0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : vampire -m 90000 --mode casc -t %d %s 0.02/0.23 % Computer : n065.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 06:56:55 CDT 2018 0.02/0.23 % CPUTime : 0.02/0.23 Hi Geoff, go and have some cold beer while I am trying to solve this very hard problem! 0.02/0.23 % remaining time: 5999 next slice time: 12 0.07/0.26 lrs+1011_3:1_av=off:cond=on:irw=on:lma=on:nm=16:nwc=1:stl=30:sos=all:updr=off_11 on theBenchmark 1.38/1.56 % (43280)Time limit reached! 1.38/1.56 % ------------------------------ 1.38/1.56 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 1.38/1.56 % Termination reason: Time limit 1.38/1.56 % Termination phase: Saturation 1.38/1.56 1.38/1.56 % Memory used [KB]: 14839 1.38/1.56 % Time elapsed: 1.300 s 1.38/1.56 % ------------------------------ 1.38/1.56 % ------------------------------ 1.38/1.57 % remaining time: 5986 next slice time: 4 1.38/1.57 lrs+1002_8_add=large:afp=40000:afq=1.0:amm=off:anc=none:cond=on:gs=on:irw=on:nm=16:newcnf=on:nwc=1:stl=30:sos=on:sp=reverse_arity:updr=off_2 on theBenchmark 1.86/2.07 % (43281)Time limit reached! 1.86/2.07 % ------------------------------ 1.86/2.07 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 1.86/2.07 % Termination reason: Time limit 1.86/2.07 % Termination phase: Saturation 1.86/2.07 1.86/2.07 % Memory used [KB]: 12281 1.86/2.07 % Time elapsed: 0.500 s 1.86/2.07 % ------------------------------ 1.86/2.07 % ------------------------------ 1.86/2.07 % remaining time: 5981 next slice time: 10 1.86/2.07 lrs+10_50_add=large:afp=40000:afq=1.2:amm=sco:anc=none:br=off:cond=on:fsr=off:gsp=input_only:gs=on:irw=on:lma=on:nm=64:nwc=1:stl=30:sos=all:sp=reverse_arity:urr=on_8 on theBenchmark 2.98/3.17 % (43282)Time limit reached! 2.98/3.17 % ------------------------------ 2.98/3.17 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 2.98/3.17 % Termination reason: Time limit 2.98/3.17 % Termination phase: Saturation 2.98/3.17 2.98/3.17 % Memory used [KB]: 31342 2.98/3.17 % Time elapsed: 1.100 s 2.98/3.17 % ------------------------------ 2.98/3.17 % ------------------------------ 2.98/3.17 % remaining time: 5970 next slice time: 7 2.98/3.18 dis+1002_3:1_acc=model:afr=on:afp=40000:afq=1.1:anc=none:ccuc=first:fsr=off:gsp=input_only:irw=on:nm=16:nwc=1:sos=all_5 on theBenchmark 3.79/3.97 % (43283)Time limit reached! 3.79/3.97 % ------------------------------ 3.79/3.97 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 3.79/3.97 % Termination reason: Time limit 3.79/3.97 % Termination phase: Saturation 3.79/3.97 3.79/3.97 % Memory used [KB]: 12153 3.79/3.97 % Time elapsed: 0.800 s 3.79/3.97 % ------------------------------ 3.79/3.97 % ------------------------------ 3.79/3.98 % remaining time: 5962 next slice time: 38 3.79/3.98 ott+11_8_amm=off:anc=none:bsr=on:cond=on:irw=on:nm=2:nwc=1.1:ss=axioms:st=2.0:sac=on_36 on theBenchmark 4.98/5.16 % Refutation found. Thanks to Tanya! 4.98/5.16 % SZS status Theorem for theBenchmark 4.98/5.16 % SZS output start Proof for theBenchmark 4.98/5.16 fof(f2,axiom,( 4.98/5.16 ! [X2,X0,X1] : (path(X0,X1,X2) => ! [X5,X6] : ((on_path(X5,X2) & (? [X7] : (precedes(X7,X6,X2) & sequential(X5,X7)) | sequential(X5,X6)) & on_path(X6,X2)) => precedes(X5,X6,X2)))), 4.98/5.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn)). 4.98/5.16 fof(f4,axiom,( 4.98/5.16 ! [X0,X1,X5,X6,X2] : ((precedes(X5,X6,X2) & shortest_path(X0,X1,X2)) => (~? [X7] : (tail_of(X5) = tail_of(X7) & head_of(X6) = head_of(X7)) & ~precedes(X6,X5,X2)))), 4.98/5.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties)). 4.98/5.16 fof(f5,axiom,( 4.98/5.16 complete => ! [X0,X1] : ((vertex(X0) & vertex(X1) & X0 != X1) => ? [X4] : (edge(X4) & ((tail_of(X4) = X1 & head_of(X4) = X0) <~> (tail_of(X4) = X0 & head_of(X4) = X1))))), 4.98/5.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_properties)). 4.98/5.16 fof(f6,axiom,( 4.98/5.16 ! [X0,X1,X9] : ((! [X2] : (path(X0,X1,X2) => less_or_equal(length_of(X9),length_of(X2))) & X0 != X1 & path(X0,X1,X9)) <=> shortest_path(X0,X1,X9))), 4.98/5.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn)). 4.98/5.16 fof(f10,axiom,( 4.98/5.16 ! [X4] : (edge(X4) => (vertex(tail_of(X4)) & vertex(head_of(X4))))), 4.98/5.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices)). 4.98/5.16 fof(f11,axiom,( 4.98/5.16 ! [X4] : (edge(X4) => tail_of(X4) != head_of(X4))), 4.98/5.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops)). 4.98/5.16 fof(f12,axiom,( 4.98/5.16 ! [X5,X6] : (sequential(X5,X6) <=> (edge(X6) & X5 != X6 & tail_of(X6) = head_of(X5) & edge(X5)))), 4.98/5.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn)). 4.98/5.16 fof(f14,conjecture,( 4.98/5.16 complete => ! [X0,X1,X2,X5,X6] : ((on_path(X6,X2) & sequential(X5,X6) & on_path(X5,X2) & shortest_path(X0,X1,X2)) => ? [X7] : triangle(X5,X6,X7))), 4.98/5.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_path_and_stuff_means_triangles)). 4.98/5.16 fof(f15,negated_conjecture,( 4.98/5.16 ~(complete => ! [X0,X1,X2,X5,X6] : ((on_path(X6,X2) & sequential(X5,X6) & on_path(X5,X2) & shortest_path(X0,X1,X2)) => ? [X7] : triangle(X5,X6,X7)))), 4.98/5.16 inference(negated_conjecture,[],[f14])). 4.98/5.16 fof(f18,axiom,( 4.98/5.16 ! [X5,X6,X7] : (triangle(X5,X6,X7) <=> (edge(X5) & edge(X6) & edge(X7) & sequential(X5,X6) & sequential(X6,X7) & sequential(X7,X5)))), 4.98/5.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn)). 4.98/5.16 fof(f20,plain,( 4.98/5.16 ~(complete => ! [X0,X1,X2,X3,X4] : ((on_path(X4,X2) & sequential(X3,X4) & on_path(X3,X2) & shortest_path(X0,X1,X2)) => ? [X5] : triangle(X3,X4,X5)))), 4.98/5.16 inference(rectify,[],[f15])). 4.98/5.16 fof(f21,plain,( 4.98/5.16 ! [X0,X1,X2] : (triangle(X0,X1,X2) <=> (edge(X0) & edge(X1) & edge(X2) & sequential(X0,X1) & sequential(X1,X2) & sequential(X2,X0)))), 4.98/5.16 inference(rectify,[],[f18])). 4.98/5.16 fof(f22,plain,( 4.98/5.16 ! [X0,X1,X2] : (path(X1,X2,X0) => ! [X3,X4] : ((on_path(X3,X0) & (? [X5] : (precedes(X5,X4,X0) & sequential(X3,X5)) | sequential(X3,X4)) & on_path(X4,X0)) => precedes(X3,X4,X0)))), 4.98/5.16 inference(rectify,[],[f2])). 4.98/5.16 fof(f24,plain,( 4.98/5.16 ! [X0,X1] : (sequential(X0,X1) <=> (edge(X1) & X0 != X1 & tail_of(X1) = head_of(X0) & edge(X0)))), 4.98/5.16 inference(rectify,[],[f12])). 4.98/5.16 fof(f25,plain,( 4.98/5.16 ! [X0,X1,X2,X3,X4] : ((precedes(X2,X3,X4) & shortest_path(X0,X1,X4)) => (~? [X5] : (tail_of(X2) = tail_of(X5) & head_of(X3) = head_of(X5)) & ~precedes(X3,X2,X4)))), 4.98/5.16 inference(rectify,[],[f4])). 4.98/5.16 fof(f26,plain,( 4.98/5.16 ! [X0,X1,X2] : ((! [X3] : (path(X0,X1,X3) => less_or_equal(length_of(X2),length_of(X3))) & X0 != X1 & path(X0,X1,X2)) <=> shortest_path(X0,X1,X2))), 4.98/5.16 inference(rectify,[],[f6])). 4.98/5.16 fof(f27,plain,( 4.98/5.16 complete => ! [X0,X1] : ((vertex(X0) & vertex(X1) & X0 != X1) => ? [X2] : (edge(X2) & ((tail_of(X2) = X1 & head_of(X2) = X0) <~> (tail_of(X2) = X0 & head_of(X2) = X1))))), 4.98/5.16 inference(rectify,[],[f5])). 4.98/5.16 fof(f28,plain,( 4.98/5.16 ! [X0] : (edge(X0) => (vertex(tail_of(X0)) & vertex(head_of(X0))))), 4.98/5.16 inference(rectify,[],[f10])). 4.98/5.16 fof(f29,plain,( 4.98/5.16 ! [X0] : (edge(X0) => tail_of(X0) != head_of(X0))), 4.98/5.16 inference(rectify,[],[f11])). 4.98/5.16 fof(f31,plain,( 4.98/5.16 ! [X0,X1,X2] : ((edge(X0) & edge(X1) & edge(X2) & sequential(X0,X1) & sequential(X1,X2) & sequential(X2,X0)) => triangle(X0,X1,X2))), 4.98/5.16 inference(unused_predicate_definition_removal,[],[f21])). 4.98/5.16 fof(f32,plain,( 4.98/5.16 ? [X0,X1,X2,X3,X4] : (! [X5] : ~triangle(X3,X4,X5) & (on_path(X4,X2) & sequential(X3,X4) & on_path(X3,X2) & shortest_path(X0,X1,X2))) & complete), 4.98/5.16 inference(ennf_transformation,[],[f20])). 4.98/5.16 fof(f33,plain,( 4.98/5.16 ? [X0,X1,X2,X3,X4] : (! [X5] : ~triangle(X3,X4,X5) & on_path(X4,X2) & sequential(X3,X4) & on_path(X3,X2) & shortest_path(X0,X1,X2)) & complete), 4.98/5.16 inference(flattening,[],[f32])). 4.98/5.16 fof(f34,plain,( 4.98/5.16 ! [X0,X1,X2] : (triangle(X0,X1,X2) | (~edge(X0) | ~edge(X1) | ~edge(X2) | ~sequential(X0,X1) | ~sequential(X1,X2) | ~sequential(X2,X0)))), 4.98/5.16 inference(ennf_transformation,[],[f31])). 4.98/5.16 fof(f35,plain,( 4.98/5.16 ! [X0,X1,X2] : (triangle(X0,X1,X2) | ~edge(X0) | ~edge(X1) | ~edge(X2) | ~sequential(X0,X1) | ~sequential(X1,X2) | ~sequential(X2,X0))), 4.98/5.16 inference(flattening,[],[f34])). 4.98/5.16 fof(f36,plain,( 4.98/5.16 ! [X0,X1,X2] : (! [X3,X4] : (precedes(X3,X4,X0) | (~on_path(X3,X0) | (! [X5] : (~precedes(X5,X4,X0) | ~sequential(X3,X5)) & ~sequential(X3,X4)) | ~on_path(X4,X0))) | ~path(X1,X2,X0))), 4.98/5.16 inference(ennf_transformation,[],[f22])). 4.98/5.16 fof(f37,plain,( 4.98/5.16 ! [X0,X1,X2] : (! [X3,X4] : (precedes(X3,X4,X0) | ~on_path(X3,X0) | (! [X5] : (~precedes(X5,X4,X0) | ~sequential(X3,X5)) & ~sequential(X3,X4)) | ~on_path(X4,X0)) | ~path(X1,X2,X0))), 4.98/5.16 inference(flattening,[],[f36])). 