TSTP Solution File: SET918+1 by PyRes---1.3
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- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n010.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 04:41:19 EDT 2022
% Result : Theorem 2.13s 2.30s
% Output : Refutation 2.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.14 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 22:55:45 EDT 2022
% 0.14/0.36 % CPUTime :
% 2.13/2.30 # Version: 1.3
% 2.13/2.30 # SZS status Theorem
% 2.13/2.30 # SZS output start CNFRefutation
% 2.13/2.30 fof(t59_zfmisc_1,conjecture,(![A]:(![B]:(![C]:(~((set_intersection2(unordered_pair(A,B),C)=singleton(A)&in(B,C))&A!=B))))),input).
% 2.13/2.30 fof(c5,negated_conjecture,(~(![A]:(![B]:(![C]:(~((set_intersection2(unordered_pair(A,B),C)=singleton(A)&in(B,C))&A!=B)))))),inference(assume_negation,status(cth),[t59_zfmisc_1])).
% 2.13/2.30 fof(c6,negated_conjecture,(?[A]:(?[B]:(?[C]:((set_intersection2(unordered_pair(A,B),C)=singleton(A)&in(B,C))&A!=B)))),inference(fof_nnf,status(thm),[c5])).
% 2.13/2.30 fof(c7,negated_conjecture,(?[A]:(?[B]:((?[C]:(set_intersection2(unordered_pair(A,B),C)=singleton(A)&in(B,C)))&A!=B))),inference(shift_quantors,status(thm),[c6])).
% 2.13/2.30 fof(c8,negated_conjecture,(?[X2]:(?[X3]:((?[X4]:(set_intersection2(unordered_pair(X2,X3),X4)=singleton(X2)&in(X3,X4)))&X2!=X3))),inference(variable_rename,status(thm),[c7])).
% 2.13/2.30 fof(c9,negated_conjecture,((set_intersection2(unordered_pair(skolem0001,skolem0002),skolem0003)=singleton(skolem0001)&in(skolem0002,skolem0003))&skolem0001!=skolem0002),inference(skolemize,status(esa),[c8])).
% 2.13/2.30 cnf(c12,negated_conjecture,skolem0001!=skolem0002,inference(split_conjunct,status(thm),[c9])).
% 2.13/2.30 cnf(symmetry,axiom,X41!=X40|X40=X41,eq_axiom).
% 2.13/2.30 cnf(c10,negated_conjecture,set_intersection2(unordered_pair(skolem0001,skolem0002),skolem0003)=singleton(skolem0001),inference(split_conjunct,status(thm),[c9])).
% 2.13/2.30 fof(d1_tarski,axiom,(![A]:(![B]:(B=singleton(A)<=>(![C]:(in(C,B)<=>C=A))))),input).
% 2.13/2.30 fof(c47,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])).
% 2.13/2.30 fof(c48,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),[c47])).
% 2.13/2.30 fof(c49,axiom,((![X26]:(![X27]:(X27!=singleton(X26)|((![X28]:(~in(X28,X27)|X28=X26))&(![X29]:(X29!=X26|in(X29,X27)))))))&(![X30]:(![X31]:((?[X32]:((~in(X32,X31)|X32!=X30)&(in(X32,X31)|X32=X30)))|X31=singleton(X30))))),inference(variable_rename,status(thm),[c48])).
% 2.13/2.30 fof(c51,axiom,(![X26]:(![X27]:(![X28]:(![X29]:(![X30]:(![X31]:((X27!=singleton(X26)|((~in(X28,X27)|X28=X26)&(X29!=X26|in(X29,X27))))&(((~in(skolem0008(X30,X31),X31)|skolem0008(X30,X31)!=X30)&(in(skolem0008(X30,X31),X31)|skolem0008(X30,X31)=X30))|X31=singleton(X30))))))))),inference(shift_quantors,status(thm),[fof(c50,axiom,((![X26]:(![X27]:(X27!=singleton(X26)|((![X28]:(~in(X28,X27)|X28=X26))&(![X29]:(X29!=X26|in(X29,X27)))))))&(![X30]:(![X31]:(((~in(skolem0008(X30,X31),X31)|skolem0008(X30,X31)!=X30)&(in(skolem0008(X30,X31),X31)|skolem0008(X30,X31)=X30))|X31=singleton(X30))))),inference(skolemize,status(esa),[c49])).])).
