TSTP Solution File: SET662+3 by PyRes---1.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n014.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 04:39:27 EDT 2022
% Result : Theorem 0.78s 1.01s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.35 % Computer : n014.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 03:40:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.78/1.01 # Version: 1.3
% 0.78/1.01 # SZS status Theorem
% 0.78/1.01 # SZS output start CNFRefutation
% 0.78/1.01 fof(prove_relset_1_25,conjecture,(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>ilf_type(empty_set,relation_type(B,C)))))),input).
% 0.78/1.01 fof(c12,negated_conjecture,(~(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>ilf_type(empty_set,relation_type(B,C))))))),inference(assume_negation,status(cth),[prove_relset_1_25])).
% 0.78/1.01 fof(c13,negated_conjecture,(?[B]:(ilf_type(B,set_type)&(?[C]:(ilf_type(C,set_type)&~ilf_type(empty_set,relation_type(B,C)))))),inference(fof_nnf,status(thm),[c12])).
% 0.78/1.01 fof(c14,negated_conjecture,(?[X2]:(ilf_type(X2,set_type)&(?[X3]:(ilf_type(X3,set_type)&~ilf_type(empty_set,relation_type(X2,X3)))))),inference(variable_rename,status(thm),[c13])).
% 0.78/1.01 fof(c15,negated_conjecture,(ilf_type(skolem0001,set_type)&(ilf_type(skolem0002,set_type)&~ilf_type(empty_set,relation_type(skolem0001,skolem0002)))),inference(skolemize,status(esa),[c14])).
% 0.78/1.01 cnf(c18,negated_conjecture,~ilf_type(empty_set,relation_type(skolem0001,skolem0002)),inference(split_conjunct,status(thm),[c15])).
% 0.78/1.01 fof(p20,axiom,(![B]:ilf_type(B,set_type)),input).
% 0.78/1.01 fof(c19,axiom,(![X4]:ilf_type(X4,set_type)),inference(variable_rename,status(thm),[p20])).
% 0.78/1.01 cnf(c20,axiom,ilf_type(X52,set_type),inference(split_conjunct,status(thm),[c19])).
% 0.78/1.01 fof(p2,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).
% 0.78/1.01 fof(c116,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),[p2])).
% 0.78/1.01 fof(c118,axiom,(![X45]:(![X46]:(![X47]:(![X48]:(~ilf_type(X45,set_type)|(~ilf_type(X46,set_type)|((~ilf_type(X47,subset_type(cross_product(X45,X46)))|ilf_type(X47,relation_type(X45,X46)))&(~ilf_type(X48,relation_type(X45,X46))|ilf_type(X48,subset_type(cross_product(X45,X46))))))))))),inference(shift_quantors,status(thm),[fof(c117,axiom,(![X45]:(~ilf_type(X45,set_type)|(![X46]:(~ilf_type(X46,set_type)|((![X47]:(~ilf_type(X47,subset_type(cross_product(X45,X46)))|ilf_type(X47,relation_type(X45,X46))))&(![X48]:(~ilf_type(X48,relation_type(X45,X46))|ilf_type(X48,subset_type(cross_product(X45,X46)))))))))),inference(variable_rename,status(thm),[c116])).])).
% 0.78/1.01 fof(c119,axiom,(![X45]:(![X46]:(![X47]:(![X48]:((~ilf_type(X45,set_type)|(~ilf_type(X46,set_type)|(~ilf_type(X47,subset_type(cross_product(X45,X46)))|ilf_type(X47,relation_type(X45,X46)))))&(~ilf_type(X45,set_type)|(~ilf_type(X46,set_type)|(~ilf_type(X48,relation_type(X45,X46))|ilf_type(X48,subset_type(cross_product(X45,X46))))))))))),inference(distribute,status(thm),[c118])).
% 0.78/1.01 cnf(c120,axiom,~ilf_type(X354,set_type)|~ilf_type(X353,set_type)|~ilf_type(X352,subset_type(cross_product(X354,X353)))|ilf_type(X352,relation_type(X354,X353)),inference(split_conjunct,status(thm),[c119])).
% 0.78/1.01 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).
% 0.78/1.01 fof(c95,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])).