4.98/5.16 fof(f39,plain,( 4.98/5.16 ! [X0,X1,X2,X3,X4] : ((! [X5] : (tail_of(X2) != tail_of(X5) | head_of(X3) != head_of(X5)) & ~precedes(X3,X2,X4)) | (~precedes(X2,X3,X4) | ~shortest_path(X0,X1,X4)))), 4.98/5.16 inference(ennf_transformation,[],[f25])). 4.98/5.16 fof(f40,plain,( 4.98/5.16 ! [X0,X1,X2,X3,X4] : ((! [X5] : (tail_of(X2) != tail_of(X5) | head_of(X3) != head_of(X5)) & ~precedes(X3,X2,X4)) | ~precedes(X2,X3,X4) | ~shortest_path(X0,X1,X4))), 4.98/5.16 inference(flattening,[],[f39])). 4.98/5.16 fof(f41,plain,( 4.98/5.16 ! [X0,X1,X2] : ((! [X3] : (less_or_equal(length_of(X2),length_of(X3)) | ~path(X0,X1,X3)) & X0 != X1 & path(X0,X1,X2)) <=> shortest_path(X0,X1,X2))), 4.98/5.16 inference(ennf_transformation,[],[f26])). 4.98/5.16 fof(f42,plain,( 4.98/5.16 ! [X0,X1] : (? [X2] : (edge(X2) & ((tail_of(X2) = X1 & head_of(X2) = X0) <~> (tail_of(X2) = X0 & head_of(X2) = X1))) | (~vertex(X0) | ~vertex(X1) | X0 = X1)) | ~complete), 4.98/5.16 inference(ennf_transformation,[],[f27])). 4.98/5.16 fof(f43,plain,( 4.98/5.16 ! [X0,X1] : (? [X2] : (edge(X2) & ((tail_of(X2) = X1 & head_of(X2) = X0) <~> (tail_of(X2) = X0 & head_of(X2) = X1))) | ~vertex(X0) | ~vertex(X1) | X0 = X1) | ~complete), 4.98/5.16 inference(flattening,[],[f42])). 4.98/5.16 fof(f44,plain,( 4.98/5.16 ! [X0] : ((vertex(tail_of(X0)) & vertex(head_of(X0))) | ~edge(X0))), 4.98/5.16 inference(ennf_transformation,[],[f28])). 4.98/5.16 fof(f45,plain,( 4.98/5.16 ! [X0] : (tail_of(X0) != head_of(X0) | ~edge(X0))), 4.98/5.16 inference(ennf_transformation,[],[f29])). 4.98/5.16 fof(f50,plain,( 4.98/5.16 ! [X2,X1,X0] : (sP3(X2,X1,X0) <=> (! [X3] : (less_or_equal(length_of(X2),length_of(X3)) | ~path(X0,X1,X3)) & X0 != X1 & path(X0,X1,X2)))), 4.98/5.16 introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])])). 4.98/5.16 fof(f51,plain,( 4.98/5.16 ! [X0,X1,X2] : (sP3(X2,X1,X0) <=> shortest_path(X0,X1,X2))), 4.98/5.16 inference(definition_folding,[],[f41,f50])). 4.98/5.16 fof(f52,plain,( 4.98/5.16 ! [X1,X2,X0] : (sP4(X1,X2,X0) <=> (tail_of(X2) = X1 & head_of(X2) = X0))), 4.98/5.16 introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])])). 4.98/5.16 fof(f53,plain,( 4.98/5.16 ! [X0,X2,X1] : (sP5(X0,X2,X1) <=> (tail_of(X2) = X0 & head_of(X2) = X1))), 4.98/5.16 introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])])). 4.98/5.16 fof(f54,plain,( 4.98/5.16 ! [X1,X2,X0] : ((sP4(X1,X2,X0) <~> sP5(X0,X2,X1)) | ~sP6(X1,X2,X0))), 4.98/5.16 introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])])). 4.98/5.16 fof(f55,plain,( 4.98/5.16 ! [X0,X1] : (? [X2] : (edge(X2) & sP6(X1,X2,X0)) | ~vertex(X0) | ~vertex(X1) | X0 = X1) | ~complete), 4.98/5.16 inference(definition_folding,[],[f43,f54,f53,f52])). 4.98/5.16 fof(f56,plain,( 4.98/5.16 ? [X0,X1,X2,X3,X4] : (! [X5] : ~triangle(X3,X4,X5) & on_path(X4,X2) & sequential(X3,X4) & on_path(X3,X2) & shortest_path(X0,X1,X2)) => (! [X5] : ~triangle(sK10,sK11,X5) & on_path(sK11,sK9) & sequential(sK10,sK11) & on_path(sK10,sK9) & shortest_path(sK7,sK8,sK9))), 4.98/5.16 introduced(choice_axiom,[])). 4.98/5.16 fof(f57,plain,( 4.98/5.16 (! [X5] : ~triangle(sK10,sK11,X5) & on_path(sK11,sK9) & sequential(sK10,sK11) & on_path(sK10,sK9) & shortest_path(sK7,sK8,sK9)) & complete), 4.98/5.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f33,f56])). 4.98/5.16 fof(f66,plain,( 4.98/5.16 ! [X0,X1] : ((sequential(X0,X1) | (~edge(X1) | X0 = X1 | tail_of(X1) != head_of(X0) | ~edge(X0))) & ((edge(X1) & X0 != X1 & tail_of(X1) = head_of(X0) & edge(X0)) | ~sequential(X0,X1)))), 4.98/5.16 inference(nnf_transformation,[],[f24])). 4.98/5.16 fof(f67,plain,( 4.98/5.16 ! [X0,X1] : ((sequential(X0,X1) | ~edge(X1) | X0 = X1 | tail_of(X1) != head_of(X0) | ~edge(X0)) & ((edge(X1) & X0 != X1 & tail_of(X1) = head_of(X0) & edge(X0)) | ~sequential(X0,X1)))), 4.98/5.16 inference(flattening,[],[f66])). 4.98/5.16 fof(f68,plain,( 4.98/5.16 ! [X2,X1,X0] : ((sP3(X2,X1,X0) | (? [X3] : (~less_or_equal(length_of(X2),length_of(X3)) & path(X0,X1,X3)) | X0 = X1 | ~path(X0,X1,X2))) & ((! [X3] : (less_or_equal(length_of(X2),length_of(X3)) | ~path(X0,X1,X3)) & X0 != X1 & path(X0,X1,X2)) | ~sP3(X2,X1,X0)))), 4.98/5.16 inference(nnf_transformation,[],[f50])). 4.98/5.16 fof(f69,plain,( 4.98/5.16 ! [X2,X1,X0] : ((sP3(X2,X1,X0) | ? [X3] : (~less_or_equal(length_of(X2),length_of(X3)) & path(X0,X1,X3)) | X0 = X1 | ~path(X0,X1,X2)) & ((! [X3] : (less_or_equal(length_of(X2),length_of(X3)) | ~path(X0,X1,X3)) & X0 != X1 & path(X0,X1,X2)) | ~sP3(X2,X1,X0)))), 4.98/5.16 inference(flattening,[],[f68])). 4.98/5.16 fof(f70,plain,( 4.98/5.16 ! [X0,X1,X2] : ((sP3(X0,X1,X2) | ? [X3] : (~less_or_equal(length_of(X0),length_of(X3)) & path(X2,X1,X3)) | X1 = X2 | ~path(X2,X1,X0)) & ((! [X4] : (less_or_equal(length_of(X0),length_of(X4)) | ~path(X2,X1,X4)) & X1 != X2 & path(X2,X1,X0)) | ~sP3(X0,X1,X2)))), 4.98/5.16 inference(rectify,[],[f69])). 4.98/5.16 fof(f71,plain,( 4.98/5.16 ! [X2,X1,X0] : (? [X3] : (~less_or_equal(length_of(X0),length_of(X3)) & path(X2,X1,X3)) => (~less_or_equal(length_of(X0),length_of(sK13(X0,X1,X2))) & path(X2,X1,sK13(X0,X1,X2))))), 4.98/5.16 introduced(choice_axiom,[])). 4.98/5.16 fof(f72,plain,( 4.98/5.16 ! [X0,X1,X2] : ((sP3(X0,X1,X2) | (~less_or_equal(length_of(X0),length_of(sK13(X0,X1,X2))) & path(X2,X1,sK13(X0,X1,X2))) | X1 = X2 | ~path(X2,X1,X0)) & ((! [X4] : (less_or_equal(length_of(X0),length_of(X4)) | ~path(X2,X1,X4)) & X1 != X2 & path(X2,X1,X0)) | ~sP3(X0,X1,X2)))), 4.98/5.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f70,f71])). 4.98/5.16 fof(f73,plain,( 4.98/5.16 ! [X0,X1,X2] : ((sP3(X2,X1,X0) | ~shortest_path(X0,X1,X2)) & (shortest_path(X0,X1,X2) | ~sP3(X2,X1,X0)))), 4.98/5.16 inference(nnf_transformation,[],[f51])). 4.98/5.16 fof(f74,plain,( 4.98/5.16 ! [X1,X2,X0] : (((~sP5(X0,X2,X1) | ~sP4(X1,X2,X0)) & (sP5(X0,X2,X1) | sP4(X1,X2,X0))) | ~sP6(X1,X2,X0))), 4.98/5.16 inference(nnf_transformation,[],[f54])). 4.98/5.16 fof(f75,plain,( 4.98/5.16 ! [X0,X1,X2] : (((~sP5(X2,X1,X0) | ~sP4(X0,X1,X2)) & (sP5(X2,X1,X0) | sP4(X0,X1,X2))) | ~sP6(X0,X1,X2))), 4.98/5.16 inference(rectify,[],[f74])). 4.98/5.16 fof(f76,plain,( 4.98/5.16 ! [X0,X2,X1] : ((sP5(X0,X2,X1) | (tail_of(X2) != X0 | head_of(X2) != X1)) & ((tail_of(X2) = X0 & head_of(X2) = X1) | ~sP5(X0,X2,X1)))), 4.98/5.16 inference(nnf_transformation,[],[f53])). 4.98/5.16 fof(f77,plain,( 4.98/5.16 ! [X0,X2,X1] : ((sP5(X0,X2,X1) | tail_of(X2) != X0 | head_of(X2) != X1) & ((tail_of(X2) = X0 & head_of(X2) = X1) | ~sP5(X0,X2,X1)))), 4.98/5.16 inference(flattening,[],[f76])). 4.98/5.16 fof(f78,plain,( 4.98/5.16 ! [X0,X1,X2] : ((sP5(X0,X1,X2) | tail_of(X1) != X0 | head_of(X1) != X2) & ((tail_of(X1) = X0 & head_of(X1) = X2) | ~sP5(X0,X1,X2)))), 4.98/5.16 inference(rectify,[],[f77])). 4.98/5.16 fof(f79,plain,( 4.98/5.16 ! [X1,X2,X0] : ((sP4(X1,X2,X0) | (tail_of(X2) != X1 | head_of(X2) != X0)) & ((tail_of(X2) = X1 & head_of(X2) = X0) | ~sP4(X1,X2,X0)))), 4.98/5.16 inference(nnf_transformation,[],[f52])). 4.98/5.16 fof(f80,plain,( 4.98/5.16 ! [X1,X2,X0] : ((sP4(X1,X2,X0) | tail_of(X2) != X1 | head_of(X2) != X0) & ((tail_of(X2) = X1 & head_of(X2) = X0) | ~sP4(X1,X2,X0)))), 4.98/5.16 inference(flattening,[],[f79])). 4.98/5.16 fof(f81,plain,( 4.98/5.16 ! [X0,X1,X2] : ((sP4(X0,X1,X2) | tail_of(X1) != X0 | head_of(X1) != X2) & ((tail_of(X1) = X0 & head_of(X1) = X2) | ~sP4(X0,X1,X2)))), 4.98/5.16 inference(rectify,[],[f80])). 4.98/5.16 fof(f82,plain,( 4.98/5.16 ! [X1,X0] : (? [X2] : (edge(X2) & sP6(X1,X2,X0)) => (edge(sK14(X0,X1)) & sP6(X1,sK14(X0,X1),X0)))), 4.98/5.16 introduced(choice_axiom,[])). 4.98/5.16 fof(f83,plain,( 4.98/5.16 ! [X0,X1] : ((edge(sK14(X0,X1)) & sP6(X1,sK14(X0,X1),X0)) | ~vertex(X0) | ~vertex(X1) | X0 = X1) | ~complete), 4.98/5.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f55,f82])). 4.98/5.16 fof(f84,plain,( 4.98/5.16 complete), 4.98/5.16 inference(cnf_transformation,[],[f57])). 4.98/5.16 fof(f85,plain,( 4.98/5.16 shortest_path(sK7,sK8,sK9)), 4.98/5.16 inference(cnf_transformation,[],[f57])). 4.98/5.16 fof(f86,plain,( 4.98/5.16 on_path(sK10,sK9)), 4.98/5.16 inference(cnf_transformation,[],[f57])). 4.98/5.16 fof(f87,plain,( 4.98/5.16 sequential(sK10,sK11)), 4.98/5.16 inference(cnf_transformation,[],[f57])). 4.98/5.16 fof(f88,plain,( 4.98/5.16 on_path(sK11,sK9)), 4.98/5.16 inference(cnf_transformation,[],[f57])). 4.98/5.16 fof(f89,plain,( 4.98/5.16 ( ! [X5] : (~triangle(sK10,sK11,X5)) )), 4.98/5.16 inference(cnf_transformation,[],[f57])). 4.98/5.16 fof(f90,plain,( 4.98/5.16 ( ! [X2,X0,X1] : (~sequential(X2,X0) | ~edge(X0) | ~edge(X1) | ~edge(X2) | ~sequential(X0,X1) | ~sequential(X1,X2) | triangle(X0,X1,X2)) )), 4.98/5.16 inference(cnf_transformation,[],[f35])). 4.98/5.16 fof(f91,plain,( 4.98/5.16 ( ! [X4,X2,X0,X3,X1] : (~sequential(X3,X4) | ~on_path(X3,X0) | precedes(X3,X4,X0) | ~on_path(X4,X0) | ~path(X1,X2,X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f37])). 