TSTP Solution File: SET663+3 by PyRes---1.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : SET663+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n029.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 04:39:28 EDT 2022
% Result : Theorem 44.52s 44.75s
% Output : Refutation 44.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET663+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 09:55:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 44.52/44.75 # Version: 1.3
% 44.52/44.75 # SZS status Theorem
% 44.52/44.75 # SZS output start CNFRefutation
% 44.52/44.75 fof(prove_relset_1_26,conjecture,(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>(![D]:(ilf_type(D,relation_type(B,C))=>(ilf_type(D,relation_type(empty_set,C))=>D=empty_set))))))),input).
% 44.52/44.75 fof(c16,negated_conjecture,(~(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>(![D]:(ilf_type(D,relation_type(B,C))=>(ilf_type(D,relation_type(empty_set,C))=>D=empty_set)))))))),inference(assume_negation,status(cth),[prove_relset_1_26])).
% 44.52/44.75 fof(c17,negated_conjecture,(?[B]:(ilf_type(B,set_type)&(?[C]:(ilf_type(C,set_type)&(?[D]:(ilf_type(D,relation_type(B,C))&(ilf_type(D,relation_type(empty_set,C))&D!=empty_set))))))),inference(fof_nnf,status(thm),[c16])).
% 44.52/44.75 fof(c18,negated_conjecture,(?[X2]:(ilf_type(X2,set_type)&(?[X3]:(ilf_type(X3,set_type)&(?[X4]:(ilf_type(X4,relation_type(X2,X3))&(ilf_type(X4,relation_type(empty_set,X3))&X4!=empty_set))))))),inference(variable_rename,status(thm),[c17])).
% 44.52/44.75 fof(c19,negated_conjecture,(ilf_type(skolem0001,set_type)&(ilf_type(skolem0002,set_type)&(ilf_type(skolem0003,relation_type(skolem0001,skolem0002))&(ilf_type(skolem0003,relation_type(empty_set,skolem0002))&skolem0003!=empty_set)))),inference(skolemize,status(esa),[c18])).
% 44.52/44.75 cnf(c24,negated_conjecture,skolem0003!=empty_set,inference(split_conjunct,status(thm),[c19])).
% 44.52/44.75 fof(p33,axiom,(![B]:ilf_type(B,set_type)),input).
% 44.52/44.75 fof(c25,axiom,(![X5]:ilf_type(X5,set_type)),inference(variable_rename,status(thm),[p33])).
% 44.52/44.75 cnf(c26,axiom,ilf_type(X81,set_type),inference(split_conjunct,status(thm),[c25])).
% 44.52/44.75 fof(p13,axiom,(![B]:(ilf_type(B,set_type)=>(ilf_type(B,binary_relation_type)<=>(relation_like(B)&ilf_type(B,set_type))))),input).
% 44.52/44.75 fof(c129,axiom,(![B]:(~ilf_type(B,set_type)|((~ilf_type(B,binary_relation_type)|(relation_like(B)&ilf_type(B,set_type)))&((~relation_like(B)|~ilf_type(B,set_type))|ilf_type(B,binary_relation_type))))),inference(fof_nnf,status(thm),[p13])).
% 44.52/44.75 fof(c130,axiom,(![X54]:(~ilf_type(X54,set_type)|((~ilf_type(X54,binary_relation_type)|(relation_like(X54)&ilf_type(X54,set_type)))&((~relation_like(X54)|~ilf_type(X54,set_type))|ilf_type(X54,binary_relation_type))))),inference(variable_rename,status(thm),[c129])).
% 44.52/44.75 fof(c131,axiom,(![X54]:(((~ilf_type(X54,set_type)|(~ilf_type(X54,binary_relation_type)|relation_like(X54)))&(~ilf_type(X54,set_type)|(~ilf_type(X54,binary_relation_type)|ilf_type(X54,set_type))))&(~ilf_type(X54,set_type)|((~relation_like(X54)|~ilf_type(X54,set_type))|ilf_type(X54,binary_relation_type))))),inference(distribute,status(thm),[c130])).
