TSTP Solution File: SET643+3 by PyRes---1.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n028.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 04:39:20 EDT 2022
% Result : Theorem 0.78s 0.94s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 04:19:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.78/0.94 # Version: 1.3
% 0.78/0.94 # SZS status Theorem
% 0.78/0.94 # SZS output start CNFRefutation
% 0.78/0.94 fof(prove_relset_1_5,conjecture,(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>ilf_type(cross_product(B,C),relation_type(B,C)))))),input).
% 0.78/0.94 fof(c11,negated_conjecture,(~(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>ilf_type(cross_product(B,C),relation_type(B,C))))))),inference(assume_negation,status(cth),[prove_relset_1_5])).
% 0.78/0.94 fof(c12,negated_conjecture,(?[B]:(ilf_type(B,set_type)&(?[C]:(ilf_type(C,set_type)&~ilf_type(cross_product(B,C),relation_type(B,C)))))),inference(fof_nnf,status(thm),[c11])).
% 0.78/0.94 fof(c13,negated_conjecture,(?[X2]:(ilf_type(X2,set_type)&(?[X3]:(ilf_type(X3,set_type)&~ilf_type(cross_product(X2,X3),relation_type(X2,X3)))))),inference(variable_rename,status(thm),[c12])).
% 0.78/0.94 fof(c14,negated_conjecture,(ilf_type(skolem0001,set_type)&(ilf_type(skolem0002,set_type)&~ilf_type(cross_product(skolem0001,skolem0002),relation_type(skolem0001,skolem0002)))),inference(skolemize,status(esa),[c13])).
% 0.78/0.94 cnf(c17,negated_conjecture,~ilf_type(cross_product(skolem0001,skolem0002),relation_type(skolem0001,skolem0002)),inference(split_conjunct,status(thm),[c14])).
% 0.78/0.94 fof(p19,axiom,(![B]:ilf_type(B,set_type)),input).
% 0.78/0.94 fof(c18,axiom,(![X4]:ilf_type(X4,set_type)),inference(variable_rename,status(thm),[p19])).
% 0.78/0.94 cnf(c19,axiom,ilf_type(X59,set_type),inference(split_conjunct,status(thm),[c18])).
% 0.78/0.94 fof(p4,axiom,(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>((![D]:(ilf_type(D,subset_type(cross_product(B,C)))=>ilf_type(D,relation_type(B,C))))&(![E]:(ilf_type(E,relation_type(B,C))=>ilf_type(E,subset_type(cross_product(B,C)))))))))),input).
% 0.78/0.94 fof(c105,axiom,(![B]:(~ilf_type(B,set_type)|(![C]:(~ilf_type(C,set_type)|((![D]:(~ilf_type(D,subset_type(cross_product(B,C)))|ilf_type(D,relation_type(B,C))))&(![E]:(~ilf_type(E,relation_type(B,C))|ilf_type(E,subset_type(cross_product(B,C)))))))))),inference(fof_nnf,status(thm),[p4])).
% 0.78/0.94 fof(c107,axiom,(![X42]:(![X43]:(![X44]:(![X45]:(~ilf_type(X42,set_type)|(~ilf_type(X43,set_type)|((~ilf_type(X44,subset_type(cross_product(X42,X43)))|ilf_type(X44,relation_type(X42,X43)))&(~ilf_type(X45,relation_type(X42,X43))|ilf_type(X45,subset_type(cross_product(X42,X43))))))))))),inference(shift_quantors,status(thm),[fof(c106,axiom,(![X42]:(~ilf_type(X42,set_type)|(![X43]:(~ilf_type(X43,set_type)|((![X44]:(~ilf_type(X44,subset_type(cross_product(X42,X43)))|ilf_type(X44,relation_type(X42,X43))))&(![X45]:(~ilf_type(X45,relation_type(X42,X43))|ilf_type(X45,subset_type(cross_product(X42,X43)))))))))),inference(variable_rename,status(thm),[c105])).])).
% 0.78/0.94 fof(c108,axiom,(![X42]:(![X43]:(![X44]:(![X45]:((~ilf_type(X42,set_type)|(~ilf_type(X43,set_type)|(~ilf_type(X44,subset_type(cross_product(X42,X43)))|ilf_type(X44,relation_type(X42,X43)))))&(~ilf_type(X42,set_type)|(~ilf_type(X43,set_type)|(~ilf_type(X45,relation_type(X42,X43))|ilf_type(X45,subset_type(cross_product(X42,X43))))))))))),inference(distribute,status(thm),[c107])).
