TSTP Solution File: SET909+1 by PyRes---1.3
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- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n022.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 04:41:15 EDT 2022
% Result : Theorem 0.49s 0.66s
% Output : Refutation 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 10 16:39:25 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.49/0.66 # Version: 1.3
% 0.49/0.66 # SZS status Theorem
% 0.49/0.66 # SZS output start CNFRefutation
% 0.49/0.66 fof(t50_zfmisc_1,conjecture,(![A]:(![B]:(![C]:set_union2(unordered_pair(A,B),C)!=empty_set))),input).
% 0.49/0.66 fof(c4,negated_conjecture,(~(![A]:(![B]:(![C]:set_union2(unordered_pair(A,B),C)!=empty_set)))),inference(assume_negation,status(cth),[t50_zfmisc_1])).
% 0.49/0.66 fof(c5,negated_conjecture,(?[A]:(?[B]:(?[C]:set_union2(unordered_pair(A,B),C)=empty_set))),inference(fof_nnf,status(thm),[c4])).
% 0.49/0.66 fof(c6,negated_conjecture,(?[X2]:(?[X3]:(?[X4]:set_union2(unordered_pair(X2,X3),X4)=empty_set))),inference(variable_rename,status(thm),[c5])).
% 0.49/0.66 fof(c7,negated_conjecture,set_union2(unordered_pair(skolem0001,skolem0002),skolem0003)=empty_set,inference(skolemize,status(esa),[c6])).
% 0.49/0.66 cnf(c8,negated_conjecture,set_union2(unordered_pair(skolem0001,skolem0002),skolem0003)=empty_set,inference(split_conjunct,status(thm),[c7])).
% 0.49/0.66 fof(d1_xboole_0,axiom,(![A]:(A=empty_set<=>(![B]:(~in(B,A))))),input).
% 0.49/0.66 fof(c56,axiom,(![A]:(A=empty_set<=>(![B]:~in(B,A)))),inference(fof_simplification,status(thm),[d1_xboole_0])).
% 0.49/0.66 fof(c57,axiom,(![A]:((A!=empty_set|(![B]:~in(B,A)))&((?[B]:in(B,A))|A=empty_set))),inference(fof_nnf,status(thm),[c56])).
% 0.49/0.66 fof(c58,axiom,((![A]:(A!=empty_set|(![B]:~in(B,A))))&(![A]:((?[B]:in(B,A))|A=empty_set))),inference(shift_quantors,status(thm),[c57])).
% 0.49/0.66 fof(c59,axiom,((![X30]:(X30!=empty_set|(![X31]:~in(X31,X30))))&(![X32]:((?[X33]:in(X33,X32))|X32=empty_set))),inference(variable_rename,status(thm),[c58])).
% 0.49/0.66 fof(c61,axiom,(![X30]:(![X31]:(![X32]:((X30!=empty_set|~in(X31,X30))&(in(skolem0008(X32),X32)|X32=empty_set))))),inference(shift_quantors,status(thm),[fof(c60,axiom,((![X30]:(X30!=empty_set|(![X31]:~in(X31,X30))))&(![X32]:(in(skolem0008(X32),X32)|X32=empty_set))),inference(skolemize,status(esa),[c59])).])).
% 0.49/0.66 cnf(c62,axiom,X59!=empty_set|~in(X58,X59),inference(split_conjunct,status(thm),[c61])).
% 0.49/0.66 cnf(reflexivity,axiom,X40=X40,eq_axiom).
% 0.49/0.66 fof(d2_xboole_0,axiom,(![A]:(![B]:(![C]:(C=set_union2(A,B)<=>(![D]:(in(D,C)<=>(in(D,A)|in(D,B)))))))),input).
% 0.49/0.66 fof(c32,axiom,(![A]:(![B]:(![C]:((C!=set_union2(A,B)|(![D]:((~in(D,C)|(in(D,A)|in(D,B)))&((~in(D,A)&~in(D,B))|in(D,C)))))&((?[D]:((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))|C=set_union2(A,B)))))),inference(fof_nnf,status(thm),[d2_xboole_0])).
% 0.49/0.66 fof(c33,axiom,((![A]:(![B]:(![C]:(C!=set_union2(A,B)|((![D]:(~in(D,C)|(in(D,A)|in(D,B))))&(![D]:((~in(D,A)&~in(D,B))|in(D,C))))))))&(![A]:(![B]:(![C]:((?[D]:((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))|C=set_union2(A,B)))))),inference(shift_quantors,status(thm),[c32])).
