%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU146+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 12:38:44 EDT 2022
% Result : Theorem 0.45s 0.66s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 41
% Syntax : Number of formulae : 197 ( 79 unt; 0 def)
% Number of atoms : 397 ( 266 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 359 ( 159 ~; 150 |; 22 &)
% ( 23 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 232 ( 4 sgn 110 !; 10 ?)
% 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_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ) ).
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(l4_zfmisc_1,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ) ).
fof(t2_xboole_1,lemma,
! [A] : subset(empty_set,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(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ).
fof(subgoal_0,plain,
! [A,B] :
( ( subset(A,singleton(B))
& A != empty_set )
=> A = singleton(B) ),
inference(strip,[],[l4_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B] :
( ( A = empty_set
| A = singleton(B) )
=> subset(A,singleton(B)) ),
inference(strip,[],[l4_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ( subset(A,singleton(B))
& A != empty_set )
=> A = singleton(B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_0_1,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(canonicalize,[],[l2_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( ~ subset(singleton(A),B)
| in(A,B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(canonicalize,[],[t28_xboole_1]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_11,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_13,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(canonicalize,[],[d3_xboole_0]) ).
fof(normalize_0_17,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A,B,C,D] :
( ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) )
& ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D_2(A,B,C),A)
| in(skolemFOFtoCNF_D_2(A,B,C),C) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D_2(A,B,C),B)
| in(skolemFOFtoCNF_D_2(A,B,C),C) )
& ( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D_2(A,B,C),A)
| ~ in(skolemFOFtoCNF_D_2(A,B,C),B)
| ~ in(skolemFOFtoCNF_D_2(A,B,C),C)
| C = set_intersection2(A,B) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[t39_xboole_1]) ).
fof(normalize_0_21,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[t48_xboole_1]) ).
fof(normalize_0_23,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_25,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
? [A,B] :
( A != empty_set
& A != singleton(B)
& subset(A,singleton(B)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_27,plain,
( skolemFOFtoCNF_A_2 != empty_set
& skolemFOFtoCNF_A_2 != singleton(skolemFOFtoCNF_B_1)
& subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) ),
inference(skolemize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_0_30,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,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_30]) ).
fof(normalize_0_32,plain,
! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(conjunct,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [A] : set_union2(A,empty_set) = A,
inference(canonicalize,[],[t1_boole]) ).
fof(normalize_0_34,plain,
! [A] : set_union2(A,empty_set) = A,
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
skolemFOFtoCNF_A_2 != empty_set,
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_36,plain,
skolemFOFtoCNF_A_2 != singleton(skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_27]) ).
cnf(refute_0_0,plain,
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( X_169 = empty_set
| in(skolemFOFtoCNF_B(X_169),X_169) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_169))]]) ).
cnf(refute_0_2,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ in(skolemFOFtoCNF_B(X_169),X_169)
| subset(singleton(skolemFOFtoCNF_B(X_169)),X_169) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B(X_169))),bind(B,$fot(X_169))]]) ).
cnf(refute_0_4,plain,
( X_169 = empty_set
| subset(singleton(skolemFOFtoCNF_B(X_169)),X_169) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(X_169),X_169) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( X_294 = empty_set
| subset(singleton(skolemFOFtoCNF_B(X_294)),X_294) ),
inference(subst,[],[refute_0_4:[bind(X_169,$fot(X_294))]]) ).
cnf(refute_0_6,plain,
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ subset(singleton(skolemFOFtoCNF_B(X_294)),X_294)
| set_intersection2(singleton(skolemFOFtoCNF_B(X_294)),X_294) = singleton(skolemFOFtoCNF_B(X_294)) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(singleton(skolemFOFtoCNF_B(X_294)))),bind(B,$fot(X_294))]]) ).
