0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : vampire --mode casc -t %d %s 0.12/0.34 % Computer : n024.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % DateTime : Thu Jul 2 08:41:11 EDT 2020 0.12/0.34 % CPUTime : 0.20/0.41 % lrs-11_12_av=off:nm=32:nwc=1.3:stl=30:sd=3:ss=axioms:sos=all_2 on theBenchmark 0.68/0.91 % Time limit reached! 0.68/0.91 % ------------------------------ 0.68/0.91 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 0.68/0.91 % Termination reason: Time limit 0.68/0.91 % Termination phase: Saturation 0.68/0.91 0.68/0.91 % Memory used [KB]: 4605 0.68/0.91 % Time elapsed: 0.500 s 0.68/0.91 % ------------------------------ 0.68/0.91 % ------------------------------ 0.75/0.97 % lrs+2_3:1_add=large:afr=on:afp=10000:afq=1.1:amm=off:anc=none:er=known:fde=unused:gs=on:gsaa=from_current:gsem=on:lma=on:nm=32:newcnf=on:nwc=4:sas=z3:stl=30:sd=1:ss=axioms:st=5.0:sac=on:sp=occurrence:updr=off_2 on theBenchmark 0.75/1.04 % Refutation found. Thanks to Tanya! 0.75/1.04 % SZS status Theorem for theBenchmark 0.75/1.04 % SZS output start Proof for theBenchmark 0.75/1.04 fof(f398,plain,( 0.75/1.04 $false), 0.75/1.04 inference(avatar_sat_refutation,[],[f50,f97,f102,f116,f121,f128,f139,f143,f162,f194,f201,f217,f267,f274,f290,f298,f301,f303,f318,f369,f395])). 0.75/1.04 fof(f395,plain,( 0.75/1.04 spl9_3 | ~spl9_4 | ~spl9_24), 0.75/1.04 inference(avatar_contradiction_clause,[],[f394])). 0.75/1.04 fof(f394,plain,( 0.75/1.04 $false | (~spl9_3 | ~spl9_4 | ~spl9_24)), 0.75/1.04 inference(subsumption_resolution,[],[f383,f43])). 0.75/1.04 fof(f43,plain,( 0.75/1.04 ( ! [X2] : (in(X2,singleton(X2))) )), 0.75/1.04 inference(equality_resolution,[],[f42])). 0.75/1.04 fof(f42,plain,( 0.75/1.04 ( ! [X2,X0] : (X0 != X2 | in(X2,singleton(X0))) )), 0.75/1.04 inference(equality_resolution,[],[f26])). 0.75/1.04 fof(f26,plain,( 0.75/1.04 ( ! [X2,X0,X1] : (singleton(X0) != X1 | X0 != X2 | in(X2,X1)) )), 0.75/1.04 inference(cnf_transformation,[],[f5])). 0.75/1.04 fof(f5,axiom,( 0.75/1.04 ! [X0,X1] : (! [X2] : (in(X2,X1) <=> X0 = X2) <=> singleton(X0) = X1)), 0.75/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski)). 0.75/1.04 fof(f383,plain,( 0.75/1.04 ~in(ordered_pair(sK0,sK1),singleton(ordered_pair(sK0,sK1))) | (~spl9_3 | ~spl9_4 | ~spl9_24)), 0.75/1.04 inference(backward_demodulation,[],[f382,f90])). 0.75/1.04 fof(f90,plain,( 0.75/1.04 ~in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),singleton(ordered_pair(sK0,sK1))) | ~spl9_3), 0.75/1.04 inference(avatar_component_clause,[],[f89])). 0.75/1.04 fof(f89,plain,( 0.75/1.04 spl9_3 <=> ~in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),singleton(ordered_pair(sK0,sK1)))), 0.75/1.04 introduced(avatar_definition,[new_symbols(naming,[spl9_3])])). 0.75/1.04 fof(f382,plain,( 0.75/1.04 ordered_pair(sK0,sK1) = sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))) | (~spl9_4 | ~spl9_24)), 0.75/1.04 inference(backward_demodulation,[],[f350,f289])). 0.75/1.04 fof(f289,plain,( 0.75/1.04 ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) = sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_24), 0.75/1.04 inference(avatar_component_clause,[],[f288])). 