0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.12 % Command : vampire --mode casc -t %d %s 0.12/0.33 % Computer : n027.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 : 960 0.12/0.33 % DateTime : Thu Jul 2 08:41:16 EDT 2020 0.12/0.33 % CPUTime : 0.12/0.39 % lrs-11_12_av=off:nm=32:nwc=1.3:stl=30:sd=3:ss=axioms:sos=all_2 on theBenchmark 0.17/0.41 % Refutation found. Thanks to Tanya! 0.17/0.41 % SZS status Theorem for theBenchmark 0.17/0.41 % SZS output start Proof for theBenchmark 0.17/0.41 fof(f593,plain,( 0.17/0.41 $false), 0.17/0.41 inference(subsumption_resolution,[],[f592,f591])). 0.17/0.41 fof(f591,plain,( 0.17/0.41 member(sK6(sK0,sK0),sK0)), 0.17/0.41 inference(resolution,[],[f590,f66])). 0.17/0.41 fof(f66,plain,( 0.17/0.41 ( ! [X0,X1] : (subset(X0,X1) | member(sK6(X0,X1),X0)) )), 0.17/0.41 inference(cnf_transformation,[],[f40])). 0.17/0.41 fof(f40,plain,( 0.17/0.41 ! [X0,X1] : (subset(X0,X1) | (~member(sK6(X0,X1),X1) & member(sK6(X0,X1),X0)))), 0.17/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f30,f39])). 0.17/0.41 fof(f39,plain,( 0.17/0.41 ! [X1,X0] : (? [X2] : (~member(X2,X1) & member(X2,X0)) => (~member(sK6(X0,X1),X1) & member(sK6(X0,X1),X0)))), 0.17/0.41 introduced(choice_axiom,[])). 0.17/0.41 fof(f30,plain,( 0.17/0.41 ! [X0,X1] : (subset(X0,X1) | ? [X2] : (~member(X2,X1) & member(X2,X0)))), 0.17/0.41 inference(ennf_transformation,[],[f26])). 0.17/0.41 fof(f26,plain,( 0.17/0.41 ! [X0,X1] : (! [X2] : (member(X2,X0) => member(X2,X1)) => subset(X0,X1))), 0.17/0.41 inference(unused_predicate_definition_removal,[],[f24])). 0.17/0.41 fof(f24,plain,( 0.17/0.41 ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (member(X2,X0) => member(X2,X1)))), 0.17/0.41 inference(rectify,[],[f6])). 0.17/0.41 fof(f6,axiom,( 0.17/0.41 ! [X1,X2] : (subset(X1,X2) <=> ! [X0] : (member(X0,X1) => member(X0,X2)))), 0.17/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset)). 0.17/0.41 fof(f590,plain,( 0.17/0.41 ~subset(sK0,sK0)), 0.17/0.41 inference(duplicate_literal_removal,[],[f589])). 0.17/0.41 fof(f589,plain,( 0.17/0.41 ~subset(sK0,sK0) | ~subset(sK0,sK0)), 0.17/0.41 inference(forward_demodulation,[],[f588,f513])). 0.17/0.41 fof(f513,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f512,f199])). 0.17/0.41 fof(f199,plain,( 0.17/0.41 sK0 = sK1(singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f198,f197])). 0.17/0.41 fof(f197,plain,( 0.17/0.41 sK0 = sK1(singleton(sK0)) | member(sK6(sK0,sK0),sK0)), 0.17/0.41 inference(resolution,[],[f196,f66])). 0.17/0.41 fof(f196,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK1(singleton(sK0))), 0.17/0.41 inference(duplicate_literal_removal,[],[f195])). 0.17/0.41 fof(f195,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK1(singleton(sK0)) | ~subset(sK0,sK0) | sK0 = sK1(singleton(sK0))), 0.17/0.41 inference(superposition,[],[f192,f140])). 0.17/0.41 fof(f140,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK1(singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f139,f63])). 0.17/0.41 fof(f63,plain,( 0.17/0.41 ( ! [X0,X1] : (X0 = X1 | ~member(X0,singleton(X1))) )), 0.17/0.41 inference(cnf_transformation,[],[f38])). 