% 0.49/0.66 fof(c34,axiom,((![X12]:(![X13]:(![X14]:(X14!=set_union2(X12,X13)|((![X15]:(~in(X15,X14)|(in(X15,X12)|in(X15,X13))))&(![X16]:((~in(X16,X12)&~in(X16,X13))|in(X16,X14))))))))&(![X17]:(![X18]:(![X19]:((?[X20]:((~in(X20,X19)|(~in(X20,X17)&~in(X20,X18)))&(in(X20,X19)|(in(X20,X17)|in(X20,X18)))))|X19=set_union2(X17,X18)))))),inference(variable_rename,status(thm),[c33])).
% 0.49/0.66 fof(c36,axiom,(![X12]:(![X13]:(![X14]:(![X15]:(![X16]:(![X17]:(![X18]:(![X19]:((X14!=set_union2(X12,X13)|((~in(X15,X14)|(in(X15,X12)|in(X15,X13)))&((~in(X16,X12)&~in(X16,X13))|in(X16,X14))))&(((~in(skolem0006(X17,X18,X19),X19)|(~in(skolem0006(X17,X18,X19),X17)&~in(skolem0006(X17,X18,X19),X18)))&(in(skolem0006(X17,X18,X19),X19)|(in(skolem0006(X17,X18,X19),X17)|in(skolem0006(X17,X18,X19),X18))))|X19=set_union2(X17,X18))))))))))),inference(shift_quantors,status(thm),[fof(c35,axiom,((![X12]:(![X13]:(![X14]:(X14!=set_union2(X12,X13)|((![X15]:(~in(X15,X14)|(in(X15,X12)|in(X15,X13))))&(![X16]:((~in(X16,X12)&~in(X16,X13))|in(X16,X14))))))))&(![X17]:(![X18]:(![X19]:(((~in(skolem0006(X17,X18,X19),X19)|(~in(skolem0006(X17,X18,X19),X17)&~in(skolem0006(X17,X18,X19),X18)))&(in(skolem0006(X17,X18,X19),X19)|(in(skolem0006(X17,X18,X19),X17)|in(skolem0006(X17,X18,X19),X18))))|X19=set_union2(X17,X18)))))),inference(skolemize,status(esa),[c34])).])).
% 0.49/0.66 fof(c37,axiom,(![X12]:(![X13]:(![X14]:(![X15]:(![X16]:(![X17]:(![X18]:(![X19]:(((X14!=set_union2(X12,X13)|(~in(X15,X14)|(in(X15,X12)|in(X15,X13))))&((X14!=set_union2(X12,X13)|(~in(X16,X12)|in(X16,X14)))&(X14!=set_union2(X12,X13)|(~in(X16,X13)|in(X16,X14)))))&((((~in(skolem0006(X17,X18,X19),X19)|~in(skolem0006(X17,X18,X19),X17))|X19=set_union2(X17,X18))&((~in(skolem0006(X17,X18,X19),X19)|~in(skolem0006(X17,X18,X19),X18))|X19=set_union2(X17,X18)))&((in(skolem0006(X17,X18,X19),X19)|(in(skolem0006(X17,X18,X19),X17)|in(skolem0006(X17,X18,X19),X18)))|X19=set_union2(X17,X18)))))))))))),inference(distribute,status(thm),[c36])).
% 0.49/0.66 cnf(c39,axiom,X105!=set_union2(X106,X108)|~in(X107,X106)|in(X107,X105),inference(split_conjunct,status(thm),[c37])).
% 0.49/0.66 cnf(c144,plain,~in(X114,X113)|in(X114,set_union2(X113,X115)),inference(resolution,status(thm),[c39, reflexivity])).
% 0.49/0.66 fof(d2_tarski,axiom,(![A]:(![B]:(![C]:(C=unordered_pair(A,B)<=>(![D]:(in(D,C)<=>(D=A|D=B))))))),input).
% 0.49/0.66 fof(c44,axiom,(![A]:(![B]:(![C]:((C!=unordered_pair(A,B)|(![D]:((~in(D,C)|(D=A|D=B))&((D!=A&D!=B)|in(D,C)))))&((?[D]:((~in(D,C)|(D!=A&D!=B))&(in(D,C)|(D=A|D=B))))|C=unordered_pair(A,B)))))),inference(fof_nnf,status(thm),[d2_tarski])).
% 0.49/0.66 fof(c45,axiom,((![A]:(![B]:(![C]:(C!=unordered_pair(A,B)|((![D]:(~in(D,C)|(D=A|D=B)))&(![D]:((D!=A&D!=B)|in(D,C))))))))&(![A]:(![B]:(![C]:((?[D]:((~in(D,C)|(D!=A&D!=B))&(in(D,C)|(D=A|D=B))))|C=unordered_pair(A,B)))))),inference(shift_quantors,status(thm),[c44])).