4.98/5.16 fof(f102,plain,( 4.98/5.16 ( ! [X0,X1] : (~sequential(X0,X1) | edge(X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f67])). 4.98/5.16 fof(f103,plain,( 4.98/5.16 ( ! [X0,X1] : (~sequential(X0,X1) | tail_of(X1) = head_of(X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f67])). 4.98/5.16 fof(f104,plain,( 4.98/5.16 ( ! [X0,X1] : (X0 != X1 | ~sequential(X0,X1)) )), 4.98/5.16 inference(cnf_transformation,[],[f67])). 4.98/5.16 fof(f105,plain,( 4.98/5.16 ( ! [X0,X1] : (~sequential(X0,X1) | edge(X1)) )), 4.98/5.16 inference(cnf_transformation,[],[f67])). 4.98/5.16 fof(f106,plain,( 4.98/5.16 ( ! [X0,X1] : (tail_of(X1) != head_of(X0) | ~edge(X1) | X0 = X1 | sequential(X0,X1) | ~edge(X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f67])). 4.98/5.16 fof(f107,plain,( 4.98/5.16 ( ! [X4,X2,X0,X3,X1] : (~shortest_path(X0,X1,X4) | ~precedes(X2,X3,X4) | ~precedes(X3,X2,X4)) )), 4.98/5.16 inference(cnf_transformation,[],[f40])). 4.98/5.16 fof(f108,plain,( 4.98/5.16 ( ! [X4,X2,X0,X5,X3,X1] : (tail_of(X2) != tail_of(X5) | head_of(X3) != head_of(X5) | ~precedes(X2,X3,X4) | ~shortest_path(X0,X1,X4)) )), 4.98/5.16 inference(cnf_transformation,[],[f40])). 4.98/5.16 fof(f109,plain,( 4.98/5.16 ( ! [X2,X0,X1] : (~sP3(X0,X1,X2) | path(X2,X1,X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f72])). 4.98/5.16 fof(f115,plain,( 4.98/5.16 ( ! [X2,X0,X1] : (~shortest_path(X0,X1,X2) | sP3(X2,X1,X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f73])). 4.98/5.16 fof(f116,plain,( 4.98/5.16 ( ! [X2,X0,X1] : (~sP6(X0,X1,X2) | sP4(X0,X1,X2) | sP5(X2,X1,X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f75])). 4.98/5.16 fof(f118,plain,( 4.98/5.16 ( ! [X2,X0,X1] : (~sP5(X0,X1,X2) | head_of(X1) = X2) )), 4.98/5.16 inference(cnf_transformation,[],[f78])). 4.98/5.16 fof(f119,plain,( 4.98/5.16 ( ! [X2,X0,X1] : (~sP5(X0,X1,X2) | tail_of(X1) = X0) )), 4.98/5.16 inference(cnf_transformation,[],[f78])). 4.98/5.16 fof(f121,plain,( 4.98/5.16 ( ! [X2,X0,X1] : (~sP4(X0,X1,X2) | head_of(X1) = X2) )), 4.98/5.16 inference(cnf_transformation,[],[f81])). 4.98/5.16 fof(f122,plain,( 4.98/5.16 ( ! [X2,X0,X1] : (~sP4(X0,X1,X2) | tail_of(X1) = X0) )), 4.98/5.16 inference(cnf_transformation,[],[f81])). 4.98/5.16 fof(f124,plain,( 4.98/5.16 ( ! [X0,X1] : (sP6(X1,sK14(X0,X1),X0) | ~vertex(X0) | ~vertex(X1) | X0 = X1 | ~complete) )), 4.98/5.16 inference(cnf_transformation,[],[f83])). 4.98/5.16 fof(f125,plain,( 4.98/5.16 ( ! [X0,X1] : (edge(sK14(X0,X1)) | ~vertex(X0) | ~vertex(X1) | X0 = X1 | ~complete) )), 4.98/5.16 inference(cnf_transformation,[],[f83])). 4.98/5.16 fof(f126,plain,( 4.98/5.16 ( ! [X0] : (vertex(head_of(X0)) | ~edge(X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f44])). 4.98/5.16 fof(f127,plain,( 4.98/5.16 ( ! [X0] : (vertex(tail_of(X0)) | ~edge(X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f44])). 4.98/5.16 fof(f128,plain,( 4.98/5.16 ( ! [X0] : (tail_of(X0) != head_of(X0) | ~edge(X0)) )), 4.98/5.16 inference(cnf_transformation,[],[f45])). 4.98/5.16 fof(f130,plain,( 4.98/5.16 ( ! [X1] : (~sequential(X1,X1)) )), 4.98/5.16 inference(equality_resolution,[],[f104])). 4.98/5.16 fof(f136,plain,( 4.98/5.16 ( ! [X0,X1] : (edge(sK14(X0,X1)) | ~vertex(X0) | ~vertex(X1) | X0 = X1) )), 4.98/5.16 inference(subsumption_resolution,[],[f125,f84])). 4.98/5.16 fof(f137,plain,( 4.98/5.16 ( ! [X0,X1] : (sP6(X1,sK14(X0,X1),X0) | ~vertex(X0) | ~vertex(X1) | X0 = X1) )), 4.98/5.16 inference(subsumption_resolution,[],[f124,f84])). 4.98/5.16 fof(f138,plain,( 4.98/5.16 edge(sK10)), 4.98/5.16 inference(resolution,[],[f102,f87])). 4.98/5.16 fof(f139,plain,( 4.98/5.16 edge(sK11)), 4.98/5.16 inference(resolution,[],[f105,f87])). 4.98/5.16 fof(f140,plain,( 4.98/5.16 tail_of(sK11) = head_of(sK10)), 4.98/5.16 inference(resolution,[],[f103,f87])). 4.98/5.16 fof(f141,plain,( 4.98/5.16 tail_of(sK10) != tail_of(sK11) | ~edge(sK10)), 4.98/5.16 inference(superposition,[],[f128,f140])). 4.98/5.16 fof(f144,plain,( 4.98/5.16 vertex(tail_of(sK11)) | ~edge(sK10)), 4.98/5.16 inference(superposition,[],[f126,f140])). 4.98/5.16 fof(f145,plain,( 4.98/5.16 tail_of(sK10) != tail_of(sK11)), 4.98/5.16 inference(subsumption_resolution,[],[f141,f138])). 4.98/5.16 fof(f146,plain,( 4.98/5.16 vertex(tail_of(sK11))), 4.98/5.16 inference(subsumption_resolution,[],[f144,f138])). 4.98/5.16 fof(f147,plain,( 4.98/5.16 sP3(sK9,sK8,sK7)), 4.98/5.16 inference(resolution,[],[f115,f85])). 4.98/5.16 fof(f149,plain,( 4.98/5.16 path(sK7,sK8,sK9)), 4.98/5.16 inference(resolution,[],[f147,f109])). 4.98/5.16 fof(f160,plain,( 4.98/5.16 ( ! [X0,X1] : (~precedes(X1,X0,sK9) | ~precedes(X0,X1,sK9)) )), 4.98/5.17 inference(resolution,[],[f107,f85])). 4.98/5.17 fof(f161,plain,( 4.98/5.17 ( ! [X0,X1] : (sP5(X1,sK14(X1,X0),X0) | sP4(X0,sK14(X1,X0),X1) | ~vertex(X1) | ~vertex(X0) | X0 = X1) )), 4.98/5.17 inference(resolution,[],[f116,f137])). 4.98/5.17 fof(f168,plain,( 4.98/5.17 ( ! [X2,X0,X1] : (~on_path(sK11,X0) | precedes(sK10,sK11,X0) | ~on_path(sK10,X0) | ~path(X1,X2,X0)) )), 4.98/5.17 inference(resolution,[],[f91,f87])). 4.98/5.17 fof(f169,plain,( 4.98/5.17 ( ! [X0,X1] : (precedes(sK10,sK11,sK9) | ~on_path(sK10,sK9) | ~path(X0,X1,sK9)) )), 4.98/5.17 inference(resolution,[],[f168,f88])). 4.98/5.17 fof(f170,plain,( 4.98/5.17 ( ! [X0,X1] : (precedes(sK10,sK11,sK9) | ~path(X0,X1,sK9)) )), 4.98/5.17 inference(subsumption_resolution,[],[f169,f86])). 4.98/5.17 fof(f172,plain,( 4.98/5.17 spl15_0 <=> ! [X1,X0] : ~path(X0,X1,sK9)), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_0])])). 4.98/5.17 fof(f173,plain,( 4.98/5.17 ( ! [X0,X1] : (~path(X0,X1,sK9)) ) | ~spl15_0), 4.98/5.17 inference(avatar_component_clause,[],[f172])). 4.98/5.17 fof(f178,plain,( 4.98/5.17 spl15_2 <=> precedes(sK10,sK11,sK9)), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_2])])). 4.98/5.17 fof(f179,plain,( 4.98/5.17 precedes(sK10,sK11,sK9) | ~spl15_2), 4.98/5.17 inference(avatar_component_clause,[],[f178])). 4.98/5.17 fof(f180,plain,( 4.98/5.17 spl15_0 | spl15_2), 4.98/5.17 inference(avatar_split_clause,[],[f170,f178,f172])). 4.98/5.17 fof(f181,plain,( 4.98/5.17 ~precedes(sK11,sK10,sK9) | ~spl15_2), 4.98/5.17 inference(resolution,[],[f179,f160])). 4.98/5.17 fof(f190,plain,( 4.98/5.17 $false | ~spl15_0), 4.98/5.17 inference(subsumption_resolution,[],[f149,f173])). 4.98/5.17 fof(f191,plain,( 4.98/5.17 ~spl15_0), 4.98/5.17 inference(avatar_contradiction_clause,[],[f190])). 4.98/5.17 fof(f198,plain,( 4.98/5.17 ( ! [X4,X2,X0,X3,X1] : (~shortest_path(X3,X4,X2) | ~precedes(X1,X0,X2) | head_of(X0) != head_of(X1)) )), 4.98/5.17 inference(equality_resolution,[],[f108])). 4.98/5.17 fof(f199,plain,( 4.98/5.17 ( ! [X0,X1] : (~precedes(X0,X1,sK9) | head_of(X0) != head_of(X1)) )), 4.98/5.17 inference(resolution,[],[f198,f85])). 4.98/5.17 fof(f201,plain,( 4.98/5.17 head_of(sK10) != head_of(sK11) | ~spl15_2), 4.98/5.17 inference(resolution,[],[f199,f179])). 4.98/5.17 fof(f202,plain,( 4.98/5.17 tail_of(sK11) != head_of(sK11) | ~spl15_2), 4.98/5.17 inference(forward_demodulation,[],[f201,f140])). 4.98/5.17 fof(f203,plain,( 4.98/5.17 ( ! [X0,X1] : (~vertex(X0) | ~vertex(X1) | sP4(X0,sK14(X1,X0),X1) | X0 = X1 | tail_of(sK14(X1,X0)) = X1) )), 4.98/5.17 inference(resolution,[],[f161,f119])). 4.98/5.17 fof(f204,plain,( 4.98/5.17 ( ! [X2,X3] : (~vertex(X2) | ~vertex(X3) | sP4(X2,sK14(X3,X2),X3) | X2 = X3 | head_of(sK14(X3,X2)) = X2) )), 4.98/5.17 inference(resolution,[],[f161,f118])). 4.98/5.17 fof(f205,plain,( 4.98/5.17 ( ! [X0,X1] : (~edge(X1) | sP4(head_of(X1),sK14(X0,head_of(X1)),X0) | head_of(X1) = X0 | tail_of(sK14(X0,head_of(X1))) = X0 | ~vertex(X0)) )), 4.98/5.17 inference(resolution,[],[f203,f126])). 4.98/5.17 fof(f207,plain,( 4.98/5.17 ( ! [X4] : (sP4(tail_of(sK11),sK14(X4,tail_of(sK11)),X4) | ~vertex(X4) | tail_of(sK11) = X4 | tail_of(sK14(X4,tail_of(sK11))) = X4) )), 4.98/5.17 inference(resolution,[],[f203,f146])). 4.98/5.17 fof(f208,plain,( 4.98/5.17 ( ! [X0,X1] : (~vertex(X0) | sP4(head_of(X1),sK14(X0,head_of(X1)),X0) | head_of(X1) = X0 | head_of(X1) = head_of(sK14(X0,head_of(X1))) | ~edge(X1)) )), 4.98/5.17 inference(resolution,[],[f204,f126])). 4.98/5.17 fof(f220,plain,( 4.98/5.17 ( ! [X2] : (~vertex(X2) | tail_of(sK11) = X2 | tail_of(sK14(X2,tail_of(sK11))) = X2 | head_of(sK14(X2,tail_of(sK11))) = X2) )), 4.98/5.17 inference(resolution,[],[f207,f121])). 4.98/5.17 fof(f223,plain,( 4.98/5.17 ( ! [X1] : (~edge(X1) | tail_of(X1) = tail_of(sK14(tail_of(X1),tail_of(sK11))) | tail_of(X1) = head_of(sK14(tail_of(X1),tail_of(sK11))) | tail_of(sK11) = tail_of(X1)) )), 4.98/5.17 inference(resolution,[],[f220,f127])). 4.98/5.17 fof(f242,plain,( 4.98/5.17 ( ! [X1] : (sP4(head_of(sK11),sK14(X1,head_of(sK11)),X1) | head_of(sK11) = X1 | tail_of(sK14(X1,head_of(sK11))) = X1 | ~vertex(X1)) )), 4.98/5.17 inference(resolution,[],[f205,f139])). 4.98/5.17 fof(f248,plain,( 4.98/5.17 ( ! [X1] : (~vertex(X1) | tail_of(sK14(X1,head_of(sK11))) = X1 | head_of(sK11) = X1 | tail_of(sK14(X1,head_of(sK11))) = head_of(sK11)) )), 4.98/5.17 inference(resolution,[],[f242,f122])). 