% 2.13/2.30 fof(c52,axiom,(![X26]:(![X27]:(![X28]:(![X29]:(![X30]:(![X31]:(((X27!=singleton(X26)|(~in(X28,X27)|X28=X26))&(X27!=singleton(X26)|(X29!=X26|in(X29,X27))))&(((~in(skolem0008(X30,X31),X31)|skolem0008(X30,X31)!=X30)|X31=singleton(X30))&((in(skolem0008(X30,X31),X31)|skolem0008(X30,X31)=X30)|X31=singleton(X30)))))))))),inference(distribute,status(thm),[c51])).
% 2.13/2.30 cnf(c53,axiom,X146!=singleton(X144)|~in(X145,X146)|X145=X144,inference(split_conjunct,status(thm),[c52])).
% 2.13/2.30 cnf(c175,plain,~in(X845,set_intersection2(unordered_pair(skolem0001,skolem0002),skolem0003))|X845=skolem0001,inference(resolution,status(thm),[c53, c10])).
% 2.13/2.30 cnf(reflexivity,axiom,X39=X39,eq_axiom).
% 2.13/2.30 fof(commutativity_k2_tarski,axiom,(![A]:(![B]:unordered_pair(A,B)=unordered_pair(B,A))),input).
% 2.13/2.30 fof(c59,axiom,(![X35]:(![X36]:unordered_pair(X35,X36)=unordered_pair(X36,X35))),inference(variable_rename,status(thm),[commutativity_k2_tarski])).
% 2.13/2.30 cnf(c60,axiom,unordered_pair(X64,X65)=unordered_pair(X65,X64),inference(split_conjunct,status(thm),[c59])).
% 2.13/2.30 fof(d2_tarski,axiom,(![A]:(![B]:(![C]:(C=unordered_pair(A,B)<=>(![D]:(in(D,C)<=>(D=A|D=B))))))),input).
% 2.13/2.30 fof(c35,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])).
% 2.13/2.30 fof(c36,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),[c35])).
% 2.13/2.30 fof(c37,axiom,((![X17]:(![X18]:(![X19]:(X19!=unordered_pair(X17,X18)|((![X20]:(~in(X20,X19)|(X20=X17|X20=X18)))&(![X21]:((X21!=X17&X21!=X18)|in(X21,X19))))))))&(![X22]:(![X23]:(![X24]:((?[X25]:((~in(X25,X24)|(X25!=X22&X25!=X23))&(in(X25,X24)|(X25=X22|X25=X23))))|X24=unordered_pair(X22,X23)))))),inference(variable_rename,status(thm),[c36])).
% 2.13/2.30 fof(c39,axiom,(![X17]:(![X18]:(![X19]:(![X20]:(![X21]:(![X22]:(![X23]:(![X24]:((X19!=unordered_pair(X17,X18)|((~in(X20,X19)|(X20=X17|X20=X18))&((X21!=X17&X21!=X18)|in(X21,X19))))&(((~in(skolem0007(X22,X23,X24),X24)|(skolem0007(X22,X23,X24)!=X22&skolem0007(X22,X23,X24)!=X23))&(in(skolem0007(X22,X23,X24),X24)|(skolem0007(X22,X23,X24)=X22|skolem0007(X22,X23,X24)=X23)))|X24=unordered_pair(X22,X23))))))))))),inference(shift_quantors,status(thm),[fof(c38,axiom,((![X17]:(![X18]:(![X19]:(X19!=unordered_pair(X17,X18)|((![X20]:(~in(X20,X19)|(X20=X17|X20=X18)))&(![X21]:((X21!=X17&X21!=X18)|in(X21,X19))))))))&(![X22]:(![X23]:(![X24]:(((~in(skolem0007(X22,X23,X24),X24)|(skolem0007(X22,X23,X24)!=X22&skolem0007(X22,X23,X24)!=X23))&(in(skolem0007(X22,X23,X24),X24)|(skolem0007(X22,X23,X24)=X22|skolem0007(X22,X23,X24)=X23)))|X24=unordered_pair(X22,X23)))))),inference(skolemize,status(esa),[c37])).])).
