TSTP Solution File: SET762+4 by PyRes---1.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : SET762+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n024.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 04:40:01 EDT 2022
% Result : Theorem 48.55s 48.79s
% Output : Refutation 48.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET762+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.12 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.33 % Computer : n024.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 06:03:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 48.55/48.79 # Version: 1.3
% 48.55/48.79 # SZS status Theorem
% 48.55/48.79 # SZS output start CNFRefutation
% 48.55/48.79 fof(thIIa12,conjecture,(![F]:(![A]:(![B]:(maps(F,A,B)=>equal_set(image2(F,empty_set),empty_set))))),input).
% 48.55/48.79 fof(c29,negated_conjecture,(~(![F]:(![A]:(![B]:(maps(F,A,B)=>equal_set(image2(F,empty_set),empty_set)))))),inference(assume_negation,status(cth),[thIIa12])).
% 48.55/48.79 fof(c30,negated_conjecture,(?[F]:(?[A]:(?[B]:(maps(F,A,B)&~equal_set(image2(F,empty_set),empty_set))))),inference(fof_nnf,status(thm),[c29])).
% 48.55/48.79 fof(c31,negated_conjecture,(?[F]:((?[A]:(?[B]:maps(F,A,B)))&~equal_set(image2(F,empty_set),empty_set))),inference(shift_quantors,status(thm),[c30])).
% 48.55/48.79 fof(c32,negated_conjecture,(?[X2]:((?[X3]:(?[X4]:maps(X2,X3,X4)))&~equal_set(image2(X2,empty_set),empty_set))),inference(variable_rename,status(thm),[c31])).
% 48.55/48.79 fof(c33,negated_conjecture,(maps(skolem0001,skolem0002,skolem0003)&~equal_set(image2(skolem0001,empty_set),empty_set)),inference(skolemize,status(esa),[c32])).
% 48.55/48.79 cnf(c35,negated_conjecture,~equal_set(image2(skolem0001,empty_set),empty_set),inference(split_conjunct,status(thm),[c33])).
% 48.55/48.79 fof(empty_set,axiom,(![X]:(~member(X,empty_set))),input).
% 48.55/48.79 fof(c279,axiom,(![X]:~member(X,empty_set)),inference(fof_simplification,status(thm),[empty_set])).
% 48.55/48.79 fof(c280,axiom,(![X233]:~member(X233,empty_set)),inference(variable_rename,status(thm),[c279])).
% 48.55/48.79 cnf(c281,axiom,~member(X261,empty_set),inference(split_conjunct,status(thm),[c280])).
% 48.55/48.79 fof(subset,axiom,(![A]:(![B]:(subset(A,B)<=>(![X]:(member(X,A)=>member(X,B)))))),input).
% 48.55/48.79 fof(c312,axiom,(![A]:(![B]:((~subset(A,B)|(![X]:(~member(X,A)|member(X,B))))&((?[X]:(member(X,A)&~member(X,B)))|subset(A,B))))),inference(fof_nnf,status(thm),[subset])).
% 48.55/48.79 fof(c313,axiom,((![A]:(![B]:(~subset(A,B)|(![X]:(~member(X,A)|member(X,B))))))&(![A]:(![B]:((?[X]:(member(X,A)&~member(X,B)))|subset(A,B))))),inference(shift_quantors,status(thm),[c312])).
% 48.55/48.79 fof(c314,axiom,((![X254]:(![X255]:(~subset(X254,X255)|(![X256]:(~member(X256,X254)|member(X256,X255))))))&(![X257]:(![X258]:((?[X259]:(member(X259,X257)&~member(X259,X258)))|subset(X257,X258))))),inference(variable_rename,status(thm),[c313])).
% 48.55/48.79 fof(c316,axiom,(![X254]:(![X255]:(![X256]:(![X257]:(![X258]:((~subset(X254,X255)|(~member(X256,X254)|member(X256,X255)))&((member(skolem0043(X257,X258),X257)&~member(skolem0043(X257,X258),X258))|subset(X257,X258)))))))),inference(shift_quantors,status(thm),[fof(c315,axiom,((![X254]:(![X255]:(~subset(X254,X255)|(![X256]:(~member(X256,X254)|member(X256,X255))))))&(![X257]:(![X258]:((member(skolem0043(X257,X258),X257)&~member(skolem0043(X257,X258),X258))|subset(X257,X258))))),inference(skolemize,status(esa),[c314])).])).
