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 : n125.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 05:48:09 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 0.06/0.26 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 1.37/1.56 % (33031)Time limit reached! 1.37/1.56 % ------------------------------ 1.37/1.56 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 1.37/1.56 % Termination reason: Time limit 1.37/1.56 % Termination phase: Saturation 1.37/1.56 1.37/1.56 % Memory used [KB]: 10746 1.37/1.56 % Time elapsed: 1.300 s 1.37/1.56 % ------------------------------ 1.37/1.56 % ------------------------------ 1.37/1.56 % remaining time: 5986 next slice time: 4 1.37/1.56 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 1.89/2.06 % (33032)Time limit reached! 1.89/2.06 % ------------------------------ 1.89/2.06 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 1.89/2.06 % Termination reason: Time limit 1.89/2.06 % Termination phase: Saturation 1.89/2.06 1.89/2.06 % Memory used [KB]: 13304 1.89/2.06 % Time elapsed: 0.500 s 1.89/2.06 % ------------------------------ 1.89/2.06 % ------------------------------ 1.89/2.06 % remaining time: 5981 next slice time: 10 1.89/2.06 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 2.96/3.16 % (33033)Time limit reached! 2.96/3.16 % ------------------------------ 2.96/3.16 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 2.96/3.16 % Termination reason: Time limit 2.96/3.16 % Termination phase: Saturation 2.96/3.16 2.96/3.16 % Memory used [KB]: 31726 2.96/3.16 % Time elapsed: 1.100 s 2.96/3.16 % ------------------------------ 2.96/3.16 % ------------------------------ 2.96/3.17 % remaining time: 5970 next slice time: 7 2.96/3.17 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 3.77/3.97 % (33034)Time limit reached! 3.77/3.97 % ------------------------------ 3.77/3.97 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 3.77/3.97 % Termination reason: Time limit 3.77/3.97 % Termination phase: Saturation 3.77/3.97 3.77/3.97 % Memory used [KB]: 16375 3.77/3.97 % Time elapsed: 0.800 s 3.77/3.97 % ------------------------------ 3.77/3.97 % ------------------------------ 3.77/3.97 % remaining time: 5962 next slice time: 38 3.77/3.97 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 4.36/4.61 % Refutation found. Thanks to Tanya! 4.36/4.61 % SZS status Theorem for theBenchmark 4.36/4.61 % SZS output start Proof for theBenchmark 4.36/4.61 fof(f2,axiom,( 4.36/4.61 ! [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)))), 4.36/4.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn)). 4.36/4.61 fof(f4,axiom,( 4.36/4.61 ! [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)))), 4.36/4.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties)). 4.36/4.61 fof(f5,axiom,( 4.36/4.61 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))))), 4.36/4.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_properties)). 4.36/4.61 fof(f6,axiom,( 4.36/4.61 ! [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))), 4.36/4.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn)). 4.36/4.61 fof(f10,axiom,( 4.36/4.61 ! [X4] : (edge(X4) => (vertex(tail_of(X4)) & vertex(head_of(X4))))), 4.36/4.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices)). 4.36/4.61 fof(f11,axiom,( 4.36/4.61 ! [X4] : (edge(X4) => tail_of(X4) != head_of(X4))), 4.36/4.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops)). 4.36/4.62 fof(f12,axiom,( 4.36/4.62 ! [X5,X6] : (sequential(X5,X6) <=> (edge(X6) & X5 != X6 & tail_of(X6) = head_of(X5) & edge(X5)))), 4.36/4.