TSTP Solution File: SET013-4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET013-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 03:31:05 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of clauses : 59 ( 11 unt; 10 nHn; 56 RR)
% Number of literals : 124 ( 20 equ; 50 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(extensionality2,axiom,
( member(f1(X,Y),X)
| member(f1(X,Y),Y)
| X = Y ) ).
cnf(extensionality3,axiom,
( ~ member(f1(X,Y),X)
| ~ member(f1(X,Y),Y)
| X = Y ) ).
cnf(intersection1,axiom,
( ~ member(Z,intersection(X,Y))
| member(Z,X) ) ).
cnf(intersection2,axiom,
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) ).
cnf(intersection3,axiom,
( member(Z,intersection(X,Y))
| ~ member(Z,X)
| ~ member(Z,Y) ) ).
cnf(intersection_of_a_and_b_is_c,hypothesis,
intersection(as,bs) = cs ).
cnf(intersection_of_b_and_a_is_d,hypothesis,
intersection(bs,as) = ds ).
cnf(prove_c_equals_d,negated_conjecture,
cs != ds ).
cnf(refute_0_0,plain,
( ~ member(f1(cs,ds),cs)
| ~ member(f1(cs,ds),ds)
| cs = ds ),
inference(subst,[],[extensionality3:[bind(X,$fot(cs)),bind(Y,$fot(ds))]]) ).
cnf(refute_0_1,plain,
( ~ member(X_14,intersection(as,bs))
| member(X_14,as) ),
inference(subst,[],[intersection1:[bind(X,$fot(as)),bind(Y,$fot(bs)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_2,plain,
( intersection(as,bs) != cs
| ~ member(X_14,cs)
| member(X_14,intersection(as,bs)) ),
introduced(tautology,[equality,[$cnf( ~ member(X_14,intersection(as,bs)) ),[1],$fot(cs)]]) ).
cnf(refute_0_3,plain,
( ~ member(X_14,cs)
| member(X_14,intersection(as,bs)) ),
inference(resolve,[$cnf( $equal(intersection(as,bs),cs) )],[intersection_of_a_and_b_is_c,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ member(X_14,cs)
| member(X_14,as) ),
inference(resolve,[$cnf( member(X_14,intersection(as,bs)) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
( ~ member(f1(cs,ds),cs)
| member(f1(cs,ds),as) ),
inference(subst,[],[refute_0_4:[bind(X_14,$fot(f1(cs,ds)))]]) ).
cnf(refute_0_6,plain,
( ~ member(X_19,intersection(bs,as))
| member(X_19,as) ),
inference(subst,[],[intersection2:[bind(X,$fot(bs)),bind(Y,$fot(as)),bind(Z,$fot(X_19))]]) ).
cnf(refute_0_7,plain,
( intersection(bs,as) != ds
| ~ member(X_19,ds)
| member(X_19,intersection(bs,as)) ),
introduced(tautology,[equality,[$cnf( ~ member(X_19,intersection(bs,as)) ),[1],$fot(ds)]]) ).
cnf(refute_0_8,plain,
( ~ member(X_19,ds)
| member(X_19,intersection(bs,as)) ),
inference(resolve,[$cnf( $equal(intersection(bs,as),ds) )],[intersection_of_b_and_a_is_d,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ member(X_19,ds)
| member(X_19,as) ),
inference(resolve,[$cnf( member(X_19,intersection(bs,as)) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
( ~ member(f1(cs,ds),ds)
| member(f1(cs,ds),as) ),
inference(subst,[],[refute_0_9:[bind(X_19,$fot(f1(cs,ds)))]]) ).
cnf(refute_0_11,plain,
( ~ member(f1(cs,ds),intersection(ds,bs))
| member(f1(cs,ds),ds) ),
inference(subst,[],[intersection1:[bind(X,$fot(ds)),bind(Y,$fot(bs)),bind(Z,$fot(f1(cs,ds)))]]) ).
cnf(refute_0_12,plain,
( cs = ds
| member(f1(cs,ds),cs)
| member(f1(cs,ds),ds) ),
inference(subst,[],[extensionality2:[bind(X,$fot(cs)),bind(Y,$fot(ds))]]) ).
cnf(refute_0_13,plain,
( ~ member(f1(cs,ds),X)
| ~ member(f1(cs,ds),bs)
| member(f1(cs,ds),intersection(X,bs)) ),
inference(subst,[],[intersection3:[bind(Y,$fot(bs)),bind(Z,$fot(f1(cs,ds)))]]) ).