% 2.13/2.30 fof(c40,axiom,(![X17]:(![X18]:(![X19]:(![X20]:(![X21]:(![X22]:(![X23]:(![X24]:(((X19!=unordered_pair(X17,X18)|(~in(X20,X19)|(X20=X17|X20=X18)))&((X19!=unordered_pair(X17,X18)|(X21!=X17|in(X21,X19)))&(X19!=unordered_pair(X17,X18)|(X21!=X18|in(X21,X19)))))&((((~in(skolem0007(X22,X23,X24),X24)|skolem0007(X22,X23,X24)!=X22)|X24=unordered_pair(X22,X23))&((~in(skolem0007(X22,X23,X24),X24)|skolem0007(X22,X23,X24)!=X23)|X24=unordered_pair(X22,X23)))&((in(skolem0007(X22,X23,X24),X24)|(skolem0007(X22,X23,X24)=X22|skolem0007(X22,X23,X24)=X23))|X24=unordered_pair(X22,X23)))))))))))),inference(distribute,status(thm),[c39])).
% 2.13/2.30 cnf(c42,axiom,X182!=unordered_pair(X179,X181)|X180!=X179|in(X180,X182),inference(split_conjunct,status(thm),[c40])).
% 2.13/2.30 cnf(c280,plain,X210!=X211|in(X210,unordered_pair(X212,X211)),inference(resolution,status(thm),[c42, c60])).
% 2.13/2.30 cnf(c313,plain,in(X214,unordered_pair(X213,X214)),inference(resolution,status(thm),[c280, reflexivity])).
% 2.13/2.30 cnf(c11,negated_conjecture,in(skolem0002,skolem0003),inference(split_conjunct,status(thm),[c9])).
% 2.13/2.30 fof(d3_xboole_0,axiom,(![A]:(![B]:(![C]:(C=set_intersection2(A,B)<=>(![D]:(in(D,C)<=>(in(D,A)&in(D,B)))))))),input).
% 2.13/2.30 fof(c23,axiom,(![A]:(![B]:(![C]:((C!=set_intersection2(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_intersection2(A,B)))))),inference(fof_nnf,status(thm),[d3_xboole_0])).
% 2.13/2.30 fof(c24,axiom,((![A]:(![B]:(![C]:(C!=set_intersection2(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_intersection2(A,B)))))),inference(shift_quantors,status(thm),[c23])).
% 2.13/2.30 fof(c25,axiom,((![X8]:(![X9]:(![X10]:(X10!=set_intersection2(X8,X9)|((![X11]:(~in(X11,X10)|(in(X11,X8)&in(X11,X9))))&(![X12]:((~in(X12,X8)|~in(X12,X9))|in(X12,X10))))))))&(![X13]:(![X14]:(![X15]:((?[X16]:((~in(X16,X15)|(~in(X16,X13)|~in(X16,X14)))&(in(X16,X15)|(in(X16,X13)&in(X16,X14)))))|X15=set_intersection2(X13,X14)))))),inference(variable_rename,status(thm),[c24])).
