TSTP Solution File: SET173+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 03:33:19 EDT 2022
% Result : Theorem 0.39s 0.56s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 128 ( 43 unt; 0 def)
% Number of atoms : 264 ( 73 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 240 ( 104 ~; 109 |; 14 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 279 ( 27 sgn 81 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ) ).
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(prove_absorbtion_for_intersection,conjecture,
! [B,C] : intersection(B,union(B,C)) = B ).
fof(subgoal_0,plain,
! [B,C] : intersection(B,union(B,C)) = B,
inference(strip,[],[prove_absorbtion_for_intersection]) ).
fof(negate_0_0,plain,
~ ! [B,C] : intersection(B,union(B,C)) = B,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] : intersection(B,union(B,C)) != B,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != skolemFOFtoCNF_B,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_0_3,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] :
( ( B != C
| subset(B,C) )
& ( B != C
| subset(C,B) )
& ( ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,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_12]) ).
fof(normalize_0_14,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_0_16,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_0_18,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,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_18]) ).
fof(normalize_0_20,plain,
! [B,C,D] :
( ~ member(D,C)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_22,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_23,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(conjunct,[],[normalize_0_19]) ).
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]) ).
cnf(refute_0_0,plain,
intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ subset(X_45,intersection(X_44,X_45))
| ~ subset(intersection(X_44,X_45),X_45)
| X_45 = intersection(X_44,X_45) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_45)),bind(C,$fot(intersection(X_44,X_45)))]]) ).
cnf(refute_0_3,plain,
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( ~ member(skolemFOFtoCNF_D(intersection(X_42,X_43),X_43),X_43)
| subset(intersection(X_42,X_43),X_43) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(intersection(X_42,X_43))),bind(C,$fot(X_43))]]) ).
cnf(refute_0_5,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( member(skolemFOFtoCNF_D(intersection(X_23,X_24),C),intersection(X_23,X_24))
| subset(intersection(X_23,X_24),C) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(intersection(X_23,X_24)))]]) ).
cnf(refute_0_7,plain,
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_8,plain,
( ~ member(skolemFOFtoCNF_D(intersection(X_23,X_24),C),intersection(X_23,X_24))
| member(skolemFOFtoCNF_D(intersection(X_23,X_24),C),X_24) ),
inference(subst,[],[refute_0_7:[bind(B,$fot(X_23)),bind(C,$fot(X_24)),bind(D,$fot(skolemFOFtoCNF_D(intersection(X_23,X_24),C)))]]) ).
cnf(refute_0_9,plain,
( member(skolemFOFtoCNF_D(intersection(X_23,X_24),C),X_24)
| subset(intersection(X_23,X_24),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(X_23,X_24),C),intersection(X_23,X_24)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( member(skolemFOFtoCNF_D(intersection(X_42,X_43),X_43),X_43)
| subset(intersection(X_42,X_43),X_43) ),
inference(subst,[],[refute_0_9:[bind(C,$fot(X_43)),bind(X_23,$fot(X_42)),bind(X_24,$fot(X_43))]]) ).
cnf(refute_0_11,plain,
subset(intersection(X_42,X_43),X_43),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(X_42,X_43),X_43),X_43) )],[refute_0_10,refute_0_4]) ).
cnf(refute_0_12,plain,
subset(intersection(X_44,X_45),X_45),
inference(subst,[],[refute_0_11:[bind(X_42,$fot(X_44)),bind(X_43,$fot(X_45))]]) ).
cnf(refute_0_13,plain,
( ~ subset(X_45,intersection(X_44,X_45))
| X_45 = intersection(X_44,X_45) ),
inference(resolve,[$cnf( subset(intersection(X_44,X_45),X_45) )],[refute_0_12,refute_0_2]) ).
cnf(refute_0_14,plain,
( ~ subset(X_83,intersection(X_82,X_83))
| X_83 = intersection(X_82,X_83) ),
inference(subst,[],[refute_0_13:[bind(X_44,$fot(X_82)),bind(X_45,$fot(X_83))]]) ).
cnf(refute_0_15,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_16,plain,
intersection(X_83,X_82) = intersection(X_82,X_83),
inference(subst,[],[refute_0_15:[bind(B,$fot(X_83)),bind(C,$fot(X_82))]]) ).
cnf(refute_0_17,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_18,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_19,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( intersection(X_83,X_82) != intersection(X_82,X_83)
| intersection(X_82,X_83) = intersection(X_83,X_82) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(intersection(X_83,X_82))),bind(Y,$fot(intersection(X_82,X_83)))]]) ).
