TSTP Solution File: SET009-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 03:30:59 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 49 ( 7 unt; 23 nHn; 36 RR)
% Number of literals : 112 ( 0 equ; 45 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 58 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(membership_in_subsets,axiom,
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) ) ).
cnf(subsets_axiom1,axiom,
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ) ).
cnf(subsets_axiom2,axiom,
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ) ).
cnf(member_of_difference,axiom,
( ~ difference(Set1,Set2,Difference)
| ~ member(Element,Difference)
| member(Element,Set1) ) ).
cnf(not_member_of_difference,axiom,
( ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ difference(A_set,Set1,Set2) ) ).
cnf(member_of_difference_or_set2,axiom,
( ~ member(Element,Set1)
| ~ difference(Set1,Set2,Difference)
| member(Element,Difference)
| member(Element,Set2) ) ).
cnf(difference_axiom2,axiom,
( difference(Set1,Set2,Difference)
| member(k(Set1,Set2,Difference),Set1)
| member(k(Set1,Set2,Difference),Difference) ) ).
cnf(difference_axiom3,axiom,
( ~ member(k(Set1,Set2,Difference),Difference)
| ~ member(k(Set1,Set2,Difference),Set1)
| member(k(Set1,Set2,Difference),Set2)
| difference(Set1,Set2,Difference) ) ).
cnf(d_is_a_subset_of_a,hypothesis,
subset(d,a) ).
cnf(b_minus_a,hypothesis,
difference(b,a,bDa) ).
cnf(b_minus_d,hypothesis,
difference(b,d,bDd) ).
cnf(prove_bDa_is_a_subset_of_bDd,negated_conjecture,
~ subset(bDa,bDd) ).
cnf(refute_0_0,plain,
( ~ member(member_of_1_not_of_2(bDa,bDd),bDd)
| subset(bDa,bDd) ),
inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(bDa)),bind(Superset,$fot(bDd))]]) ).
cnf(refute_0_1,plain,
( member(member_of_1_not_of_2(bDa,X_242),bDa)
| subset(bDa,X_242) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(bDa)),bind(Superset,$fot(X_242))]]) ).
cnf(refute_0_2,plain,
( ~ difference(bDa,d,bDa)
| ~ member(Element,bDa)
| ~ member(Element,d) ),
inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(bDa)),bind(Set1,$fot(d)),bind(Set2,$fot(bDa))]]) ).
cnf(refute_0_3,plain,
( ~ member(X_24,d)
| ~ subset(d,a)
| member(X_24,a) ),
inference(subst,[],[membership_in_subsets:[bind(Element,$fot(X_24)),bind(Subset,$fot(d)),bind(Superset,$fot(a))]]) ).
cnf(refute_0_4,plain,
( ~ member(X_24,d)
| member(X_24,a) ),
inference(resolve,[$cnf( subset(d,a) )],[d_is_a_subset_of_a,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ member(k(X_36,d,X_36),d)
| member(k(X_36,d,X_36),a) ),
inference(subst,[],[refute_0_4:[bind(X_24,$fot(k(X_36,d,X_36)))]]) ).
cnf(refute_0_6,plain,
( difference(X_34,X_35,X_34)
| member(k(X_34,X_35,X_34),X_34) ),
inference(subst,[],[difference_axiom2:[bind(Difference,$fot(X_34)),bind(Set1,$fot(X_34)),bind(Set2,$fot(X_35))]]) ).
cnf(refute_0_7,plain,
( ~ member(k(X_34,X_35,X_34),X_34)
| difference(X_34,X_35,X_34)
| member(k(X_34,X_35,X_34),X_35) ),
inference(subst,[],[difference_axiom3:[bind(Difference,$fot(X_34)),bind(Set1,$fot(X_34)),bind(Set2,$fot(X_35))]]) ).
cnf(refute_0_8,plain,
( difference(X_34,X_35,X_34)
| member(k(X_34,X_35,X_34),X_35) ),
inference(resolve,[$cnf( member(k(X_34,X_35,X_34),X_34) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( difference(X_36,d,X_36)
| member(k(X_36,d,X_36),d) ),
inference(subst,[],[refute_0_8:[bind(X_34,$fot(X_36)),bind(X_35,$fot(d))]]) ).
cnf(refute_0_10,plain,
( difference(X_36,d,X_36)
| member(k(X_36,d,X_36),a) ),
inference(resolve,[$cnf( member(k(X_36,d,X_36),d) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
( difference(bDa,d,bDa)
| member(k(bDa,d,bDa),a) ),
inference(subst,[],[refute_0_10:[bind(X_36,$fot(bDa))]]) ).
cnf(refute_0_12,plain,
( difference(bDa,Set2,bDa)
| member(k(bDa,Set2,bDa),bDa) ),
inference(subst,[],[difference_axiom2:[bind(Difference,$fot(bDa)),bind(Set1,$fot(bDa))]]) ).
cnf(refute_0_13,plain,
( ~ difference(b,a,bDa)
| ~ member(X_71,a)
| ~ member(X_71,bDa) ),
inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(b)),bind(Element,$fot(X_71)),bind(Set1,$fot(a)),bind(Set2,$fot(bDa))]]) ).
cnf(refute_0_14,plain,
( ~ member(X_71,a)
| ~ member(X_71,bDa) ),
inference(resolve,[$cnf( difference(b,a,bDa) )],[b_minus_a,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ member(k(bDa,Set2,bDa),a)
| ~ member(k(bDa,Set2,bDa),bDa) ),
inference(subst,[],[refute_0_14:[bind(X_71,$fot(k(bDa,Set2,bDa)))]]) ).