% 44.52/44.75 cnf(c134,axiom,~ilf_type(X257,set_type)|~relation_like(X257)|~ilf_type(X257,set_type)|ilf_type(X257,binary_relation_type),inference(split_conjunct,status(thm),[c131])).
% 44.52/44.75 cnf(c269,plain,~ilf_type(X258,set_type)|~relation_like(X258)|ilf_type(X258,binary_relation_type),inference(resolution,status(thm),[c134, c26])).
% 44.52/44.75 cnf(c270,plain,~relation_like(X261)|ilf_type(X261,binary_relation_type),inference(resolution,status(thm),[c269, c26])).
% 44.52/44.75 fof(p28,axiom,(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>(![D]:(ilf_type(D,subset_type(cross_product(B,C)))=>relation_like(D))))))),input).
% 44.52/44.75 fof(c43,axiom,(![B]:(~ilf_type(B,set_type)|(![C]:(~ilf_type(C,set_type)|(![D]:(~ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D))))))),inference(fof_nnf,status(thm),[p28])).
% 44.52/44.75 fof(c45,axiom,(![X18]:(![X19]:(![X20]:(~ilf_type(X18,set_type)|(~ilf_type(X19,set_type)|(~ilf_type(X20,subset_type(cross_product(X18,X19)))|relation_like(X20))))))),inference(shift_quantors,status(thm),[fof(c44,axiom,(![X18]:(~ilf_type(X18,set_type)|(![X19]:(~ilf_type(X19,set_type)|(![X20]:(~ilf_type(X20,subset_type(cross_product(X18,X19)))|relation_like(X20))))))),inference(variable_rename,status(thm),[c43])).])).
% 44.52/44.75 cnf(c46,axiom,~ilf_type(X252,set_type)|~ilf_type(X250,set_type)|~ilf_type(X251,subset_type(cross_product(X252,X250)))|relation_like(X251),inference(split_conjunct,status(thm),[c45])).
% 44.52/44.75 cnf(c23,negated_conjecture,ilf_type(skolem0003,relation_type(empty_set,skolem0002)),inference(split_conjunct,status(thm),[c19])).
% 44.52/44.75 fof(p6,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).
% 44.52/44.75 fof(c165,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),[p6])).
% 44.52/44.75 fof(c167,axiom,(![X70]:(![X71]:(![X72]:(![X73]:(~ilf_type(X70,set_type)|(~ilf_type(X71,set_type)|((~ilf_type(X72,subset_type(cross_product(X70,X71)))|ilf_type(X72,relation_type(X70,X71)))&(~ilf_type(X73,relation_type(X70,X71))|ilf_type(X73,subset_type(cross_product(X70,X71))))))))))),inference(shift_quantors,status(thm),[fof(c166,axiom,(![X70]:(~ilf_type(X70,set_type)|(![X71]:(~ilf_type(X71,set_type)|((![X72]:(~ilf_type(X72,subset_type(cross_product(X70,X71)))|ilf_type(X72,relation_type(X70,X71))))&(![X73]:(~ilf_type(X73,relation_type(X70,X71))|ilf_type(X73,subset_type(cross_product(X70,X71)))))))))),inference(variable_rename,status(thm),[c165])).])).
% 44.52/44.75 fof(c168,axiom,(![X70]:(![X71]:(![X72]:(![X73]:((~ilf_type(X70,set_type)|(~ilf_type(X71,set_type)|(~ilf_type(X72,subset_type(cross_product(X70,X71)))|ilf_type(X72,relation_type(X70,X71)))))&(~ilf_type(X70,set_type)|(~ilf_type(X71,set_type)|(~ilf_type(X73,relation_type(X70,X71))|ilf_type(X73,subset_type(cross_product(X70,X71))))))))))),inference(distribute,status(thm),[c167])).