0.75/1.04 fof(f288,plain,( 0.75/1.04 spl9_24 <=> ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) = sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.04 introduced(avatar_definition,[new_symbols(naming,[spl9_24])])). 0.75/1.04 fof(f350,plain,( 0.75/1.04 sK1 = sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))) | ~spl9_4), 0.75/1.04 inference(resolution,[],[f69,f93])). 0.75/1.04 fof(f93,plain,( 0.75/1.04 in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_4), 0.75/1.04 inference(avatar_component_clause,[],[f92])). 0.75/1.04 fof(f92,plain,( 0.75/1.04 spl9_4 <=> in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.04 introduced(avatar_definition,[new_symbols(naming,[spl9_4])])). 0.75/1.04 fof(f69,plain,( 0.75/1.04 ( ! [X2,X0,X1] : (~in(X0,cartesian_product2(X1,singleton(X2))) | sK4(X1,singleton(X2),X0) = X2) )), 0.75/1.04 inference(resolution,[],[f40,f41])). 0.75/1.04 fof(f41,plain,( 0.75/1.04 ( ! [X2,X0] : (~in(X2,singleton(X0)) | X0 = X2) )), 0.75/1.04 inference(equality_resolution,[],[f27])). 0.75/1.04 fof(f27,plain,( 0.75/1.04 ( ! [X2,X0,X1] : (singleton(X0) != X1 | X0 = X2 | ~in(X2,X1)) )), 0.75/1.04 inference(cnf_transformation,[],[f5])). 0.75/1.04 fof(f40,plain,( 0.75/1.04 ( ! [X0,X3,X1] : (in(sK4(X0,X1,X3),X1) | ~in(X3,cartesian_product2(X0,X1))) )), 0.75/1.04 inference(equality_resolution,[],[f20])). 0.75/1.04 fof(f20,plain,( 0.75/1.04 ( ! [X2,X0,X3,X1] : (in(sK4(X0,X1,X3),X1) | ~in(X3,X2) | cartesian_product2(X0,X1) != X2) )), 0.75/1.04 inference(cnf_transformation,[],[f2])). 0.75/1.04 fof(f2,axiom,( 0.75/1.04 ! [X0,X1,X2] : (cartesian_product2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> ? [X4,X5] : (in(X4,X0) & ordered_pair(X4,X5) = X3 & in(X5,X1))))), 0.75/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1)). 0.75/1.04 fof(f369,plain,( 0.75/1.04 ~spl9_6 | spl9_9 | ~spl9_26), 0.75/1.04 inference(avatar_contradiction_clause,[],[f368])). 0.75/1.04 fof(f368,plain,( 0.75/1.04 $false | (~spl9_6 | ~spl9_9 | ~spl9_26)), 0.75/1.04 inference(subsumption_resolution,[],[f363,f43])). 0.75/1.04 fof(f363,plain,( 0.75/1.04 ~in(ordered_pair(sK0,sK1),singleton(ordered_pair(sK0,sK1))) | (~spl9_6 | ~spl9_9 | ~spl9_26)), 0.75/1.04 inference(backward_demodulation,[],[f356,f115])). 0.75/1.04 fof(f115,plain,( 0.75/1.04 ~in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),singleton(ordered_pair(sK0,sK1))) | ~spl9_9), 0.75/1.04 inference(avatar_component_clause,[],[f114])). 0.75/1.04 fof(f114,plain,( 0.75/1.04 spl9_9 <=> ~in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),singleton(ordered_pair(sK0,sK1)))), 0.75/1.04 introduced(avatar_definition,[new_symbols(naming,[spl9_9])])). 0.75/1.04 fof(f356,plain,( 0.75/1.04 ordered_pair(sK0,sK1) = sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))) | (~spl9_6 | ~spl9_26)), 0.75/1.04 inference(backward_demodulation,[],[f349,f317])). 0.75/1.04 fof(f317,plain,( 0.75/1.04 ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))))) = sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))) | ~spl9_26), 0.75/1.04 inference(avatar_component_clause,[],[f316])). 