% 0.78/0.94 cnf(c109,axiom,~ilf_type(X337,set_type)|~ilf_type(X338,set_type)|~ilf_type(X339,subset_type(cross_product(X337,X338)))|ilf_type(X339,relation_type(X337,X338)),inference(split_conjunct,status(thm),[c108])).
% 0.78/0.94 fof(p7,axiom,(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>(ilf_type(C,subset_type(B))<=>ilf_type(C,member_type(power_set(B)))))))),input).
% 0.78/0.94 fof(c90,axiom,(![B]:(~ilf_type(B,set_type)|(![C]:(~ilf_type(C,set_type)|((~ilf_type(C,subset_type(B))|ilf_type(C,member_type(power_set(B))))&(~ilf_type(C,member_type(power_set(B)))|ilf_type(C,subset_type(B)))))))),inference(fof_nnf,status(thm),[p7])).
% 0.78/0.94 fof(c92,axiom,(![X35]:(![X36]:(~ilf_type(X35,set_type)|(~ilf_type(X36,set_type)|((~ilf_type(X36,subset_type(X35))|ilf_type(X36,member_type(power_set(X35))))&(~ilf_type(X36,member_type(power_set(X35)))|ilf_type(X36,subset_type(X35)))))))),inference(shift_quantors,status(thm),[fof(c91,axiom,(![X35]:(~ilf_type(X35,set_type)|(![X36]:(~ilf_type(X36,set_type)|((~ilf_type(X36,subset_type(X35))|ilf_type(X36,member_type(power_set(X35))))&(~ilf_type(X36,member_type(power_set(X35)))|ilf_type(X36,subset_type(X35)))))))),inference(variable_rename,status(thm),[c90])).])).
% 0.78/0.94 fof(c93,axiom,(![X35]:(![X36]:((~ilf_type(X35,set_type)|(~ilf_type(X36,set_type)|(~ilf_type(X36,subset_type(X35))|ilf_type(X36,member_type(power_set(X35))))))&(~ilf_type(X35,set_type)|(~ilf_type(X36,set_type)|(~ilf_type(X36,member_type(power_set(X35)))|ilf_type(X36,subset_type(X35)))))))),inference(distribute,status(thm),[c92])).
% 0.78/0.94 cnf(c95,axiom,~ilf_type(X322,set_type)|~ilf_type(X321,set_type)|~ilf_type(X321,member_type(power_set(X322)))|ilf_type(X321,subset_type(X322)),inference(split_conjunct,status(thm),[c93])).
% 0.78/0.94 fof(p12,axiom,(![B]:(ilf_type(B,set_type)=>((~empty(power_set(B)))&ilf_type(power_set(B),set_type)))),input).
% 0.78/0.94 fof(c59,axiom,(![B]:(ilf_type(B,set_type)=>(~empty(power_set(B))&ilf_type(power_set(B),set_type)))),inference(fof_simplification,status(thm),[p12])).
% 0.78/0.94 fof(c60,axiom,(![B]:(~ilf_type(B,set_type)|(~empty(power_set(B))&ilf_type(power_set(B),set_type)))),inference(fof_nnf,status(thm),[c59])).
% 0.78/0.94 fof(c61,axiom,(![X23]:(~ilf_type(X23,set_type)|(~empty(power_set(X23))&ilf_type(power_set(X23),set_type)))),inference(variable_rename,status(thm),[c60])).
% 0.78/0.94 fof(c62,axiom,(![X23]:((~ilf_type(X23,set_type)|~empty(power_set(X23)))&(~ilf_type(X23,set_type)|ilf_type(power_set(X23),set_type)))),inference(distribute,status(thm),[c61])).
% 0.78/0.94 cnf(c63,axiom,~ilf_type(X80,set_type)|~empty(power_set(X80)),inference(split_conjunct,status(thm),[c62])).
% 0.78/0.94 fof(p15,axiom,(![B]:(ilf_type(B,set_type)=>(empty(B)<=>(![C]:(ilf_type(C,set_type)=>(~member(C,B))))))),input).