% 44.52/44.75 cnf(c170,axiom,~ilf_type(X459,set_type)|~ilf_type(X461,set_type)|~ilf_type(X460,relation_type(X459,X461))|ilf_type(X460,subset_type(cross_product(X459,X461))),inference(split_conjunct,status(thm),[c168])).
% 44.52/44.75 cnf(c748,plain,~ilf_type(empty_set,set_type)|~ilf_type(skolem0002,set_type)|ilf_type(skolem0003,subset_type(cross_product(empty_set,skolem0002))),inference(resolution,status(thm),[c170, c23])).
% 44.52/44.75 cnf(c47869,plain,~ilf_type(empty_set,set_type)|ilf_type(skolem0003,subset_type(cross_product(empty_set,skolem0002))),inference(resolution,status(thm),[c748, c26])).
% 44.52/44.75 cnf(c47870,plain,ilf_type(skolem0003,subset_type(cross_product(empty_set,skolem0002))),inference(resolution,status(thm),[c47869, c26])).
% 44.52/44.75 cnf(c47871,plain,~ilf_type(empty_set,set_type)|~ilf_type(skolem0002,set_type)|relation_like(skolem0003),inference(resolution,status(thm),[c47870, c46])).
% 44.52/44.75 cnf(c47875,plain,~ilf_type(empty_set,set_type)|relation_like(skolem0003),inference(resolution,status(thm),[c47871, c26])).
% 44.52/44.75 cnf(c47876,plain,relation_like(skolem0003),inference(resolution,status(thm),[c47875, c26])).
% 44.52/44.75 cnf(c47877,plain,ilf_type(skolem0003,binary_relation_type),inference(resolution,status(thm),[c47876, c270])).
% 44.52/44.75 fof(p2,axiom,(![B]:(ilf_type(B,binary_relation_type)=>((domain_of(B)=empty_set|range_of(B)=empty_set)=>B=empty_set))),input).
% 44.52/44.75 fof(c183,axiom,(![B]:(~ilf_type(B,binary_relation_type)|((domain_of(B)!=empty_set&range_of(B)!=empty_set)|B=empty_set))),inference(fof_nnf,status(thm),[p2])).
% 44.52/44.75 fof(c184,axiom,(![X78]:(~ilf_type(X78,binary_relation_type)|((domain_of(X78)!=empty_set&range_of(X78)!=empty_set)|X78=empty_set))),inference(variable_rename,status(thm),[c183])).
% 44.52/44.75 fof(c185,axiom,(![X78]:((~ilf_type(X78,binary_relation_type)|(domain_of(X78)!=empty_set|X78=empty_set))&(~ilf_type(X78,binary_relation_type)|(range_of(X78)!=empty_set|X78=empty_set)))),inference(distribute,status(thm),[c184])).
% 44.52/44.75 cnf(c186,axiom,~ilf_type(X224,binary_relation_type)|domain_of(X224)!=empty_set|X224=empty_set,inference(split_conjunct,status(thm),[c185])).
% 44.52/44.75 fof(p1,axiom,(![B]:(ilf_type(B,set_type)=>(subset(B,empty_set)=>B=empty_set))),input).
% 44.52/44.75 fof(c188,axiom,(![B]:(~ilf_type(B,set_type)|(~subset(B,empty_set)|B=empty_set))),inference(fof_nnf,status(thm),[p1])).
% 44.52/44.75 fof(c189,axiom,(![X79]:(~ilf_type(X79,set_type)|(~subset(X79,empty_set)|X79=empty_set))),inference(variable_rename,status(thm),[c188])).
% 44.52/44.75 cnf(c190,axiom,~ilf_type(X204,set_type)|~subset(X204,empty_set)|X204=empty_set,inference(split_conjunct,status(thm),[c189])).
% 44.52/44.75 fof(p3,axiom,(![B]:(ilf_type(B,set_type)=>(![C]:(ilf_type(C,set_type)=>(![D]:(ilf_type(D,relation_type(B,C))=>(subset(domain_of(D),B)&subset(range_of(D),C)))))))),input).