0.17/0.41 fof(f38,plain,( 0.17/0.41 ! [X0,X1] : ((member(X0,singleton(X1)) | X0 != X1) & (X0 = X1 | ~member(X0,singleton(X1))))), 0.17/0.41 inference(nnf_transformation,[],[f5])). 0.17/0.41 fof(f5,axiom,( 0.17/0.41 ! [X0,X1] : (member(X0,singleton(X1)) <=> X0 = X1)), 0.17/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)). 0.17/0.41 fof(f139,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK1(singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f138,f63])). 0.17/0.41 fof(f138,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK1(singleton(sK0)) | member(sK1(singleton(sK0)),singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f137,f68])). 0.17/0.41 fof(f68,plain,( 0.17/0.41 ( ! [X1] : (member(X1,singleton(X1))) )), 0.17/0.41 inference(equality_resolution,[],[f64])). 0.17/0.41 fof(f64,plain,( 0.17/0.41 ( ! [X0,X1] : (member(X0,singleton(X1)) | X0 != X1) )), 0.17/0.41 inference(cnf_transformation,[],[f38])). 0.17/0.41 fof(f137,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK1(singleton(sK0)) | member(sK1(singleton(sK0)),singleton(sK0)) | ~member(sK0,singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f117,f42])). 0.17/0.41 fof(f42,plain,( 0.17/0.41 ~partition(singleton(sK0),sK0)), 0.17/0.41 inference(cnf_transformation,[],[f32])). 0.17/0.41 fof(f32,plain,( 0.17/0.41 ~partition(singleton(sK0),sK0) & empty_set != sK0), 0.17/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f31])). 0.17/0.41 fof(f31,plain,( 0.17/0.41 ? [X0] : (~partition(singleton(X0),X0) & empty_set != X0) => (~partition(singleton(sK0),sK0) & empty_set != sK0)), 0.17/0.41 introduced(choice_axiom,[])). 0.17/0.41 fof(f27,plain,( 0.17/0.41 ? [X0] : (~partition(singleton(X0),X0) & empty_set != X0)), 0.17/0.41 inference(ennf_transformation,[],[f22])). 0.17/0.41 fof(f22,plain,( 0.17/0.41 ~! [X0] : (empty_set != X0 => partition(singleton(X0),X0))), 0.17/0.41 inference(rectify,[],[f19])). 0.17/0.41 fof(f19,negated_conjecture,( 0.17/0.41 ~! [X4] : (empty_set != X4 => partition(singleton(X4),X4))), 0.17/0.41 inference(negated_conjecture,[],[f18])). 0.17/0.41 fof(f18,conjecture,( 0.17/0.41 ! [X4] : (empty_set != X4 => partition(singleton(X4),X4))), 0.17/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_partitions_itself)). 0.17/0.41 fof(f117,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK1(singleton(sK0)) | partition(singleton(sK0),sK0) | member(sK1(singleton(sK0)),singleton(sK0)) | ~member(sK0,singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(resolution,[],[f106,f45])). 0.17/0.41 fof(f45,plain,( 0.17/0.41 ( ! [X6,X0,X1] : (partition(X0,X1) | member(sK1(X0),X0) | ~member(sK4(X0,X1),X6) | ~member(X6,X0) | member(sK5(X0,X1),X0)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f37,plain,( 0.17/0.41 ! [X0,X1] : (partition(X0,X1) | (sK1(X0) != sK2(X0) & (member(sK3(X0),sK2(X0)) & member(sK3(X0),sK1(X0))) & member(sK2(X0),X0) & member(sK1(X0),X0)) | (! [X6] : (~member(sK4(X0,X1),X6) | ~member(X6,X0)) & member(sK4(X0,X1),X1)) | (~subset(sK5(X0,X1),X1) & member(sK5(X0,X1),X0)))), 0.17/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f29,f36,f35,f34,f33])). 