% 48.55/48.79 fof(c317,axiom,(![X254]:(![X255]:(![X256]:(![X257]:(![X258]:((~subset(X254,X255)|(~member(X256,X254)|member(X256,X255)))&((member(skolem0043(X257,X258),X257)|subset(X257,X258))&(~member(skolem0043(X257,X258),X258)|subset(X257,X258))))))))),inference(distribute,status(thm),[c316])).
% 48.55/48.79 cnf(c319,axiom,member(skolem0043(X359,X360),X359)|subset(X359,X360),inference(split_conjunct,status(thm),[c317])).
% 48.55/48.79 cnf(c364,plain,subset(empty_set,X361),inference(resolution,status(thm),[c319, c281])).
% 48.55/48.79 fof(equal_set,axiom,(![A]:(![B]:(equal_set(A,B)<=>(subset(A,B)&subset(B,A))))),input).
% 48.55/48.79 fof(c304,axiom,(![A]:(![B]:((~equal_set(A,B)|(subset(A,B)&subset(B,A)))&((~subset(A,B)|~subset(B,A))|equal_set(A,B))))),inference(fof_nnf,status(thm),[equal_set])).
% 48.55/48.79 fof(c305,axiom,((![A]:(![B]:(~equal_set(A,B)|(subset(A,B)&subset(B,A)))))&(![A]:(![B]:((~subset(A,B)|~subset(B,A))|equal_set(A,B))))),inference(shift_quantors,status(thm),[c304])).
% 48.55/48.79 fof(c307,axiom,(![X250]:(![X251]:(![X252]:(![X253]:((~equal_set(X250,X251)|(subset(X250,X251)&subset(X251,X250)))&((~subset(X252,X253)|~subset(X253,X252))|equal_set(X252,X253))))))),inference(shift_quantors,status(thm),[fof(c306,axiom,((![X250]:(![X251]:(~equal_set(X250,X251)|(subset(X250,X251)&subset(X251,X250)))))&(![X252]:(![X253]:((~subset(X252,X253)|~subset(X253,X252))|equal_set(X252,X253))))),inference(variable_rename,status(thm),[c305])).])).
% 48.55/48.79 fof(c308,axiom,(![X250]:(![X251]:(![X252]:(![X253]:(((~equal_set(X250,X251)|subset(X250,X251))&(~equal_set(X250,X251)|subset(X251,X250)))&((~subset(X252,X253)|~subset(X253,X252))|equal_set(X252,X253))))))),inference(distribute,status(thm),[c307])).
% 48.55/48.79 cnf(c311,axiom,~subset(X418,X417)|~subset(X417,X418)|equal_set(X418,X417),inference(split_conjunct,status(thm),[c308])).
% 48.55/48.79 cnf(c395,plain,~subset(X427,empty_set)|equal_set(X427,empty_set),inference(resolution,status(thm),[c311, c364])).
% 48.55/48.79 fof(power_set,axiom,(![X]:(![A]:(member(X,power_set(A))<=>subset(X,A)))),input).
% 48.55/48.79 fof(c298,axiom,(![X]:(![A]:((~member(X,power_set(A))|subset(X,A))&(~subset(X,A)|member(X,power_set(A)))))),inference(fof_nnf,status(thm),[power_set])).
% 48.55/48.79 fof(c299,axiom,((![X]:(![A]:(~member(X,power_set(A))|subset(X,A))))&(![X]:(![A]:(~subset(X,A)|member(X,power_set(A)))))),inference(shift_quantors,status(thm),[c298])).
% 48.55/48.79 fof(c301,axiom,(![X246]:(![X247]:(![X248]:(![X249]:((~member(X246,power_set(X247))|subset(X246,X247))&(~subset(X248,X249)|member(X248,power_set(X249)))))))),inference(shift_quantors,status(thm),[fof(c300,axiom,((![X246]:(![X247]:(~member(X246,power_set(X247))|subset(X246,X247))))&(![X248]:(![X249]:(~subset(X248,X249)|member(X248,power_set(X249)))))),inference(variable_rename,status(thm),[c299])).])).
% 48.55/48.79 cnf(c302,axiom,~member(X294,power_set(X293))|subset(X294,X293),inference(split_conjunct,status(thm),[c301])).
% 48.55/48.79 cnf(c303,axiom,~subset(X296,X295)|member(X296,power_set(X295)),inference(split_conjunct,status(thm),[c301])).
% 48.55/48.79 cnf(c369,plain,member(skolem0043(X847,X846),X847)|member(X847,power_set(X846)),inference(resolution,status(thm),[c319, c303])).