% 0.78/1.01 fof(c97,axiom,(![X37]:(![X38]:(~ilf_type(X37,set_type)|(~ilf_type(X38,set_type)|((~ilf_type(X38,subset_type(X37))|ilf_type(X38,member_type(power_set(X37))))&(~ilf_type(X38,member_type(power_set(X37)))|ilf_type(X38,subset_type(X37)))))))),inference(shift_quantors,status(thm),[fof(c96,axiom,(![X37]:(~ilf_type(X37,set_type)|(![X38]:(~ilf_type(X38,set_type)|((~ilf_type(X38,subset_type(X37))|ilf_type(X38,member_type(power_set(X37))))&(~ilf_type(X38,member_type(power_set(X37)))|ilf_type(X38,subset_type(X37)))))))),inference(variable_rename,status(thm),[c95])).])).
% 0.78/1.01 fof(c98,axiom,(![X37]:(![X38]:((~ilf_type(X37,set_type)|(~ilf_type(X38,set_type)|(~ilf_type(X38,subset_type(X37))|ilf_type(X38,member_type(power_set(X37))))))&(~ilf_type(X37,set_type)|(~ilf_type(X38,set_type)|(~ilf_type(X38,member_type(power_set(X37)))|ilf_type(X38,subset_type(X37)))))))),inference(distribute,status(thm),[c97])).
% 0.78/1.01 cnf(c100,axiom,~ilf_type(X340,set_type)|~ilf_type(X339,set_type)|~ilf_type(X339,member_type(power_set(X340)))|ilf_type(X339,subset_type(X340)),inference(split_conjunct,status(thm),[c98])).
% 0.78/1.01 fof(p11,axiom,(![B]:(ilf_type(B,set_type)=>(empty(B)<=>(![C]:(ilf_type(C,set_type)=>(~member(C,B))))))),input).
% 0.78/1.01 fof(c70,axiom,(![B]:(ilf_type(B,set_type)=>(empty(B)<=>(![C]:(ilf_type(C,set_type)=>~member(C,B)))))),inference(fof_simplification,status(thm),[p11])).
% 0.78/1.01 fof(c71,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),[c70])).
% 0.78/1.01 fof(c72,axiom,(![X27]:(~ilf_type(X27,set_type)|((~empty(X27)|(![X28]:(~ilf_type(X28,set_type)|~member(X28,X27))))&((?[X29]:(ilf_type(X29,set_type)&member(X29,X27)))|empty(X27))))),inference(variable_rename,status(thm),[c71])).
% 0.78/1.01 fof(c74,axiom,(![X27]:(![X28]:(~ilf_type(X27,set_type)|((~empty(X27)|(~ilf_type(X28,set_type)|~member(X28,X27)))&((ilf_type(skolem0008(X27),set_type)&member(skolem0008(X27),X27))|empty(X27)))))),inference(shift_quantors,status(thm),[fof(c73,axiom,(![X27]:(~ilf_type(X27,set_type)|((~empty(X27)|(![X28]:(~ilf_type(X28,set_type)|~member(X28,X27))))&((ilf_type(skolem0008(X27),set_type)&member(skolem0008(X27),X27))|empty(X27))))),inference(skolemize,status(esa),[c72])).])).
% 0.78/1.01 fof(c75,axiom,(![X27]:(![X28]:((~ilf_type(X27,set_type)|(~empty(X27)|(~ilf_type(X28,set_type)|~member(X28,X27))))&((~ilf_type(X27,set_type)|(ilf_type(skolem0008(X27),set_type)|empty(X27)))&(~ilf_type(X27,set_type)|(member(skolem0008(X27),X27)|empty(X27))))))),inference(distribute,status(thm),[c74])).
% 0.78/1.01 cnf(c76,axiom,~ilf_type(X166,set_type)|~empty(X166)|~ilf_type(X165,set_type)|~member(X165,X166),inference(split_conjunct,status(thm),[c75])).
% 0.78/1.01 fof(p4,axiom,(![B]:(ilf_type(B,set_type)=>(~member(B,empty_set)))),input).
% 0.78/1.01 fof(c107,axiom,(![B]:(ilf_type(B,set_type)=>~member(B,empty_set))),inference(fof_simplification,status(thm),[p4])).
% 0.78/1.01 fof(c108,axiom,(![B]:(~ilf_type(B,set_type)|~member(B,empty_set))),inference(fof_nnf,status(thm),[c107])).
% 0.78/1.01 fof(c109,axiom,(![X41]:(~ilf_type(X41,set_type)|~member(X41,empty_set))),inference(variable_rename,status(thm),[c108])).