cnf(refute_0_16,plain,
( ~ member(k(bDa,Set2,bDa),a)
| difference(bDa,Set2,bDa) ),
inference(resolve,[$cnf( member(k(bDa,Set2,bDa),bDa) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(k(bDa,d,bDa),a)
| difference(bDa,d,bDa) ),
inference(subst,[],[refute_0_16:[bind(Set2,$fot(d))]]) ).
cnf(refute_0_18,plain,
difference(bDa,d,bDa),
inference(resolve,[$cnf( member(k(bDa,d,bDa),a) )],[refute_0_11,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ member(Element,bDa)
| ~ member(Element,d) ),
inference(resolve,[$cnf( difference(bDa,d,bDa) )],[refute_0_18,refute_0_2]) ).
cnf(refute_0_20,plain,
( ~ member(member_of_1_not_of_2(bDa,X_214),bDa)
| ~ member(member_of_1_not_of_2(bDa,X_214),d) ),
inference(subst,[],[refute_0_19:[bind(Element,$fot(member_of_1_not_of_2(bDa,X_214)))]]) ).
cnf(refute_0_21,plain,
( member(member_of_1_not_of_2(bDa,Superset),bDa)
| subset(bDa,Superset) ),
inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(bDa))]]) ).
cnf(refute_0_22,plain,
( ~ difference(b,a,bDa)
| ~ member(X_47,bDa)
| member(X_47,b) ),
inference(subst,[],[member_of_difference:[bind(Difference,$fot(bDa)),bind(Element,$fot(X_47)),bind(Set1,$fot(b)),bind(Set2,$fot(a))]]) ).
cnf(refute_0_23,plain,
( ~ member(X_47,bDa)
| member(X_47,b) ),
inference(resolve,[$cnf( difference(b,a,bDa) )],[b_minus_a,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ member(member_of_1_not_of_2(bDa,Superset),bDa)
| member(member_of_1_not_of_2(bDa,Superset),b) ),
inference(subst,[],[refute_0_23:[bind(X_47,$fot(member_of_1_not_of_2(bDa,Superset)))]]) ).
cnf(refute_0_25,plain,
( member(member_of_1_not_of_2(bDa,Superset),b)
| subset(bDa,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(bDa,Superset),bDa) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ difference(b,d,bDd)
| ~ member(X_207,b)
| member(X_207,bDd)
| member(X_207,d) ),
inference(subst,[],[member_of_difference_or_set2:[bind(Difference,$fot(bDd)),bind(Element,$fot(X_207)),bind(Set1,$fot(b)),bind(Set2,$fot(d))]]) ).
cnf(refute_0_27,plain,
( ~ member(X_207,b)
| member(X_207,bDd)
| member(X_207,d) ),
inference(resolve,[$cnf( difference(b,d,bDd) )],[b_minus_d,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ member(member_of_1_not_of_2(bDa,Superset),b)
| member(member_of_1_not_of_2(bDa,Superset),bDd)
| member(member_of_1_not_of_2(bDa,Superset),d) ),
inference(subst,[],[refute_0_27:[bind(X_207,$fot(member_of_1_not_of_2(bDa,Superset)))]]) ).
cnf(refute_0_29,plain,
( member(member_of_1_not_of_2(bDa,Superset),bDd)
| member(member_of_1_not_of_2(bDa,Superset),d)
| subset(bDa,Superset) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(bDa,Superset),b) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( member(member_of_1_not_of_2(bDa,X_214),bDd)
| member(member_of_1_not_of_2(bDa,X_214),d)
| subset(bDa,X_214) ),
inference(subst,[],[refute_0_29:[bind(Superset,$fot(X_214))]]) ).
cnf(refute_0_31,plain,
( ~ member(member_of_1_not_of_2(bDa,X_214),bDa)
| member(member_of_1_not_of_2(bDa,X_214),bDd)
| subset(bDa,X_214) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(bDa,X_214),d) )],[refute_0_30,refute_0_20]) ).
cnf(refute_0_32,plain,
( ~ member(member_of_1_not_of_2(bDa,X_242),bDa)
| member(member_of_1_not_of_2(bDa,X_242),bDd)
| subset(bDa,X_242) ),
inference(subst,[],[refute_0_31:[bind(X_214,$fot(X_242))]]) ).
cnf(refute_0_33,plain,
( member(member_of_1_not_of_2(bDa,X_242),bDd)
| subset(bDa,X_242) ),
inference(resolve,[$cnf( member(member_of_1_not_of_2(bDa,X_242),bDa) )],[refute_0_1,refute_0_32]) ).
cnf(refute_0_34,plain,
( member(member_of_1_not_of_2(bDa,bDd),bDd)
| subset(bDa,bDd) ),
inference(subst,[],[refute_0_33:[bind(X_242,$fot(bDd))]]) ).
cnf(refute_0_35,plain,
subset(bDa,bDd),
inference(resolve,[$cnf( member(member_of_1_not_of_2(bDa,bDd),bDd) )],[refute_0_34,refute_0_0]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( subset(bDa,bDd) )],[refute_0_35,prove_bDa_is_a_subset_of_bDd]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 600
% 0.12/0.35 % DateTime : Sun Jul 10 08:06:13 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48
% 0.20/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.48
%------------------------------------------------------------------------------