% 0.49/0.66 fof(c46,axiom,((![X21]:(![X22]:(![X23]:(X23!=unordered_pair(X21,X22)|((![X24]:(~in(X24,X23)|(X24=X21|X24=X22)))&(![X25]:((X25!=X21&X25!=X22)|in(X25,X23))))))))&(![X26]:(![X27]:(![X28]:((?[X29]:((~in(X29,X28)|(X29!=X26&X29!=X27))&(in(X29,X28)|(X29=X26|X29=X27))))|X28=unordered_pair(X26,X27)))))),inference(variable_rename,status(thm),[c45])).
% 0.49/0.66 fof(c48,axiom,(![X21]:(![X22]:(![X23]:(![X24]:(![X25]:(![X26]:(![X27]:(![X28]:((X23!=unordered_pair(X21,X22)|((~in(X24,X23)|(X24=X21|X24=X22))&((X25!=X21&X25!=X22)|in(X25,X23))))&(((~in(skolem0007(X26,X27,X28),X28)|(skolem0007(X26,X27,X28)!=X26&skolem0007(X26,X27,X28)!=X27))&(in(skolem0007(X26,X27,X28),X28)|(skolem0007(X26,X27,X28)=X26|skolem0007(X26,X27,X28)=X27)))|X28=unordered_pair(X26,X27))))))))))),inference(shift_quantors,status(thm),[fof(c47,axiom,((![X21]:(![X22]:(![X23]:(X23!=unordered_pair(X21,X22)|((![X24]:(~in(X24,X23)|(X24=X21|X24=X22)))&(![X25]:((X25!=X21&X25!=X22)|in(X25,X23))))))))&(![X26]:(![X27]:(![X28]:(((~in(skolem0007(X26,X27,X28),X28)|(skolem0007(X26,X27,X28)!=X26&skolem0007(X26,X27,X28)!=X27))&(in(skolem0007(X26,X27,X28),X28)|(skolem0007(X26,X27,X28)=X26|skolem0007(X26,X27,X28)=X27)))|X28=unordered_pair(X26,X27)))))),inference(skolemize,status(esa),[c46])).])).
% 0.49/0.66 fof(c49,axiom,(![X21]:(![X22]:(![X23]:(![X24]:(![X25]:(![X26]:(![X27]:(![X28]:(((X23!=unordered_pair(X21,X22)|(~in(X24,X23)|(X24=X21|X24=X22)))&((X23!=unordered_pair(X21,X22)|(X25!=X21|in(X25,X23)))&(X23!=unordered_pair(X21,X22)|(X25!=X22|in(X25,X23)))))&((((~in(skolem0007(X26,X27,X28),X28)|skolem0007(X26,X27,X28)!=X26)|X28=unordered_pair(X26,X27))&((~in(skolem0007(X26,X27,X28),X28)|skolem0007(X26,X27,X28)!=X27)|X28=unordered_pair(X26,X27)))&((in(skolem0007(X26,X27,X28),X28)|(skolem0007(X26,X27,X28)=X26|skolem0007(X26,X27,X28)=X27))|X28=unordered_pair(X26,X27)))))))))))),inference(distribute,status(thm),[c48])).
% 0.49/0.66 cnf(c51,axiom,X165!=unordered_pair(X163,X164)|X166!=X163|in(X166,X165),inference(split_conjunct,status(thm),[c49])).
% 0.49/0.66 cnf(c249,plain,X177!=X175|in(X177,unordered_pair(X175,X176)),inference(resolution,status(thm),[c51, reflexivity])).
% 0.49/0.66 cnf(c273,plain,in(X178,unordered_pair(X178,X179)),inference(resolution,status(thm),[c249, reflexivity])).
% 0.49/0.66 cnf(c285,plain,in(X193,set_union2(unordered_pair(X193,X194),X195)),inference(resolution,status(thm),[c273, c144])).
% 0.49/0.66 cnf(c305,plain,set_union2(unordered_pair(X276,X275),X277)!=empty_set,inference(resolution,status(thm),[c285, c62])).
% 0.49/0.66 cnf(c456,plain,$false,inference(resolution,status(thm),[c305, c8])).
% 0.49/0.66 # SZS output end CNFRefutation
% 0.49/0.66
% 0.49/0.66 # Initial clauses : 31
% 0.49/0.66 # Processed clauses : 89
% 0.49/0.66 # Factors computed : 4
% 0.49/0.66 # Resolvents computed: 396
% 0.49/0.66 # Tautologies deleted: 6
% 0.49/0.66 # Forward subsumed : 43
% 0.49/0.66 # Backward subsumed : 1
% 0.49/0.66 # -------- CPU Time ---------
% 0.49/0.66 # User time : 0.295 s
% 0.49/0.66 # System time : 0.014 s
% 0.49/0.66 # Total time : 0.310 s
%------------------------------------------------------------------------------