0.75/1.04 fof(f316,plain,( 0.75/1.04 spl9_26 <=> ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))))) = sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1)))), 0.75/1.04 introduced(avatar_definition,[new_symbols(naming,[spl9_26])])). 0.75/1.04 fof(f349,plain,( 0.75/1.04 sK1 = sK4(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1)))) | ~spl9_6), 0.75/1.04 inference(resolution,[],[f69,f106])). 0.75/1.05 fof(f106,plain,( 0.75/1.05 in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_6), 0.75/1.05 inference(avatar_component_clause,[],[f105])). 0.75/1.05 fof(f105,plain,( 0.75/1.05 spl9_6 <=> in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_6])])). 0.75/1.05 fof(f318,plain,( 0.75/1.05 spl9_26 | ~spl9_6 | ~spl9_16), 0.75/1.05 inference(avatar_split_clause,[],[f260,f199,f105,f316])). 0.75/1.05 fof(f199,plain,( 0.75/1.05 spl9_16 <=> ordered_pair(sK3(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1)))),sK4(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))))) = sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_16])])). 0.75/1.05 fof(f260,plain,( 0.75/1.05 ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))))) = sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))) | (~spl9_6 | ~spl9_16)), 0.75/1.05 inference(backward_demodulation,[],[f240,f200])). 0.75/1.05 fof(f200,plain,( 0.75/1.05 ordered_pair(sK3(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1)))),sK4(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))))) = sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))) | ~spl9_16), 0.75/1.05 inference(avatar_component_clause,[],[f199])). 0.75/1.05 fof(f240,plain,( 0.75/1.05 sK0 = sK3(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1)))) | ~spl9_6), 0.75/1.05 inference(resolution,[],[f68,f106])). 0.75/1.05 fof(f68,plain,( 0.75/1.05 ( ! [X2,X0,X1] : (~in(X0,cartesian_product2(singleton(X1),X2)) | sK3(singleton(X1),X2,X0) = X1) )), 0.75/1.05 inference(resolution,[],[f38,f41])). 0.75/1.05 fof(f38,plain,( 0.75/1.05 ( ! [X0,X3,X1] : (in(sK3(X0,X1,X3),X0) | ~in(X3,cartesian_product2(X0,X1))) )), 0.75/1.05 inference(equality_resolution,[],[f22])). 0.75/1.05 fof(f22,plain,( 0.75/1.05 ( ! [X2,X0,X3,X1] : (in(sK3(X0,X1,X3),X0) | ~in(X3,X2) | cartesian_product2(X0,X1) != X2) )), 0.75/1.05 inference(cnf_transformation,[],[f2])). 0.75/1.05 fof(f303,plain,( 0.75/1.05 ~spl9_2 | ~spl9_20 | spl9_25), 0.75/1.05 inference(avatar_contradiction_clause,[],[f302])). 0.75/1.05 fof(f302,plain,( 0.75/1.05 $false | (~spl9_2 | ~spl9_20 | ~spl9_25)), 0.75/1.05 inference(subsumption_resolution,[],[f296,f266])). 0.75/1.05 fof(f266,plain,( 0.75/1.05 ordered_pair(sK0,sK1) = ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1))) | ~spl9_20), 0.75/1.05 inference(avatar_component_clause,[],[f265])). 0.75/1.05 fof(f265,plain,( 0.75/1.05 spl9_20 <=> ordered_pair(sK0,sK1) = ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_20])])). 0.75/1.05 fof(f296,plain,( 0.75/1.05 ordered_pair(sK0,sK1) != ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1))) | (~spl9_2 | ~spl9_25)), 0.75/1.05 inference(backward_demodulation,[],[f291,f286])). 