TSTP Solution File: SET908+1 by PyRes---1.3
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- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %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 04:41:14 EDT 2022
% Result : Theorem 0.37s 0.60s
% Output : Refutation 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.33 % Computer : n020.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 19:20:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.37/0.60 # Version: 1.3
% 0.37/0.60 # SZS status Theorem
% 0.37/0.60 # SZS output start CNFRefutation
% 0.37/0.60 cnf(reflexivity,axiom,X35=X35,eq_axiom).
% 0.37/0.60 fof(d1_xboole_0,axiom,(![A]:(A=empty_set<=>(![B]:(~in(B,A))))),input).
% 0.37/0.60 fof(c44,axiom,(![A]:(A=empty_set<=>(![B]:~in(B,A)))),inference(fof_simplification,status(thm),[d1_xboole_0])).
% 0.37/0.60 fof(c45,axiom,(![A]:((A!=empty_set|(![B]:~in(B,A)))&((?[B]:in(B,A))|A=empty_set))),inference(fof_nnf,status(thm),[c44])).
% 0.37/0.60 fof(c46,axiom,((![A]:(A!=empty_set|(![B]:~in(B,A))))&(![A]:((?[B]:in(B,A))|A=empty_set))),inference(shift_quantors,status(thm),[c45])).
% 0.37/0.60 fof(c47,axiom,((![X20]:(X20!=empty_set|(![X21]:~in(X21,X20))))&(![X22]:((?[X23]:in(X23,X22))|X22=empty_set))),inference(variable_rename,status(thm),[c46])).
% 0.37/0.60 fof(c49,axiom,(![X20]:(![X21]:(![X22]:((X20!=empty_set|~in(X21,X20))&(in(skolem0006(X22),X22)|X22=empty_set))))),inference(shift_quantors,status(thm),[fof(c48,axiom,((![X20]:(X20!=empty_set|(![X21]:~in(X21,X20))))&(![X22]:(in(skolem0006(X22),X22)|X22=empty_set))),inference(skolemize,status(esa),[c47])).])).
% 0.37/0.60 cnf(c50,axiom,X53!=empty_set|~in(X54,X53),inference(split_conjunct,status(thm),[c49])).
% 0.37/0.60 fof(d2_xboole_0,axiom,(![A]:(![B]:(![C]:(C=set_union2(A,B)<=>(![D]:(in(D,C)<=>(in(D,A)|in(D,B)))))))),input).
% 0.37/0.60 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])).
% 0.37/0.60 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])).
% 0.37/0.60 fof(c34,axiom,((![X11]:(![X12]:(![X13]:(X13!=set_union2(X11,X12)|((![X14]:(~in(X14,X13)|(in(X14,X11)|in(X14,X12))))&(![X15]:((~in(X15,X11)&~in(X15,X12))|in(X15,X13))))))))&(![X16]:(![X17]:(![X18]:((?[X19]:((~in(X19,X18)|(~in(X19,X16)&~in(X19,X17)))&(in(X19,X18)|(in(X19,X16)|in(X19,X17)))))|X18=set_union2(X16,X17)))))),inference(variable_rename,status(thm),[c33])).
% 0.37/0.60 fof(c36,axiom,(![X11]:(![X12]:(![X13]:(![X14]:(![X15]:(![X16]:(![X17]:(![X18]:((X13!=set_union2(X11,X12)|((~in(X14,X13)|(in(X14,X11)|in(X14,X12)))&((~in(X15,X11)&~in(X15,X12))|in(X15,X13))))&(((~in(skolem0005(X16,X17,X18),X18)|(~in(skolem0005(X16,X17,X18),X16)&~in(skolem0005(X16,X17,X18),X17)))&(in(skolem0005(X16,X17,X18),X18)|(in(skolem0005(X16,X17,X18),X16)|in(skolem0005(X16,X17,X18),X17))))|X18=set_union2(X16,X17))))))))))),inference(shift_quantors,status(thm),[fof(c35,axiom,((![X11]:(![X12]:(![X13]:(X13!=set_union2(X11,X12)|((![X14]:(~in(X14,X13)|(in(X14,X11)|in(X14,X12))))&(![X15]:((~in(X15,X11)&~in(X15,X12))|in(X15,X13))))))))&(![X16]:(![X17]:(![X18]:(((~in(skolem0005(X16,X17,X18),X18)|(~in(skolem0005(X16,X17,X18),X16)&~in(skolem0005(X16,X17,X18),X17)))&(in(skolem0005(X16,X17,X18),X18)|(in(skolem0005(X16,X17,X18),X16)|in(skolem0005(X16,X17,X18),X17))))|X18=set_union2(X16,X17)))))),inference(skolemize,status(esa),[c34])).])).