0.17/0.41 fof(f33,plain,( 0.17/0.41 ! [X0] : (? [X2,X3] : (X2 != X3 & ? [X4] : (member(X4,X3) & member(X4,X2)) & member(X3,X0) & member(X2,X0)) => (sK1(X0) != sK2(X0) & ? [X4] : (member(X4,sK2(X0)) & member(X4,sK1(X0))) & member(sK2(X0),X0) & member(sK1(X0),X0)))), 0.17/0.41 introduced(choice_axiom,[])). 0.17/0.41 fof(f34,plain,( 0.17/0.41 ( ! [X2,X3] : (! [X0] : (? [X4] : (member(X4,X3) & member(X4,X2)) => (member(sK3(X0),X3) & member(sK3(X0),X2)))) )), 0.17/0.41 introduced(choice_axiom,[])). 0.17/0.41 fof(f35,plain,( 0.17/0.41 ! [X1,X0] : (? [X5] : (! [X6] : (~member(X5,X6) | ~member(X6,X0)) & member(X5,X1)) => (! [X6] : (~member(sK4(X0,X1),X6) | ~member(X6,X0)) & member(sK4(X0,X1),X1)))), 0.17/0.41 introduced(choice_axiom,[])). 0.17/0.41 fof(f36,plain,( 0.17/0.41 ! [X1,X0] : (? [X7] : (~subset(X7,X1) & member(X7,X0)) => (~subset(sK5(X0,X1),X1) & member(sK5(X0,X1),X0)))), 0.17/0.41 introduced(choice_axiom,[])). 0.17/0.41 fof(f29,plain,( 0.17/0.41 ! [X0,X1] : (partition(X0,X1) | ? [X2,X3] : (X2 != X3 & ? [X4] : (member(X4,X3) & member(X4,X2)) & member(X3,X0) & member(X2,X0)) | ? [X5] : (! [X6] : (~member(X5,X6) | ~member(X6,X0)) & member(X5,X1)) | ? [X7] : (~subset(X7,X1) & member(X7,X0)))), 0.17/0.41 inference(flattening,[],[f28])). 0.17/0.41 fof(f28,plain,( 0.17/0.41 ! [X0,X1] : (partition(X0,X1) | (? [X2,X3] : ((X2 != X3 & ? [X4] : (member(X4,X3) & member(X4,X2))) & (member(X3,X0) & member(X2,X0))) | ? [X5] : (! [X6] : (~member(X5,X6) | ~member(X6,X0)) & member(X5,X1)) | ? [X7] : (~subset(X7,X1) & member(X7,X0))))), 0.17/0.41 inference(ennf_transformation,[],[f25])). 0.17/0.41 fof(f25,plain,( 0.17/0.41 ! [X0,X1] : ((! [X2,X3] : ((member(X3,X0) & member(X2,X0)) => (? [X4] : (member(X4,X3) & member(X4,X2)) => X2 = X3)) & ! [X5] : (member(X5,X1) => ? [X6] : (member(X5,X6) & member(X6,X0))) & ! [X7] : (member(X7,X0) => subset(X7,X1))) => partition(X0,X1))), 0.17/0.41 inference(unused_predicate_definition_removal,[],[f23])). 0.17/0.41 fof(f23,plain,( 0.17/0.41 ! [X0,X1] : (partition(X0,X1) <=> (! [X2,X3] : ((member(X3,X0) & member(X2,X0)) => (? [X4] : (member(X4,X3) & member(X4,X2)) => X2 = X3)) & ! [X5] : (member(X5,X1) => ? [X6] : (member(X5,X6) & member(X6,X0))) & ! [X7] : (member(X7,X0) => subset(X7,X1))))), 0.17/0.41 inference(rectify,[],[f13])). 0.17/0.41 fof(f13,axiom,( 0.17/0.41 ! [X1,X4] : (partition(X1,X4) <=> (! [X0,X3] : ((member(X3,X1) & member(X0,X1)) => (? [X6] : (member(X6,X3) & member(X6,X0)) => X0 = X3)) & ! [X0] : (member(X0,X4) => ? [X3] : (member(X0,X3) & member(X3,X1))) & ! [X0] : (member(X0,X1) => subset(X0,X4))))), 0.17/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition)). 0.17/0.41 fof(f106,plain,( 0.17/0.41 member(sK4(singleton(sK0),sK0),sK0) | sK0 = sK5(singleton(sK0),sK0) | sK0 = sK1(singleton(sK0))), 0.17/0.41 inference(resolution,[],[f93,f63])). 0.17/0.41 fof(f93,plain,( 0.17/0.41 member(sK1(singleton(sK0)),singleton(sK0)) | member(sK4(singleton(sK0),sK0),sK0) | sK0 = sK5(singleton(sK0),sK0)), 0.17/0.41 inference(resolution,[],[f69,f63])). 