0.75/1.05 fof(f286,plain,( 0.75/1.05 ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) != sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_25), 0.75/1.05 inference(avatar_component_clause,[],[f285])). 0.75/1.05 fof(f285,plain,( 0.75/1.05 spl9_25 <=> ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) != sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_25])])). 0.75/1.05 fof(f291,plain,( 0.75/1.05 ordered_pair(sK0,sK1) = sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_2), 0.75/1.05 inference(resolution,[],[f87,f41])). 0.75/1.05 fof(f87,plain,( 0.75/1.05 in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),singleton(ordered_pair(sK0,sK1))) | ~spl9_2), 0.75/1.05 inference(avatar_component_clause,[],[f86])). 0.75/1.05 fof(f86,plain,( 0.75/1.05 spl9_2 <=> in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),singleton(ordered_pair(sK0,sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_2])])). 0.75/1.05 fof(f301,plain,( 0.75/1.05 ~spl9_2 | spl9_15 | ~spl9_20 | ~spl9_22), 0.75/1.05 inference(avatar_contradiction_clause,[],[f300])). 0.75/1.05 fof(f300,plain,( 0.75/1.05 $false | (~spl9_2 | ~spl9_15 | ~spl9_20 | ~spl9_22)), 0.75/1.05 inference(subsumption_resolution,[],[f299,f266])). 0.75/1.05 fof(f299,plain,( 0.75/1.05 ordered_pair(sK0,sK1) != ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1))) | (~spl9_2 | ~spl9_15 | ~spl9_22)), 0.75/1.05 inference(forward_demodulation,[],[f294,f273])). 0.75/1.05 fof(f273,plain,( 0.75/1.05 sK0 = sK3(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1)) | ~spl9_22), 0.75/1.05 inference(avatar_component_clause,[],[f272])). 0.75/1.05 fof(f272,plain,( 0.75/1.05 spl9_22 <=> sK0 = sK3(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_22])])). 0.75/1.05 fof(f294,plain,( 0.75/1.05 ordered_pair(sK0,sK1) != ordered_pair(sK3(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1)),sK4(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1))) | (~spl9_2 | ~spl9_15)), 0.75/1.05 inference(backward_demodulation,[],[f291,f190])). 0.75/1.05 fof(f190,plain,( 0.75/1.05 ordered_pair(sK3(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))),sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) != sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_15), 0.75/1.05 inference(avatar_component_clause,[],[f189])). 0.75/1.05 fof(f189,plain,( 0.75/1.05 spl9_15 <=> ordered_pair(sK3(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))),sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) != sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_15])])). 0.75/1.05 fof(f298,plain,( 0.75/1.05 ~spl9_2 | spl9_5 | ~spl9_10), 0.75/1.05 inference(avatar_contradiction_clause,[],[f297])). 0.75/1.05 fof(f297,plain,( 0.75/1.05 $false | (~spl9_2 | ~spl9_5 | ~spl9_10)), 0.75/1.05 inference(subsumption_resolution,[],[f293,f135])). 0.75/1.05 fof(f135,plain,( 0.75/1.05 in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_10), 0.75/1.05 inference(avatar_component_clause,[],[f134])). 0.75/1.05 fof(f134,plain,( 0.75/1.05 spl9_10 <=> in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_10])])). 0.75/1.05 fof(f293,plain,( 0.75/1.05 ~in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1))) | (~spl9_2 | ~spl9_5)), 0.75/1.05 inference(backward_demodulation,[],[f291,f96])). 