% 48.55/48.79 fof(image2,axiom,(![F]:(![A]:(![Y]:(member(Y,image2(F,A))<=>(?[X]:(member(X,A)&apply(F,X,Y))))))),input).
% 48.55/48.79 fof(c113,axiom,(![F]:(![A]:(![Y]:((~member(Y,image2(F,A))|(?[X]:(member(X,A)&apply(F,X,Y))))&((![X]:(~member(X,A)|~apply(F,X,Y)))|member(Y,image2(F,A))))))),inference(fof_nnf,status(thm),[image2])).
% 48.55/48.79 fof(c114,axiom,((![F]:(![A]:(![Y]:(~member(Y,image2(F,A))|(?[X]:(member(X,A)&apply(F,X,Y)))))))&(![F]:(![A]:(![Y]:((![X]:(~member(X,A)|~apply(F,X,Y)))|member(Y,image2(F,A))))))),inference(shift_quantors,status(thm),[c113])).
% 48.55/48.79 fof(c115,axiom,((![X87]:(![X88]:(![X89]:(~member(X89,image2(X87,X88))|(?[X90]:(member(X90,X88)&apply(X87,X90,X89)))))))&(![X91]:(![X92]:(![X93]:((![X94]:(~member(X94,X92)|~apply(X91,X94,X93)))|member(X93,image2(X91,X92))))))),inference(variable_rename,status(thm),[c114])).
% 48.55/48.79 fof(c117,axiom,(![X87]:(![X88]:(![X89]:(![X91]:(![X92]:(![X93]:(![X94]:((~member(X89,image2(X87,X88))|(member(skolem0019(X87,X88,X89),X88)&apply(X87,skolem0019(X87,X88,X89),X89)))&((~member(X94,X92)|~apply(X91,X94,X93))|member(X93,image2(X91,X92))))))))))),inference(shift_quantors,status(thm),[fof(c116,axiom,((![X87]:(![X88]:(![X89]:(~member(X89,image2(X87,X88))|(member(skolem0019(X87,X88,X89),X88)&apply(X87,skolem0019(X87,X88,X89),X89))))))&(![X91]:(![X92]:(![X93]:((![X94]:(~member(X94,X92)|~apply(X91,X94,X93)))|member(X93,image2(X91,X92))))))),inference(skolemize,status(esa),[c115])).])).
% 48.55/48.79 fof(c118,axiom,(![X87]:(![X88]:(![X89]:(![X91]:(![X92]:(![X93]:(![X94]:(((~member(X89,image2(X87,X88))|member(skolem0019(X87,X88,X89),X88))&(~member(X89,image2(X87,X88))|apply(X87,skolem0019(X87,X88,X89),X89)))&((~member(X94,X92)|~apply(X91,X94,X93))|member(X93,image2(X91,X92))))))))))),inference(distribute,status(thm),[c117])).
% 48.55/48.79 cnf(c119,axiom,~member(X1325,image2(X1324,X1323))|member(skolem0019(X1324,X1323,X1325),X1323),inference(split_conjunct,status(thm),[c118])).
% 48.55/48.79 cnf(c1410,plain,member(skolem0019(X13000,X13001,skolem0043(image2(X13000,X13001),X13002)),X13001)|member(image2(X13000,X13001),power_set(X13002)),inference(resolution,status(thm),[c119, c369])).
% 48.55/48.79 cnf(c74368,plain,member(image2(X13004,empty_set),power_set(X13003)),inference(resolution,status(thm),[c1410, c281])).
% 48.55/48.79 cnf(c74477,plain,subset(image2(X13005,empty_set),X13006),inference(resolution,status(thm),[c74368, c302])).
% 48.55/48.79 cnf(c74535,plain,equal_set(image2(X13007,empty_set),empty_set),inference(resolution,status(thm),[c74477, c395])).
% 48.55/48.79 cnf(c74541,plain,$false,inference(resolution,status(thm),[c74535, c35])).
% 48.55/48.79 # SZS output end CNFRefutation
% 48.55/48.79
% 48.55/48.79 # Initial clauses : 168
% 48.55/48.79 # Processed clauses : 1527
% 48.55/48.79 # Factors computed : 2
% 48.55/48.79 # Resolvents computed: 74221
% 48.55/48.79 # Tautologies deleted: 3
% 48.55/48.79 # Forward subsumed : 3945
% 48.55/48.79 # Backward subsumed : 3
% 48.55/48.79 # -------- CPU Time ---------
% 48.55/48.79 # User time : 48.285 s
% 48.55/48.79 # System time : 0.146 s
% 48.55/48.79 # Total time : 48.431 s
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