4.98/5.17 fof(f249,plain,( 4.98/5.17 ( ! [X2] : (~vertex(X2) | tail_of(sK14(X2,head_of(sK11))) = X2 | head_of(sK11) = X2 | head_of(sK14(X2,head_of(sK11))) = X2) )), 4.98/5.17 inference(resolution,[],[f242,f121])). 4.98/5.17 fof(f252,plain,( 4.98/5.17 ( ! [X1] : (~edge(X1) | tail_of(X1) = head_of(sK11) | tail_of(X1) = head_of(sK14(tail_of(X1),head_of(sK11))) | tail_of(X1) = tail_of(sK14(tail_of(X1),head_of(sK11)))) )), 4.98/5.17 inference(resolution,[],[f249,f127])). 4.98/5.17 fof(f262,plain,( 4.98/5.17 spl15_9 <=> tail_of(sK11) != tail_of(sK14(tail_of(sK11),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_9])])). 4.98/5.17 fof(f263,plain,( 4.98/5.17 tail_of(sK11) != tail_of(sK14(tail_of(sK11),head_of(sK11))) | ~spl15_9), 4.98/5.17 inference(avatar_component_clause,[],[f262])). 4.98/5.17 fof(f265,plain,( 4.98/5.17 spl15_8 <=> tail_of(sK11) = tail_of(sK14(tail_of(sK11),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_8])])). 4.98/5.17 fof(f266,plain,( 4.98/5.17 tail_of(sK11) = tail_of(sK14(tail_of(sK11),head_of(sK11))) | ~spl15_8), 4.98/5.17 inference(avatar_component_clause,[],[f265])). 4.98/5.17 fof(f296,plain,( 4.98/5.17 spl15_14 <=> edge(sK14(tail_of(sK11),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_14])])). 4.98/5.17 fof(f297,plain,( 4.98/5.17 edge(sK14(tail_of(sK11),head_of(sK11))) | ~spl15_14), 4.98/5.17 inference(avatar_component_clause,[],[f296])). 4.98/5.17 fof(f299,plain,( 4.98/5.17 spl15_15 <=> ~edge(sK14(tail_of(sK11),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_15])])). 4.98/5.17 fof(f300,plain,( 4.98/5.17 ~edge(sK14(tail_of(sK11),head_of(sK11))) | ~spl15_15), 4.98/5.17 inference(avatar_component_clause,[],[f299])). 4.98/5.17 fof(f302,plain,( 4.98/5.17 ~vertex(tail_of(sK11)) | ~vertex(head_of(sK11)) | tail_of(sK11) = head_of(sK11) | ~spl15_15), 4.98/5.17 inference(resolution,[],[f300,f136])). 4.98/5.17 fof(f303,plain,( 4.98/5.17 ~vertex(head_of(sK11)) | tail_of(sK11) = head_of(sK11) | ~spl15_15), 4.98/5.17 inference(subsumption_resolution,[],[f302,f146])). 4.98/5.17 fof(f304,plain,( 4.98/5.17 ~vertex(head_of(sK11)) | (~spl15_2 | ~spl15_15)), 4.98/5.17 inference(subsumption_resolution,[],[f303,f202])). 4.98/5.17 fof(f305,plain,( 4.98/5.17 ~edge(sK11) | (~spl15_2 | ~spl15_15)), 4.98/5.17 inference(resolution,[],[f304,f126])). 4.98/5.17 fof(f306,plain,( 4.98/5.17 $false | (~spl15_2 | ~spl15_15)), 4.98/5.17 inference(subsumption_resolution,[],[f305,f139])). 4.98/5.17 fof(f307,plain,( 4.98/5.17 ~spl15_2 | spl15_15), 4.98/5.17 inference(avatar_contradiction_clause,[],[f306])). 4.98/5.17 fof(f316,plain,( 4.98/5.17 ( ! [X4] : (~edge(X4) | tail_of(sK11) = head_of(X4) | head_of(X4) = head_of(sK14(tail_of(sK11),head_of(X4))) | sP4(head_of(X4),sK14(tail_of(sK11),head_of(X4)),tail_of(sK11))) )), 4.98/5.17 inference(resolution,[],[f208,f146])). 4.98/5.17 fof(f361,plain,( 4.98/5.17 ( ! [X0] : (~edge(X0) | head_of(sK11) = head_of(X0) | tail_of(sK14(head_of(X0),head_of(sK11))) = head_of(sK11) | tail_of(sK14(head_of(X0),head_of(sK11))) = head_of(X0)) )), 4.98/5.17 inference(resolution,[],[f248,f126])). 4.98/5.17 fof(f362,plain,( 4.98/5.17 ( ! [X1] : (~edge(X1) | tail_of(X1) = head_of(sK11) | tail_of(sK14(tail_of(X1),head_of(sK11))) = head_of(sK11) | tail_of(X1) = tail_of(sK14(tail_of(X1),head_of(sK11)))) )), 4.98/5.17 inference(resolution,[],[f248,f127])). 4.98/5.17 fof(f363,plain,( 4.98/5.17 tail_of(sK11) = tail_of(sK14(tail_of(sK11),head_of(sK11))) | tail_of(sK11) = head_of(sK11) | tail_of(sK14(tail_of(sK11),head_of(sK11))) = head_of(sK11)), 4.98/5.17 inference(resolution,[],[f248,f146])). 4.98/5.17 fof(f389,plain,( 4.98/5.17 spl15_23 <=> ~vertex(tail_of(sK10))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_23])])). 4.98/5.17 fof(f390,plain,( 4.98/5.17 ~vertex(tail_of(sK10)) | ~spl15_23), 4.98/5.17 inference(avatar_component_clause,[],[f389])). 4.98/5.17 fof(f392,plain,( 4.98/5.17 spl15_22 <=> vertex(tail_of(sK10))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_22])])). 4.98/5.17 fof(f393,plain,( 4.98/5.17 vertex(tail_of(sK10)) | ~spl15_22), 4.98/5.17 inference(avatar_component_clause,[],[f392])). 4.98/5.17 fof(f395,plain,( 4.98/5.17 ~edge(sK10) | ~spl15_23), 4.98/5.17 inference(resolution,[],[f390,f127])). 4.98/5.17 fof(f396,plain,( 4.98/5.17 $false | ~spl15_23), 4.98/5.17 inference(subsumption_resolution,[],[f395,f138])). 4.98/5.17 fof(f397,plain,( 4.98/5.17 spl15_23), 4.98/5.17 inference(avatar_contradiction_clause,[],[f396])). 4.98/5.17 fof(f399,plain,( 4.98/5.17 tail_of(sK11) = head_of(sK11) | head_of(sK11) = head_of(sK14(tail_of(sK11),head_of(sK11))) | sP4(head_of(sK11),sK14(tail_of(sK11),head_of(sK11)),tail_of(sK11))), 4.98/5.17 inference(resolution,[],[f316,f139])). 4.98/5.17 fof(f402,plain,( 4.98/5.17 head_of(sK11) = head_of(sK14(tail_of(sK11),head_of(sK11))) | sP4(head_of(sK11),sK14(tail_of(sK11),head_of(sK11)),tail_of(sK11)) | ~spl15_2), 4.98/5.17 inference(subsumption_resolution,[],[f399,f202])). 4.98/5.17 fof(f406,plain,( 4.98/5.17 ( ! [X2] : (~edge(X2) | tail_of(sK10) = head_of(X2) | head_of(X2) = head_of(sK14(tail_of(sK10),head_of(X2))) | sP4(head_of(X2),sK14(tail_of(sK10),head_of(X2)),tail_of(sK10))) ) | ~spl15_22), 4.98/5.17 inference(resolution,[],[f393,f208])). 4.98/5.17 fof(f412,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11))) | tail_of(sK10) = head_of(sK11) | tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11) | ~spl15_22), 4.98/5.17 inference(resolution,[],[f393,f248])). 4.98/5.17 fof(f463,plain,( 4.98/5.17 spl15_27 <=> tail_of(sK10) != tail_of(sK14(tail_of(sK10),tail_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_27])])). 4.98/5.17 fof(f464,plain,( 4.98/5.17 tail_of(sK10) != tail_of(sK14(tail_of(sK10),tail_of(sK11))) | ~spl15_27), 4.98/5.17 inference(avatar_component_clause,[],[f463])). 4.98/5.17 fof(f466,plain,( 4.98/5.17 spl15_26 <=> tail_of(sK10) = tail_of(sK14(tail_of(sK10),tail_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_26])])). 4.98/5.17 fof(f467,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK14(tail_of(sK10),tail_of(sK11))) | ~spl15_26), 4.98/5.17 inference(avatar_component_clause,[],[f466])). 4.98/5.17 fof(f519,plain,( 4.98/5.17 spl15_28 <=> sP4(head_of(sK11),sK14(tail_of(sK11),head_of(sK11)),tail_of(sK11))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_28])])). 4.98/5.17 fof(f520,plain,( 4.98/5.17 sP4(head_of(sK11),sK14(tail_of(sK11),head_of(sK11)),tail_of(sK11)) | ~spl15_28), 4.98/5.17 inference(avatar_component_clause,[],[f519])). 4.98/5.17 fof(f525,plain,( 4.98/5.17 spl15_30 <=> head_of(sK11) = head_of(sK14(tail_of(sK11),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_30])])). 4.98/5.17 fof(f526,plain,( 4.98/5.17 head_of(sK11) = head_of(sK14(tail_of(sK11),head_of(sK11))) | ~spl15_30), 4.98/5.17 inference(avatar_component_clause,[],[f525])). 4.98/5.17 fof(f527,plain,( 4.98/5.17 spl15_28 | spl15_30 | ~spl15_2), 4.98/5.17 inference(avatar_split_clause,[],[f402,f178,f525,f519])). 4.98/5.17 fof(f529,plain,( 4.98/5.17 tail_of(sK14(tail_of(sK11),head_of(sK11))) = head_of(sK11) | ~spl15_28), 4.98/5.17 inference(resolution,[],[f520,f122])). 4.98/5.17 fof(f533,plain,( 4.98/5.17 tail_of(sK11) = head_of(sK11) | (~spl15_8 | ~spl15_28)), 4.98/5.17 inference(forward_demodulation,[],[f529,f266])). 4.98/5.17 fof(f534,plain,( 4.98/5.17 $false | (~spl15_2 | ~spl15_8 | ~spl15_28)), 4.98/5.17 inference(subsumption_resolution,[],[f533,f202])). 4.98/5.17 fof(f535,plain,( 4.98/5.17 ~spl15_2 | ~spl15_8 | ~spl15_28), 4.98/5.17 inference(avatar_contradiction_clause,[],[f534])). 4.98/5.17 fof(f634,plain,( 4.98/5.17 spl15_35 <=> tail_of(sK14(head_of(sK11),tail_of(sK11))) != head_of(sK11)), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_35])])). 4.98/5.17 fof(f635,plain,( 4.98/5.17 tail_of(sK14(head_of(sK11),tail_of(sK11))) != head_of(sK11) | ~spl15_35), 4.98/5.17 inference(avatar_component_clause,[],[f634])). 4.98/5.17 fof(f637,plain,( 4.98/5.17 spl15_34 <=> tail_of(sK14(head_of(sK11),tail_of(sK11))) = head_of(sK11)), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_34])])). 4.98/5.17 fof(f638,plain,( 4.98/5.17 tail_of(sK14(head_of(sK11),tail_of(sK11))) = head_of(sK11) | ~spl15_34), 4.98/5.17 inference(avatar_component_clause,[],[f637])). 4.98/5.17 fof(f672,plain,( 4.98/5.17 tail_of(sK11) = tail_of(sK14(tail_of(sK11),head_of(sK11))) | tail_of(sK14(tail_of(sK11),head_of(sK11))) = head_of(sK11) | ~spl15_2), 4.98/5.17 inference(subsumption_resolution,[],[f363,f202])). 4.98/5.17 fof(f800,plain,( 4.98/5.17 tail_of(sK14(tail_of(sK11),head_of(sK11))) = head_of(sK11) | (~spl15_2 | ~spl15_9)), 4.98/5.17 inference(subsumption_resolution,[],[f672,f263])). 4.98/5.17 fof(f837,plain,( 4.98/5.17 vertex(head_of(sK11)) | ~edge(sK14(tail_of(sK11),head_of(sK11))) | (~spl15_2 | ~spl15_9)), 4.98/5.17 inference(superposition,[],[f127,f800])). 