% 0.78/0.94 fof(c38,axiom,(![B]:(ilf_type(B,set_type)=>(empty(B)<=>(![C]:(ilf_type(C,set_type)=>~member(C,B)))))),inference(fof_simplification,status(thm),[p15])).
% 0.78/0.94 fof(c39,axiom,(![B]:(~ilf_type(B,set_type)|((~empty(B)|(![C]:(~ilf_type(C,set_type)|~member(C,B))))&((?[C]:(ilf_type(C,set_type)&member(C,B)))|empty(B))))),inference(fof_nnf,status(thm),[c38])).
% 0.78/0.94 fof(c40,axiom,(![X16]:(~ilf_type(X16,set_type)|((~empty(X16)|(![X17]:(~ilf_type(X17,set_type)|~member(X17,X16))))&((?[X18]:(ilf_type(X18,set_type)&member(X18,X16)))|empty(X16))))),inference(variable_rename,status(thm),[c39])).
% 0.78/0.94 fof(c42,axiom,(![X16]:(![X17]:(~ilf_type(X16,set_type)|((~empty(X16)|(~ilf_type(X17,set_type)|~member(X17,X16)))&((ilf_type(skolem0006(X16),set_type)&member(skolem0006(X16),X16))|empty(X16)))))),inference(shift_quantors,status(thm),[fof(c41,axiom,(![X16]:(~ilf_type(X16,set_type)|((~empty(X16)|(![X17]:(~ilf_type(X17,set_type)|~member(X17,X16))))&((ilf_type(skolem0006(X16),set_type)&member(skolem0006(X16),X16))|empty(X16))))),inference(skolemize,status(esa),[c40])).])).
% 0.78/0.94 fof(c43,axiom,(![X16]:(![X17]:((~ilf_type(X16,set_type)|(~empty(X16)|(~ilf_type(X17,set_type)|~member(X17,X16))))&((~ilf_type(X16,set_type)|(ilf_type(skolem0006(X16),set_type)|empty(X16)))&(~ilf_type(X16,set_type)|(member(skolem0006(X16),X16)|empty(X16))))))),inference(distribute,status(thm),[c42])).
% 0.78/0.94 cnf(c46,axiom,~ilf_type(X124,set_type)|member(skolem0006(X124),X124)|empty(X124),inference(split_conjunct,status(thm),[c43])).
% 0.78/0.94 cnf(c150,plain,member(skolem0006(X125),X125)|empty(X125),inference(resolution,status(thm),[c46, c19])).
% 0.78/0.94 cnf(c151,plain,member(skolem0006(power_set(X151)),power_set(X151))|~ilf_type(X151,set_type),inference(resolution,status(thm),[c150, c63])).
% 0.78/0.94 cnf(c160,plain,member(skolem0006(power_set(X154)),power_set(X154)),inference(resolution,status(thm),[c151, c19])).
% 0.78/0.94 cnf(c44,axiom,~ilf_type(X167,set_type)|~empty(X167)|~ilf_type(X166,set_type)|~member(X166,X167),inference(split_conjunct,status(thm),[c43])).
% 0.78/0.94 cnf(c172,plain,~ilf_type(power_set(X363),set_type)|~empty(power_set(X363))|~ilf_type(skolem0006(power_set(X363)),set_type),inference(resolution,status(thm),[c44, c160])).
% 0.78/0.94 cnf(c285,plain,~ilf_type(power_set(X364),set_type)|~empty(power_set(X364)),inference(resolution,status(thm),[c172, c19])).
% 0.78/0.94 cnf(c286,plain,~empty(power_set(X365)),inference(resolution,status(thm),[c285, c19])).
% 0.78/0.94 fof(p13,axiom,(![B]:(ilf_type(B,set_type)=>(![C]:(((~empty(C))&ilf_type(C,set_type))=>(ilf_type(B,member_type(C))<=>member(B,C)))))),input).
% 0.78/0.94 fof(c52,axiom,(![B]:(ilf_type(B,set_type)=>(![C]:((~empty(C)&ilf_type(C,set_type))=>(ilf_type(B,member_type(C))<=>member(B,C)))))),inference(fof_simplification,status(thm),[p13])).
% 0.78/0.94 fof(c53,axiom,(![B]:(~ilf_type(B,set_type)|(![C]:((empty(C)|~ilf_type(C,set_type))|((~ilf_type(B,member_type(C))|member(B,C))&(~member(B,C)|ilf_type(B,member_type(C)))))))),inference(fof_nnf,status(thm),[c52])).