cnf(refute_0_21,plain,
intersection(X_82,X_83) = intersection(X_83,X_82),
inference(resolve,[$cnf( $equal(intersection(X_83,X_82),intersection(X_82,X_83)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( intersection(X_82,X_83) != intersection(X_83,X_82)
| ~ subset(X_83,intersection(X_83,X_82))
| subset(X_83,intersection(X_82,X_83)) ),
introduced(tautology,[equality,[$cnf( ~ subset(X_83,intersection(X_82,X_83)) ),[1],$fot(intersection(X_83,X_82))]]) ).
cnf(refute_0_23,plain,
( ~ subset(X_83,intersection(X_83,X_82))
| subset(X_83,intersection(X_82,X_83)) ),
inference(resolve,[$cnf( $equal(intersection(X_82,X_83),intersection(X_83,X_82)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ subset(X_83,intersection(X_83,X_82))
| X_83 = intersection(X_82,X_83) ),
inference(resolve,[$cnf( subset(X_83,intersection(X_82,X_83)) )],[refute_0_23,refute_0_14]) ).
cnf(refute_0_25,plain,
( ~ subset(X_287,intersection(X_287,union(X_287,X_288)))
| X_287 = intersection(union(X_287,X_288),X_287) ),
inference(subst,[],[refute_0_24:[bind(X_82,$fot(union(X_287,X_288))),bind(X_83,$fot(X_287))]]) ).
cnf(refute_0_26,plain,
( ~ member(skolemFOFtoCNF_D(X_280,intersection(X_280,union(X_278,union(X_280,X_281)))),intersection(X_280,union(X_278,union(X_280,X_281))))
| subset(X_280,intersection(X_280,union(X_278,union(X_280,X_281)))) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_280)),bind(C,$fot(intersection(X_280,union(X_278,union(X_280,X_281)))))]]) ).
cnf(refute_0_27,plain,
( ~ member(D,C)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_28,plain,
( ~ member(skolemFOFtoCNF_D(X_34,X_33),union(X_34,X_35))
| member(skolemFOFtoCNF_D(X_34,X_33),union(B,union(X_34,X_35))) ),
inference(subst,[],[refute_0_27:[bind(C,$fot(union(X_34,X_35))),bind(D,$fot(skolemFOFtoCNF_D(X_34,X_33)))]]) ).
cnf(refute_0_29,plain,
( member(skolemFOFtoCNF_D(X_14,C),X_14)
| subset(X_14,C) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_14))]]) ).
cnf(refute_0_30,plain,
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_31,plain,
( ~ member(skolemFOFtoCNF_D(X_14,C),X_14)
| member(skolemFOFtoCNF_D(X_14,C),union(X_14,X_15)) ),
inference(subst,[],[refute_0_30:[bind(B,$fot(X_14)),bind(C,$fot(X_15)),bind(D,$fot(skolemFOFtoCNF_D(X_14,C)))]]) ).
cnf(refute_0_32,plain,
( member(skolemFOFtoCNF_D(X_14,C),union(X_14,X_15))
| subset(X_14,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_14,C),X_14) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( member(skolemFOFtoCNF_D(X_34,X_33),union(X_34,X_35))
| subset(X_34,X_33) ),
inference(subst,[],[refute_0_32:[bind(C,$fot(X_33)),bind(X_14,$fot(X_34)),bind(X_15,$fot(X_35))]]) ).
cnf(refute_0_34,plain,
( member(skolemFOFtoCNF_D(X_34,X_33),union(B,union(X_34,X_35)))
| subset(X_34,X_33) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_34,X_33),union(X_34,X_35)) )],[refute_0_33,refute_0_28]) ).
cnf(refute_0_35,plain,
( member(skolemFOFtoCNF_D(X_276,X_275),union(B,union(X_276,X_35)))
| subset(X_276,X_275) ),
inference(subst,[],[refute_0_34:[bind(X_33,$fot(X_275)),bind(X_34,$fot(X_276))]]) ).
cnf(refute_0_36,plain,
( member(skolemFOFtoCNF_D(X_116,C),X_116)
| subset(X_116,C) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_116))]]) ).
cnf(refute_0_37,plain,
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_38,plain,
( ~ member(skolemFOFtoCNF_D(X_116,C),X_116)
| ~ member(skolemFOFtoCNF_D(X_116,C),X_117)
| member(skolemFOFtoCNF_D(X_116,C),intersection(X_116,X_117)) ),
inference(subst,[],[refute_0_37:[bind(B,$fot(X_116)),bind(C,$fot(X_117)),bind(D,$fot(skolemFOFtoCNF_D(X_116,C)))]]) ).