4.98/5.17 fof(f844,plain,( 4.98/5.17 vertex(head_of(sK11)) | (~spl15_2 | ~spl15_9 | ~spl15_14)), 4.98/5.17 inference(subsumption_resolution,[],[f837,f297])). 4.98/5.17 fof(f848,plain,( 4.98/5.17 ( ! [X1] : (sP4(head_of(sK11),sK14(X1,head_of(sK11)),X1) | ~vertex(X1) | head_of(sK11) = X1 | head_of(sK11) = head_of(sK14(X1,head_of(sK11)))) ) | (~spl15_2 | ~spl15_9 | ~spl15_14)), 4.98/5.17 inference(resolution,[],[f844,f204])). 4.98/5.17 fof(f935,plain,( 4.98/5.17 spl15_44 <=> edge(sK14(tail_of(sK10),tail_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_44])])). 4.98/5.17 fof(f936,plain,( 4.98/5.17 edge(sK14(tail_of(sK10),tail_of(sK11))) | ~spl15_44), 4.98/5.17 inference(avatar_component_clause,[],[f935])). 4.98/5.17 fof(f938,plain,( 4.98/5.17 spl15_45 <=> ~edge(sK14(tail_of(sK10),tail_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_45])])). 4.98/5.17 fof(f939,plain,( 4.98/5.17 ~edge(sK14(tail_of(sK10),tail_of(sK11))) | ~spl15_45), 4.98/5.17 inference(avatar_component_clause,[],[f938])). 4.98/5.17 fof(f941,plain,( 4.98/5.17 ~vertex(tail_of(sK10)) | ~vertex(tail_of(sK11)) | tail_of(sK10) = tail_of(sK11) | ~spl15_45), 4.98/5.17 inference(resolution,[],[f939,f136])). 4.98/5.17 fof(f942,plain,( 4.98/5.17 ~vertex(tail_of(sK11)) | tail_of(sK10) = tail_of(sK11) | (~spl15_22 | ~spl15_45)), 4.98/5.17 inference(subsumption_resolution,[],[f941,f393])). 4.98/5.17 fof(f943,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK11) | (~spl15_22 | ~spl15_45)), 4.98/5.17 inference(subsumption_resolution,[],[f942,f146])). 4.98/5.17 fof(f944,plain,( 4.98/5.17 $false | (~spl15_22 | ~spl15_45)), 4.98/5.17 inference(subsumption_resolution,[],[f943,f145])). 4.98/5.17 fof(f945,plain,( 4.98/5.17 ~spl15_22 | spl15_45), 4.98/5.17 inference(avatar_contradiction_clause,[],[f944])). 4.98/5.17 fof(f994,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK14(tail_of(sK10),tail_of(sK11))) | tail_of(sK10) = head_of(sK14(tail_of(sK10),tail_of(sK11))) | tail_of(sK10) = tail_of(sK11)), 4.98/5.17 inference(resolution,[],[f223,f138])). 4.98/5.17 fof(f1574,plain,( 4.98/5.17 ( ! [X1] : (~vertex(X1) | head_of(sK11) = X1 | head_of(sK11) = head_of(sK14(X1,head_of(sK11))) | tail_of(sK14(X1,head_of(sK11))) = head_of(sK11)) ) | (~spl15_2 | ~spl15_9 | ~spl15_14)), 4.98/5.17 inference(resolution,[],[f848,f122])). 4.98/5.17 fof(f2466,plain,( 4.98/5.17 spl15_79 <=> tail_of(sK14(tail_of(sK10),head_of(sK11))) != head_of(sK11)), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_79])])). 4.98/5.17 fof(f2467,plain,( 4.98/5.17 tail_of(sK14(tail_of(sK10),head_of(sK11))) != head_of(sK11) | ~spl15_79), 4.98/5.17 inference(avatar_component_clause,[],[f2466])). 4.98/5.17 fof(f2469,plain,( 4.98/5.17 spl15_78 <=> tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11)), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_78])])). 4.98/5.17 fof(f2470,plain,( 4.98/5.17 tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11) | ~spl15_78), 4.98/5.17 inference(avatar_component_clause,[],[f2469])). 4.98/5.17 fof(f2472,plain,( 4.98/5.17 spl15_81 <=> tail_of(sK10) != tail_of(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_81])])). 4.98/5.17 fof(f2473,plain,( 4.98/5.17 tail_of(sK10) != tail_of(sK14(tail_of(sK10),head_of(sK11))) | ~spl15_81), 4.98/5.17 inference(avatar_component_clause,[],[f2472])). 4.98/5.17 fof(f2475,plain,( 4.98/5.17 spl15_80 <=> tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_80])])). 4.98/5.17 fof(f2476,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11))) | ~spl15_80), 4.98/5.17 inference(avatar_component_clause,[],[f2475])). 4.98/5.17 fof(f2480,plain,( 4.98/5.17 ( ! [X4,X2,X5,X3,X1] : (tail_of(sK10) != tail_of(X1) | head_of(X2) != head_of(sK14(tail_of(sK10),head_of(sK11))) | ~precedes(X1,X2,X3) | ~shortest_path(X4,X5,X3)) ) | ~spl15_80), 4.98/5.17 inference(superposition,[],[f108,f2476])). 4.98/5.17 fof(f2637,plain,( 4.98/5.17 spl15_93 <=> tail_of(sK10) != head_of(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_93])])). 4.98/5.17 fof(f2638,plain,( 4.98/5.17 tail_of(sK10) != head_of(sK14(tail_of(sK10),head_of(sK11))) | ~spl15_93), 4.98/5.17 inference(avatar_component_clause,[],[f2637])). 4.98/5.17 fof(f2640,plain,( 4.98/5.17 spl15_92 <=> tail_of(sK10) = head_of(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_92])])). 4.98/5.17 fof(f2641,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK14(tail_of(sK10),head_of(sK11))) | ~spl15_92), 4.98/5.17 inference(avatar_component_clause,[],[f2640])). 4.98/5.17 fof(f2643,plain,( 4.98/5.17 spl15_95 <=> head_of(sK11) != head_of(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_95])])). 4.98/5.17 fof(f2644,plain,( 4.98/5.17 head_of(sK11) != head_of(sK14(tail_of(sK10),head_of(sK11))) | ~spl15_95), 4.98/5.17 inference(avatar_component_clause,[],[f2643])). 4.98/5.17 fof(f2646,plain,( 4.98/5.17 spl15_94 <=> head_of(sK11) = head_of(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_94])])). 4.98/5.17 fof(f2647,plain,( 4.98/5.17 head_of(sK11) = head_of(sK14(tail_of(sK10),head_of(sK11))) | ~spl15_94), 4.98/5.17 inference(avatar_component_clause,[],[f2646])). 4.98/5.17 fof(f2651,plain,( 4.98/5.17 ( ! [X4,X2,X5,X3,X1] : (~shortest_path(X4,X5,X3) | tail_of(sK10) != tail_of(X1) | ~precedes(X1,X2,X3) | head_of(sK11) != head_of(X2)) ) | (~spl15_80 | ~spl15_94)), 4.98/5.17 inference(backward_demodulation,[],[f2647,f2480])). 4.98/5.17 fof(f2671,plain,( 4.98/5.17 ( ! [X0,X1] : (~precedes(X0,X1,sK9) | tail_of(sK10) != tail_of(X0) | head_of(sK11) != head_of(X1)) ) | (~spl15_80 | ~spl15_94)), 4.98/5.17 inference(resolution,[],[f2651,f85])). 4.98/5.17 fof(f2673,plain,( 4.98/5.17 tail_of(sK10) != tail_of(sK10) | head_of(sK11) != head_of(sK11) | (~spl15_2 | ~spl15_80 | ~spl15_94)), 4.98/5.17 inference(resolution,[],[f2671,f179])). 4.98/5.17 fof(f2674,plain,( 4.98/5.17 $false | (~spl15_2 | ~spl15_80 | ~spl15_94)), 4.98/5.17 inference(trivial_inequality_removal,[],[f2673])). 4.98/5.17 fof(f2675,plain,( 4.98/5.17 ~spl15_2 | ~spl15_80 | ~spl15_94), 4.98/5.17 inference(avatar_contradiction_clause,[],[f2674])). 4.98/5.17 fof(f2702,plain,( 4.98/5.17 ( ! [X0] : (tail_of(sK10) != tail_of(X0) | ~edge(X0) | sK14(tail_of(sK10),head_of(sK11)) = X0 | sequential(sK14(tail_of(sK10),head_of(sK11)),X0) | ~edge(sK14(tail_of(sK10),head_of(sK11)))) ) | ~spl15_92), 4.98/5.17 inference(superposition,[],[f106,f2641])). 4.98/5.17 fof(f2719,plain,( 4.98/5.17 ( ! [X0] : (head_of(sK11) != head_of(X0) | ~edge(sK14(tail_of(sK10),head_of(sK11))) | sK14(tail_of(sK10),head_of(sK11)) = X0 | sequential(X0,sK14(tail_of(sK10),head_of(sK11))) | ~edge(X0)) ) | ~spl15_78), 4.98/5.17 inference(superposition,[],[f106,f2470])). 4.98/5.17 fof(f3074,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | tail_of(sK10) = head_of(sK14(tail_of(sK10),head_of(sK11))) | tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 inference(resolution,[],[f252,f138])). 4.98/5.17 fof(f3206,plain,( 4.98/5.17 ( ! [X1] : (~edge(X1) | head_of(sK11) = head_of(sK14(tail_of(X1),head_of(sK11))) | tail_of(sK14(tail_of(X1),head_of(sK11))) = head_of(sK11) | tail_of(X1) = head_of(sK11)) ) | (~spl15_2 | ~spl15_9 | ~spl15_14)), 4.98/5.17 inference(resolution,[],[f1574,f127])). 4.98/5.17 fof(f3240,plain,( 4.98/5.17 spl15_107 <=> sK14(tail_of(sK10),tail_of(sK11)) != sK14(head_of(sK11),tail_of(sK11))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_107])])). 4.98/5.17 fof(f3241,plain,( 4.98/5.17 sK14(tail_of(sK10),tail_of(sK11)) != sK14(head_of(sK11),tail_of(sK11)) | ~spl15_107), 4.98/5.17 inference(avatar_component_clause,[],[f3240])). 4.98/5.17 fof(f3243,plain,( 4.98/5.17 spl15_106 <=> sK14(tail_of(sK10),tail_of(sK11)) = sK14(head_of(sK11),tail_of(sK11))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_106])])). 4.98/5.17 fof(f3244,plain,( 4.98/5.17 sK14(tail_of(sK10),tail_of(sK11)) = sK14(head_of(sK11),tail_of(sK11)) | ~spl15_106), 4.98/5.17 inference(avatar_component_clause,[],[f3243])). 4.98/5.17 fof(f3257,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11) | tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 inference(resolution,[],[f362,f138])). 4.98/5.17 fof(f3510,plain,( 4.98/5.17 head_of(sK11) = head_of(sK14(tail_of(sK10),head_of(sK11))) | tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11) | tail_of(sK10) = head_of(sK11) | (~spl15_2 | ~spl15_9 | ~spl15_14)), 4.98/5.17 inference(resolution,[],[f3206,f138])). 4.98/5.17 fof(f4962,plain,( 4.98/5.17 spl15_140 <=> edge(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_140])])). 4.98/5.17 fof(f4963,plain,( 4.98/5.17 edge(sK14(tail_of(sK10),head_of(sK11))) | ~spl15_140), 4.98/5.17 inference(avatar_component_clause,[],[f4962])). 4.98/5.17 fof(f4965,plain,( 4.98/5.17 spl15_141 <=> ~edge(sK14(tail_of(sK10),head_of(sK11)))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_141])])). 4.98/5.17 fof(f4966,plain,( 4.98/5.17 ~edge(sK14(tail_of(sK10),head_of(sK11))) | ~spl15_141), 4.98/5.17 inference(avatar_component_clause,[],[f4965])). 