0.17/0.41 fof(f69,plain,( 0.17/0.41 member(sK5(singleton(sK0),sK0),singleton(sK0)) | member(sK4(singleton(sK0),sK0),sK0) | member(sK1(singleton(sK0)),singleton(sK0))), 0.17/0.41 inference(resolution,[],[f42,f43])). 0.17/0.41 fof(f43,plain,( 0.17/0.41 ( ! [X0,X1] : (partition(X0,X1) | member(sK1(X0),X0) | member(sK4(X0,X1),X1) | member(sK5(X0,X1),X0)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f192,plain,( 0.17/0.41 ~subset(sK5(singleton(sK0),sK0),sK0) | sK0 = sK1(singleton(sK0)) | ~subset(sK0,sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f191,f63])). 0.17/0.41 fof(f191,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK1(singleton(sK0)) | member(sK1(singleton(sK0)),singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f190,f68])). 0.17/0.41 fof(f190,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK1(singleton(sK0)) | member(sK1(singleton(sK0)),singleton(sK0)) | ~member(sK0,singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f168,f42])). 0.17/0.41 fof(f168,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK1(singleton(sK0)) | partition(singleton(sK0),sK0) | member(sK1(singleton(sK0)),singleton(sK0)) | ~member(sK0,singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(resolution,[],[f164,f46])). 0.17/0.41 fof(f46,plain,( 0.17/0.41 ( ! [X6,X0,X1] : (partition(X0,X1) | member(sK1(X0),X0) | ~member(sK4(X0,X1),X6) | ~member(X6,X0) | ~subset(sK5(X0,X1),X1)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f164,plain,( 0.17/0.41 member(sK4(singleton(sK0),sK0),sK0) | ~subset(sK0,sK0) | sK0 = sK1(singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f143,f63])). 0.17/0.41 fof(f143,plain,( 0.17/0.41 ~subset(sK0,sK0) | member(sK4(singleton(sK0),sK0),sK0) | member(sK1(singleton(sK0)),singleton(sK0)) | sK0 = sK1(singleton(sK0))), 0.17/0.41 inference(superposition,[],[f70,f140])). 0.17/0.41 fof(f70,plain,( 0.17/0.41 ~subset(sK5(singleton(sK0),sK0),sK0) | member(sK4(singleton(sK0),sK0),sK0) | member(sK1(singleton(sK0)),singleton(sK0))), 0.17/0.41 inference(resolution,[],[f42,f44])). 0.17/0.41 fof(f44,plain,( 0.17/0.41 ( ! [X0,X1] : (partition(X0,X1) | member(sK1(X0),X0) | member(sK4(X0,X1),X1) | ~subset(sK5(X0,X1),X1)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f198,plain,( 0.17/0.41 sK0 = sK1(singleton(sK0)) | ~member(sK6(sK0,sK0),sK0)), 0.17/0.41 inference(resolution,[],[f196,f67])). 0.17/0.41 fof(f67,plain,( 0.17/0.41 ( ! [X0,X1] : (subset(X0,X1) | ~member(sK6(X0,X1),X1)) )), 0.17/0.41 inference(cnf_transformation,[],[f40])). 0.17/0.41 fof(f512,plain,( 0.17/0.41 sK0 != sK1(singleton(sK0)) | sK0 = sK5(singleton(sK0),sK0)), 0.17/0.41 inference(forward_demodulation,[],[f511,f382])). 0.17/0.41 fof(f382,plain,( 0.17/0.41 sK0 = sK2(singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f381,f380])). 0.17/0.41 fof(f380,plain,( 0.17/0.41 sK0 = sK2(singleton(sK0)) | member(sK6(sK0,sK0),sK0)), 0.17/0.41 inference(resolution,[],[f379,f66])). 0.17/0.41 fof(f379,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK2(singleton(sK0))), 0.17/0.41 inference(duplicate_literal_removal,[],[f378])). 