0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : vampire --mode casc -t %d %s 0.03/0.24 % Computer : n012.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 04:37:55 CDT 2018 0.03/0.24 % CPUTime : 0.03/0.28 % lrs+1002_2:1_acc=on:add=large:afr=on:afp=10000:afq=1.4:amm=sco:anc=none:bd=off:ccuc=first:fsr=off:gs=on:irw=on:nm=32:newcnf=on:nwc=1:stl=30:sd=2:ss=axioms:sos=on:sp=reverse_arity_3 on theBenchmark 0.07/0.34 % Refutation found. Thanks to Tanya! 0.07/0.34 % SZS status Theorem for theBenchmark 0.07/0.34 % SZS output start Proof for theBenchmark 0.07/0.34 fof(f3,axiom,( 0.07/0.34 ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0))), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski)). 0.07/0.34 fof(f16,conjecture,( 0.07/0.34 empty_set = relation_dom(empty_set) & relation_rng(empty_set) = empty_set), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1)). 0.07/0.34 fof(f17,negated_conjecture,( 0.07/0.34 ~(empty_set = relation_dom(empty_set) & relation_rng(empty_set) = empty_set)), 0.07/0.34 inference(negated_conjecture,[],[f16])). 0.07/0.34 fof(f21,axiom,( 0.07/0.34 ! [X0] : (relation(X0) => ! [X1] : (! [X2] : (in(X2,X1) <=> ? [X3] : in(ordered_pair(X2,X3),X0)) <=> relation_dom(X0) = X1))), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1)). 0.07/0.34 fof(f22,axiom,( 0.07/0.34 ! [X0] : (empty_set = X0 <=> ! [X1] : ~in(X1,X0))), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0)). 0.07/0.34 fof(f52,axiom,( 0.07/0.34 relation(empty_set) & empty(empty_set)), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1)). 0.07/0.34 fof(f108,axiom,( 0.07/0.34 ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski)). 0.07/0.34 fof(f126,axiom,( 0.07/0.34 ! [X0] : singleton(X0) = unordered_pair(X0,X0)), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1)). 0.07/0.34 fof(f136,axiom,( 0.07/0.34 ! [X0] : (relation(X0) => ! [X1] : (! [X2] : (? [X3] : in(ordered_pair(X3,X2),X0) <=> in(X2,X1)) <=> relation_rng(X0) = X1))), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1)). 0.07/0.34 fof(f180,plain,( 0.07/0.34 empty_set != relation_dom(empty_set) | relation_rng(empty_set) != empty_set), 0.07/0.34 inference(ennf_transformation,[],[f17])). 0.07/0.34 fof(f247,plain,( 0.07/0.34 ! [X0] : (! [X1] : (! [X2] : (in(X2,X1) <=> ? [X3] : in(ordered_pair(X2,X3),X0)) <=> relation_dom(X0) = X1) | ~relation(X0))), 0.07/0.34 inference(ennf_transformation,[],[f21])). 0.07/0.34 fof(f250,plain,( 0.07/0.34 ! [X0] : (! [X1] : (! [X2] : (? [X3] : in(ordered_pair(X3,X2),X0) <=> in(X2,X1)) <=> relation_rng(X0) = X1) | ~relation(X0))), 0.07/0.34 inference(ennf_transformation,[],[f136])). 0.07/0.34 fof(f299,plain,( 0.07/0.34 relation_rng(empty_set) != empty_set | empty_set != relation_dom(empty_set)), 0.07/0.34 inference(cnf_transformation,[],[f180])). 0.07/0.34 fof(f304,plain,( 0.07/0.34 ( ! [X0] : (singleton(X0) = unordered_pair(X0,X0)) )), 0.07/0.34 inference(cnf_transformation,[],[f126])). 0.07/0.34 fof(f401,plain,( 0.07/0.34 ( ! [X2,X0,X1] : (~relation(X0) | relation_dom(X0) != X1 | in(ordered_pair(X2,sK8(X0,X2)),X0) | ~in(X2,X1)) )), 0.07/0.34 inference(cnf_transformation,[],[f247])). 