% 0.78/1.01 cnf(c110,axiom,~ilf_type(X74,set_type)|~member(X74,empty_set),inference(split_conjunct,status(thm),[c109])).
% 0.78/1.01 fof(p12,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).
% 0.78/1.01 fof(c61,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),[p12])).
% 0.78/1.01 fof(c62,axiom,(![X23]:(~ilf_type(X23,set_type)|(![X24]:(~ilf_type(X24,set_type)|((~member(X23,power_set(X24))|(![X25]:(~ilf_type(X25,set_type)|(~member(X25,X23)|member(X25,X24)))))&((?[X26]:(ilf_type(X26,set_type)&(member(X26,X23)&~member(X26,X24))))|member(X23,power_set(X24)))))))),inference(variable_rename,status(thm),[c61])).
% 0.78/1.01 fof(c64,axiom,(![X23]:(![X24]:(![X25]:(~ilf_type(X23,set_type)|(~ilf_type(X24,set_type)|((~member(X23,power_set(X24))|(~ilf_type(X25,set_type)|(~member(X25,X23)|member(X25,X24))))&((ilf_type(skolem0007(X23,X24),set_type)&(member(skolem0007(X23,X24),X23)&~member(skolem0007(X23,X24),X24)))|member(X23,power_set(X24))))))))),inference(shift_quantors,status(thm),[fof(c63,axiom,(![X23]:(~ilf_type(X23,set_type)|(![X24]:(~ilf_type(X24,set_type)|((~member(X23,power_set(X24))|(![X25]:(~ilf_type(X25,set_type)|(~member(X25,X23)|member(X25,X24)))))&((ilf_type(skolem0007(X23,X24),set_type)&(member(skolem0007(X23,X24),X23)&~member(skolem0007(X23,X24),X24)))|member(X23,power_set(X24)))))))),inference(skolemize,status(esa),[c62])).])).
% 0.78/1.01 fof(c65,axiom,(![X23]:(![X24]:(![X25]:((~ilf_type(X23,set_type)|(~ilf_type(X24,set_type)|(~member(X23,power_set(X24))|(~ilf_type(X25,set_type)|(~member(X25,X23)|member(X25,X24))))))&((~ilf_type(X23,set_type)|(~ilf_type(X24,set_type)|(ilf_type(skolem0007(X23,X24),set_type)|member(X23,power_set(X24)))))&((~ilf_type(X23,set_type)|(~ilf_type(X24,set_type)|(member(skolem0007(X23,X24),X23)|member(X23,power_set(X24)))))&(~ilf_type(X23,set_type)|(~ilf_type(X24,set_type)|(~member(skolem0007(X23,X24),X24)|member(X23,power_set(X24))))))))))),inference(distribute,status(thm),[c64])).
% 0.78/1.01 cnf(c68,axiom,~ilf_type(X275,set_type)|~ilf_type(X274,set_type)|member(skolem0007(X275,X274),X275)|member(X275,power_set(X274)),inference(split_conjunct,status(thm),[c65])).
% 0.78/1.01 cnf(c222,plain,~ilf_type(X289,set_type)|member(skolem0007(X289,X288),X289)|member(X289,power_set(X288)),inference(resolution,status(thm),[c68, c20])).
% 0.78/1.01 cnf(c234,plain,member(skolem0007(X290,X291),X290)|member(X290,power_set(X291)),inference(resolution,status(thm),[c222, c20])).
% 0.78/1.01 cnf(c235,plain,member(empty_set,power_set(X303))|~ilf_type(skolem0007(empty_set,X303),set_type),inference(resolution,status(thm),[c234, c110])).
% 0.78/1.01 cnf(c264,plain,member(empty_set,power_set(X304)),inference(resolution,status(thm),[c235, c20])).
% 0.78/1.01 cnf(c270,plain,~ilf_type(power_set(X319),set_type)|~empty(power_set(X319))|~ilf_type(empty_set,set_type),inference(resolution,status(thm),[c264, c76])).
% 0.78/1.01 cnf(c275,plain,~empty(power_set(X320))|~ilf_type(empty_set,set_type),inference(resolution,status(thm),[c270, c20])).
% 0.78/1.01 cnf(c276,plain,~empty(power_set(X321)),inference(resolution,status(thm),[c275, c20])).
% 0.78/1.01 fof(p14,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).
% 0.78/1.01 fof(c48,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),[p14])).