0.75/1.05 fof(f96,plain,( 0.75/1.05 ~in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_5), 0.75/1.05 inference(avatar_component_clause,[],[f95])). 0.75/1.05 fof(f95,plain,( 0.75/1.05 spl9_5 <=> ~in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_5])])). 0.75/1.05 fof(f290,plain,( 0.75/1.05 spl9_24 | ~spl9_4 | ~spl9_14), 0.75/1.05 inference(avatar_split_clause,[],[f254,f192,f92,f288])). 0.75/1.05 fof(f192,plain,( 0.75/1.05 spl9_14 <=> ordered_pair(sK3(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))),sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) = sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_14])])). 0.75/1.05 fof(f254,plain,( 0.75/1.05 ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) = sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))) | (~spl9_4 | ~spl9_14)), 0.75/1.05 inference(backward_demodulation,[],[f239,f193])). 0.75/1.05 fof(f193,plain,( 0.75/1.05 ordered_pair(sK3(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))),sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) = sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_14), 0.75/1.05 inference(avatar_component_clause,[],[f192])). 0.75/1.05 fof(f239,plain,( 0.75/1.05 sK0 = sK3(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))) | ~spl9_4), 0.75/1.05 inference(resolution,[],[f68,f93])). 0.75/1.05 fof(f274,plain,( 0.75/1.05 spl9_22 | ~spl9_10), 0.75/1.05 inference(avatar_split_clause,[],[f228,f134,f272])). 0.75/1.05 fof(f228,plain,( 0.75/1.05 sK0 = sK3(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1)) | ~spl9_10), 0.75/1.05 inference(resolution,[],[f68,f135])). 0.75/1.05 fof(f267,plain,( 0.75/1.05 spl9_20 | ~spl9_10 | ~spl9_12), 0.75/1.05 inference(avatar_split_clause,[],[f241,f160,f134,f265])). 0.75/1.05 fof(f160,plain,( 0.75/1.05 spl9_12 <=> ordered_pair(sK0,sK1) = ordered_pair(sK3(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1)),sK4(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_12])])). 0.75/1.05 fof(f241,plain,( 0.75/1.05 ordered_pair(sK0,sK1) = ordered_pair(sK0,sK4(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1))) | (~spl9_10 | ~spl9_12)), 0.75/1.05 inference(backward_demodulation,[],[f228,f161])). 0.75/1.05 fof(f161,plain,( 0.75/1.05 ordered_pair(sK0,sK1) = ordered_pair(sK3(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1)),sK4(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1))) | ~spl9_12), 0.75/1.05 inference(avatar_component_clause,[],[f160])). 0.75/1.05 fof(f217,plain,( 0.75/1.05 ~spl9_19 | ~spl9_14), 0.75/1.05 inference(avatar_split_clause,[],[f205,f192,f215])). 0.75/1.05 fof(f215,plain,( 0.75/1.05 spl9_19 <=> ~empty(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_19])])). 0.75/1.05 fof(f205,plain,( 0.75/1.05 ~empty(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))) | ~spl9_14), 0.75/1.05 inference(superposition,[],[f35,f193])). 0.75/1.05 fof(f35,plain,( 0.75/1.05 ( ! [X0,X1] : (~empty(ordered_pair(X0,X1))) )), 0.75/1.05 inference(cnf_transformation,[],[f9])). 