cnf(refute_0_8,plain,
( X_294 = empty_set
| set_intersection2(singleton(skolemFOFtoCNF_B(X_294)),X_294) = singleton(skolemFOFtoCNF_B(X_294)) ),
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_B(X_294)),X_294) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_14,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
set_intersection2(singleton(skolemFOFtoCNF_B(X_294)),X_294) = set_intersection2(X_294,singleton(skolemFOFtoCNF_B(X_294))),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_294)),bind(B,$fot(singleton(skolemFOFtoCNF_B(X_294))))]]) ).
cnf(refute_0_16,plain,
( set_intersection2(singleton(skolemFOFtoCNF_B(X_294)),X_294) != set_intersection2(X_294,singleton(skolemFOFtoCNF_B(X_294)))
| set_intersection2(singleton(skolemFOFtoCNF_B(X_294)),X_294) != singleton(skolemFOFtoCNF_B(X_294))
| set_intersection2(X_294,singleton(skolemFOFtoCNF_B(X_294))) = singleton(skolemFOFtoCNF_B(X_294)) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_B(X_294)),X_294),singleton(skolemFOFtoCNF_B(X_294))) ),[0],$fot(set_intersection2(X_294,singleton(skolemFOFtoCNF_B(X_294))))]]) ).
cnf(refute_0_17,plain,
( set_intersection2(singleton(skolemFOFtoCNF_B(X_294)),X_294) != singleton(skolemFOFtoCNF_B(X_294))
| set_intersection2(X_294,singleton(skolemFOFtoCNF_B(X_294))) = singleton(skolemFOFtoCNF_B(X_294)) ),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_B(X_294)),X_294),set_intersection2(X_294,singleton(skolemFOFtoCNF_B(X_294)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( X_294 = empty_set
| set_intersection2(X_294,singleton(skolemFOFtoCNF_B(X_294))) = singleton(skolemFOFtoCNF_B(X_294)) ),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_B(X_294)),X_294),singleton(skolemFOFtoCNF_B(X_294))) )],[refute_0_8,refute_0_17]) ).
cnf(refute_0_19,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))
| skolemFOFtoCNF_A_2 = empty_set ),
inference(subst,[],[refute_0_18:[bind(X_294,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_20,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_21,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_20:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_22,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_23,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
( ~ in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B_1))
| skolemFOFtoCNF_B(skolemFOFtoCNF_A_2) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_A_2 = empty_set
| in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_26,plain,
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_27,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,set_intersection2(A,B))
| in(D,B) ),
inference(subst,[],[refute_0_26:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_0_28,plain,
set_intersection2(A,B) = set_intersection2(A,B),
introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).
cnf(refute_0_29,plain,
( ~ in(D,set_intersection2(A,B))
| in(D,B) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
( ~ in(X_369,set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))
| in(X_369,singleton(skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B_1))),bind(D,$fot(X_369))]]) ).
cnf(refute_0_31,plain,
set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_32,plain,
set_union2(set_difference(B,X_58),set_difference(B,set_difference(B,X_58))) = set_union2(set_difference(B,X_58),B),
inference(subst,[],[refute_0_31:[bind(A,$fot(set_difference(B,X_58)))]]) ).
cnf(refute_0_33,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_34,plain,
set_difference(B,set_difference(B,X_58)) = set_intersection2(B,X_58),
inference(subst,[],[refute_0_33:[bind(A,$fot(B)),bind(B,$fot(X_58))]]) ).
cnf(refute_0_35,plain,
( set_difference(B,set_difference(B,X_58)) != set_intersection2(B,X_58)
| set_union2(set_difference(B,X_58),set_difference(B,set_difference(B,X_58))) != set_union2(set_difference(B,X_58),B)
| set_union2(set_difference(B,X_58),set_intersection2(B,X_58)) = set_union2(set_difference(B,X_58),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(B,X_58),set_difference(B,set_difference(B,X_58))),set_union2(set_difference(B,X_58),B)) ),[0,1],$fot(set_intersection2(B,X_58))]]) ).