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn)). 4.36/4.62 fof(f13,conjecture,( 4.36/4.62 complete => ! [X2,X0,X1] : (shortest_path(X0,X1,X2) => number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2))), 4.36/4.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_and_sequential_pairs)). 4.36/4.62 fof(f14,negated_conjecture,( 4.36/4.62 ~(complete => ! [X2,X0,X1] : (shortest_path(X0,X1,X2) => number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2)))), 4.36/4.62 inference(negated_conjecture,[],[f13])). 4.36/4.62 fof(f18,axiom,( 4.36/4.62 ! [X5,X6,X7] : (triangle(X5,X6,X7) <=> (edge(X6) & edge(X7) & sequential(X7,X5) & sequential(X6,X7) & sequential(X5,X6) & edge(X5)))), 4.36/4.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn)). 4.36/4.62 fof(f19,axiom,( 4.36/4.62 ! [X2,X0,X1] : ((path(X0,X1,X2) & ! [X5,X6] : ((on_path(X5,X2) & sequential(X5,X6) & on_path(X6,X2)) => ? [X7] : triangle(X5,X6,X7))) => number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2))), 4.36/4.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles)). 4.36/4.62 fof(f20,plain,( 4.36/4.62 ~(complete => ! [X0,X1,X2] : (shortest_path(X1,X2,X0) => number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0)))), 4.36/4.62 inference(rectify,[],[f14])). 4.36/4.62 fof(f21,plain,( 4.36/4.62 ! [X0] : (edge(X0) => tail_of(X0) != head_of(X0))), 4.36/4.62 inference(rectify,[],[f11])). 4.36/4.62 fof(f22,plain,( 4.36/4.62 ! [X0,X1,X2] : ((path(X1,X2,X0) & ! [X3,X4] : ((on_path(X3,X0) & sequential(X3,X4) & on_path(X4,X0)) => ? [X5] : triangle(X3,X4,X5))) => number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0))), 4.36/4.62 inference(rectify,[],[f19])). 4.36/4.62 fof(f23,plain,( 4.36/4.62 ! [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)))), 4.36/4.62 inference(rectify,[],[f4])). 4.36/4.62 fof(f24,plain,( 4.36/4.62 ! [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))), 4.36/4.62 inference(rectify,[],[f6])). 4.36/4.62 fof(f25,plain,( 4.36/4.62 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))))), 4.36/4.62 inference(rectify,[],[f5])). 4.36/4.62 fof(f26,plain,( 4.36/4.62 ! [X0,X1] : (sequential(X0,X1) <=> (edge(X1) & X0 != X1 & tail_of(X1) = head_of(X0) & edge(X0)))), 4.36/4.62 inference(rectify,[],[f12])). 4.36/4.62 fof(f27,plain,( 4.36/4.62 ! [X0] : (edge(X0) => (vertex(tail_of(X0)) & vertex(head_of(X0))))), 4.36/4.62 inference(rectify,[],[f10])). 4.36/4.62 fof(f28,plain,( 4.36/4.62 ! [X0,X1,X2] : (triangle(X0,X1,X2) <=> (edge(X1) & edge(X2) & sequential(X2,X0) & sequential(X1,X2) & sequential(X0,X1) & edge(X0)))), 4.36/4.62 inference(rectify,[],[f18])). 4.36/4.62 fof(f29,plain,( 4.36/4.62 ! [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)))), 4.36/4.62 inference(rectify,[],[f2])). 4.36/4.62 fof(f32,plain,( 4.36/4.62 ! [X0,X1,X2] : ((edge(X1) & edge(X2) & sequential(X2,X0) & sequential(X1,X2) & sequential(X0,X1) & edge(X0)) => triangle(X0,X1,X2))), 4.36/4.62 inference(unused_predicate_definition_removal,[],[f28])). 4.36/4.62 fof(f33,plain,( 4.36/4.62 ? [X0,X1,X2] : (number_of_in(triangles,X0) != number_of_in(sequential_pairs,X0) & shortest_path(X1,X2,X0)) & complete), 4.36/4.62 inference(ennf_transformation,[],[f20])). 4.36/4.62 fof(f34,plain,( 4.36/4.62 ! [X0] : (tail_of(X0) != head_of(X0) | ~edge(X0))), 4.36/4.62 inference(ennf_transformation,[],[f21])). 