% 0.78/1.01 fof(c49,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),[c48])).
% 0.78/1.01 fof(c51,axiom,(![X20]:(![X21]:(~ilf_type(X20,set_type)|((empty(X21)|~ilf_type(X21,set_type))|((~ilf_type(X20,member_type(X21))|member(X20,X21))&(~member(X20,X21)|ilf_type(X20,member_type(X21)))))))),inference(shift_quantors,status(thm),[fof(c50,axiom,(![X20]:(~ilf_type(X20,set_type)|(![X21]:((empty(X21)|~ilf_type(X21,set_type))|((~ilf_type(X20,member_type(X21))|member(X20,X21))&(~member(X20,X21)|ilf_type(X20,member_type(X21)))))))),inference(variable_rename,status(thm),[c49])).])).
% 0.78/1.01 fof(c52,axiom,(![X20]:(![X21]:((~ilf_type(X20,set_type)|((empty(X21)|~ilf_type(X21,set_type))|(~ilf_type(X20,member_type(X21))|member(X20,X21))))&(~ilf_type(X20,set_type)|((empty(X21)|~ilf_type(X21,set_type))|(~member(X20,X21)|ilf_type(X20,member_type(X21)))))))),inference(distribute,status(thm),[c51])).
% 0.78/1.01 cnf(c54,axiom,~ilf_type(X236,set_type)|empty(X235)|~ilf_type(X235,set_type)|~member(X236,X235)|ilf_type(X236,member_type(X235)),inference(split_conjunct,status(thm),[c52])).
% 0.78/1.01 cnf(c268,plain,~ilf_type(empty_set,set_type)|empty(power_set(X862))|~ilf_type(power_set(X862),set_type)|ilf_type(empty_set,member_type(power_set(X862))),inference(resolution,status(thm),[c264, c54])).
% 0.78/1.01 cnf(c783,plain,~ilf_type(empty_set,set_type)|empty(power_set(X863))|ilf_type(empty_set,member_type(power_set(X863))),inference(resolution,status(thm),[c268, c20])).
% 0.78/1.01 cnf(c784,plain,empty(power_set(X864))|ilf_type(empty_set,member_type(power_set(X864))),inference(resolution,status(thm),[c783, c20])).
% 0.78/1.01 cnf(c787,plain,ilf_type(empty_set,member_type(power_set(X865))),inference(resolution,status(thm),[c784, c276])).
% 0.78/1.01 cnf(c794,plain,~ilf_type(X879,set_type)|~ilf_type(empty_set,set_type)|ilf_type(empty_set,subset_type(X879)),inference(resolution,status(thm),[c787, c100])).
% 0.78/1.01 cnf(c804,plain,~ilf_type(X882,set_type)|ilf_type(empty_set,subset_type(X882)),inference(resolution,status(thm),[c794, c20])).
% 0.78/1.01 cnf(c806,plain,ilf_type(empty_set,subset_type(X883)),inference(resolution,status(thm),[c804, c20])).
% 0.78/1.01 cnf(c810,plain,~ilf_type(X893,set_type)|~ilf_type(X894,set_type)|ilf_type(empty_set,relation_type(X893,X894)),inference(resolution,status(thm),[c806, c120])).
% 0.78/1.01 cnf(c814,plain,~ilf_type(X896,set_type)|ilf_type(empty_set,relation_type(X896,X895)),inference(resolution,status(thm),[c810, c20])).
% 0.78/1.01 cnf(c815,plain,ilf_type(empty_set,relation_type(X897,X898)),inference(resolution,status(thm),[c814, c20])).
% 0.78/1.01 cnf(c817,plain,$false,inference(resolution,status(thm),[c815, c18])).
% 0.78/1.01 # SZS output end CNFRefutation
% 0.78/1.01
% 0.78/1.01 # Initial clauses : 56
% 0.78/1.01 # Processed clauses : 294
% 0.78/1.01 # Factors computed : 4
% 0.78/1.01 # Resolvents computed: 689
% 0.78/1.01 # Tautologies deleted: 8
% 0.78/1.01 # Forward subsumed : 134
% 0.78/1.01 # Backward subsumed : 84
% 0.78/1.01 # -------- CPU Time ---------
% 0.78/1.01 # User time : 0.639 s
% 0.78/1.01 # System time : 0.014 s
% 0.78/1.01 # Total time : 0.653 s
%------------------------------------------------------------------------------