4.98/5.17 fof(f4968,plain,( 4.98/5.17 spl15_142 <=> ! [X0] : (head_of(sK11) != head_of(X0) | ~edge(X0) | sequential(X0,sK14(tail_of(sK10),head_of(sK11))) | sK14(tail_of(sK10),head_of(sK11)) = X0)), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_142])])). 4.98/5.17 fof(f4969,plain,( 4.98/5.17 ( ! [X0] : (sequential(X0,sK14(tail_of(sK10),head_of(sK11))) | ~edge(X0) | head_of(sK11) != head_of(X0) | sK14(tail_of(sK10),head_of(sK11)) = X0) ) | ~spl15_142), 4.98/5.17 inference(avatar_component_clause,[],[f4968])). 4.98/5.17 fof(f4970,plain,( 4.98/5.17 ~spl15_141 | spl15_142 | ~spl15_78), 4.98/5.17 inference(avatar_split_clause,[],[f2719,f2469,f4968,f4965])). 4.98/5.17 fof(f4977,plain,( 4.98/5.17 ( ! [X0] : (sequential(sK14(tail_of(sK10),head_of(sK11)),X0) | ~edge(X0) | sK14(tail_of(sK10),head_of(sK11)) = X0 | tail_of(sK10) != tail_of(X0)) ) | (~spl15_92 | ~spl15_140)), 4.98/5.17 inference(subsumption_resolution,[],[f2702,f4963])). 4.98/5.17 fof(f5122,plain,( 4.98/5.17 ( ! [X0,X1] : (~edge(X0) | sK14(tail_of(sK10),head_of(sK11)) = X0 | tail_of(sK10) != tail_of(X0) | ~edge(X0) | ~edge(X1) | ~edge(sK14(tail_of(sK10),head_of(sK11))) | ~sequential(X0,X1) | ~sequential(X1,sK14(tail_of(sK10),head_of(sK11))) | triangle(X0,X1,sK14(tail_of(sK10),head_of(sK11)))) ) | (~spl15_92 | ~spl15_140)), 4.98/5.17 inference(resolution,[],[f4977,f90])). 4.98/5.17 fof(f5129,plain,( 4.98/5.17 ( ! [X0,X1] : (~edge(X0) | sK14(tail_of(sK10),head_of(sK11)) = X0 | tail_of(sK10) != tail_of(X0) | ~edge(X1) | ~edge(sK14(tail_of(sK10),head_of(sK11))) | ~sequential(X0,X1) | ~sequential(X1,sK14(tail_of(sK10),head_of(sK11))) | triangle(X0,X1,sK14(tail_of(sK10),head_of(sK11)))) ) | (~spl15_92 | ~spl15_140)), 4.98/5.17 inference(duplicate_literal_removal,[],[f5122])). 4.98/5.17 fof(f5130,plain,( 4.98/5.17 ( ! [X0,X1] : (~edge(X0) | sK14(tail_of(sK10),head_of(sK11)) = X0 | tail_of(sK10) != tail_of(X0) | ~edge(X1) | ~sequential(X0,X1) | ~sequential(X1,sK14(tail_of(sK10),head_of(sK11))) | triangle(X0,X1,sK14(tail_of(sK10),head_of(sK11)))) ) | (~spl15_92 | ~spl15_140)), 4.98/5.17 inference(subsumption_resolution,[],[f5129,f4963])). 4.98/5.17 fof(f5131,plain,( 4.98/5.17 ( ! [X0,X1] : (~edge(X0) | sK14(tail_of(sK10),head_of(sK11)) = X0 | tail_of(sK10) != tail_of(X0) | ~sequential(X0,X1) | ~sequential(X1,sK14(tail_of(sK10),head_of(sK11))) | triangle(X0,X1,sK14(tail_of(sK10),head_of(sK11)))) ) | (~spl15_92 | ~spl15_140)), 4.98/5.17 inference(subsumption_resolution,[],[f5130,f105])). 4.98/5.17 fof(f5132,plain,( 4.98/5.17 ( ! [X0,X1] : (triangle(X0,X1,sK14(tail_of(sK10),head_of(sK11))) | tail_of(sK10) != tail_of(X0) | ~sequential(X0,X1) | ~sequential(X1,sK14(tail_of(sK10),head_of(sK11))) | sK14(tail_of(sK10),head_of(sK11)) = X0) ) | (~spl15_92 | ~spl15_140)), 4.98/5.17 inference(subsumption_resolution,[],[f5131,f102])). 4.98/5.17 fof(f6046,plain,( 4.98/5.17 spl15_159 <=> sK10 != sK14(tail_of(sK10),head_of(sK11))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_159])])). 4.98/5.17 fof(f6047,plain,( 4.98/5.17 sK10 != sK14(tail_of(sK10),head_of(sK11)) | ~spl15_159), 4.98/5.17 inference(avatar_component_clause,[],[f6046])). 4.98/5.17 fof(f6049,plain,( 4.98/5.17 spl15_158 <=> sK10 = sK14(tail_of(sK10),head_of(sK11))), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_158])])). 4.98/5.17 fof(f6050,plain,( 4.98/5.17 sK10 = sK14(tail_of(sK10),head_of(sK11)) | ~spl15_158), 4.98/5.17 inference(avatar_component_clause,[],[f6049])). 4.98/5.17 fof(f6851,plain,( 4.98/5.17 tail_of(sK10) != tail_of(sK10) | ~sequential(sK10,sK11) | ~sequential(sK11,sK14(tail_of(sK10),head_of(sK11))) | sK10 = sK14(tail_of(sK10),head_of(sK11)) | (~spl15_92 | ~spl15_140)), 4.98/5.17 inference(resolution,[],[f5132,f89])). 4.98/5.17 fof(f6852,plain,( 4.98/5.17 ~sequential(sK10,sK11) | ~sequential(sK11,sK14(tail_of(sK10),head_of(sK11))) | sK10 = sK14(tail_of(sK10),head_of(sK11)) | (~spl15_92 | ~spl15_140)), 4.98/5.17 inference(trivial_inequality_removal,[],[f6851])). 4.98/5.17 fof(f6853,plain,( 4.98/5.17 ~sequential(sK11,sK14(tail_of(sK10),head_of(sK11))) | sK10 = sK14(tail_of(sK10),head_of(sK11)) | (~spl15_92 | ~spl15_140)), 4.98/5.17 inference(subsumption_resolution,[],[f6852,f87])). 4.98/5.17 fof(f6854,plain,( 4.98/5.17 ~sequential(sK11,sK14(tail_of(sK10),head_of(sK11))) | (~spl15_92 | ~spl15_140 | ~spl15_159)), 4.98/5.17 inference(subsumption_resolution,[],[f6853,f6047])). 4.98/5.17 fof(f6855,plain,( 4.98/5.17 ~edge(sK11) | head_of(sK11) != head_of(sK11) | sK11 = sK14(tail_of(sK10),head_of(sK11)) | (~spl15_92 | ~spl15_140 | ~spl15_142 | ~spl15_159)), 4.98/5.17 inference(resolution,[],[f6854,f4969])). 4.98/5.17 fof(f6856,plain,( 4.98/5.17 ~edge(sK11) | sK11 = sK14(tail_of(sK10),head_of(sK11)) | (~spl15_92 | ~spl15_140 | ~spl15_142 | ~spl15_159)), 4.98/5.17 inference(trivial_inequality_removal,[],[f6855])). 4.98/5.17 fof(f6857,plain,( 4.98/5.17 sK11 = sK14(tail_of(sK10),head_of(sK11)) | (~spl15_92 | ~spl15_140 | ~spl15_142 | ~spl15_159)), 4.98/5.17 inference(subsumption_resolution,[],[f6856,f139])). 4.98/5.17 fof(f6858,plain,( 4.98/5.17 tail_of(sK11) = head_of(sK11) | (~spl15_78 | ~spl15_92 | ~spl15_140 | ~spl15_142 | ~spl15_159)), 4.98/5.17 inference(backward_demodulation,[],[f6857,f2470])). 4.98/5.17 fof(f6935,plain,( 4.98/5.17 $false | (~spl15_2 | ~spl15_78 | ~spl15_92 | ~spl15_140 | ~spl15_142 | ~spl15_159)), 4.98/5.17 inference(subsumption_resolution,[],[f6858,f202])). 4.98/5.17 fof(f6936,plain,( 4.98/5.17 ~spl15_2 | ~spl15_78 | ~spl15_92 | ~spl15_140 | ~spl15_142 | spl15_159), 4.98/5.17 inference(avatar_contradiction_clause,[],[f6935])). 4.98/5.17 fof(f6994,plain,( 4.98/5.17 tail_of(sK10) != tail_of(sK10) | (~spl15_81 | ~spl15_158)), 4.98/5.17 inference(backward_demodulation,[],[f6050,f2473])). 4.98/5.17 fof(f7069,plain,( 4.98/5.17 $false | (~spl15_81 | ~spl15_158)), 4.98/5.17 inference(trivial_inequality_removal,[],[f6994])). 4.98/5.17 fof(f7070,plain,( 4.98/5.17 spl15_81 | ~spl15_158), 4.98/5.17 inference(avatar_contradiction_clause,[],[f7069])). 4.98/5.17 fof(f7614,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK14(tail_of(sK10),tail_of(sK11))) | tail_of(sK10) = tail_of(sK11) | ~spl15_27), 4.98/5.17 inference(subsumption_resolution,[],[f994,f464])). 4.98/5.17 fof(f7615,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK14(tail_of(sK10),tail_of(sK11))) | ~spl15_27), 4.98/5.17 inference(subsumption_resolution,[],[f7614,f145])). 4.98/5.17 fof(f7987,plain,( 4.98/5.17 head_of(sK11) = head_of(sK14(tail_of(sK10),tail_of(sK11))) | tail_of(sK14(head_of(sK14(tail_of(sK10),tail_of(sK11))),head_of(sK11))) = head_of(sK11) | tail_of(sK14(head_of(sK14(tail_of(sK10),tail_of(sK11))),head_of(sK11))) = head_of(sK14(tail_of(sK10),tail_of(sK11))) | ~spl15_44), 4.98/5.17 inference(resolution,[],[f936,f361])). 4.98/5.17 fof(f8054,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | tail_of(sK14(head_of(sK14(tail_of(sK10),tail_of(sK11))),head_of(sK11))) = head_of(sK11) | tail_of(sK14(head_of(sK14(tail_of(sK10),tail_of(sK11))),head_of(sK11))) = head_of(sK14(tail_of(sK10),tail_of(sK11))) | (~spl15_27 | ~spl15_44)), 4.98/5.17 inference(forward_demodulation,[],[f7987,f7615])). 4.98/5.17 fof(f10034,plain,( 4.98/5.17 spl15_183 <=> ~sequential(sK11,sK10)), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_183])])). 4.98/5.17 fof(f10035,plain,( 4.98/5.17 ~sequential(sK11,sK10) | ~spl15_183), 4.98/5.17 inference(avatar_component_clause,[],[f10034])). 4.98/5.17 fof(f10037,plain,( 4.98/5.17 spl15_182 <=> sequential(sK11,sK10)), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_182])])). 4.98/5.17 fof(f10038,plain,( 4.98/5.17 sequential(sK11,sK10) | ~spl15_182), 4.98/5.17 inference(avatar_component_clause,[],[f10037])). 4.98/5.17 fof(f10040,plain,( 4.98/5.17 spl15_185 <=> sK10 != sK11), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_185])])). 4.98/5.17 fof(f10041,plain,( 4.98/5.17 sK10 != sK11 | ~spl15_185), 4.98/5.17 inference(avatar_component_clause,[],[f10040])). 4.98/5.17 fof(f10043,plain,( 4.98/5.17 spl15_184 <=> sK10 = sK11), 4.98/5.17 introduced(avatar_definition,[new_symbols(naming,[spl15_184])])). 4.98/5.17 fof(f10044,plain,( 4.98/5.17 sK10 = sK11 | ~spl15_184), 4.98/5.17 inference(avatar_component_clause,[],[f10043])). 4.98/5.17 fof(f10220,plain,( 4.98/5.17 sequential(sK10,sK10) | ~spl15_184), 4.98/5.17 inference(backward_demodulation,[],[f10044,f87])). 4.98/5.17 fof(f10564,plain,( 4.98/5.17 $false | ~spl15_184), 4.98/5.17 inference(subsumption_resolution,[],[f10220,f130])). 4.98/5.17 fof(f10565,plain,( 4.98/5.17 ~spl15_184), 4.98/5.17 inference(avatar_contradiction_clause,[],[f10564])). 4.98/5.17 fof(f11190,plain,( 4.98/5.17 ( ! [X2,X3,X1] : (~on_path(sK11,X1) | precedes(sK11,sK10,X1) | ~on_path(sK10,X1) | ~path(X2,X3,X1)) ) | ~spl15_182), 4.98/5.17 inference(resolution,[],[f10038,f91])). 4.98/5.17 fof(f12787,plain,( 4.98/5.17 ( ! [X0,X1] : (precedes(sK11,sK10,sK9) | ~on_path(sK10,sK9) | ~path(X0,X1,sK9)) ) | ~spl15_182), 4.98/5.17 inference(resolution,[],[f11190,f88])). 