0.17/0.41 fof(f378,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK2(singleton(sK0)) | ~subset(sK0,sK0) | sK0 = sK2(singleton(sK0))), 0.17/0.41 inference(superposition,[],[f375,f314])). 0.17/0.41 fof(f314,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK2(singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f313,f63])). 0.17/0.41 fof(f313,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK2(singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f312,f63])). 0.17/0.41 fof(f312,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK2(singleton(sK0)) | member(sK2(singleton(sK0)),singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f311,f68])). 0.17/0.41 fof(f311,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK2(singleton(sK0)) | member(sK2(singleton(sK0)),singleton(sK0)) | ~member(sK0,singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f287,f42])). 0.17/0.41 fof(f287,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK0 = sK2(singleton(sK0)) | partition(singleton(sK0),sK0) | member(sK2(singleton(sK0)),singleton(sK0)) | ~member(sK0,singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(resolution,[],[f266,f49])). 0.17/0.41 fof(f49,plain,( 0.17/0.41 ( ! [X6,X0,X1] : (partition(X0,X1) | member(sK2(X0),X0) | ~member(sK4(X0,X1),X6) | ~member(X6,X0) | member(sK5(X0,X1),X0)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f266,plain,( 0.17/0.41 member(sK4(singleton(sK0),sK0),sK0) | sK0 = sK5(singleton(sK0),sK0) | sK0 = sK2(singleton(sK0))), 0.17/0.41 inference(resolution,[],[f251,f63])). 0.17/0.41 fof(f251,plain,( 0.17/0.41 member(sK2(singleton(sK0)),singleton(sK0)) | member(sK4(singleton(sK0),sK0),sK0) | sK0 = sK5(singleton(sK0),sK0)), 0.17/0.41 inference(resolution,[],[f73,f63])). 0.17/0.41 fof(f73,plain,( 0.17/0.41 member(sK5(singleton(sK0),sK0),singleton(sK0)) | member(sK4(singleton(sK0),sK0),sK0) | member(sK2(singleton(sK0)),singleton(sK0))), 0.17/0.41 inference(resolution,[],[f42,f47])). 0.17/0.41 fof(f47,plain,( 0.17/0.41 ( ! [X0,X1] : (partition(X0,X1) | member(sK2(X0),X0) | member(sK4(X0,X1),X1) | member(sK5(X0,X1),X0)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f375,plain,( 0.17/0.41 ~subset(sK5(singleton(sK0),sK0),sK0) | sK0 = sK2(singleton(sK0)) | ~subset(sK0,sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f374,f63])). 0.17/0.41 fof(f374,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK2(singleton(sK0)) | member(sK2(singleton(sK0)),singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f373,f68])). 0.17/0.41 fof(f373,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK2(singleton(sK0)) | member(sK2(singleton(sK0)),singleton(sK0)) | ~member(sK0,singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f347,f42])). 0.17/0.41 fof(f347,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK0 = sK2(singleton(sK0)) | partition(singleton(sK0),sK0) | member(sK2(singleton(sK0)),singleton(sK0)) | ~member(sK0,singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(resolution,[],[f339,f50])). 