% 0.78/0.94 fof(c55,axiom,(![X21]:(![X22]:(~ilf_type(X21,set_type)|((empty(X22)|~ilf_type(X22,set_type))|((~ilf_type(X21,member_type(X22))|member(X21,X22))&(~member(X21,X22)|ilf_type(X21,member_type(X22)))))))),inference(shift_quantors,status(thm),[fof(c54,axiom,(![X21]:(~ilf_type(X21,set_type)|(![X22]:((empty(X22)|~ilf_type(X22,set_type))|((~ilf_type(X21,member_type(X22))|member(X21,X22))&(~member(X21,X22)|ilf_type(X21,member_type(X22)))))))),inference(variable_rename,status(thm),[c53])).])).
% 0.78/0.94 fof(c56,axiom,(![X21]:(![X22]:((~ilf_type(X21,set_type)|((empty(X22)|~ilf_type(X22,set_type))|(~ilf_type(X21,member_type(X22))|member(X21,X22))))&(~ilf_type(X21,set_type)|((empty(X22)|~ilf_type(X22,set_type))|(~member(X21,X22)|ilf_type(X21,member_type(X22)))))))),inference(distribute,status(thm),[c55])).
% 0.78/0.94 cnf(c58,axiom,~ilf_type(X208,set_type)|empty(X209)|~ilf_type(X209,set_type)|~member(X208,X209)|ilf_type(X208,member_type(X209)),inference(split_conjunct,status(thm),[c56])).
% 0.78/0.94 fof(p11,axiom,(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>(member(B,power_set(C))<=>(![D]:(ilf_type(D,set_type)=>(member(D,B)=>member(D,C))))))))),input).
% 0.78/0.94 fof(c65,axiom,(![B]:(~ilf_type(B,set_type)|(![C]:(~ilf_type(C,set_type)|((~member(B,power_set(C))|(![D]:(~ilf_type(D,set_type)|(~member(D,B)|member(D,C)))))&((?[D]:(ilf_type(D,set_type)&(member(D,B)&~member(D,C))))|member(B,power_set(C)))))))),inference(fof_nnf,status(thm),[p11])).
% 0.78/0.94 fof(c66,axiom,(![X24]:(~ilf_type(X24,set_type)|(![X25]:(~ilf_type(X25,set_type)|((~member(X24,power_set(X25))|(![X26]:(~ilf_type(X26,set_type)|(~member(X26,X24)|member(X26,X25)))))&((?[X27]:(ilf_type(X27,set_type)&(member(X27,X24)&~member(X27,X25))))|member(X24,power_set(X25)))))))),inference(variable_rename,status(thm),[c65])).
% 0.78/0.94 fof(c68,axiom,(![X24]:(![X25]:(![X26]:(~ilf_type(X24,set_type)|(~ilf_type(X25,set_type)|((~member(X24,power_set(X25))|(~ilf_type(X26,set_type)|(~member(X26,X24)|member(X26,X25))))&((ilf_type(skolem0008(X24,X25),set_type)&(member(skolem0008(X24,X25),X24)&~member(skolem0008(X24,X25),X25)))|member(X24,power_set(X25))))))))),inference(shift_quantors,status(thm),[fof(c67,axiom,(![X24]:(~ilf_type(X24,set_type)|(![X25]:(~ilf_type(X25,set_type)|((~member(X24,power_set(X25))|(![X26]:(~ilf_type(X26,set_type)|(~member(X26,X24)|member(X26,X25)))))&((ilf_type(skolem0008(X24,X25),set_type)&(member(skolem0008(X24,X25),X24)&~member(skolem0008(X24,X25),X25)))|member(X24,power_set(X25)))))))),inference(skolemize,status(esa),[c66])).])).