cnf(refute_0_14,plain,
( ~ member(X_14,intersection(bs,as))
| member(X_14,bs) ),
inference(subst,[],[intersection1:[bind(X,$fot(bs)),bind(Y,$fot(as)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_15,plain,
( intersection(bs,as) != ds
| ~ member(X_14,ds)
| member(X_14,intersection(bs,as)) ),
introduced(tautology,[equality,[$cnf( ~ member(X_14,intersection(bs,as)) ),[1],$fot(ds)]]) ).
cnf(refute_0_16,plain,
( ~ member(X_14,ds)
| member(X_14,intersection(bs,as)) ),
inference(resolve,[$cnf( $equal(intersection(bs,as),ds) )],[intersection_of_b_and_a_is_d,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(X_14,ds)
| member(X_14,bs) ),
inference(resolve,[$cnf( member(X_14,intersection(bs,as)) )],[refute_0_16,refute_0_14]) ).
cnf(refute_0_18,plain,
( ~ member(f1(cs,ds),ds)
| member(f1(cs,ds),bs) ),
inference(subst,[],[refute_0_17:[bind(X_14,$fot(f1(cs,ds)))]]) ).
cnf(refute_0_19,plain,
( ~ member(X_19,intersection(as,bs))
| member(X_19,bs) ),
inference(subst,[],[intersection2:[bind(X,$fot(as)),bind(Y,$fot(bs)),bind(Z,$fot(X_19))]]) ).
cnf(refute_0_20,plain,
( intersection(as,bs) != cs
| ~ member(X_19,cs)
| member(X_19,intersection(as,bs)) ),
introduced(tautology,[equality,[$cnf( ~ member(X_19,intersection(as,bs)) ),[1],$fot(cs)]]) ).
cnf(refute_0_21,plain,
( ~ member(X_19,cs)
| member(X_19,intersection(as,bs)) ),
inference(resolve,[$cnf( $equal(intersection(as,bs),cs) )],[intersection_of_a_and_b_is_c,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ member(X_19,cs)
| member(X_19,bs) ),
inference(resolve,[$cnf( member(X_19,intersection(as,bs)) )],[refute_0_21,refute_0_19]) ).
cnf(refute_0_23,plain,
( ~ member(f1(cs,X_25),cs)
| member(f1(cs,X_25),bs) ),
inference(subst,[],[refute_0_22:[bind(X_19,$fot(f1(cs,X_25)))]]) ).
cnf(refute_0_24,plain,
( cs = X_25
| member(f1(cs,X_25),X_25)
| member(f1(cs,X_25),cs) ),
inference(subst,[],[extensionality2:[bind(X,$fot(cs)),bind(Y,$fot(X_25))]]) ).
cnf(refute_0_25,plain,
( cs = X_25
| member(f1(cs,X_25),X_25)
| member(f1(cs,X_25),bs) ),
inference(resolve,[$cnf( member(f1(cs,X_25),cs) )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
( cs = ds
| member(f1(cs,ds),bs)
| member(f1(cs,ds),ds) ),
inference(subst,[],[refute_0_25:[bind(X_25,$fot(ds))]]) ).
cnf(refute_0_27,plain,
( cs = ds
| member(f1(cs,ds),bs) ),
inference(resolve,[$cnf( member(f1(cs,ds),ds) )],[refute_0_26,refute_0_18]) ).
cnf(refute_0_28,plain,
member(f1(cs,ds),bs),
inference(resolve,[$cnf( $equal(cs,ds) )],[refute_0_27,prove_c_equals_d]) ).
cnf(refute_0_29,plain,
( ~ member(f1(cs,ds),X)
| member(f1(cs,ds),intersection(X,bs)) ),
inference(resolve,[$cnf( member(f1(cs,ds),bs) )],[refute_0_28,refute_0_13]) ).
cnf(refute_0_30,plain,
( ~ member(f1(cs,ds),ds)
| member(f1(cs,ds),intersection(ds,bs)) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(ds))]]) ).
cnf(refute_0_31,plain,
( cs = ds
| member(f1(cs,ds),cs)
| member(f1(cs,ds),intersection(ds,bs)) ),
inference(resolve,[$cnf( member(f1(cs,ds),ds) )],[refute_0_12,refute_0_30]) ).