cnf(refute_0_39,plain,
( ~ member(skolemFOFtoCNF_D(X_116,C),X_117)
| member(skolemFOFtoCNF_D(X_116,C),intersection(X_116,X_117))
| subset(X_116,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_116,C),X_116) )],[refute_0_36,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ member(skolemFOFtoCNF_D(X_276,X_275),union(B,union(X_276,X_35)))
| member(skolemFOFtoCNF_D(X_276,X_275),intersection(X_276,union(B,union(X_276,X_35))))
| subset(X_276,X_275) ),
inference(subst,[],[refute_0_39:[bind(C,$fot(X_275)),bind(X_116,$fot(X_276)),bind(X_117,$fot(union(B,union(X_276,X_35))))]]) ).
cnf(refute_0_41,plain,
( member(skolemFOFtoCNF_D(X_276,X_275),intersection(X_276,union(B,union(X_276,X_35))))
| subset(X_276,X_275) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_276,X_275),union(B,union(X_276,X_35))) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
( member(skolemFOFtoCNF_D(X_280,intersection(X_280,union(X_278,union(X_280,X_281)))),intersection(X_280,union(X_278,union(X_280,X_281))))
| subset(X_280,intersection(X_280,union(X_278,union(X_280,X_281)))) ),
inference(subst,[],[refute_0_41:[bind(B,$fot(X_278)),bind(X_275,$fot(intersection(X_280,union(X_278,union(X_280,X_281))))),bind(X_276,$fot(X_280)),bind(X_35,$fot(X_281))]]) ).
cnf(refute_0_43,plain,
subset(X_280,intersection(X_280,union(X_278,union(X_280,X_281)))),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_280,intersection(X_280,union(X_278,union(X_280,X_281)))),intersection(X_280,union(X_278,union(X_280,X_281)))) )],[refute_0_42,refute_0_26]) ).
cnf(refute_0_44,plain,
subset(X_283,intersection(X_283,union(union(X_283,X_284),union(X_283,X_284)))),
inference(subst,[],[refute_0_43:[bind(X_278,$fot(union(X_283,X_284))),bind(X_280,$fot(X_283)),bind(X_281,$fot(X_284))]]) ).
cnf(refute_0_45,plain,
( ~ subset(X_114,union(X_114,X_114))
| ~ subset(union(X_114,X_114),X_114)
| X_114 = union(X_114,X_114) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_114)),bind(C,$fot(union(X_114,X_114)))]]) ).
cnf(refute_0_46,plain,
( ~ member(skolemFOFtoCNF_D(union(X_113,X_113),X_113),X_113)
| subset(union(X_113,X_113),X_113) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(union(X_113,X_113))),bind(C,$fot(X_113))]]) ).
cnf(refute_0_47,plain,
( member(skolemFOFtoCNF_D(union(X_107,X_108),C),union(X_107,X_108))
| subset(union(X_107,X_108),C) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(union(X_107,X_108)))]]) ).
cnf(refute_0_48,plain,
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_49,plain,
( ~ member(skolemFOFtoCNF_D(union(X_107,X_108),C),union(X_107,X_108))
| member(skolemFOFtoCNF_D(union(X_107,X_108),C),X_107)
| member(skolemFOFtoCNF_D(union(X_107,X_108),C),X_108) ),
inference(subst,[],[refute_0_48:[bind(B,$fot(X_107)),bind(C,$fot(X_108)),bind(D,$fot(skolemFOFtoCNF_D(union(X_107,X_108),C)))]]) ).
cnf(refute_0_50,plain,
( member(skolemFOFtoCNF_D(union(X_107,X_108),C),X_107)
| member(skolemFOFtoCNF_D(union(X_107,X_108),C),X_108)
| subset(union(X_107,X_108),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(union(X_107,X_108),C),union(X_107,X_108)) )],[refute_0_47,refute_0_49]) ).
cnf(refute_0_51,plain,
( member(skolemFOFtoCNF_D(union(X_113,X_113),X_113),X_113)
| subset(union(X_113,X_113),X_113) ),
inference(subst,[],[refute_0_50:[bind(C,$fot(X_113)),bind(X_107,$fot(X_113)),bind(X_108,$fot(X_113))]]) ).
cnf(refute_0_52,plain,
subset(union(X_113,X_113),X_113),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(union(X_113,X_113),X_113),X_113) )],[refute_0_51,refute_0_46]) ).