% 0.78/0.94 fof(c69,axiom,(![X24]:(![X25]:(![X26]:((~ilf_type(X24,set_type)|(~ilf_type(X25,set_type)|(~member(X24,power_set(X25))|(~ilf_type(X26,set_type)|(~member(X26,X24)|member(X26,X25))))))&((~ilf_type(X24,set_type)|(~ilf_type(X25,set_type)|(ilf_type(skolem0008(X24,X25),set_type)|member(X24,power_set(X25)))))&((~ilf_type(X24,set_type)|(~ilf_type(X25,set_type)|(member(skolem0008(X24,X25),X24)|member(X24,power_set(X25)))))&(~ilf_type(X24,set_type)|(~ilf_type(X25,set_type)|(~member(skolem0008(X24,X25),X25)|member(X24,power_set(X25))))))))))),inference(distribute,status(thm),[c68])).
% 0.78/0.94 cnf(c72,axiom,~ilf_type(X244,set_type)|~ilf_type(X243,set_type)|member(skolem0008(X244,X243),X244)|member(X244,power_set(X243)),inference(split_conjunct,status(thm),[c69])).
% 0.78/0.94 cnf(c209,plain,~ilf_type(X251,set_type)|member(skolem0008(X251,X250),X251)|member(X251,power_set(X250)),inference(resolution,status(thm),[c72, c19])).
% 0.78/0.94 cnf(c211,plain,member(skolem0008(X252,X253),X252)|member(X252,power_set(X253)),inference(resolution,status(thm),[c209, c19])).
% 0.78/0.94 cnf(c73,axiom,~ilf_type(X258,set_type)|~ilf_type(X257,set_type)|~member(skolem0008(X258,X257),X257)|member(X258,power_set(X257)),inference(split_conjunct,status(thm),[c69])).
% 0.78/0.94 cnf(c224,plain,~ilf_type(X259,set_type)|member(X259,power_set(X259)),inference(resolution,status(thm),[c73, c211])).
% 0.78/0.94 cnf(c225,plain,member(X260,power_set(X260)),inference(resolution,status(thm),[c224, c19])).
% 0.78/0.94 cnf(c226,plain,~ilf_type(X744,set_type)|empty(power_set(X744))|~ilf_type(power_set(X744),set_type)|ilf_type(X744,member_type(power_set(X744))),inference(resolution,status(thm),[c225, c58])).
% 0.78/0.94 cnf(c689,plain,~ilf_type(X747,set_type)|empty(power_set(X747))|ilf_type(X747,member_type(power_set(X747))),inference(resolution,status(thm),[c226, c19])).
% 0.78/0.94 cnf(c690,plain,empty(power_set(X748))|ilf_type(X748,member_type(power_set(X748))),inference(resolution,status(thm),[c689, c19])).
% 0.78/0.94 cnf(c692,plain,ilf_type(X749,member_type(power_set(X749))),inference(resolution,status(thm),[c690, c286])).
% 0.78/0.94 cnf(c700,plain,~ilf_type(X750,set_type)|ilf_type(X750,subset_type(X750)),inference(resolution,status(thm),[c692, c95])).
% 0.78/0.94 cnf(c701,plain,ilf_type(X752,subset_type(X752)),inference(resolution,status(thm),[c700, c19])).
% 0.78/0.94 cnf(c703,plain,~ilf_type(X785,set_type)|~ilf_type(X784,set_type)|ilf_type(cross_product(X785,X784),relation_type(X785,X784)),inference(resolution,status(thm),[c701, c109])).
% 0.78/0.94 cnf(c716,plain,~ilf_type(X786,set_type)|ilf_type(cross_product(X786,X787),relation_type(X786,X787)),inference(resolution,status(thm),[c703, c19])).
% 0.78/0.94 cnf(c717,plain,ilf_type(cross_product(X788,X789),relation_type(X788,X789)),inference(resolution,status(thm),[c716, c19])).
% 0.78/0.94 cnf(c720,plain,$false,inference(resolution,status(thm),[c717, c17])).
% 0.78/0.94 # SZS output end CNFRefutation
% 0.78/0.94
% 0.78/0.94 # Initial clauses : 58
% 0.78/0.94 # Processed clauses : 249
% 0.78/0.94 # Factors computed : 3
% 0.78/0.94 # Resolvents computed: 588
% 0.78/0.94 # Tautologies deleted: 8
% 0.78/0.94 # Forward subsumed : 100
% 0.78/0.94 # Backward subsumed : 63
% 0.78/0.94 # -------- CPU Time ---------
% 0.78/0.94 # User time : 0.568 s
% 0.78/0.94 # System time : 0.017 s
% 0.78/0.94 # Total time : 0.585 s
%------------------------------------------------------------------------------