%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 03:33:33 EDT 2022
% Result : Theorem 45.36s 45.56s
% Output : CNFRefutation 45.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 17 unt; 0 def)
% Number of atoms : 171 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 158 ( 64 ~; 70 |; 14 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 144 ( 2 sgn 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(prove_th41,conjecture,
! [B,C,D,E] :
( ( subset(B,C)
& subset(D,E) )
=> subset(intersection(B,D),intersection(C,E)) ) ).
fof(subgoal_0,plain,
! [B,C,D,E] :
( ( subset(B,C)
& subset(D,E) )
=> subset(intersection(B,D),intersection(C,E)) ),
inference(strip,[],[prove_th41]) ).
fof(negate_0_0,plain,
~ ! [B,C,D,E] :
( ( subset(B,C)
& subset(D,E) )
=> subset(intersection(B,D),intersection(C,E)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_1,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_6,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| member(D,B) )
& ( ~ member(D,intersection(B,C))
| member(D,C) )
& ( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
? [B,C,D,E] :
( ~ subset(intersection(B,D),intersection(C,E))
& subset(B,C)
& subset(D,E) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
( ~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E))
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_13,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_14,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,B) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
subset(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_16,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_0_17,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E))
| subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))),bind(C,$fot(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_2,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),intersection(X_15,X_16))
| subset(intersection(X_15,X_16),C) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(intersection(X_15,X_16)))]]) ).
cnf(refute_0_4,plain,
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),intersection(X_15,X_16))
| member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),X_16) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(X_15)),bind(C,$fot(X_16)),bind(D,$fot(skolemFOFtoCNF_D(intersection(X_15,X_16),C)))]]) ).
cnf(refute_0_6,plain,
( member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),X_16)
| subset(intersection(X_15,X_16),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),intersection(X_15,X_16)) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( member(skolemFOFtoCNF_D(intersection(X_15,skolemFOFtoCNF_B),C),skolemFOFtoCNF_B)
| subset(intersection(X_15,skolemFOFtoCNF_B),C) ),
inference(subst,[],[refute_0_6:[bind(X_16,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_8,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ member(X_33,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| member(X_33,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(X_33))]]) ).
cnf(refute_0_11,plain,
( ~ member(X_33,skolemFOFtoCNF_B)
| member(X_33,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ member(skolemFOFtoCNF_D(intersection(X_15,skolemFOFtoCNF_B),C),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D(intersection(X_15,skolemFOFtoCNF_B),C),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_11:[bind(X_33,$fot(skolemFOFtoCNF_D(intersection(X_15,skolemFOFtoCNF_B),C)))]]) ).
cnf(refute_0_13,plain,
( member(skolemFOFtoCNF_D(intersection(X_15,skolemFOFtoCNF_B),C),skolemFOFtoCNF_C)
| subset(intersection(X_15,skolemFOFtoCNF_B),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(X_15,skolemFOFtoCNF_B),C),skolemFOFtoCNF_B) )],[refute_0_7,refute_0_12]) ).
cnf(refute_0_14,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),skolemFOFtoCNF_C)
| subset(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) ),
inference(subst,[],[refute_0_13:[bind(C,$fot(X_5213)),bind(X_15,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_15,plain,
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_16,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_81),X_80),B)
| ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_81),X_80),skolemFOFtoCNF_E)
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_81),X_80),intersection(B,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_15:[bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_81),X_80)))]]) ).
cnf(refute_0_17,plain,
( member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),intersection(X_12,X_13))
| subset(intersection(X_12,X_13),C) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(intersection(X_12,X_13)))]]) ).
cnf(refute_0_18,plain,
( ~ member(D,intersection(B,C))
| member(D,B) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_19,plain,
( ~ member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),intersection(X_12,X_13))
| member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),X_12) ),
inference(subst,[],[refute_0_18:[bind(B,$fot(X_12)),bind(C,$fot(X_13)),bind(D,$fot(skolemFOFtoCNF_D(intersection(X_12,X_13),C)))]]) ).
