%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 03:35:33 EDT 2022
% Result : Theorem 0.60s 0.81s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 92 ( 17 unt; 0 def)
% Number of atoms : 235 ( 41 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 236 ( 93 ~; 101 |; 19 &)
% ( 19 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 140 ( 6 sgn 78 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ) ).
fof(prove_th18,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
| member(E,D) ) )
=> B = union(C,D) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
| member(E,D) ) )
=> B = union(C,D) ),
inference(strip,[],[prove_th18]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
| member(E,D) ) )
=> B = union(C,D) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C,D] :
( B != union(C,D)
& ! [E] :
( ~ member(E,B)
<=> ( ~ member(E,C)
& ~ member(E,D) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_B != union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)
& ! [E] :
( ~ member(E,skolemFOFtoCNF_B)
<=> ( ~ member(E,skolemFOFtoCNF_C)
& ~ member(E,skolemFOFtoCNF_D_2) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [E] :
( ~ member(E,skolemFOFtoCNF_B)
<=> ( ~ member(E,skolemFOFtoCNF_C)
& ~ member(E,skolemFOFtoCNF_D_2) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E] :
( ~ member(E,skolemFOFtoCNF_B)
<=> ( ~ member(E,skolemFOFtoCNF_C)
& ~ member(E,skolemFOFtoCNF_D_2) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [E] :
( ( ~ member(E,skolemFOFtoCNF_C)
| member(E,skolemFOFtoCNF_B) )
& ( ~ member(E,skolemFOFtoCNF_D_2)
| member(E,skolemFOFtoCNF_B) )
& ( ~ member(E,skolemFOFtoCNF_B)
| member(E,skolemFOFtoCNF_C)
| member(E,skolemFOFtoCNF_D_2) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [E] :
( ~ member(E,skolemFOFtoCNF_C)
| member(E,skolemFOFtoCNF_B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [E] :
( ~ member(E,skolemFOFtoCNF_D_2)
| member(E,skolemFOFtoCNF_B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ( ~ member(D,B)
| member(D,union(B,C)) )
& ( ~ member(D,C)
| member(D,union(B,C)) )
& ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(canonicalize,[],[equal_member_defn]) ).
fof(normalize_0_12,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C,D] :
( ( B != C
| ~ member(D,B)
| member(D,C) )
& ( B != C
| ~ member(D,C)
| member(D,B) )
& ( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C )
& ( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B,C] :
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_16,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [B,C,D] :
( ( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) )
& ( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) )
& ( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_20,plain,
! [B,C,D] :
( ~ member(D,C)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_21,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_22,plain,
! [E] :
( ~ member(E,skolemFOFtoCNF_B)
| member(E,skolemFOFtoCNF_C)
| member(E,skolemFOFtoCNF_D_2) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_23,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_24,plain,
! [B,C] : union(B,C) = union(C,B),
inference(canonicalize,[],[commutativity_of_union]) ).
fof(normalize_0_25,plain,
! [B,C] : union(B,C) = union(C,B),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
skolemFOFtoCNF_B != union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_27,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
( ~ member(E,skolemFOFtoCNF_C)
| member(E,skolemFOFtoCNF_B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_0:[bind(E,$fot(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_2,plain,
( ~ member(E,skolemFOFtoCNF_D_2)
| member(E,skolemFOFtoCNF_B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_D_2)
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_2:[bind(E,$fot(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_4,plain,
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_6,plain,
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( B = skolemFOFtoCNF_B
| member(skolemFOFtoCNF_D_1(B,skolemFOFtoCNF_B),B)
| member(skolemFOFtoCNF_D_1(B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_6:[bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_8,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_9,plain,
( ~ member(D,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| member(D,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_10,plain,
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_11,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)),union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C))
| subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_10:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_12,plain,
( ~ member(D,C)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_13,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_438)),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_438)),union(B,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_12:[bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_438))))]]) ).
cnf(refute_0_14,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_436)),union(skolemFOFtoCNF_D_2,X_436))
| subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_436)) ),
inference(subst,[],[refute_0_10:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(union(skolemFOFtoCNF_D_2,X_436)))]]) ).
cnf(refute_0_15,plain,
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_16,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_26),skolemFOFtoCNF_D_2)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_26),union(skolemFOFtoCNF_D_2,C)) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_26)))]]) ).
cnf(refute_0_17,plain,
( ~ member(E,skolemFOFtoCNF_B)
| member(E,skolemFOFtoCNF_C)
| member(E,skolemFOFtoCNF_D_2) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_18,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_9),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_9),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_9),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_17:[bind(E,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_9)))]]) ).