cnf(refute_0_36,plain,
( set_union2(set_difference(B,X_58),set_difference(B,set_difference(B,X_58))) != set_union2(set_difference(B,X_58),B)
| set_union2(set_difference(B,X_58),set_intersection2(B,X_58)) = set_union2(set_difference(B,X_58),B) ),
inference(resolve,[$cnf( $equal(set_difference(B,set_difference(B,X_58)),set_intersection2(B,X_58)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
set_union2(set_difference(B,X_58),set_intersection2(B,X_58)) = set_union2(set_difference(B,X_58),B),
inference(resolve,[$cnf( $equal(set_union2(set_difference(B,X_58),set_difference(B,set_difference(B,X_58))),set_union2(set_difference(B,X_58),B)) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_39,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_40,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
set_union2(set_difference(B,X_58),B) = set_union2(B,set_difference(B,X_58)),
inference(subst,[],[refute_0_40:[bind(A,$fot(B)),bind(B,$fot(set_difference(B,X_58)))]]) ).
cnf(refute_0_42,plain,
( set_union2(set_difference(B,X_58),B) != set_union2(B,set_difference(B,X_58))
| set_union2(set_difference(B,X_58),set_intersection2(B,X_58)) != set_union2(set_difference(B,X_58),B)
| set_union2(set_difference(B,X_58),set_intersection2(B,X_58)) = set_union2(B,set_difference(B,X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(B,X_58),set_intersection2(B,X_58)),set_union2(set_difference(B,X_58),B)) ),[1],$fot(set_union2(B,set_difference(B,X_58)))]]) ).
cnf(refute_0_43,plain,
( set_union2(set_difference(B,X_58),set_intersection2(B,X_58)) != set_union2(set_difference(B,X_58),B)
| set_union2(set_difference(B,X_58),set_intersection2(B,X_58)) = set_union2(B,set_difference(B,X_58)) ),
inference(resolve,[$cnf( $equal(set_union2(set_difference(B,X_58),B),set_union2(B,set_difference(B,X_58))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
set_union2(set_difference(B,X_58),set_intersection2(B,X_58)) = set_union2(B,set_difference(B,X_58)),
inference(resolve,[$cnf( $equal(set_union2(set_difference(B,X_58),set_intersection2(B,X_58)),set_union2(set_difference(B,X_58),B)) )],[refute_0_37,refute_0_43]) ).
cnf(refute_0_45,plain,
set_union2(set_difference(X_154,X_155),set_intersection2(X_154,X_155)) = set_union2(X_154,set_difference(X_154,X_155)),
inference(subst,[],[refute_0_44:[bind(B,$fot(X_154)),bind(X_58,$fot(X_155))]]) ).
cnf(refute_0_46,plain,
set_intersection2(X_155,X_154) = set_intersection2(X_154,X_155),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_155)),bind(B,$fot(X_154))]]) ).
cnf(refute_0_47,plain,
( set_intersection2(X_155,X_154) != set_intersection2(X_154,X_155)
| set_intersection2(X_154,X_155) = set_intersection2(X_155,X_154) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(set_intersection2(X_155,X_154))),bind(Y,$fot(set_intersection2(X_154,X_155)))]]) ).
cnf(refute_0_48,plain,
set_intersection2(X_154,X_155) = set_intersection2(X_155,X_154),
inference(resolve,[$cnf( $equal(set_intersection2(X_155,X_154),set_intersection2(X_154,X_155)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( set_intersection2(X_154,X_155) != set_intersection2(X_155,X_154)
| set_union2(set_difference(X_154,X_155),set_intersection2(X_154,X_155)) != set_union2(X_154,set_difference(X_154,X_155))
| set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) = set_union2(X_154,set_difference(X_154,X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(X_154,X_155),set_intersection2(X_154,X_155)),set_union2(X_154,set_difference(X_154,X_155))) ),[0,1],$fot(set_intersection2(X_155,X_154))]]) ).
