%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET935+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:38:29 EDT 2022
% Result : Theorem 0.55s 0.76s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 20
% Syntax : Number of formulae : 127 ( 46 unt; 0 def)
% Number of atoms : 293 ( 94 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 286 ( 120 ~; 128 |; 17 &)
% ( 18 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 171 ( 10 sgn 82 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ) ).
fof(d9_xboole_0,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(A,B)
| subset(B,A) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(reflexivity_r3_xboole_0,axiom,
! [A,B] : inclusion_comparable(A,A) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)) ).
fof(t82_zfmisc_1,conjecture,
! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ) ).
fof(subgoal_0,plain,
! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
inference(strip,[],[t82_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( ~ inclusion_comparable(A,B)
& set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
& set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)) = powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(canonicalize,[],[t7_xboole_1]) ).
fof(normalize_0_4,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_6,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ inclusion_comparable(A,B)
<=> ( ~ subset(A,B)
& ~ subset(B,A) ) ),
inference(canonicalize,[],[d9_xboole_0]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ inclusion_comparable(A,B)
<=> ( ~ subset(A,B)
& ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ( ~ subset(A,B)
| inclusion_comparable(A,B) )
& ( ~ subset(B,A)
| inclusion_comparable(A,B) )
& ( ~ inclusion_comparable(A,B)
| subset(A,B)
| subset(B,A) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ subset(A,B)
| inclusion_comparable(A,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( A != B
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[d10_xboole_0]) ).
fof(normalize_0_12,plain,
! [A,B] :
( A != B
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ( A != B
| subset(A,B) )
& ( A != B
| subset(B,A) )
& ( ~ subset(A,B)
| ~ subset(B,A)
| A = B ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(canonicalize,[],[d1_zfmisc_1]) ).
fof(normalize_0_16,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,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(A,B),B)
| ~ subset(skolemFOFtoCNF_C(A,B),A)
| B = powerset(A) )
& ( B = powerset(A)
| in(skolemFOFtoCNF_C(A,B),B)
| subset(skolemFOFtoCNF_C(A,B),A) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A,B,C] :
( B != powerset(A)
| ~ in(C,B)
| subset(C,A) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A] : subset(A,A),
inference(canonicalize,[],[reflexivity_r1_tarski]) ).
fof(normalize_0_20,plain,
! [A] : subset(A,A),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B,C] :
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_22,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(canonicalize,[],[d2_xboole_0]) ).
fof(normalize_0_23,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B,C,D] :
( ( C != set_union2(A,B)
| ~ in(D,A)
| in(D,C) )
& ( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( C != set_union2(A,B)
| ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( C = set_union2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B,C,D] :
( C != set_union2(A,B)
| ~ in(D,C)
| in(D,A)
| in(D,B) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)) = powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_27,plain,
! [A,B] :
( ~ subset(B,A)
| inclusion_comparable(A,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_28,plain,
! [A] : inclusion_comparable(A,A),
inference(canonicalize,[],[reflexivity_r3_xboole_0]) ).
fof(normalize_0_29,plain,
! [A] : inclusion_comparable(A,A),
inference(specialize,[],[normalize_0_28]) ).
cnf(refute_0_0,plain,
~ inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
subset(A,set_union2(A,B)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,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_4,plain,
( ~ subset(A,set_union2(A,B))
| subset(A,set_union2(B,A)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
subset(A,set_union2(B,A)),
inference(resolve,[$cnf( subset(A,set_union2(A,B)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
subset(X_12,set_union2(B,X_12)),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_7,plain,
( ~ subset(A,B)
| inclusion_comparable(A,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ subset(X_12,set_union2(B,X_12))
| inclusion_comparable(X_12,set_union2(B,X_12)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_12)),bind(B,$fot(set_union2(B,X_12)))]]) ).
cnf(refute_0_9,plain,
inclusion_comparable(X_12,set_union2(B,X_12)),
inference(resolve,[$cnf( subset(X_12,set_union2(B,X_12)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
inclusion_comparable(X_15,set_union2(X_14,X_15)),
inference(subst,[],[refute_0_9:[bind(B,$fot(X_14)),bind(X_12,$fot(X_15))]]) ).