0.07/0.34 fof(f405,plain,( 0.07/0.34 ( ! [X2,X0,X1] : (~relation(X0) | relation_rng(X0) != X1 | ~in(X2,X1) | in(ordered_pair(sK11(X0,X2),X2),X0)) )), 0.07/0.34 inference(cnf_transformation,[],[f250])). 0.07/0.34 fof(f407,plain,( 0.07/0.34 ( ! [X0] : (in(sK12(X0),X0) | empty_set = X0) )), 0.07/0.34 inference(cnf_transformation,[],[f22])). 0.07/0.34 fof(f408,plain,( 0.07/0.34 ( ! [X0,X1] : (~in(X1,X0) | empty_set != X0) )), 0.07/0.34 inference(cnf_transformation,[],[f22])). 0.07/0.34 fof(f411,plain,( 0.07/0.34 relation(empty_set)), 0.07/0.34 inference(cnf_transformation,[],[f52])). 0.07/0.34 fof(f441,plain,( 0.07/0.34 ( ! [X0,X1] : (ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0))) )), 0.07/0.34 inference(cnf_transformation,[],[f3])). 0.07/0.34 fof(f442,plain,( 0.07/0.34 ( ! [X0,X1] : (unordered_pair(X0,X1) = unordered_pair(X1,X0)) )), 0.07/0.34 inference(cnf_transformation,[],[f108])). 0.07/0.34 fof(f555,plain,( 0.07/0.34 ( ! [X0,X1] : (ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) )), 0.07/0.34 inference(definition_unfolding,[],[f441,f304])). 0.07/0.34 fof(f597,plain,( 0.07/0.34 ( ! [X2,X0,X1] : (~relation(X0) | relation_dom(X0) != X1 | in(unordered_pair(unordered_pair(X2,sK8(X0,X2)),unordered_pair(X2,X2)),X0) | ~in(X2,X1)) )), 0.07/0.34 inference(definition_unfolding,[],[f401,f555])). 0.07/0.34 fof(f602,plain,( 0.07/0.34 ( ! [X2,X0,X1] : (~relation(X0) | relation_rng(X0) != X1 | ~in(X2,X1) | in(unordered_pair(unordered_pair(sK11(X0,X2),X2),unordered_pair(sK11(X0,X2),sK11(X0,X2))),X0)) )), 0.07/0.34 inference(definition_unfolding,[],[f405,f555])). 0.07/0.34 fof(f642,plain,( 0.07/0.34 ( ! [X2,X0] : (~relation(X0) | in(unordered_pair(unordered_pair(X2,sK8(X0,X2)),unordered_pair(X2,X2)),X0) | ~in(X2,relation_dom(X0))) )), 0.07/0.34 inference(equality_resolution,[],[f597])). 0.07/0.34 fof(f645,plain,( 0.07/0.34 ( ! [X2,X0] : (~relation(X0) | ~in(X2,relation_rng(X0)) | in(unordered_pair(unordered_pair(sK11(X0,X2),X2),unordered_pair(sK11(X0,X2),sK11(X0,X2))),X0)) )), 0.07/0.34 inference(equality_resolution,[],[f602])). 0.07/0.34 fof(f646,plain,( 0.07/0.34 ( ! [X1] : (~in(X1,empty_set)) )), 0.07/0.34 inference(equality_resolution,[],[f408])). 0.07/0.34 fof(f684,plain,( 0.07/0.34 spl48_0 <=> empty_set = relation_dom(empty_set)), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl48_0])])). 0.07/0.34 fof(f687,plain,( 0.07/0.34 spl48_1 <=> empty_set != relation_dom(empty_set)), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl48_1])])). 0.07/0.34 fof(f690,plain,( 0.07/0.34 spl48_2 <=> relation_rng(empty_set) = empty_set), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl48_2])])). 0.07/0.34 fof(f693,plain,( 0.07/0.34 spl48_3 <=> relation_rng(empty_set) != empty_set), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl48_3])])). 0.07/0.34 fof(f695,plain,( 0.07/0.34 ~spl48_1 | ~spl48_3), 0.07/0.34 inference(avatar_split_clause,[],[f299,f693,f687])). 0.07/0.34 fof(f707,plain,( 0.07/0.34 ( ! [X2,X0] : (in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,sK8(X0,X2))),X0) | ~relation(X0) | ~in(X2,relation_dom(X0))) )), 0.07/0.34 inference(forward_demodulation,[],[f642,f442])). 