0.75/1.05 fof(f9,axiom,( 0.75/1.05 ! [X0,X1] : ~empty(ordered_pair(X0,X1))), 0.75/1.05 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1)). 0.75/1.05 fof(f201,plain,( 0.75/1.05 spl9_16 | ~spl9_6), 0.75/1.05 inference(avatar_split_clause,[],[f155,f105,f199])). 0.75/1.05 fof(f155,plain,( 0.75/1.05 ordered_pair(sK3(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1)))),sK4(singleton(sK0),singleton(sK1),sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))))) = sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))) | ~spl9_6), 0.75/1.05 inference(resolution,[],[f39,f106])). 0.75/1.05 fof(f39,plain,( 0.75/1.05 ( ! [X0,X3,X1] : (~in(X3,cartesian_product2(X0,X1)) | ordered_pair(sK3(X0,X1,X3),sK4(X0,X1,X3)) = X3) )), 0.75/1.05 inference(equality_resolution,[],[f21])). 0.75/1.05 fof(f21,plain,( 0.75/1.05 ( ! [X2,X0,X3,X1] : (ordered_pair(sK3(X0,X1,X3),sK4(X0,X1,X3)) = X3 | ~in(X3,X2) | cartesian_product2(X0,X1) != X2) )), 0.75/1.05 inference(cnf_transformation,[],[f2])). 0.75/1.05 fof(f194,plain,( 0.75/1.05 spl9_14 | ~spl9_4), 0.75/1.05 inference(avatar_split_clause,[],[f154,f92,f192])). 0.75/1.05 fof(f154,plain,( 0.75/1.05 ordered_pair(sK3(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))),sK4(singleton(sK0),singleton(sK1),sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))))) = sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_4), 0.75/1.05 inference(resolution,[],[f39,f93])). 0.75/1.05 fof(f162,plain,( 0.75/1.05 spl9_12 | ~spl9_10), 0.75/1.05 inference(avatar_split_clause,[],[f148,f134,f160])). 0.75/1.05 fof(f148,plain,( 0.75/1.05 ordered_pair(sK0,sK1) = ordered_pair(sK3(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1)),sK4(singleton(sK0),singleton(sK1),ordered_pair(sK0,sK1))) | ~spl9_10), 0.75/1.05 inference(resolution,[],[f39,f135])). 0.75/1.05 fof(f143,plain,( 0.75/1.05 spl9_11), 0.75/1.05 inference(avatar_contradiction_clause,[],[f142])). 0.75/1.05 fof(f142,plain,( 0.75/1.05 $false | ~spl9_11), 0.75/1.05 inference(subsumption_resolution,[],[f141,f43])). 0.75/1.05 fof(f141,plain,( 0.75/1.05 ~in(sK1,singleton(sK1)) | ~spl9_11), 0.75/1.05 inference(subsumption_resolution,[],[f140,f43])). 0.75/1.05 fof(f140,plain,( 0.75/1.05 ~in(sK0,singleton(sK0)) | ~in(sK1,singleton(sK1)) | ~spl9_11), 0.75/1.05 inference(resolution,[],[f138,f37])). 0.75/1.05 fof(f37,plain,( 0.75/1.05 ( ! [X4,X0,X5,X1] : (in(ordered_pair(X4,X5),cartesian_product2(X0,X1)) | ~in(X4,X0) | ~in(X5,X1)) )), 0.75/1.05 inference(equality_resolution,[],[f36])). 0.75/1.05 fof(f36,plain,( 0.75/1.05 ( ! [X4,X2,X0,X5,X1] : (~in(X5,X1) | ~in(X4,X0) | in(ordered_pair(X4,X5),X2) | cartesian_product2(X0,X1) != X2) )), 0.75/1.05 inference(equality_resolution,[],[f23])). 0.75/1.05 fof(f23,plain,( 0.75/1.05 ( ! [X4,X2,X0,X5,X3,X1] : (~in(X5,X1) | ordered_pair(X4,X5) != X3 | ~in(X4,X0) | in(X3,X2) | cartesian_product2(X0,X1) != X2) )), 0.75/1.05 inference(cnf_transformation,[],[f2])). 0.75/1.05 fof(f138,plain,( 0.75/1.05 ~in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_11), 0.75/1.05 inference(avatar_component_clause,[],[f137])). 0.75/1.05 fof(f137,plain,( 0.75/1.05 spl9_11 <=> ~in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_11])])). 