cnf(refute_0_11,plain,
set_union2(X_15,X_14) = set_union2(X_14,X_15),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_15)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( set_union2(X_15,X_14) != set_union2(X_14,X_15)
| set_union2(X_14,X_15) = set_union2(X_15,X_14) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(set_union2(X_15,X_14))),bind(Y,$fot(set_union2(X_14,X_15)))]]) ).
cnf(refute_0_16,plain,
set_union2(X_14,X_15) = set_union2(X_15,X_14),
inference(resolve,[$cnf( $equal(set_union2(X_15,X_14),set_union2(X_14,X_15)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( set_union2(X_14,X_15) != set_union2(X_15,X_14)
| ~ inclusion_comparable(X_15,set_union2(X_14,X_15))
| inclusion_comparable(X_15,set_union2(X_15,X_14)) ),
introduced(tautology,[equality,[$cnf( inclusion_comparable(X_15,set_union2(X_14,X_15)) ),[1],$fot(set_union2(X_15,X_14))]]) ).
cnf(refute_0_18,plain,
( ~ inclusion_comparable(X_15,set_union2(X_14,X_15))
| inclusion_comparable(X_15,set_union2(X_15,X_14)) ),
inference(resolve,[$cnf( $equal(set_union2(X_14,X_15),set_union2(X_15,X_14)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
inclusion_comparable(X_15,set_union2(X_15,X_14)),
inference(resolve,[$cnf( inclusion_comparable(X_15,set_union2(X_14,X_15)) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
inclusion_comparable(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_19:[bind(X_14,$fot(skolemFOFtoCNF_B)),bind(X_15,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_21,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_22,plain,
( ~ subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_A_2)
| ~ subset(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| skolemFOFtoCNF_A_2 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_23,plain,
( ~ subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_24,plain,
( B != powerset(A)
| ~ in(C,B)
| subset(C,A) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_25,plain,
( powerset(A) != powerset(A)
| ~ in(C,powerset(A))
| subset(C,A) ),
inference(subst,[],[refute_0_24:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_26,plain,
powerset(A) = powerset(A),
introduced(tautology,[refl,[$fot(powerset(A))]]) ).
cnf(refute_0_27,plain,
( ~ in(C,powerset(A))
| subset(C,A) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
( ~ in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(skolemFOFtoCNF_A_2))
| subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_29,plain,
( ~ in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(skolemFOFtoCNF_B))
| subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_B)),bind(C,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_30,plain,
subset(A,A),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_31,plain,
subset(X_32,X_32),
inference(subst,[],[refute_0_30:[bind(A,$fot(X_32))]]) ).
cnf(refute_0_32,plain,
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_33,plain,
( powerset(A) != powerset(A)
| ~ subset(C,A)
| in(C,powerset(A)) ),
inference(subst,[],[refute_0_32:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_34,plain,
( ~ subset(C,A)
| in(C,powerset(A)) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_26,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ subset(X_32,X_32)
| in(X_32,powerset(X_32)) ),
inference(subst,[],[refute_0_34:[bind(A,$fot(X_32)),bind(C,$fot(X_32))]]) ).
cnf(refute_0_36,plain,
in(X_32,powerset(X_32)),
inference(resolve,[$cnf( subset(X_32,X_32) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))),
inference(subst,[],[refute_0_36:[bind(X_32,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_38,plain,
( C != set_union2(A,B)
| ~ in(D,C)
| in(D,A)
| in(D,B) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_39,plain,
( set_union2(A,B) != set_union2(A,B)
| ~ in(D,set_union2(A,B))
| in(D,A)
| in(D,B) ),
inference(subst,[],[refute_0_38:[bind(C,$fot(set_union2(A,B)))]]) ).
cnf(refute_0_40,plain,
set_union2(A,B) = set_union2(A,B),
introduced(tautology,[refl,[$fot(set_union2(A,B))]]) ).
cnf(refute_0_41,plain,
( ~ in(D,set_union2(A,B))
| in(D,A)
| in(D,B) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(A,B)) )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
( ~ in(X_620,set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)))
| in(X_620,powerset(skolemFOFtoCNF_A_2))
| in(X_620,powerset(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_41:[bind(A,$fot(powerset(skolemFOFtoCNF_A_2))),bind(B,$fot(powerset(skolemFOFtoCNF_B))),bind(D,$fot(X_620))]]) ).