cnf(refute_0_19,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_20,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_9),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_B,X_9) ),
inference(subst,[],[refute_0_19:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_9))]]) ).
cnf(refute_0_21,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_9),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_9),skolemFOFtoCNF_D_2)
| subset(skolemFOFtoCNF_B,X_9) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_9),skolemFOFtoCNF_B) )],[refute_0_20,refute_0_18]) ).
cnf(refute_0_22,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_26),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_26),skolemFOFtoCNF_D_2)
| subset(skolemFOFtoCNF_B,X_26) ),
inference(subst,[],[refute_0_21:[bind(X_9,$fot(X_26))]]) ).
cnf(refute_0_23,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_26),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_26),union(skolemFOFtoCNF_D_2,C))
| subset(skolemFOFtoCNF_B,X_26) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_26),skolemFOFtoCNF_D_2) )],[refute_0_22,refute_0_16]) ).
cnf(refute_0_24,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_436)),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_436)),union(skolemFOFtoCNF_D_2,X_436))
| subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_436)) ),
inference(subst,[],[refute_0_23:[bind(C,$fot(X_436)),bind(X_26,$fot(union(skolemFOFtoCNF_D_2,X_436)))]]) ).
cnf(refute_0_25,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_436)),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_436)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_436)),union(skolemFOFtoCNF_D_2,X_436)) )],[refute_0_24,refute_0_14]) ).
cnf(refute_0_26,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_438)),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_438)) ),
inference(subst,[],[refute_0_25:[bind(X_436,$fot(X_438))]]) ).
cnf(refute_0_27,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_438)),union(B,skolemFOFtoCNF_C))
| subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_438)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,X_438)),skolemFOFtoCNF_C) )],[refute_0_26,refute_0_13]) ).
cnf(refute_0_28,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)),union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C))
| subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_27:[bind(B,$fot(skolemFOFtoCNF_D_2)),bind(X_438,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_29,plain,
subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)),union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)) )],[refute_0_28,refute_0_11]) ).
cnf(refute_0_30,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_31,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_32,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_33,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( union(B,C) != union(C,B)
| union(C,B) = union(B,C) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(union(B,C))),bind(Y,$fot(union(C,B)))]]) ).
cnf(refute_0_35,plain,
union(C,B) = union(B,C),
inference(resolve,[$cnf( $equal(union(B,C),union(C,B)) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C) = union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),
inference(subst,[],[refute_0_35:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_37,plain,
( union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C) != union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)
| ~ subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C))
| subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)) ),[1],$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_38,plain,
( ~ subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C))
| subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_D_2,skolemFOFtoCNF_C)) )],[refute_0_29,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ member(D,skolemFOFtoCNF_B)
| member(D,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_39,refute_0_9]) ).
cnf(refute_0_41,plain,
( ~ member(skolemFOFtoCNF_D_1(B,skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D_1(B,skolemFOFtoCNF_B),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_40:[bind(D,$fot(skolemFOFtoCNF_D_1(B,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_42,plain,
( B = skolemFOFtoCNF_B
| member(skolemFOFtoCNF_D_1(B,skolemFOFtoCNF_B),B)
| member(skolemFOFtoCNF_D_1(B,skolemFOFtoCNF_B),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_7,refute_0_41]) ).
cnf(refute_0_43,plain,
( union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) = skolemFOFtoCNF_B
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_42:[bind(B,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_44,plain,
skolemFOFtoCNF_B != union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_45,plain,
( union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) != skolemFOFtoCNF_B
| skolemFOFtoCNF_B = union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_46,plain,
union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_47,refute_0_5]) ).
cnf(refute_0_49,plain,
( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_D_2) )],[refute_0_48,refute_0_3]) ).
cnf(refute_0_50,plain,
( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_51,plain,
( ~ member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| ~ member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_50:[bind(B,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_52,plain,
( ~ member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
~ member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B) )],[refute_0_52,refute_0_46]) ).
cnf(refute_0_54,plain,
member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_C),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_49,refute_0_53]) ).
cnf(refute_0_55,plain,
member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_B),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_C) )],[refute_0_54,refute_0_1]) ).
cnf(refute_0_56,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_55,refute_0_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 01:59:13 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.81
% 0.60/0.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.60/0.82
%------------------------------------------------------------------------------