4.98/5.17 fof(f12788,plain,( 4.98/5.17 ( ! [X0,X1] : (~on_path(sK10,sK9) | ~path(X0,X1,sK9)) ) | (~spl15_2 | ~spl15_182)), 4.98/5.17 inference(subsumption_resolution,[],[f12787,f181])). 4.98/5.17 fof(f12789,plain,( 4.98/5.17 ( ! [X0,X1] : (~path(X0,X1,sK9)) ) | (~spl15_2 | ~spl15_182)), 4.98/5.17 inference(subsumption_resolution,[],[f12788,f86])). 4.98/5.17 fof(f12790,plain,( 4.98/5.17 $false | (~spl15_2 | ~spl15_182)), 4.98/5.17 inference(subsumption_resolution,[],[f149,f12789])). 4.98/5.17 fof(f12791,plain,( 4.98/5.17 ~spl15_2 | ~spl15_182), 4.98/5.17 inference(avatar_contradiction_clause,[],[f12790])). 4.98/5.17 fof(f13407,plain,( 4.98/5.17 tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11) | tail_of(sK10) = head_of(sK11) | tail_of(sK14(head_of(sK14(tail_of(sK10),tail_of(sK11))),head_of(sK11))) = head_of(sK14(tail_of(sK10),tail_of(sK11))) | (~spl15_27 | ~spl15_44)), 4.98/5.17 inference(forward_demodulation,[],[f8054,f7615])). 4.98/5.17 fof(f13408,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11))) | tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11) | tail_of(sK10) = head_of(sK11) | (~spl15_27 | ~spl15_44)), 4.98/5.17 inference(forward_demodulation,[],[f13407,f7615])). 4.98/5.17 fof(f13409,plain,( 4.98/5.17 tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11) | tail_of(sK10) = head_of(sK11) | (~spl15_27 | ~spl15_44 | ~spl15_81)), 4.98/5.17 inference(subsumption_resolution,[],[f13408,f2473])). 4.98/5.17 fof(f13493,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | (~spl15_27 | ~spl15_44 | ~spl15_79 | ~spl15_81)), 4.98/5.17 inference(subsumption_resolution,[],[f13409,f2467])). 4.98/5.17 fof(f14018,plain,( 4.98/5.17 ( ! [X0] : (tail_of(sK10) != tail_of(X0) | ~edge(X0) | sK11 = X0 | sequential(sK11,X0) | ~edge(sK11)) ) | (~spl15_27 | ~spl15_44 | ~spl15_79 | ~spl15_81)), 4.98/5.17 inference(superposition,[],[f106,f13493])). 4.98/5.17 fof(f14023,plain,( 4.98/5.17 ( ! [X0] : (tail_of(sK10) != tail_of(X0) | ~edge(X0) | sK11 = X0 | sequential(sK11,X0)) ) | (~spl15_27 | ~spl15_44 | ~spl15_79 | ~spl15_81)), 4.98/5.17 inference(subsumption_resolution,[],[f14018,f139])). 4.98/5.17 fof(f14256,plain,( 4.98/5.17 ~edge(sK10) | sK10 = sK11 | sequential(sK11,sK10) | (~spl15_27 | ~spl15_44 | ~spl15_79 | ~spl15_81)), 4.98/5.17 inference(equality_resolution,[],[f14023])). 4.98/5.17 fof(f14260,plain,( 4.98/5.17 sK10 = sK11 | sequential(sK11,sK10) | (~spl15_27 | ~spl15_44 | ~spl15_79 | ~spl15_81)), 4.98/5.17 inference(subsumption_resolution,[],[f14256,f138])). 4.98/5.17 fof(f14261,plain,( 4.98/5.17 sequential(sK11,sK10) | (~spl15_27 | ~spl15_44 | ~spl15_79 | ~spl15_81 | ~spl15_185)), 4.98/5.17 inference(subsumption_resolution,[],[f14260,f10041])). 4.98/5.17 fof(f14262,plain,( 4.98/5.17 $false | (~spl15_27 | ~spl15_44 | ~spl15_79 | ~spl15_81 | ~spl15_183 | ~spl15_185)), 4.98/5.17 inference(subsumption_resolution,[],[f14261,f10035])). 4.98/5.17 fof(f14263,plain,( 4.98/5.17 spl15_27 | ~spl15_44 | spl15_79 | spl15_81 | spl15_183 | spl15_185), 4.98/5.17 inference(avatar_contradiction_clause,[],[f14262])). 4.98/5.17 fof(f14773,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11))) | ~spl15_93), 4.98/5.17 inference(subsumption_resolution,[],[f3074,f2638])). 4.98/5.17 fof(f14787,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | (~spl15_81 | ~spl15_93)), 4.98/5.17 inference(subsumption_resolution,[],[f14773,f2473])). 4.98/5.17 fof(f14864,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK14(tail_of(sK10),tail_of(sK10))) | (~spl15_78 | ~spl15_81 | ~spl15_93)), 4.98/5.17 inference(backward_demodulation,[],[f14787,f2470])). 4.98/5.17 fof(f14865,plain,( 4.98/5.17 tail_of(sK10) != tail_of(sK14(tail_of(sK10),tail_of(sK10))) | (~spl15_81 | ~spl15_93)), 4.98/5.17 inference(backward_demodulation,[],[f14787,f2473])). 4.98/5.17 fof(f14866,plain,( 4.98/5.17 tail_of(sK10) != head_of(sK14(tail_of(sK10),tail_of(sK10))) | (~spl15_81 | ~spl15_93)), 4.98/5.17 inference(backward_demodulation,[],[f14787,f2638])). 4.98/5.17 fof(f14938,plain,( 4.98/5.17 $false | (~spl15_78 | ~spl15_81 | ~spl15_93)), 4.98/5.17 inference(subsumption_resolution,[],[f14865,f14864])). 4.98/5.17 fof(f14939,plain,( 4.98/5.17 ~spl15_78 | spl15_81 | spl15_93), 4.98/5.17 inference(avatar_contradiction_clause,[],[f14938])). 4.98/5.17 fof(f15280,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK14(tail_of(sK10),tail_of(sK10))) | (~spl15_81 | ~spl15_93 | ~spl15_94)), 4.98/5.17 inference(forward_demodulation,[],[f2647,f14787])). 4.98/5.17 fof(f15281,plain,( 4.98/5.17 $false | (~spl15_81 | ~spl15_93 | ~spl15_94)), 4.98/5.17 inference(subsumption_resolution,[],[f15280,f14866])). 4.98/5.17 fof(f15282,plain,( 4.98/5.17 spl15_81 | spl15_93 | ~spl15_94), 4.98/5.17 inference(avatar_contradiction_clause,[],[f15281])). 4.98/5.17 fof(f15297,plain,( 4.98/5.17 sK14(tail_of(sK10),tail_of(sK11)) != sK14(tail_of(sK10),tail_of(sK11)) | (~spl15_81 | ~spl15_93 | ~spl15_107)), 4.98/5.17 inference(forward_demodulation,[],[f3241,f14787])). 4.98/5.17 fof(f15298,plain,( 4.98/5.17 $false | (~spl15_81 | ~spl15_93 | ~spl15_107)), 4.98/5.17 inference(trivial_inequality_removal,[],[f15297])). 4.98/5.17 fof(f15299,plain,( 4.98/5.17 spl15_81 | spl15_93 | spl15_107), 4.98/5.17 inference(avatar_contradiction_clause,[],[f15298])). 4.98/5.17 fof(f15814,plain,( 4.98/5.17 tail_of(sK10) != head_of(sK11) | (~spl15_92 | ~spl15_95)), 4.98/5.17 inference(forward_demodulation,[],[f2644,f2641])). 4.98/5.17 fof(f15890,plain,( 4.98/5.17 tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11) | tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11))) | (~spl15_92 | ~spl15_95)), 4.98/5.17 inference(subsumption_resolution,[],[f3257,f15814])). 4.98/5.17 fof(f17000,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11))) | (~spl15_79 | ~spl15_92 | ~spl15_95)), 4.98/5.17 inference(subsumption_resolution,[],[f15890,f2467])). 4.98/5.17 fof(f17001,plain,( 4.98/5.17 $false | (~spl15_79 | ~spl15_81 | ~spl15_92 | ~spl15_95)), 4.98/5.17 inference(subsumption_resolution,[],[f17000,f2473])). 4.98/5.17 fof(f17002,plain,( 4.98/5.17 spl15_79 | spl15_81 | ~spl15_92 | spl15_95), 4.98/5.17 inference(avatar_contradiction_clause,[],[f17001])). 4.98/5.17 fof(f18394,plain,( 4.98/5.17 head_of(sK11) = head_of(sK14(tail_of(sK10),head_of(sK11))) | tail_of(sK10) = head_of(sK11) | (~spl15_2 | ~spl15_9 | ~spl15_14 | ~spl15_79)), 4.98/5.17 inference(subsumption_resolution,[],[f3510,f2467])). 4.98/5.17 fof(f18395,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | (~spl15_2 | ~spl15_9 | ~spl15_14 | ~spl15_79 | ~spl15_95)), 4.98/5.17 inference(subsumption_resolution,[],[f18394,f2644])). 4.98/5.17 fof(f18416,plain,( 4.98/5.17 tail_of(sK10) != tail_of(sK14(tail_of(sK10),tail_of(sK10))) | (~spl15_2 | ~spl15_9 | ~spl15_14 | ~spl15_79 | ~spl15_95)), 4.98/5.17 inference(backward_demodulation,[],[f18395,f2467])). 4.98/5.17 fof(f18763,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK14(tail_of(sK10),tail_of(sK10))) | (~spl15_2 | ~spl15_9 | ~spl15_14 | ~spl15_79 | ~spl15_80 | ~spl15_95)), 4.98/5.17 inference(forward_demodulation,[],[f2476,f18395])). 4.98/5.17 fof(f18764,plain,( 4.98/5.17 $false | (~spl15_2 | ~spl15_9 | ~spl15_14 | ~spl15_79 | ~spl15_80 | ~spl15_95)), 4.98/5.17 inference(subsumption_resolution,[],[f18763,f18416])). 4.98/5.17 fof(f18765,plain,( 4.98/5.17 ~spl15_2 | spl15_9 | ~spl15_14 | spl15_79 | ~spl15_80 | spl15_95), 4.98/5.17 inference(avatar_contradiction_clause,[],[f18764])). 4.98/5.17 fof(f21682,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | (~spl15_92 | ~spl15_94)), 4.98/5.17 inference(forward_demodulation,[],[f2647,f2641])). 4.98/5.17 fof(f23154,plain,( 4.98/5.17 ( ! [X0] : (tail_of(sK10) != tail_of(X0) | ~edge(X0) | sK11 = X0 | sequential(sK11,X0) | ~edge(sK11)) ) | (~spl15_92 | ~spl15_94)), 4.98/5.17 inference(superposition,[],[f106,f21682])). 4.98/5.17 fof(f23159,plain,( 4.98/5.17 ( ! [X0] : (tail_of(sK10) != tail_of(X0) | ~edge(X0) | sK11 = X0 | sequential(sK11,X0)) ) | (~spl15_92 | ~spl15_94)), 4.98/5.17 inference(subsumption_resolution,[],[f23154,f139])). 4.98/5.17 fof(f23523,plain,( 4.98/5.17 ~edge(sK10) | sK10 = sK11 | sequential(sK11,sK10) | (~spl15_92 | ~spl15_94)), 4.98/5.17 inference(equality_resolution,[],[f23159])). 4.98/5.17 fof(f23528,plain,( 4.98/5.17 sK10 = sK11 | sequential(sK11,sK10) | (~spl15_92 | ~spl15_94)), 4.98/5.17 inference(subsumption_resolution,[],[f23523,f138])). 4.98/5.17 fof(f23529,plain,( 4.98/5.17 sequential(sK11,sK10) | (~spl15_92 | ~spl15_94 | ~spl15_185)), 4.98/5.17 inference(subsumption_resolution,[],[f23528,f10041])). 4.98/5.17 fof(f23530,plain,( 4.98/5.17 $false | (~spl15_92 | ~spl15_94 | ~spl15_183 | ~spl15_185)), 4.98/5.17 inference(subsumption_resolution,[],[f23529,f10035])). 4.98/5.17 fof(f23531,plain,( 4.98/5.17 ~spl15_92 | ~spl15_94 | spl15_183 | spl15_185), 4.98/5.17 inference(avatar_contradiction_clause,[],[f23530])). 