4.36/4.62 fof(f35,plain,( 4.36/4.62 ! [X0,X1,X2] : (number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) | (~path(X1,X2,X0) | ? [X3,X4] : (! [X5] : ~triangle(X3,X4,X5) & (on_path(X3,X0) & sequential(X3,X4) & on_path(X4,X0)))))), 4.36/4.62 inference(ennf_transformation,[],[f22])). 4.36/4.62 fof(f36,plain,( 4.36/4.62 ! [X0,X1,X2] : (number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) | ~path(X1,X2,X0) | ? [X3,X4] : (! [X5] : ~triangle(X3,X4,X5) & on_path(X3,X0) & sequential(X3,X4) & on_path(X4,X0)))), 4.36/4.62 inference(flattening,[],[f35])). 4.36/4.62 fof(f37,plain,( 4.36/4.62 ! [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)))), 4.36/4.62 inference(ennf_transformation,[],[f23])). 4.36/4.62 fof(f38,plain,( 4.36/4.62 ! [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))), 4.36/4.62 inference(flattening,[],[f37])). 4.36/4.62 fof(f39,plain,( 4.36/4.62 ! [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))), 4.36/4.62 inference(ennf_transformation,[],[f24])). 4.36/4.62 fof(f40,plain,( 4.36/4.62 ! [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), 4.36/4.62 inference(ennf_transformation,[],[f25])). 4.36/4.62 fof(f41,plain,( 4.36/4.62 ! [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), 4.36/4.62 inference(flattening,[],[f40])). 4.36/4.62 fof(f42,plain,( 4.36/4.62 ! [X0] : ((vertex(tail_of(X0)) & vertex(head_of(X0))) | ~edge(X0))), 4.36/4.62 inference(ennf_transformation,[],[f27])). 4.36/4.62 fof(f43,plain,( 4.36/4.62 ! [X0,X1,X2] : (triangle(X0,X1,X2) | (~edge(X1) | ~edge(X2) | ~sequential(X2,X0) | ~sequential(X1,X2) | ~sequential(X0,X1) | ~edge(X0)))), 4.36/4.62 inference(ennf_transformation,[],[f32])). 4.36/4.62 fof(f44,plain,( 4.36/4.62 ! [X0,X1,X2] : (triangle(X0,X1,X2) | ~edge(X1) | ~edge(X2) | ~sequential(X2,X0) | ~sequential(X1,X2) | ~sequential(X0,X1) | ~edge(X0))), 4.36/4.62 inference(flattening,[],[f43])). 4.36/4.62 fof(f45,plain,( 4.36/4.62 ! [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))), 4.36/4.62 inference(ennf_transformation,[],[f29])). 4.36/4.62 fof(f46,plain,( 4.36/4.62 ! [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))), 4.36/4.62 inference(flattening,[],[f45])). 4.36/4.62 fof(f48,plain,( 4.36/4.62 ! [X0] : (? [X3,X4] : (! [X5] : ~triangle(X3,X4,X5) & on_path(X3,X0) & sequential(X3,X4) & on_path(X4,X0)) | ~sP0(X0))), 4.36/4.62 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])). 4.36/4.62 fof(f49,plain,( 4.36/4.62 ! [X0,X1,X2] : (number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) | ~path(X1,X2,X0) | sP0(X0))), 4.36/4.62 inference(definition_folding,[],[f36,f48])). 4.36/4.62 fof(f50,plain,( 4.36/4.62 ! [X2,X1,X0] : (sP1(X2,X1,X0) <=> (! [X3] : (less_or_equal(length_of(X2),length_of(X3)) | ~path(X0,X1,X3)) & X0 != X1 & path(X0,X1,X2)))), 4.36/4.62 introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])). 4.36/4.62 fof(f51,plain,( 4.36/4.62 ! [X0,X1,X2] : (sP1(X2,X1,X0) <=> shortest_path(X0,X1,X2))), 4.36/4.62 inference(definition_folding,[],[f39,f50])). 4.36/4.62 fof(f52,plain,( 4.36/4.62 ! [X1,X2,X0] : (sP2(X1,X2,X0) <=> (tail_of(X2) = X1 & head_of(X2) = X0))), 4.36/4.62 introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])])). 4.36/4.62 fof(f53,plain,( 4.36/4.62 ! [X0,X2,X1] : (sP3(X0,X2,X1) <=> (tail_of(X2) = X0 & head_of(X2) = X1))), 4.36/4.62 introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])])). 4.36/4.62 fof(f54,plain,( 4.36/4.62 ! [X1,X2,X0] : ((sP2(X1,X2,X0) <~> sP3(X0,X2,X1)) | ~sP4(X1,X2,X0))), 4.36/4.62 introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])])). 