cnf(refute_0_43,plain,
set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)) = powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_44,plain,
( set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)) != powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| ~ in(X_620,powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))
| in(X_620,set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B))) ),
introduced(tautology,[equality,[$cnf( ~ in(X_620,set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B))) ),[1],$fot(powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_45,plain,
( ~ in(X_620,powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))
| in(X_620,set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B))) ),
inference(resolve,[$cnf( $equal(set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)),powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ in(X_620,powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))
| in(X_620,powerset(skolemFOFtoCNF_A_2))
| in(X_620,powerset(skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( in(X_620,set_union2(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B))) )],[refute_0_45,refute_0_42]) ).
cnf(refute_0_47,plain,
( ~ in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))
| in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(skolemFOFtoCNF_A_2))
| in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_46:[bind(X_620,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_48,plain,
( in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(skolemFOFtoCNF_A_2))
| in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) )],[refute_0_37,refute_0_47]) ).
cnf(refute_0_49,plain,
( in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(skolemFOFtoCNF_A_2))
| subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(skolemFOFtoCNF_B)) )],[refute_0_48,refute_0_29]) ).
cnf(refute_0_50,plain,
( subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_A_2)
| subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( in(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),powerset(skolemFOFtoCNF_A_2)) )],[refute_0_49,refute_0_28]) ).
cnf(refute_0_51,plain,
( ~ subset(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_50,refute_0_23]) ).
cnf(refute_0_52,plain,
subset(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
( ~ subset(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| skolemFOFtoCNF_A_2 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) )],[refute_0_53,refute_0_22]) ).
cnf(refute_0_55,plain,
subset(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_56,plain,
( skolemFOFtoCNF_A_2 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
( skolemFOFtoCNF_B != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_58,plain,
( set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = skolemFOFtoCNF_B
| skolemFOFtoCNF_A_2 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
| ~ inclusion_comparable(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[1],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_60,plain,
( ~ inclusion_comparable(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| skolemFOFtoCNF_A_2 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( skolemFOFtoCNF_A_2 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_20,refute_0_60]) ).
cnf(refute_0_62,plain,
subset(X_19,set_union2(B,X_19)),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_19))]]) ).
cnf(refute_0_63,plain,
( ~ subset(B,A)
| inclusion_comparable(A,B) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_64,plain,
( ~ subset(X_19,set_union2(B,X_19))
| inclusion_comparable(set_union2(B,X_19),X_19) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(set_union2(B,X_19))),bind(B,$fot(X_19))]]) ).
cnf(refute_0_65,plain,
inclusion_comparable(set_union2(B,X_19),X_19),
inference(resolve,[$cnf( subset(X_19,set_union2(B,X_19)) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
inclusion_comparable(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B),
inference(subst,[],[refute_0_65:[bind(B,$fot(skolemFOFtoCNF_A_2)),bind(X_19,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_67,plain,
( skolemFOFtoCNF_A_2 != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_68,plain,
( set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = skolemFOFtoCNF_A_2
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_56,refute_0_67]) ).
cnf(refute_0_69,plain,
( set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != skolemFOFtoCNF_A_2
| ~ inclusion_comparable(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( inclusion_comparable(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_70,plain,
( ~ inclusion_comparable(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( inclusion_comparable(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_66,refute_0_70]) ).
cnf(refute_0_72,plain,
skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_71,refute_0_0]) ).
cnf(refute_0_73,plain,
set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_72,refute_0_57]) ).
cnf(refute_0_74,plain,
( set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
| skolemFOFtoCNF_A_2 != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[1],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_75,plain,
( skolemFOFtoCNF_A_2 != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B
| inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_61,refute_0_75]) ).
cnf(refute_0_77,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B,
inference(resolve,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_76,refute_0_0]) ).
cnf(refute_0_78,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B
| skolemFOFtoCNF_B = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_79,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_A_2
| ~ inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)
| inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( ~ inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),[1],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_81,plain,
( ~ inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)
| inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
~ inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_81,refute_0_0]) ).
cnf(refute_0_83,plain,
inclusion_comparable(A,A),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_84,plain,
inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_83:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) )],[refute_0_84,refute_0_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET935+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 23:28:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.55/0.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.76
% 0.55/0.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.62/0.77
%------------------------------------------------------------------------------