$fot(singleton(set_difference(empty_set,X_457)))]]) ).
cnf(refute_0_553,plain,
( set_difference(empty_set,X_457) != empty_set
| singleton(set_difference(empty_set,X_457)) != singleton(set_difference(empty_set,X_457))
| singleton(set_difference(empty_set,X_457)) = singleton(empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(set_difference(empty_set,X_457)),singleton(set_difference(empty_set,X_457))) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_0_554,plain,
( set_difference(empty_set,X_457) != empty_set
| singleton(set_difference(empty_set,X_457)) = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(singleton(set_difference(empty_set,X_457)),singleton(set_difference(empty_set,X_457))) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
singleton(set_difference(empty_set,X_457)) = singleton(empty_set),
inference(resolve,[$cnf( $equal(set_difference(empty_set,X_457),empty_set) )],[refute_0_551,refute_0_554]) ).
cnf(refute_0_556,plain,
( empty_set != singleton(set_difference(empty_set,X_457))
| singleton(set_difference(empty_set,X_457)) != singleton(empty_set)
| empty_set = singleton(empty_set) ),
introduced(tautology,[equality,[$cnf( ~ $equal(empty_set,singleton(empty_set)) ),[0],$fot(singleton(set_difference(empty_set,X_457)))]]) ).
cnf(refute_0_557,plain,
( empty_set != singleton(set_difference(empty_set,X_457))
| empty_set = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(singleton(set_difference(empty_set,X_457)),singleton(empty_set)) )],[refute_0_555,refute_0_556]) ).
cnf(refute_0_558,plain,
( set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))) != singleton(set_difference(empty_set,X_457))
| empty_set = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(empty_set,singleton(set_difference(empty_set,X_457))) )],[refute_0_549,refute_0_557]) ).
cnf(refute_0_559,plain,
empty_set = singleton(empty_set),
inference(resolve,[$cnf( $equal(set_intersection2(empty_set,singleton(set_difference(empty_set,X_457))),singleton(set_difference(empty_set,X_457))) )],[refute_0_542,refute_0_558]) ).
cnf(refute_0_560,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,singleton(empty_set)) )],[refute_0_559,refute_0_530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU147+2 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 20 05:12:00 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 22.24/22.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.24/22.42
% 22.24/22.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.33/22.49
%------------------------------------------------------------------------------