4.98/5.17 fof(f24156,plain,( 4.98/5.17 tail_of(sK10) != head_of(sK11) | (~spl15_92 | ~spl15_95)), 4.98/5.17 inference(backward_demodulation,[],[f2641,f2644])). 4.98/5.17 fof(f24926,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK14(tail_of(sK11),head_of(sK11))) | head_of(sK14(tail_of(sK11),head_of(sK11))) = head_of(sK14(tail_of(sK10),head_of(sK14(tail_of(sK11),head_of(sK11))))) | sP4(head_of(sK14(tail_of(sK11),head_of(sK11))),sK14(tail_of(sK10),head_of(sK14(tail_of(sK11),head_of(sK11)))),tail_of(sK10)) | (~spl15_14 | ~spl15_22)), 4.98/5.17 inference(resolution,[],[f297,f406])). 4.98/5.17 fof(f24974,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | head_of(sK14(tail_of(sK11),head_of(sK11))) = head_of(sK14(tail_of(sK10),head_of(sK14(tail_of(sK11),head_of(sK11))))) | sP4(head_of(sK14(tail_of(sK11),head_of(sK11))),sK14(tail_of(sK10),head_of(sK14(tail_of(sK11),head_of(sK11)))),tail_of(sK10)) | (~spl15_14 | ~spl15_22 | ~spl15_30)), 4.98/5.17 inference(forward_demodulation,[],[f24926,f526])). 4.98/5.17 fof(f25241,plain,( 4.98/5.17 ~vertex(tail_of(sK10)) | ~vertex(head_of(sK11)) | tail_of(sK10) = head_of(sK11) | ~spl15_141), 4.98/5.17 inference(resolution,[],[f4966,f136])). 4.98/5.17 fof(f25242,plain,( 4.98/5.17 ~vertex(head_of(sK11)) | tail_of(sK10) = head_of(sK11) | (~spl15_22 | ~spl15_141)), 4.98/5.17 inference(subsumption_resolution,[],[f25241,f393])). 4.98/5.17 fof(f25243,plain,( 4.98/5.17 ~vertex(head_of(sK11)) | (~spl15_22 | ~spl15_92 | ~spl15_95 | ~spl15_141)), 4.98/5.17 inference(subsumption_resolution,[],[f25242,f24156])). 4.98/5.17 fof(f25244,plain,( 4.98/5.17 ~edge(sK11) | (~spl15_22 | ~spl15_92 | ~spl15_95 | ~spl15_141)), 4.98/5.17 inference(resolution,[],[f25243,f126])). 4.98/5.17 fof(f25245,plain,( 4.98/5.17 $false | (~spl15_22 | ~spl15_92 | ~spl15_95 | ~spl15_141)), 4.98/5.17 inference(subsumption_resolution,[],[f25244,f139])). 4.98/5.17 fof(f25246,plain,( 4.98/5.17 ~spl15_22 | ~spl15_92 | spl15_95 | spl15_141), 4.98/5.17 inference(avatar_contradiction_clause,[],[f25245])). 4.98/5.17 fof(f25526,plain,( 4.98/5.17 tail_of(sK10) = tail_of(sK14(tail_of(sK10),head_of(sK11))) | tail_of(sK10) = head_of(sK11) | (~spl15_22 | ~spl15_79)), 4.98/5.17 inference(subsumption_resolution,[],[f412,f2467])). 4.98/5.17 fof(f25533,plain,( 4.98/5.17 head_of(sK11) = head_of(sK14(tail_of(sK10),head_of(sK11))) | tail_of(sK10) = head_of(sK11) | sP4(head_of(sK14(tail_of(sK11),head_of(sK11))),sK14(tail_of(sK10),head_of(sK14(tail_of(sK11),head_of(sK11)))),tail_of(sK10)) | (~spl15_14 | ~spl15_22 | ~spl15_30)), 4.98/5.17 inference(forward_demodulation,[],[f24974,f526])). 4.98/5.17 fof(f25534,plain,( 4.98/5.17 sP4(head_of(sK11),sK14(tail_of(sK10),head_of(sK11)),tail_of(sK10)) | head_of(sK11) = head_of(sK14(tail_of(sK10),head_of(sK11))) | tail_of(sK10) = head_of(sK11) | (~spl15_14 | ~spl15_22 | ~spl15_30)), 4.98/5.17 inference(forward_demodulation,[],[f25533,f526])). 4.98/5.17 fof(f25554,plain,( 4.98/5.17 tail_of(sK14(tail_of(sK10),tail_of(sK11))) = head_of(sK11) | (~spl15_34 | ~spl15_106)), 4.98/5.17 inference(backward_demodulation,[],[f3244,f638])). 4.98/5.17 fof(f25580,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | (~spl15_26 | ~spl15_34 | ~spl15_106)), 4.98/5.17 inference(forward_demodulation,[],[f25554,f467])). 4.98/5.17 fof(f26195,plain,( 4.98/5.17 ( ! [X0] : (tail_of(sK10) != tail_of(X0) | ~edge(X0) | sK11 = X0 | sequential(sK11,X0) | ~edge(sK11)) ) | (~spl15_26 | ~spl15_34 | ~spl15_106)), 4.98/5.17 inference(superposition,[],[f106,f25580])). 4.98/5.17 fof(f26200,plain,( 4.98/5.17 ( ! [X0] : (tail_of(sK10) != tail_of(X0) | ~edge(X0) | sK11 = X0 | sequential(sK11,X0)) ) | (~spl15_26 | ~spl15_34 | ~spl15_106)), 4.98/5.17 inference(subsumption_resolution,[],[f26195,f139])). 4.98/5.17 fof(f26640,plain,( 4.98/5.17 ~edge(sK10) | sK10 = sK11 | sequential(sK11,sK10) | (~spl15_26 | ~spl15_34 | ~spl15_106)), 4.98/5.17 inference(equality_resolution,[],[f26200])). 4.98/5.17 fof(f26644,plain,( 4.98/5.17 sK10 = sK11 | sequential(sK11,sK10) | (~spl15_26 | ~spl15_34 | ~spl15_106)), 4.98/5.17 inference(subsumption_resolution,[],[f26640,f138])). 4.98/5.17 fof(f26645,plain,( 4.98/5.17 sequential(sK11,sK10) | (~spl15_26 | ~spl15_34 | ~spl15_106 | ~spl15_185)), 4.98/5.17 inference(subsumption_resolution,[],[f26644,f10041])). 4.98/5.17 fof(f26646,plain,( 4.98/5.17 $false | (~spl15_26 | ~spl15_34 | ~spl15_106 | ~spl15_183 | ~spl15_185)), 4.98/5.17 inference(subsumption_resolution,[],[f26645,f10035])). 4.98/5.17 fof(f26647,plain,( 4.98/5.17 ~spl15_26 | ~spl15_34 | ~spl15_106 | spl15_183 | spl15_185), 4.98/5.17 inference(avatar_contradiction_clause,[],[f26646])). 4.98/5.17 fof(f26758,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | (~spl15_22 | ~spl15_79 | ~spl15_81)), 4.98/5.17 inference(subsumption_resolution,[],[f25526,f2473])). 4.98/5.17 fof(f27271,plain,( 4.98/5.17 tail_of(sK10) != tail_of(sK14(tail_of(sK10),tail_of(sK11))) | (~spl15_22 | ~spl15_35 | ~spl15_79 | ~spl15_81)), 4.98/5.17 inference(forward_demodulation,[],[f635,f26758])). 4.98/5.17 fof(f27272,plain,( 4.98/5.17 $false | (~spl15_22 | ~spl15_26 | ~spl15_35 | ~spl15_79 | ~spl15_81)), 4.98/5.17 inference(subsumption_resolution,[],[f27271,f467])). 4.98/5.17 fof(f27273,plain,( 4.98/5.17 ~spl15_22 | ~spl15_26 | spl15_35 | spl15_79 | spl15_81), 4.98/5.17 inference(avatar_contradiction_clause,[],[f27272])). 4.98/5.17 fof(f27290,plain,( 4.98/5.17 sP4(head_of(sK11),sK14(tail_of(sK10),head_of(sK11)),tail_of(sK10)) | tail_of(sK10) = head_of(sK11) | (~spl15_14 | ~spl15_22 | ~spl15_30 | ~spl15_95)), 4.98/5.17 inference(subsumption_resolution,[],[f25534,f2644])). 4.98/5.17 fof(f28435,plain,( 4.98/5.17 tail_of(sK10) != head_of(sK11) | (~spl15_79 | ~spl15_80)), 4.98/5.17 inference(backward_demodulation,[],[f2476,f2467])). 4.98/5.17 fof(f29493,plain,( 4.98/5.17 sP4(head_of(sK11),sK14(tail_of(sK10),head_of(sK11)),tail_of(sK10)) | (~spl15_14 | ~spl15_22 | ~spl15_30 | ~spl15_79 | ~spl15_80 | ~spl15_95)), 4.98/5.17 inference(subsumption_resolution,[],[f27290,f28435])). 4.98/5.17 fof(f30000,plain,( 4.98/5.17 tail_of(sK14(tail_of(sK10),head_of(sK11))) = head_of(sK11) | (~spl15_14 | ~spl15_22 | ~spl15_30 | ~spl15_79 | ~spl15_80 | ~spl15_95)), 4.98/5.17 inference(resolution,[],[f29493,f122])). 4.98/5.17 fof(f30005,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | (~spl15_14 | ~spl15_22 | ~spl15_30 | ~spl15_79 | ~spl15_80 | ~spl15_95)), 4.98/5.17 inference(forward_demodulation,[],[f30000,f2476])). 4.98/5.17 fof(f30006,plain,( 4.98/5.17 $false | (~spl15_14 | ~spl15_22 | ~spl15_30 | ~spl15_79 | ~spl15_80 | ~spl15_95)), 4.98/5.17 inference(subsumption_resolution,[],[f30005,f28435])). 4.98/5.17 fof(f30007,plain,( 4.98/5.17 ~spl15_14 | ~spl15_22 | ~spl15_30 | spl15_79 | ~spl15_80 | spl15_95), 4.98/5.17 inference(avatar_contradiction_clause,[],[f30006])). 4.98/5.17 fof(f30106,plain,( 4.98/5.17 tail_of(sK10) = head_of(sK11) | (~spl15_78 | ~spl15_80)), 4.98/5.17 inference(forward_demodulation,[],[f2470,f2476])). 4.98/5.17 fof(f31195,plain,( 4.98/5.17 ( ! [X0] : (tail_of(sK10) != tail_of(X0) | ~edge(X0) | sK11 = X0 | sequential(sK11,X0) | ~edge(sK11)) ) | (~spl15_78 | ~spl15_80)), 4.98/5.17 inference(superposition,[],[f106,f30106])). 4.98/5.17 fof(f31200,plain,( 4.98/5.17 ( ! [X0] : (tail_of(sK10) != tail_of(X0) | ~edge(X0) | sK11 = X0 | sequential(sK11,X0)) ) | (~spl15_78 | ~spl15_80)), 4.98/5.17 inference(subsumption_resolution,[],[f31195,f139])). 4.98/5.17 fof(f31645,plain,( 4.98/5.17 ~edge(sK10) | sK10 = sK11 | sequential(sK11,sK10) | (~spl15_78 | ~spl15_80)), 4.98/5.17 inference(equality_resolution,[],[f31200])). 4.98/5.17 fof(f31648,plain,( 4.98/5.17 sK10 = sK11 | sequential(sK11,sK10) | (~spl15_78 | ~spl15_80)), 4.98/5.17 inference(subsumption_resolution,[],[f31645,f138])). 4.98/5.17 fof(f31649,plain,( 4.98/5.17 sequential(sK11,sK10) | (~spl15_78 | ~spl15_80 | ~spl15_185)), 4.98/5.17 inference(subsumption_resolution,[],[f31648,f10041])). 4.98/5.17 fof(f31650,plain,( 4.98/5.17 $false | (~spl15_78 | ~spl15_80 | ~spl15_183 | ~spl15_185)), 4.98/5.17 inference(subsumption_resolution,[],[f31649,f10035])). 4.98/5.17 fof(f31651,plain,( 4.98/5.17 ~spl15_78 | ~spl15_80 | spl15_183 | spl15_185), 4.98/5.17 inference(avatar_contradiction_clause,[],[f31650])). 4.98/5.17 fof(f31652,plain,( 4.98/5.17 $false), 4.98/5.17 inference(avatar_sat_refutation,[],[f180,f191,f307,f397,f527,f535,f945,f2675,f4970,f6936,f7070,f10565,f12791,f14263,f14939,f15282,f15299,f17002,f18765,f23531,f25246,f26647,f27273,f30007,f31651])). 4.98/5.17 % SZS output end Proof for theBenchmark 4.98/5.17 % ------------------------------ 4.98/5.17 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 4.98/5.17 % Termination reason: Refutation 4.98/5.17 4.98/5.17 % Memory used [KB]: 18933 4.98/5.17 % Time elapsed: 1.189 s 4.98/5.17 % ------------------------------ 4.98/5.17 % ------------------------------ 4.98/5.17 % Success in time 4.934 s 4.98/5.17 EOF