0.75/1.05 fof(f139,plain,( 0.75/1.05 ~spl9_11 | spl9_7 | ~spl9_8), 0.75/1.05 inference(avatar_split_clause,[],[f132,f111,f108,f137])). 0.75/1.05 fof(f108,plain,( 0.75/1.05 spl9_7 <=> ~in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),cartesian_product2(singleton(sK0),singleton(sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_7])])). 0.75/1.05 fof(f111,plain,( 0.75/1.05 spl9_8 <=> in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),singleton(ordered_pair(sK0,sK1)))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_8])])). 0.75/1.05 fof(f132,plain,( 0.75/1.05 ~in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1))) | (~spl9_7 | ~spl9_8)), 0.75/1.05 inference(backward_demodulation,[],[f130,f109])). 0.75/1.05 fof(f109,plain,( 0.75/1.05 ~in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_7), 0.75/1.05 inference(avatar_component_clause,[],[f108])). 0.75/1.05 fof(f130,plain,( 0.75/1.05 ordered_pair(sK0,sK1) = sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))) | ~spl9_8), 0.75/1.05 inference(resolution,[],[f112,f41])). 0.75/1.05 fof(f112,plain,( 0.75/1.05 in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),singleton(ordered_pair(sK0,sK1))) | ~spl9_8), 0.75/1.05 inference(avatar_component_clause,[],[f111])). 0.75/1.05 fof(f128,plain,( 0.75/1.05 spl9_8 | spl9_1 | spl9_7), 0.75/1.05 inference(avatar_split_clause,[],[f122,f108,f48,f111])). 0.75/1.05 fof(f48,plain,( 0.75/1.05 spl9_1 <=> singleton(ordered_pair(sK0,sK1)) != cartesian_product2(singleton(sK0),singleton(sK1))), 0.75/1.05 introduced(avatar_definition,[new_symbols(naming,[spl9_1])])). 0.75/1.05 fof(f122,plain,( 0.75/1.05 in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),singleton(ordered_pair(sK0,sK1))) | (~spl9_1 | ~spl9_7)), 0.75/1.05 inference(subsumption_resolution,[],[f118,f49])). 0.75/1.05 fof(f49,plain,( 0.75/1.05 singleton(ordered_pair(sK0,sK1)) != cartesian_product2(singleton(sK0),singleton(sK1)) | ~spl9_1), 0.75/1.05 inference(avatar_component_clause,[],[f48])). 0.75/1.05 fof(f118,plain,( 0.75/1.05 in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),singleton(ordered_pair(sK0,sK1))) | singleton(ordered_pair(sK0,sK1)) = cartesian_product2(singleton(sK0),singleton(sK1)) | ~spl9_7), 0.75/1.05 inference(resolution,[],[f109,f28])). 0.75/1.05 fof(f28,plain,( 0.75/1.05 ( ! [X0,X1] : (in(sK8(X0,X1),X1) | in(sK8(X0,X1),X0) | X0 = X1) )), 0.75/1.05 inference(cnf_transformation,[],[f14])). 0.75/1.05 fof(f14,plain,( 0.75/1.05 ! [X0,X1] : (X0 = X1 | ? [X2] : (in(X2,X0) <~> in(X2,X1)))), 0.75/1.05 inference(ennf_transformation,[],[f8])). 0.75/1.05 fof(f8,axiom,( 0.75/1.05 ! [X0,X1] : (! [X2] : (in(X2,X0) <=> in(X2,X1)) => X0 = X1)), 0.75/1.05 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski)). 0.75/1.05 fof(f121,plain,( 0.75/1.05 spl9_1 | spl9_7 | spl9_9), 0.75/1.05 inference(avatar_contradiction_clause,[],[f120])). 0.75/1.05 fof(f120,plain,( 0.75/1.05 $false | (~spl9_1 | ~spl9_7 | ~spl9_9)), 0.75/1.05 inference(subsumption_resolution,[],[f119,f49])). 0.75/1.05 fof(f119,plain,( 0.75/1.05 singleton(ordered_pair(sK0,sK1)) = cartesian_product2(singleton(sK0),singleton(sK1)) | (~spl9_7 | ~spl9_9)), 0.75/1.05 inference(subsumption_resolution,[],[f118,f115])). 