0.17/0.41 fof(f50,plain,( 0.17/0.41 ( ! [X6,X0,X1] : (partition(X0,X1) | member(sK2(X0),X0) | ~member(sK4(X0,X1),X6) | ~member(X6,X0) | ~subset(sK5(X0,X1),X1)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f339,plain,( 0.17/0.41 member(sK4(singleton(sK0),sK0),sK0) | ~subset(sK0,sK0) | sK0 = sK2(singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f318,f63])). 0.17/0.41 fof(f318,plain,( 0.17/0.41 ~subset(sK0,sK0) | member(sK4(singleton(sK0),sK0),sK0) | member(sK2(singleton(sK0)),singleton(sK0)) | sK0 = sK2(singleton(sK0))), 0.17/0.41 inference(superposition,[],[f74,f314])). 0.17/0.41 fof(f74,plain,( 0.17/0.41 ~subset(sK5(singleton(sK0),sK0),sK0) | member(sK4(singleton(sK0),sK0),sK0) | member(sK2(singleton(sK0)),singleton(sK0))), 0.17/0.41 inference(resolution,[],[f42,f48])). 0.17/0.41 fof(f48,plain,( 0.17/0.41 ( ! [X0,X1] : (partition(X0,X1) | member(sK2(X0),X0) | member(sK4(X0,X1),X1) | ~subset(sK5(X0,X1),X1)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f381,plain,( 0.17/0.41 sK0 = sK2(singleton(sK0)) | ~member(sK6(sK0,sK0),sK0)), 0.17/0.41 inference(resolution,[],[f379,f67])). 0.17/0.41 fof(f511,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK1(singleton(sK0)) != sK2(singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f510,f63])). 0.17/0.41 fof(f510,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK1(singleton(sK0)) != sK2(singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f509,f68])). 0.17/0.41 fof(f509,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | sK1(singleton(sK0)) != sK2(singleton(sK0)) | ~member(sK0,singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(subsumption_resolution,[],[f471,f42])). 0.17/0.41 fof(f471,plain,( 0.17/0.41 sK0 = sK5(singleton(sK0),sK0) | partition(singleton(sK0),sK0) | sK1(singleton(sK0)) != sK2(singleton(sK0)) | ~member(sK0,singleton(sK0)) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(resolution,[],[f440,f61])). 0.17/0.41 fof(f61,plain,( 0.17/0.41 ( ! [X6,X0,X1] : (partition(X0,X1) | sK1(X0) != sK2(X0) | ~member(sK4(X0,X1),X6) | ~member(X6,X0) | member(sK5(X0,X1),X0)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f440,plain,( 0.17/0.41 member(sK4(singleton(sK0),sK0),sK0) | sK0 = sK5(singleton(sK0),sK0)), 0.17/0.41 inference(resolution,[],[f421,f63])). 0.17/0.41 fof(f421,plain,( 0.17/0.41 member(sK5(singleton(sK0),sK0),singleton(sK0)) | member(sK4(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(trivial_inequality_removal,[],[f393])). 0.17/0.41 fof(f393,plain,( 0.17/0.41 sK0 != sK0 | member(sK4(singleton(sK0),sK0),sK0) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(backward_demodulation,[],[f382,f208])). 0.17/0.41 fof(f208,plain,( 0.17/0.41 sK0 != sK2(singleton(sK0)) | member(sK4(singleton(sK0),sK0),sK0) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(backward_demodulation,[],[f199,f85])). 0.17/0.41 fof(f85,plain,( 0.17/0.41 sK1(singleton(sK0)) != sK2(singleton(sK0)) | member(sK4(singleton(sK0),sK0),sK0) | member(sK5(singleton(sK0),sK0),singleton(sK0))), 0.17/0.41 inference(resolution,[],[f42,f59])). 