cnf(refute_0_53,plain,
subset(union(X_114,X_114),X_114),
inference(subst,[],[refute_0_52:[bind(X_113,$fot(X_114))]]) ).
cnf(refute_0_54,plain,
( ~ subset(X_114,union(X_114,X_114))
| X_114 = union(X_114,X_114) ),
inference(resolve,[$cnf( subset(union(X_114,X_114),X_114) )],[refute_0_53,refute_0_45]) ).
cnf(refute_0_55,plain,
( ~ member(skolemFOFtoCNF_D(X_28,union(X_27,X_28)),union(X_27,X_28))
| subset(X_28,union(X_27,X_28)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_28)),bind(C,$fot(union(X_27,X_28)))]]) ).
cnf(refute_0_56,plain,
( member(skolemFOFtoCNF_D(X_18,C),X_18)
| subset(X_18,C) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_18))]]) ).
cnf(refute_0_57,plain,
( ~ member(skolemFOFtoCNF_D(X_18,C),X_18)
| member(skolemFOFtoCNF_D(X_18,C),union(X_17,X_18)) ),
inference(subst,[],[refute_0_27:[bind(B,$fot(X_17)),bind(C,$fot(X_18)),bind(D,$fot(skolemFOFtoCNF_D(X_18,C)))]]) ).
cnf(refute_0_58,plain,
( member(skolemFOFtoCNF_D(X_18,C),union(X_17,X_18))
| subset(X_18,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_18,C),X_18) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( member(skolemFOFtoCNF_D(X_28,union(X_27,X_28)),union(X_27,X_28))
| subset(X_28,union(X_27,X_28)) ),
inference(subst,[],[refute_0_58:[bind(C,$fot(union(X_27,X_28))),bind(X_17,$fot(X_27)),bind(X_18,$fot(X_28))]]) ).
cnf(refute_0_60,plain,
subset(X_28,union(X_27,X_28)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_28,union(X_27,X_28)),union(X_27,X_28)) )],[refute_0_59,refute_0_55]) ).
cnf(refute_0_61,plain,
subset(X_30,union(X_29,X_30)),
inference(subst,[],[refute_0_60:[bind(X_27,$fot(X_29)),bind(X_28,$fot(X_30))]]) ).
cnf(refute_0_62,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_63,plain,
union(X_30,X_29) = union(X_29,X_30),
inference(subst,[],[refute_0_62:[bind(B,$fot(X_30)),bind(C,$fot(X_29))]]) ).
cnf(refute_0_64,plain,
( union(X_30,X_29) != union(X_29,X_30)
| union(X_29,X_30) = union(X_30,X_29) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(union(X_30,X_29))),bind(Y,$fot(union(X_29,X_30)))]]) ).
cnf(refute_0_65,plain,
union(X_29,X_30) = union(X_30,X_29),
inference(resolve,[$cnf( $equal(union(X_30,X_29),union(X_29,X_30)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( union(X_29,X_30) != union(X_30,X_29)
| ~ subset(X_30,union(X_29,X_30))
| subset(X_30,union(X_30,X_29)) ),
introduced(tautology,[equality,[$cnf( subset(X_30,union(X_29,X_30)) ),[1],$fot(union(X_30,X_29))]]) ).
cnf(refute_0_67,plain,
( ~ subset(X_30,union(X_29,X_30))
| subset(X_30,union(X_30,X_29)) ),
inference(resolve,[$cnf( $equal(union(X_29,X_30),union(X_30,X_29)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
subset(X_30,union(X_30,X_29)),
inference(resolve,[$cnf( subset(X_30,union(X_29,X_30)) )],[refute_0_61,refute_0_67]) ).
cnf(refute_0_69,plain,
subset(X_114,union(X_114,X_114)),
inference(subst,[],[refute_0_68:[bind(X_29,$fot(X_114)),bind(X_30,$fot(X_114))]]) ).
cnf(refute_0_70,plain,
X_114 = union(X_114,X_114),
inference(resolve,[$cnf( subset(X_114,union(X_114,X_114)) )],[refute_0_69,refute_0_54]) ).
cnf(refute_0_71,plain,
union(X_283,X_284) = union(union(X_283,X_284),union(X_283,X_284)),
inference(subst,[],[refute_0_70:[bind(X_114,$fot(union(X_283,X_284)))]]) ).
cnf(refute_0_72,plain,
( union(X_283,X_284) != union(union(X_283,X_284),union(X_283,X_284))
| union(union(X_283,X_284),union(X_283,X_284)) = union(X_283,X_284) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(union(X_283,X_284))),bind(Y,$fot(union(union(X_283,X_284),union(X_283,X_284))))]]) ).