cnf(refute_0_50,plain,
( set_union2(set_difference(X_154,X_155),set_intersection2(X_154,X_155)) != set_union2(X_154,set_difference(X_154,X_155))
| set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) = set_union2(X_154,set_difference(X_154,X_155)) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_154,X_155),set_intersection2(X_155,X_154)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
set_union2(set_difference(X_154,X_155),set_intersection2(X_155,X_154)) = set_union2(X_154,set_difference(X_154,X_155)),
inference(resolve,[$cnf( $equal(set_union2(set_difference(X_154,X_155),set_intersection2(X_154,X_155)),set_union2(X_154,set_difference(X_154,X_155))) )],[refute_0_45,refute_0_50]) ).
cnf(refute_0_52,plain,
set_union2(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) = set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))),
inference(subst,[],[refute_0_51:[bind(X_154,$fot(skolemFOFtoCNF_A_2)),bind(X_155,$fot(singleton(skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_53,plain,
subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_54,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_55,plain,
( ~ subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))
| set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) = empty_set ),
inference(subst,[],[refute_0_54:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_56,plain,
set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) = empty_set,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) )],[refute_0_53,refute_0_55]) ).
cnf(refute_0_57,plain,
( set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) != empty_set
| set_union2(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))
| set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) = set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)),set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))) ),[0,0],$fot(empty_set)]]) ).
cnf(refute_0_58,plain,
( set_union2(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))
| set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) = set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),empty_set) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) = set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))),
inference(resolve,[$cnf( $equal(set_union2(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)),set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))) )],[refute_0_52,refute_0_58]) ).
cnf(refute_0_60,plain,
set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) = set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_61,plain,
set_union2(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_62,plain,
set_union2(A,empty_set) = set_union2(empty_set,A),
inference(subst,[],[refute_0_38:[bind(B,$fot(empty_set))]]) ).
cnf(refute_0_63,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_64,plain,
( set_union2(A,empty_set) != A
| set_union2(empty_set,A) = A ),
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),set_union2(empty_set,A)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
set_union2(empty_set,A) = A,
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),A) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) = set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_65:[bind(A,$fot(set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_67,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_68,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_12,refute_0_67]) ).
cnf(refute_0_69,plain,
( set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) != set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))
| set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) != set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)
| set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) = set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_0_68:[bind(X,$fot(set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)))),bind(Y,$fot(set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2))),bind(Z,$fot(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_0_70,plain,
( set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) != set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))
| set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) = set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)),set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) = set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) )],[refute_0_60,refute_0_70]) ).
cnf(refute_0_72,plain,
( set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) != set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))
| set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) = set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)),set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))) ),[0],$fot(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_73,plain,
( set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) = set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)),set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
set_union2(skolemFOFtoCNF_A_2,empty_set) = skolemFOFtoCNF_A_2,
inference(subst,[],[refute_0_61:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_75,plain,
set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) = set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))),
introduced(tautology,[refl,[$fot(set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_0_76,plain,
( set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) != empty_set
| set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))
| set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) = set_union2(skolemFOFtoCNF_A_2,empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))),set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))) ),[1,1],$fot(empty_set)]]) ).
cnf(refute_0_77,plain,
( set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) != empty_set
| set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) = set_union2(skolemFOFtoCNF_A_2,empty_set) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))),set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) = set_union2(skolemFOFtoCNF_A_2,empty_set),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),empty_set) )],[refute_0_56,refute_0_77]) ).
cnf(refute_0_79,plain,
( set_union2(skolemFOFtoCNF_A_2,empty_set) != skolemFOFtoCNF_A_2
| set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) != set_union2(skolemFOFtoCNF_A_2,empty_set)
| set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_68:[bind(X,$fot(set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))))),bind(Y,$fot(set_union2(skolemFOFtoCNF_A_2,empty_set))),bind(Z,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_80,plain,
( set_union2(skolemFOFtoCNF_A_2,empty_set) != skolemFOFtoCNF_A_2
| set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))),set_union2(skolemFOFtoCNF_A_2,empty_set)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,empty_set),skolemFOFtoCNF_A_2) )],[refute_0_74,refute_0_80]) ).