% 0.37/0.60 fof(c37,axiom,(![X11]:(![X12]:(![X13]:(![X14]:(![X15]:(![X16]:(![X17]:(![X18]:(((X13!=set_union2(X11,X12)|(~in(X14,X13)|(in(X14,X11)|in(X14,X12))))&((X13!=set_union2(X11,X12)|(~in(X15,X11)|in(X15,X13)))&(X13!=set_union2(X11,X12)|(~in(X15,X12)|in(X15,X13)))))&((((~in(skolem0005(X16,X17,X18),X18)|~in(skolem0005(X16,X17,X18),X16))|X18=set_union2(X16,X17))&((~in(skolem0005(X16,X17,X18),X18)|~in(skolem0005(X16,X17,X18),X17))|X18=set_union2(X16,X17)))&((in(skolem0005(X16,X17,X18),X18)|(in(skolem0005(X16,X17,X18),X16)|in(skolem0005(X16,X17,X18),X17)))|X18=set_union2(X16,X17)))))))))))),inference(distribute,status(thm),[c36])).
% 0.37/0.60 cnf(c39,axiom,X98!=set_union2(X96,X97)|~in(X99,X96)|in(X99,X98),inference(split_conjunct,status(thm),[c37])).
% 0.37/0.60 cnf(symmetry,axiom,X37!=X38|X38=X37,eq_axiom).
% 0.37/0.60 fof(t49_zfmisc_1,conjecture,(![A]:(![B]:set_union2(singleton(A),B)!=empty_set)),input).
% 0.37/0.60 fof(c4,negated_conjecture,(~(![A]:(![B]:set_union2(singleton(A),B)!=empty_set))),inference(assume_negation,status(cth),[t49_zfmisc_1])).
% 0.37/0.60 fof(c5,negated_conjecture,(?[A]:(?[B]:set_union2(singleton(A),B)=empty_set)),inference(fof_nnf,status(thm),[c4])).
% 0.37/0.60 fof(c6,negated_conjecture,(?[X2]:(?[X3]:set_union2(singleton(X2),X3)=empty_set)),inference(variable_rename,status(thm),[c5])).
% 0.37/0.60 fof(c7,negated_conjecture,set_union2(singleton(skolem0001),skolem0002)=empty_set,inference(skolemize,status(esa),[c6])).
% 0.37/0.60 cnf(c8,negated_conjecture,set_union2(singleton(skolem0001),skolem0002)=empty_set,inference(split_conjunct,status(thm),[c7])).
% 0.37/0.60 cnf(c111,plain,empty_set=set_union2(singleton(skolem0001),skolem0002),inference(resolution,status(thm),[c8, symmetry])).
% 0.37/0.60 cnf(c169,plain,~in(X134,singleton(skolem0001))|in(X134,empty_set),inference(resolution,status(thm),[c111, c39])).
% 0.37/0.60 fof(d1_tarski,axiom,(![A]:(![B]:(B=singleton(A)<=>(![C]:(in(C,B)<=>C=A))))),input).
% 0.37/0.60 fof(c52,axiom,(![A]:(![B]:((B!=singleton(A)|(![C]:((~in(C,B)|C=A)&(C!=A|in(C,B)))))&((?[C]:((~in(C,B)|C!=A)&(in(C,B)|C=A)))|B=singleton(A))))),inference(fof_nnf,status(thm),[d1_tarski])).