cnf(refute_0_32,plain,
( member(f1(cs,ds),cs)
| member(f1(cs,ds),intersection(ds,bs)) ),
inference(resolve,[$cnf( $equal(cs,ds) )],[refute_0_31,prove_c_equals_d]) ).
cnf(refute_0_33,plain,
( member(f1(cs,ds),cs)
| member(f1(cs,ds),ds) ),
inference(resolve,[$cnf( member(f1(cs,ds),intersection(ds,bs)) )],[refute_0_32,refute_0_11]) ).
cnf(refute_0_34,plain,
( member(f1(cs,ds),as)
| member(f1(cs,ds),cs) ),
inference(resolve,[$cnf( member(f1(cs,ds),ds) )],[refute_0_33,refute_0_10]) ).
cnf(refute_0_35,plain,
member(f1(cs,ds),as),
inference(resolve,[$cnf( member(f1(cs,ds),cs) )],[refute_0_34,refute_0_5]) ).
cnf(refute_0_36,plain,
( ~ member(f1(cs,ds),Y)
| ~ member(f1(cs,ds),bs)
| member(f1(cs,ds),intersection(bs,Y)) ),
inference(subst,[],[intersection3:[bind(X,$fot(bs)),bind(Z,$fot(f1(cs,ds)))]]) ).
cnf(refute_0_37,plain,
( ~ member(f1(cs,ds),Y)
| member(f1(cs,ds),intersection(bs,Y)) ),
inference(resolve,[$cnf( member(f1(cs,ds),bs) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ member(f1(cs,ds),as)
| member(f1(cs,ds),intersection(bs,as)) ),
inference(subst,[],[refute_0_37:[bind(Y,$fot(as))]]) ).
cnf(refute_0_39,plain,
member(f1(cs,ds),intersection(bs,as)),
inference(resolve,[$cnf( member(f1(cs,ds),as) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
( intersection(bs,as) != ds
| ~ member(f1(cs,ds),intersection(bs,as))
| member(f1(cs,ds),ds) ),
introduced(tautology,[equality,[$cnf( member(f1(cs,ds),intersection(bs,as)) ),[1],$fot(ds)]]) ).
cnf(refute_0_41,plain,
( ~ member(f1(cs,ds),intersection(bs,as))
| member(f1(cs,ds),ds) ),
inference(resolve,[$cnf( $equal(intersection(bs,as),ds) )],[intersection_of_b_and_a_is_d,refute_0_40]) ).
cnf(refute_0_42,plain,
member(f1(cs,ds),ds),
inference(resolve,[$cnf( member(f1(cs,ds),intersection(bs,as)) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ member(f1(cs,ds),cs)
| cs = ds ),
inference(resolve,[$cnf( member(f1(cs,ds),ds) )],[refute_0_42,refute_0_0]) ).
cnf(refute_0_44,plain,
( ~ member(f1(cs,ds),as)
| member(f1(cs,ds),intersection(as,bs)) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(as))]]) ).
cnf(refute_0_45,plain,
member(f1(cs,ds),intersection(as,bs)),
inference(resolve,[$cnf( member(f1(cs,ds),as) )],[refute_0_35,refute_0_44]) ).
cnf(refute_0_46,plain,
( intersection(as,bs) != cs
| ~ member(f1(cs,ds),intersection(as,bs))
| member(f1(cs,ds),cs) ),
introduced(tautology,[equality,[$cnf( member(f1(cs,ds),intersection(as,bs)) ),[1],$fot(cs)]]) ).
cnf(refute_0_47,plain,
( ~ member(f1(cs,ds),intersection(as,bs))
| member(f1(cs,ds),cs) ),
inference(resolve,[$cnf( $equal(intersection(as,bs),cs) )],[intersection_of_a_and_b_is_c,refute_0_46]) ).
cnf(refute_0_48,plain,
member(f1(cs,ds),cs),
inference(resolve,[$cnf( member(f1(cs,ds),intersection(as,bs)) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
cs = ds,
inference(resolve,[$cnf( member(f1(cs,ds),cs) )],[refute_0_48,refute_0_43]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( $equal(cs,ds) )],[refute_0_49,prove_c_equals_d]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET013-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n020.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 05:37:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46
% 0.19/0.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.47
%------------------------------------------------------------------------------