cnf(refute_0_82,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))
| set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) != skolemFOFtoCNF_A_2
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_A_2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) ),[0],$fot(set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_0_83,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))),skolemFOFtoCNF_A_2) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))) )],[refute_0_73,refute_0_83]) ).
cnf(refute_0_85,plain,
set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(set_union2(empty_set,set_intersection2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)),set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))) )],[refute_0_59,refute_0_84]) ).
cnf(refute_0_86,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_A_2
| ~ in(X_369,skolemFOFtoCNF_A_2)
| in(X_369,set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) ),
introduced(tautology,[equality,[$cnf( ~ in(X_369,set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) ),[1],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_87,plain,
( ~ in(X_369,skolemFOFtoCNF_A_2)
| in(X_369,set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ in(X_369,skolemFOFtoCNF_A_2)
| in(X_369,singleton(skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( in(X_369,set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) )],[refute_0_87,refute_0_30]) ).
cnf(refute_0_89,plain,
( ~ in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_0_88:[bind(X_369,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_90,plain,
( skolemFOFtoCNF_A_2 = empty_set
| in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),skolemFOFtoCNF_A_2) )],[refute_0_25,refute_0_89]) ).
cnf(refute_0_91,plain,
skolemFOFtoCNF_A_2 != empty_set,
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_92,plain,
in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
skolemFOFtoCNF_B(skolemFOFtoCNF_A_2) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B_1)) )],[refute_0_92,refute_0_24]) ).
cnf(refute_0_94,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) != singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))
| skolemFOFtoCNF_B(skolemFOFtoCNF_A_2) != skolemFOFtoCNF_B_1
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = singleton(skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))),singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) ),[1,0],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_95,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) != singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = singleton(skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = singleton(skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_A_2 = empty_set ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))),singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) )],[refute_0_19,refute_0_95]) ).
cnf(refute_0_97,plain,
singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_98,plain,
( singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)) != singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))
| skolemFOFtoCNF_B(skolemFOFtoCNF_A_2) != skolemFOFtoCNF_B_1
| singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) ),[1,0],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_99,plain,
( skolemFOFtoCNF_B(skolemFOFtoCNF_A_2) != skolemFOFtoCNF_B_1
| singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) )],[refute_0_93,refute_0_99]) ).
cnf(refute_0_101,plain,
set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))),
introduced(tautology,[refl,[$fot(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))))]]) ).
cnf(refute_0_102,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) != set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)))
| singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)) != singleton(skolemFOFtoCNF_B_1)
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))),set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)))) ),[1,1],$fot(singleton(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_103,plain,
( singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)) != singleton(skolemFOFtoCNF_B_1)
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))),set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_B_1)) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) != set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_A_2
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_68:[bind(X,$fot(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))))),bind(Y,$fot(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)))),bind(Z,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_106,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_A_2
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))),set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) )],[refute_0_85,refute_0_106]) ).
cnf(refute_0_108,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) != singleton(skolemFOFtoCNF_B_1)
| set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 = singleton(skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))),singleton(skolemFOFtoCNF_B_1)) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_109,plain,
( set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))) != singleton(skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_A_2 = singleton(skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))),skolemFOFtoCNF_A_2) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( skolemFOFtoCNF_A_2 = empty_set
| skolemFOFtoCNF_A_2 = singleton(skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))),singleton(skolemFOFtoCNF_B_1)) )],[refute_0_96,refute_0_109]) ).
cnf(refute_0_111,plain,
skolemFOFtoCNF_A_2 = singleton(skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_110,refute_0_91]) ).