% 44.52/44.75 fof(c177,axiom,(![B]:(~ilf_type(B,set_type)|(![C]:(~ilf_type(C,set_type)|(![D]:(~ilf_type(D,relation_type(B,C))|(subset(domain_of(D),B)&subset(range_of(D),C)))))))),inference(fof_nnf,status(thm),[p3])).
% 44.52/44.75 fof(c179,axiom,(![X75]:(![X76]:(![X77]:(~ilf_type(X75,set_type)|(~ilf_type(X76,set_type)|(~ilf_type(X77,relation_type(X75,X76))|(subset(domain_of(X77),X75)&subset(range_of(X77),X76)))))))),inference(shift_quantors,status(thm),[fof(c178,axiom,(![X75]:(~ilf_type(X75,set_type)|(![X76]:(~ilf_type(X76,set_type)|(![X77]:(~ilf_type(X77,relation_type(X75,X76))|(subset(domain_of(X77),X75)&subset(range_of(X77),X76)))))))),inference(variable_rename,status(thm),[c177])).])).
% 44.52/44.75 fof(c180,axiom,(![X75]:(![X76]:(![X77]:((~ilf_type(X75,set_type)|(~ilf_type(X76,set_type)|(~ilf_type(X77,relation_type(X75,X76))|subset(domain_of(X77),X75))))&(~ilf_type(X75,set_type)|(~ilf_type(X76,set_type)|(~ilf_type(X77,relation_type(X75,X76))|subset(range_of(X77),X76)))))))),inference(distribute,status(thm),[c179])).
% 44.52/44.75 cnf(c181,axiom,~ilf_type(X467,set_type)|~ilf_type(X469,set_type)|~ilf_type(X468,relation_type(X467,X469))|subset(domain_of(X468),X467),inference(split_conjunct,status(thm),[c180])).
% 44.52/44.75 cnf(c922,plain,~ilf_type(empty_set,set_type)|~ilf_type(skolem0002,set_type)|subset(domain_of(skolem0003),empty_set),inference(resolution,status(thm),[c181, c23])).
% 44.52/44.75 cnf(c71390,plain,~ilf_type(empty_set,set_type)|subset(domain_of(skolem0003),empty_set),inference(resolution,status(thm),[c922, c26])).
% 44.52/44.75 cnf(c71427,plain,subset(domain_of(skolem0003),empty_set),inference(resolution,status(thm),[c71390, c26])).
% 44.52/44.75 cnf(c71429,plain,~ilf_type(domain_of(skolem0003),set_type)|domain_of(skolem0003)=empty_set,inference(resolution,status(thm),[c71427, c190])).
% 44.52/44.75 cnf(c71775,plain,domain_of(skolem0003)=empty_set,inference(resolution,status(thm),[c71429, c26])).
% 44.52/44.75 cnf(c71899,plain,~ilf_type(skolem0003,binary_relation_type)|skolem0003=empty_set,inference(resolution,status(thm),[c71775, c186])).
% 44.52/44.75 cnf(c74116,plain,skolem0003=empty_set,inference(resolution,status(thm),[c71899, c47877])).
% 44.52/44.75 cnf(c74254,plain,$false,inference(resolution,status(thm),[c74116, c24])).
% 44.52/44.75 # SZS output end CNFRefutation
% 44.52/44.75
% 44.52/44.75 # Initial clauses : 84
% 44.52/44.75 # Processed clauses : 1715
% 44.52/44.75 # Factors computed : 19
% 44.52/44.75 # Resolvents computed: 74078
% 44.52/44.75 # Tautologies deleted: 11
% 44.52/44.75 # Forward subsumed : 1324
% 44.52/44.75 # Backward subsumed : 151
% 44.52/44.75 # -------- CPU Time ---------
% 44.52/44.75 # User time : 44.190 s
% 44.52/44.75 # System time : 0.204 s
% 44.52/44.75 # Total time : 44.394 s
%------------------------------------------------------------------------------