cnf(refute_0_73,plain,
union(union(X_283,X_284),union(X_283,X_284)) = union(X_283,X_284),
inference(resolve,[$cnf( $equal(union(X_283,X_284),union(union(X_283,X_284),union(X_283,X_284))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( union(union(X_283,X_284),union(X_283,X_284)) != union(X_283,X_284)
| ~ subset(X_283,intersection(X_283,union(union(X_283,X_284),union(X_283,X_284))))
| subset(X_283,intersection(X_283,union(X_283,X_284))) ),
introduced(tautology,[equality,[$cnf( subset(X_283,intersection(X_283,union(union(X_283,X_284),union(X_283,X_284)))) ),[1,1],$fot(union(X_283,X_284))]]) ).
cnf(refute_0_75,plain,
( ~ subset(X_283,intersection(X_283,union(union(X_283,X_284),union(X_283,X_284))))
| subset(X_283,intersection(X_283,union(X_283,X_284))) ),
inference(resolve,[$cnf( $equal(union(union(X_283,X_284),union(X_283,X_284)),union(X_283,X_284)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
subset(X_283,intersection(X_283,union(X_283,X_284))),
inference(resolve,[$cnf( subset(X_283,intersection(X_283,union(union(X_283,X_284),union(X_283,X_284)))) )],[refute_0_44,refute_0_75]) ).
cnf(refute_0_77,plain,
subset(X_287,intersection(X_287,union(X_287,X_288))),
inference(subst,[],[refute_0_76:[bind(X_283,$fot(X_287)),bind(X_284,$fot(X_288))]]) ).
cnf(refute_0_78,plain,
X_287 = intersection(union(X_287,X_288),X_287),
inference(resolve,[$cnf( subset(X_287,intersection(X_287,union(X_287,X_288))) )],[refute_0_77,refute_0_25]) ).
cnf(refute_0_79,plain,
( intersection(B,C) != intersection(C,B)
| intersection(C,B) = intersection(B,C) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(intersection(B,C))),bind(Y,$fot(intersection(C,B)))]]) ).
cnf(refute_0_80,plain,
intersection(C,B) = intersection(B,C),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_0_15,refute_0_79]) ).
cnf(refute_0_81,plain,
intersection(union(X_287,X_288),X_287) = intersection(X_287,union(X_287,X_288)),
inference(subst,[],[refute_0_80:[bind(B,$fot(X_287)),bind(C,$fot(union(X_287,X_288)))]]) ).
cnf(refute_0_82,plain,
( X_287 != intersection(union(X_287,X_288),X_287)
| intersection(union(X_287,X_288),X_287) != intersection(X_287,union(X_287,X_288))
| X_287 = intersection(X_287,union(X_287,X_288)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_287,intersection(X_287,union(X_287,X_288))) ),[0],$fot(intersection(union(X_287,X_288),X_287))]]) ).
cnf(refute_0_83,plain,
( X_287 != intersection(union(X_287,X_288),X_287)
| X_287 = intersection(X_287,union(X_287,X_288)) ),
inference(resolve,[$cnf( $equal(intersection(union(X_287,X_288),X_287),intersection(X_287,union(X_287,X_288))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
X_287 = intersection(X_287,union(X_287,X_288)),
inference(resolve,[$cnf( $equal(X_287,intersection(union(X_287,X_288),X_287)) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
( X_287 != intersection(X_287,union(X_287,X_288))
| intersection(X_287,union(X_287,X_288)) = X_287 ),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_287)),bind(Y,$fot(intersection(X_287,union(X_287,X_288))))]]) ).
cnf(refute_0_86,plain,
intersection(X_287,union(X_287,X_288)) = X_287,
inference(resolve,[$cnf( $equal(X_287,intersection(X_287,union(X_287,X_288))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = skolemFOFtoCNF_B,
inference(subst,[],[refute_0_86:[bind(X_287,$fot(skolemFOFtoCNF_B)),bind(X_288,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_88,plain,
( intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != skolemFOFtoCNF_B
| skolemFOFtoCNF_B != skolemFOFtoCNF_B
| intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( ~ $equal(intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),skolemFOFtoCNF_B) ),[0],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_89,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),skolemFOFtoCNF_B) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),skolemFOFtoCNF_B) )],[refute_0_89,refute_0_0]) ).
cnf(refute_0_91,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_B,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_92,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_91,refute_0_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 09:50:19 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.56
% 0.39/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.40/0.57
%------------------------------------------------------------------------------