cnf(refute_0_112,plain,
skolemFOFtoCNF_A_2 != singleton(skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_113,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B_1)) )],[refute_0_111,refute_0_112]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( ( A = empty_set
| A = singleton(B) )
=> subset(A,singleton(B)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B] :
( ~ subset(A,singleton(B))
& ( A = empty_set
| A = singleton(B) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2))
& ( skolemFOFtoCNF_A_3 = empty_set
| skolemFOFtoCNF_A_3 = singleton(skolemFOFtoCNF_B_2) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( skolemFOFtoCNF_A_3 = empty_set
| skolemFOFtoCNF_A_3 = singleton(skolemFOFtoCNF_B_2) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_4,plain,
! [A] : subset(A,A),
inference(canonicalize,[],[reflexivity_r1_tarski]) ).
fof(normalize_1_5,plain,
! [A] : subset(A,A),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A] : subset(empty_set,A),
inference(canonicalize,[],[t2_xboole_1]) ).
fof(normalize_1_7,plain,
! [A] : subset(empty_set,A),
inference(specialize,[],[normalize_1_6]) ).
cnf(refute_1_0,plain,
~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( skolemFOFtoCNF_A_3 = empty_set
| skolemFOFtoCNF_A_3 = singleton(skolemFOFtoCNF_B_2) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( skolemFOFtoCNF_A_3 != singleton(skolemFOFtoCNF_B_2)
| singleton(skolemFOFtoCNF_B_2) = skolemFOFtoCNF_A_3 ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_A_3)),bind(Y,$fot(singleton(skolemFOFtoCNF_B_2)))]]) ).
cnf(refute_1_6,plain,
( singleton(skolemFOFtoCNF_B_2) = skolemFOFtoCNF_A_3
| skolemFOFtoCNF_A_3 = empty_set ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) )],[refute_1_1,refute_1_5]) ).
cnf(refute_1_7,plain,
( singleton(skolemFOFtoCNF_B_2) != skolemFOFtoCNF_A_3
| ~ subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3)
| subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) ),[1],$fot(skolemFOFtoCNF_A_3)]]) ).
cnf(refute_1_8,plain,
( ~ subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_A_3 = empty_set
| subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3) )],[refute_1_6,refute_1_7]) ).
cnf(refute_1_9,plain,
( ~ subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_A_3 = empty_set ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) )],[refute_1_8,refute_1_0]) ).
cnf(refute_1_10,plain,
subset(A,A),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_11,plain,
subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3),
inference(subst,[],[refute_1_10:[bind(A,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_12,plain,
skolemFOFtoCNF_A_3 = empty_set,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3) )],[refute_1_11,refute_1_9]) ).
cnf(refute_1_13,plain,
( skolemFOFtoCNF_A_3 != empty_set
| ~ subset(empty_set,singleton(skolemFOFtoCNF_B_2))
| subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) ),[0],$fot(empty_set)]]) ).
cnf(refute_1_14,plain,
( ~ subset(empty_set,singleton(skolemFOFtoCNF_B_2))
| subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,empty_set) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
~ subset(empty_set,singleton(skolemFOFtoCNF_B_2)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) )],[refute_1_14,refute_1_0]) ).
cnf(refute_1_16,plain,
subset(empty_set,A),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_17,plain,
subset(empty_set,singleton(skolemFOFtoCNF_B_2)),
inference(subst,[],[refute_1_16:[bind(A,$fot(singleton(skolemFOFtoCNF_B_2)))]]) ).
cnf(refute_1_18,plain,
$false,
inference(resolve,[$cnf( subset(empty_set,singleton(skolemFOFtoCNF_B_2)) )],[refute_1_17,refute_1_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU146+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.09 % Command : metis --show proof --show saturation %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 600
% 0.08/0.27 % DateTime : Sun Jun 19 01:03:17 EDT 2022
% 0.08/0.27 % CPUTime :
% 0.11/0.28 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.45/0.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.66
% 0.45/0.66 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.45/0.67
%------------------------------------------------------------------------------