% 2.13/2.30 fof(c27,axiom,(![X8]:(![X9]:(![X10]:(![X11]:(![X12]:(![X13]:(![X14]:(![X15]:((X10!=set_intersection2(X8,X9)|((~in(X11,X10)|(in(X11,X8)&in(X11,X9)))&((~in(X12,X8)|~in(X12,X9))|in(X12,X10))))&(((~in(skolem0006(X13,X14,X15),X15)|(~in(skolem0006(X13,X14,X15),X13)|~in(skolem0006(X13,X14,X15),X14)))&(in(skolem0006(X13,X14,X15),X15)|(in(skolem0006(X13,X14,X15),X13)&in(skolem0006(X13,X14,X15),X14))))|X15=set_intersection2(X13,X14))))))))))),inference(shift_quantors,status(thm),[fof(c26,axiom,((![X8]:(![X9]:(![X10]:(X10!=set_intersection2(X8,X9)|((![X11]:(~in(X11,X10)|(in(X11,X8)&in(X11,X9))))&(![X12]:((~in(X12,X8)|~in(X12,X9))|in(X12,X10))))))))&(![X13]:(![X14]:(![X15]:(((~in(skolem0006(X13,X14,X15),X15)|(~in(skolem0006(X13,X14,X15),X13)|~in(skolem0006(X13,X14,X15),X14)))&(in(skolem0006(X13,X14,X15),X15)|(in(skolem0006(X13,X14,X15),X13)&in(skolem0006(X13,X14,X15),X14))))|X15=set_intersection2(X13,X14)))))),inference(skolemize,status(esa),[c25])).])).
% 2.13/2.30 fof(c28,axiom,(![X8]:(![X9]:(![X10]:(![X11]:(![X12]:(![X13]:(![X14]:(![X15]:((((X10!=set_intersection2(X8,X9)|(~in(X11,X10)|in(X11,X8)))&(X10!=set_intersection2(X8,X9)|(~in(X11,X10)|in(X11,X9))))&(X10!=set_intersection2(X8,X9)|((~in(X12,X8)|~in(X12,X9))|in(X12,X10))))&(((~in(skolem0006(X13,X14,X15),X15)|(~in(skolem0006(X13,X14,X15),X13)|~in(skolem0006(X13,X14,X15),X14)))|X15=set_intersection2(X13,X14))&(((in(skolem0006(X13,X14,X15),X15)|in(skolem0006(X13,X14,X15),X13))|X15=set_intersection2(X13,X14))&((in(skolem0006(X13,X14,X15),X15)|in(skolem0006(X13,X14,X15),X14))|X15=set_intersection2(X13,X14))))))))))))),inference(distribute,status(thm),[c27])).
% 2.13/2.30 cnf(c31,axiom,X124!=set_intersection2(X125,X127)|~in(X126,X125)|~in(X126,X127)|in(X126,X124),inference(split_conjunct,status(thm),[c28])).
% 2.13/2.30 cnf(c165,plain,~in(X801,X800)|~in(X801,X799)|in(X801,set_intersection2(X800,X799)),inference(resolution,status(thm),[c31, reflexivity])).
% 2.13/2.30 cnf(c2848,plain,~in(skolem0002,X1138)|in(skolem0002,set_intersection2(X1138,skolem0003)),inference(resolution,status(thm),[c165, c11])).
% 2.13/2.30 cnf(c6232,plain,in(skolem0002,set_intersection2(unordered_pair(X1139,skolem0002),skolem0003)),inference(resolution,status(thm),[c2848, c313])).
% 2.13/2.30 cnf(c6262,plain,skolem0002=skolem0001,inference(resolution,status(thm),[c6232, c175])).
% 2.13/2.30 cnf(c6372,plain,skolem0001=skolem0002,inference(resolution,status(thm),[c6262, symmetry])).
% 2.13/2.30 cnf(c6424,plain,$false,inference(resolution,status(thm),[c6372, c12])).
% 2.13/2.30 # SZS output end CNFRefutation
% 2.13/2.30
% 2.13/2.30 # Initial clauses : 33
% 2.13/2.30 # Processed clauses : 320
% 2.13/2.30 # Factors computed : 13
% 2.13/2.30 # Resolvents computed: 6353
% 2.13/2.30 # Tautologies deleted: 9
% 2.13/2.30 # Forward subsumed : 352
% 2.13/2.30 # Backward subsumed : 0
% 2.13/2.30 # -------- CPU Time ---------
% 2.13/2.30 # User time : 1.912 s
% 2.13/2.30 # System time : 0.030 s
% 2.13/2.30 # Total time : 1.942 s
%------------------------------------------------------------------------------