cnf(refute_0_20,plain,
( member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),X_12)
| subset(intersection(X_12,X_13),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),intersection(X_12,X_13)) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_13),C),skolemFOFtoCNF_D_2)
| subset(intersection(skolemFOFtoCNF_D_2,X_13),C) ),
inference(subst,[],[refute_0_20:[bind(X_12,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_22,plain,
subset(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_23,plain,
( ~ member(X_33,skolemFOFtoCNF_D_2)
| ~ subset(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E)
| member(X_33,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(skolemFOFtoCNF_D_2)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_33))]]) ).
cnf(refute_0_24,plain,
( ~ member(X_33,skolemFOFtoCNF_D_2)
| member(X_33,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_13),C),skolemFOFtoCNF_D_2)
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_13),C),skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_24:[bind(X_33,$fot(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_13),C)))]]) ).
cnf(refute_0_26,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_13),C),skolemFOFtoCNF_E)
| subset(intersection(skolemFOFtoCNF_D_2,X_13),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_13),C),skolemFOFtoCNF_D_2) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_81),X_80),skolemFOFtoCNF_E)
| subset(intersection(skolemFOFtoCNF_D_2,X_81),X_80) ),
inference(subst,[],[refute_0_26:[bind(C,$fot(X_80)),bind(X_13,$fot(X_81))]]) ).
cnf(refute_0_28,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_81),X_80),B)
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_81),X_80),intersection(B,skolemFOFtoCNF_E))
| subset(intersection(skolemFOFtoCNF_D_2,X_81),X_80) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,X_81),X_80),skolemFOFtoCNF_E) )],[refute_0_27,refute_0_16]) ).
cnf(refute_0_29,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E))
| subset(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) ),
inference(subst,[],[refute_0_28:[bind(B,$fot(skolemFOFtoCNF_C)),bind(X_80,$fot(X_5213)),bind(X_81,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_30,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E))
| subset(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),skolemFOFtoCNF_C) )],[refute_0_14,refute_0_29]) ).
cnf(refute_0_31,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_32,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_33,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_34,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( intersection(B,C) != intersection(C,B)
| intersection(C,B) = intersection(B,C) ),
inference(subst,[],[refute_0_34:[bind(X,$fot(intersection(B,C))),bind(Y,$fot(intersection(C,B)))]]) ).
cnf(refute_0_36,plain,
intersection(C,B) = intersection(B,C),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B) = intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(subst,[],[refute_0_36:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_38,plain,
skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) = skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213))]]) ).
cnf(refute_0_39,plain,
( intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B) != intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
| skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) != skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213)
| skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) = skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213)) ),[1,0],$fot(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_40,plain,
( intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B) != intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
| skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) = skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) = skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) != skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213)
| ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E))
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)) ),[0],$fot(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213))]]) ).
cnf(refute_0_43,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E))
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E))
| subset(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)) )],[refute_0_30,refute_0_43]) ).
cnf(refute_0_45,plain,
( intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B) != intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
| ~ subset(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213)
| subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213) ),
introduced(tautology,[equality,[$cnf( subset(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) ),[0],$fot(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_46,plain,
( ~ subset(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213)
| subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) )],[refute_0_37,refute_0_45]) ).
cnf(refute_0_47,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E))
| subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),X_5213) ),
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),X_5213) )],[refute_0_44,refute_0_46]) ).
cnf(refute_0_48,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E))
| subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_47:[bind(X_5213,$fot(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_49,plain,
subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)) )],[refute_0_48,refute_0_1]) ).
cnf(refute_0_50,plain,
~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_E)) )],[refute_0_49,refute_0_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 600
% 0.18/0.33 % DateTime : Sat Jul 9 18:56:26 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 45.36/45.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.36/45.56
% 45.36/45.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 45.36/45.56
%------------------------------------------------------------------------------