% 0.37/0.60 fof(c53,axiom,((![A]:(![B]:(B!=singleton(A)|((![C]:(~in(C,B)|C=A))&(![C]:(C!=A|in(C,B)))))))&(![A]:(![B]:((?[C]:((~in(C,B)|C!=A)&(in(C,B)|C=A)))|B=singleton(A))))),inference(shift_quantors,status(thm),[c52])).
% 0.37/0.60 fof(c54,axiom,((![X24]:(![X25]:(X25!=singleton(X24)|((![X26]:(~in(X26,X25)|X26=X24))&(![X27]:(X27!=X24|in(X27,X25)))))))&(![X28]:(![X29]:((?[X30]:((~in(X30,X29)|X30!=X28)&(in(X30,X29)|X30=X28)))|X29=singleton(X28))))),inference(variable_rename,status(thm),[c53])).
% 0.37/0.60 fof(c56,axiom,(![X24]:(![X25]:(![X26]:(![X27]:(![X28]:(![X29]:((X25!=singleton(X24)|((~in(X26,X25)|X26=X24)&(X27!=X24|in(X27,X25))))&(((~in(skolem0007(X28,X29),X29)|skolem0007(X28,X29)!=X28)&(in(skolem0007(X28,X29),X29)|skolem0007(X28,X29)=X28))|X29=singleton(X28))))))))),inference(shift_quantors,status(thm),[fof(c55,axiom,((![X24]:(![X25]:(X25!=singleton(X24)|((![X26]:(~in(X26,X25)|X26=X24))&(![X27]:(X27!=X24|in(X27,X25)))))))&(![X28]:(![X29]:(((~in(skolem0007(X28,X29),X29)|skolem0007(X28,X29)!=X28)&(in(skolem0007(X28,X29),X29)|skolem0007(X28,X29)=X28))|X29=singleton(X28))))),inference(skolemize,status(esa),[c54])).])).
% 0.37/0.60 fof(c57,axiom,(![X24]:(![X25]:(![X26]:(![X27]:(![X28]:(![X29]:(((X25!=singleton(X24)|(~in(X26,X25)|X26=X24))&(X25!=singleton(X24)|(X27!=X24|in(X27,X25))))&(((~in(skolem0007(X28,X29),X29)|skolem0007(X28,X29)!=X28)|X29=singleton(X28))&((in(skolem0007(X28,X29),X29)|skolem0007(X28,X29)=X28)|X29=singleton(X28)))))))))),inference(distribute,status(thm),[c56])).
% 0.37/0.60 cnf(c59,axiom,X158!=singleton(X157)|X159!=X157|in(X159,X158),inference(split_conjunct,status(thm),[c57])).
% 0.37/0.60 cnf(c269,plain,X165!=X166|in(X165,singleton(X166)),inference(resolution,status(thm),[c59, reflexivity])).
% 0.37/0.60 cnf(c289,plain,in(X169,singleton(X169)),inference(resolution,status(thm),[c269, reflexivity])).
% 0.37/0.60 cnf(c340,plain,in(skolem0001,empty_set),inference(resolution,status(thm),[c289, c169])).
% 0.37/0.60 cnf(c346,plain,empty_set!=empty_set,inference(resolution,status(thm),[c340, c50])).
% 0.37/0.60 cnf(c362,plain,$false,inference(resolution,status(thm),[c346, reflexivity])).
% 0.37/0.60 # SZS output end CNFRefutation
% 0.37/0.60
% 0.37/0.60 # Initial clauses : 28
% 0.37/0.60 # Processed clauses : 65
% 0.37/0.60 # Factors computed : 3
% 0.37/0.60 # Resolvents computed: 294
% 0.37/0.60 # Tautologies deleted: 6
% 0.37/0.60 # Forward subsumed : 32
% 0.37/0.60 # Backward subsumed : 1
% 0.37/0.60 # -------- CPU Time ---------
% 0.37/0.60 # User time : 0.245 s
% 0.37/0.60 # System time : 0.016 s
% 0.37/0.60 # Total time : 0.261 s
%------------------------------------------------------------------------------