0.07/0.34 fof(f709,plain,( 0.07/0.34 ( ! [X2,X0] : (in(unordered_pair(unordered_pair(X2,sK11(X0,X2)),unordered_pair(sK11(X0,X2),sK11(X0,X2))),X0) | ~relation(X0) | ~in(X2,relation_rng(X0))) )), 0.07/0.34 inference(forward_demodulation,[],[f645,f442])). 0.07/0.34 fof(f2345,plain,( 0.07/0.34 ( ! [X26] : (~relation(empty_set) | ~in(X26,relation_dom(empty_set))) )), 0.07/0.34 inference(resolution,[],[f707,f646])). 0.07/0.34 fof(f2358,plain,( 0.07/0.34 spl48_26 <=> ! [X26] : ~in(X26,relation_dom(empty_set))), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl48_26])])). 0.07/0.34 fof(f2359,plain,( 0.07/0.34 ( ! [X26] : (~in(X26,relation_dom(empty_set))) ) | ~spl48_26), 0.07/0.34 inference(avatar_component_clause,[],[f2358])). 0.07/0.34 fof(f2364,plain,( 0.07/0.34 spl48_29 <=> ~relation(empty_set)), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl48_29])])). 0.07/0.34 fof(f2365,plain,( 0.07/0.34 ~relation(empty_set) | ~spl48_29), 0.07/0.34 inference(avatar_component_clause,[],[f2364])). 0.07/0.34 fof(f2366,plain,( 0.07/0.34 spl48_26 | ~spl48_29), 0.07/0.34 inference(avatar_split_clause,[],[f2345,f2364,f2358])). 0.07/0.34 fof(f2409,plain,( 0.07/0.34 $false | ~spl48_29), 0.07/0.34 inference(resolution,[],[f2365,f411])). 0.07/0.34 fof(f2412,plain,( 0.07/0.34 spl48_29), 0.07/0.34 inference(avatar_contradiction_clause,[],[f2409])). 0.07/0.34 fof(f2487,plain,( 0.07/0.34 empty_set = relation_dom(empty_set) | ~spl48_26), 0.07/0.34 inference(resolution,[],[f2359,f407])). 0.07/0.34 fof(f2515,plain,( 0.07/0.34 spl48_0 | ~spl48_26), 0.07/0.34 inference(avatar_split_clause,[],[f2487,f2358,f684])). 0.07/0.34 fof(f2860,plain,( 0.07/0.34 ( ! [X26] : (~relation(empty_set) | ~in(X26,relation_rng(empty_set))) )), 0.07/0.34 inference(resolution,[],[f709,f646])). 0.07/0.34 fof(f2869,plain,( 0.07/0.34 spl48_44 <=> ! [X26] : ~in(X26,relation_rng(empty_set))), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl48_44])])). 0.07/0.34 fof(f2870,plain,( 0.07/0.34 ( ! [X26] : (~in(X26,relation_rng(empty_set))) ) | ~spl48_44), 0.07/0.34 inference(avatar_component_clause,[],[f2869])). 0.07/0.34 fof(f2871,plain,( 0.07/0.34 spl48_44 | ~spl48_29), 0.07/0.34 inference(avatar_split_clause,[],[f2860,f2364,f2869])). 0.07/0.34 fof(f2883,plain,( 0.07/0.34 relation_rng(empty_set) = empty_set | ~spl48_44), 0.07/0.34 inference(resolution,[],[f2870,f407])). 0.07/0.34 fof(f2916,plain,( 0.07/0.34 spl48_2 | ~spl48_44), 0.07/0.34 inference(avatar_split_clause,[],[f2883,f2869,f690])). 0.07/0.34 fof(f2918,plain,( 0.07/0.34 $false), 0.07/0.34 inference(avatar_sat_refutation,[],[f695,f2366,f2412,f2515,f2871,f2916])). 0.07/0.34 % SZS output end Proof for theBenchmark 0.07/0.34 % ------------------------------ 0.07/0.34 % Version: Vampire 4.2.2 (commit 552c234 on 2018-07-02 14:53:33 +0100) 0.07/0.34 % Termination reason: Refutation 0.07/0.34 0.07/0.34 % Memory used [KB]: 12665 0.07/0.34 % Time elapsed: 0.064 s 0.07/0.34 % ------------------------------ 0.07/0.34 % ------------------------------ 0.07/0.34 % Success in time 0.102 s 0.07/0.35 EOF