0.75/1.05 fof(f116,plain,( 0.75/1.05 ~spl9_7 | ~spl9_9 | spl9_1), 0.75/1.05 inference(avatar_split_clause,[],[f81,f48,f114,f108])). 0.75/1.05 fof(f81,plain,( 0.75/1.05 ~in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),singleton(ordered_pair(sK0,sK1))) | ~in(sK8(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(ordered_pair(sK0,sK1))),cartesian_product2(singleton(sK0),singleton(sK1))) | ~spl9_1), 0.75/1.05 inference(extensionality_resolution,[],[f29,f49])). 0.75/1.05 fof(f29,plain,( 0.75/1.05 ( ! [X0,X1] : (~in(sK8(X0,X1),X1) | ~in(sK8(X0,X1),X0) | X0 = X1) )), 0.75/1.05 inference(cnf_transformation,[],[f14])). 0.75/1.05 fof(f102,plain,( 0.75/1.05 spl9_1 | spl9_3 | spl9_5), 0.75/1.05 inference(avatar_contradiction_clause,[],[f101])). 0.75/1.05 fof(f101,plain,( 0.75/1.05 $false | (~spl9_1 | ~spl9_3 | ~spl9_5)), 0.75/1.05 inference(subsumption_resolution,[],[f100,f49])). 0.75/1.05 fof(f100,plain,( 0.75/1.05 singleton(ordered_pair(sK0,sK1)) = cartesian_product2(singleton(sK0),singleton(sK1)) | (~spl9_3 | ~spl9_5)), 0.75/1.05 inference(subsumption_resolution,[],[f99,f90])). 0.75/1.05 fof(f99,plain,( 0.75/1.05 in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),singleton(ordered_pair(sK0,sK1))) | singleton(ordered_pair(sK0,sK1)) = cartesian_product2(singleton(sK0),singleton(sK1)) | ~spl9_5), 0.75/1.05 inference(resolution,[],[f96,f28])). 0.75/1.05 fof(f97,plain,( 0.75/1.05 ~spl9_3 | ~spl9_5 | spl9_1), 0.75/1.05 inference(avatar_split_clause,[],[f80,f48,f95,f89])). 0.75/1.05 fof(f80,plain,( 0.75/1.05 ~in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),cartesian_product2(singleton(sK0),singleton(sK1))) | ~in(sK8(singleton(ordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1))),singleton(ordered_pair(sK0,sK1))) | ~spl9_1), 0.75/1.05 inference(extensionality_resolution,[],[f29,f49])). 0.75/1.05 fof(f50,plain,( 0.75/1.05 ~spl9_1), 0.75/1.05 inference(avatar_split_clause,[],[f15,f48])). 0.75/1.05 fof(f15,plain,( 0.75/1.05 singleton(ordered_pair(sK0,sK1)) != cartesian_product2(singleton(sK0),singleton(sK1))), 0.75/1.05 inference(cnf_transformation,[],[f13])). 0.75/1.05 fof(f13,plain,( 0.75/1.05 ? [X0,X1] : singleton(ordered_pair(X0,X1)) != cartesian_product2(singleton(X0),singleton(X1))), 0.75/1.05 inference(ennf_transformation,[],[f12])). 0.75/1.05 fof(f12,negated_conjecture,( 0.75/1.05 ~! [X0,X1] : singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1))), 0.75/1.05 inference(negated_conjecture,[],[f11])). 0.75/1.05 fof(f11,conjecture,( 0.75/1.05 ! [X0,X1] : singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1))), 0.75/1.05 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1)). 0.75/1.05 % SZS output end Proof for theBenchmark 0.75/1.05 % ------------------------------ 0.75/1.05 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 0.75/1.05 % Termination reason: Refutation 0.75/1.05 0.75/1.05 % Memory used [KB]: 5500 0.75/1.05 % Time elapsed: 0.080 s 0.75/1.05 % ------------------------------ 0.75/1.05 % ------------------------------ 0.75/1.05 % Success in time 0.698 s 0.75/1.05 EOF