0.17/0.41 fof(f59,plain,( 0.17/0.41 ( ! [X0,X1] : (partition(X0,X1) | sK1(X0) != sK2(X0) | member(sK4(X0,X1),X1) | member(sK5(X0,X1),X0)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f588,plain,( 0.17/0.41 ~subset(sK0,sK0) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f587,f199])). 0.17/0.41 fof(f587,plain,( 0.17/0.41 sK0 != sK1(singleton(sK0)) | ~subset(sK0,sK0) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(forward_demodulation,[],[f586,f382])). 0.17/0.41 fof(f586,plain,( 0.17/0.41 ~subset(sK0,sK0) | sK1(singleton(sK0)) != sK2(singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f585,f42])). 0.17/0.41 fof(f585,plain,( 0.17/0.41 ~subset(sK0,sK0) | partition(singleton(sK0),sK0) | sK1(singleton(sK0)) != sK2(singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(subsumption_resolution,[],[f551,f68])). 0.17/0.41 fof(f551,plain,( 0.17/0.41 ~subset(sK0,sK0) | ~member(sK0,singleton(sK0)) | partition(singleton(sK0),sK0) | sK1(singleton(sK0)) != sK2(singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)), 0.17/0.41 inference(resolution,[],[f532,f60])). 0.17/0.41 fof(f60,plain,( 0.17/0.41 ( ! [X0,X1] : (partition(X0,X1) | sK1(X0) != sK2(X0) | member(sK4(X0,X1),X1) | ~subset(sK5(X0,X1),X1)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f532,plain,( 0.17/0.41 ( ! [X9] : (~member(sK4(singleton(sK0),sK0),X9) | ~subset(sK0,sK0) | ~member(X9,singleton(sK0))) )), 0.17/0.41 inference(backward_demodulation,[],[f513,f418])). 0.17/0.41 fof(f418,plain,( 0.17/0.41 ( ! [X9] : (~member(sK4(singleton(sK0),sK0),X9) | ~member(X9,singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)) )), 0.17/0.41 inference(trivial_inequality_removal,[],[f396])). 0.17/0.41 fof(f396,plain,( 0.17/0.41 ( ! [X9] : (sK0 != sK0 | ~member(sK4(singleton(sK0),sK0),X9) | ~member(X9,singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)) )), 0.17/0.41 inference(backward_demodulation,[],[f382,f211])). 0.17/0.41 fof(f211,plain,( 0.17/0.41 ( ! [X9] : (sK0 != sK2(singleton(sK0)) | ~member(sK4(singleton(sK0),sK0),X9) | ~member(X9,singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)) )), 0.17/0.41 inference(backward_demodulation,[],[f199,f88])). 0.17/0.41 fof(f88,plain,( 0.17/0.41 ( ! [X9] : (sK1(singleton(sK0)) != sK2(singleton(sK0)) | ~member(sK4(singleton(sK0),sK0),X9) | ~member(X9,singleton(sK0)) | ~subset(sK5(singleton(sK0),sK0),sK0)) )), 0.17/0.41 inference(resolution,[],[f42,f62])). 0.17/0.41 fof(f62,plain,( 0.17/0.41 ( ! [X6,X0,X1] : (partition(X0,X1) | sK1(X0) != sK2(X0) | ~member(sK4(X0,X1),X6) | ~member(X6,X0) | ~subset(sK5(X0,X1),X1)) )), 0.17/0.41 inference(cnf_transformation,[],[f37])). 0.17/0.41 fof(f592,plain,( 0.17/0.41 ~member(sK6(sK0,sK0),sK0)), 0.17/0.41 inference(resolution,[],[f590,f67])). 0.17/0.41 % SZS output end Proof for theBenchmark 0.17/0.41 % ------------------------------ 0.17/0.41 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 0.17/0.41 % Termination reason: Refutation 0.17/0.41 0.17/0.41 % Memory used [KB]: 895 0.17/0.41 % Time elapsed: 0.018 s 0.17/0.41 % ------------------------------ 0.17/0.41 % ------------------------------ 0.17/0.41 % Success in time 0.077 s 0.17/0.41 EOF