4.36/4.62 fof(f55,plain,( 4.36/4.62 ! [X0,X1] : (? [X2] : (edge(X2) & sP4(X1,X2,X0)) | ~vertex(X0) | ~vertex(X1) | X0 = X1) | ~complete), 4.36/4.62 inference(definition_folding,[],[f41,f54,f53,f52])). 4.36/4.62 fof(f60,plain,( 4.36/4.62 ? [X0,X1,X2] : (number_of_in(triangles,X0) != number_of_in(sequential_pairs,X0) & shortest_path(X1,X2,X0)) => (number_of_in(triangles,sK8) != number_of_in(sequential_pairs,sK8) & shortest_path(sK9,sK10,sK8))), 4.36/4.62 introduced(choice_axiom,[])). 4.36/4.62 fof(f61,plain,( 4.36/4.62 (number_of_in(triangles,sK8) != number_of_in(sequential_pairs,sK8) & shortest_path(sK9,sK10,sK8)) & complete), 4.36/4.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f33,f60])). 4.36/4.62 fof(f62,plain,( 4.36/4.62 ! [X0] : (? [X3,X4] : (! [X5] : ~triangle(X3,X4,X5) & on_path(X3,X0) & sequential(X3,X4) & on_path(X4,X0)) | ~sP0(X0))), 4.36/4.62 inference(nnf_transformation,[],[f48])). 4.36/4.62 fof(f63,plain,( 4.36/4.62 ! [X0] : (? [X1,X2] : (! [X3] : ~triangle(X1,X2,X3) & on_path(X1,X0) & sequential(X1,X2) & on_path(X2,X0)) | ~sP0(X0))), 4.36/4.62 inference(rectify,[],[f62])). 4.36/4.62 fof(f64,plain,( 4.36/4.62 ! [X0] : (? [X1,X2] : (! [X3] : ~triangle(X1,X2,X3) & on_path(X1,X0) & sequential(X1,X2) & on_path(X2,X0)) => (! [X3] : ~triangle(sK11(X0),sK12(X0),X3) & on_path(sK11(X0),X0) & sequential(sK11(X0),sK12(X0)) & on_path(sK12(X0),X0)))), 4.36/4.62 introduced(choice_axiom,[])). 4.36/4.62 fof(f65,plain,( 4.36/4.62 ! [X0] : ((! [X3] : ~triangle(sK11(X0),sK12(X0),X3) & on_path(sK11(X0),X0) & sequential(sK11(X0),sK12(X0)) & on_path(sK12(X0),X0)) | ~sP0(X0))), 4.36/4.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f63,f64])). 4.36/4.62 fof(f66,plain,( 4.36/4.62 ! [X2,X1,X0] : ((sP1(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)) | ~sP1(X2,X1,X0)))), 4.36/4.62 inference(nnf_transformation,[],[f50])). 4.36/4.62 fof(f67,plain,( 4.36/4.62 ! [X2,X1,X0] : ((sP1(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)) | ~sP1(X2,X1,X0)))), 4.36/4.62 inference(flattening,[],[f66])). 4.36/4.62 fof(f68,plain,( 4.36/4.62 ! [X0,X1,X2] : ((sP1(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)) | ~sP1(X0,X1,X2)))), 4.36/4.62 inference(rectify,[],[f67])). 4.36/4.62 fof(f69,plain,( 4.36/4.62 ! [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))))), 4.36/4.62 introduced(choice_axiom,[])). 4.36/4.62 fof(f70,plain,( 4.36/4.62 ! [X0,X1,X2] : ((sP1(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)) | ~sP1(X0,X1,X2)))), 4.36/4.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f68,f69])). 4.36/4.62 fof(f71,plain,( 4.36/4.62 ! [X0,X1,X2] : ((sP1(X2,X1,X0) | ~shortest_path(X0,X1,X2)) & (shortest_path(X0,X1,X2) | ~sP1(X2,X1,X0)))), 4.36/4.62 inference(nnf_transformation,[],[f51])). 4.36/4.62 fof(f72,plain,( 4.36/4.62 ! [X1,X2,X0] : (((~sP3(X0,X2,X1) | ~sP2(X1,X2,X0)) & (sP3(X0,X2,X1) | sP2(X1,X2,X0))) | ~sP4(X1,X2,X0))), 4.36/4.62 inference(nnf_transformation,[],[f54])). 4.36/4.62 fof(f73,plain,( 4.36/4.62 ! [X0,X1,X2] : (((~sP3(X2,X1,X0) | ~sP2(X0,X1,X2)) & (sP3(X2,X1,X0) | sP2(X0,X1,X2))) | ~sP4(X0,X1,X2))), 4.36/4.62 inference(rectify,[],[f72])). 4.36/4.62 fof(f74,plain,( 4.36/4.62 ! [X0,X2,X1] : ((sP3(X0,X2,X1) | (tail_of(X2) != X0 | head_of(X2) != X1)) & ((tail_of(X2) = X0 & head_of(X2) = X1) | ~sP3(X0,X2,X1)))), 4.36/4.62 inference(nnf_transformation,[],[f53])). 4.36/4.62 fof(f75,plain,( 4.36/4.62 ! [X0,X2,X1] : ((sP3(X0,X2,X1) | tail_of(X2) != X0 | head_of(X2) != X1) & ((tail_of(X2) = X0 & head_of(X2) = X1) | ~sP3(X0,X2,X1)))), 4.36/4.62 inference(flattening,[],[f74])). 4.36/4.62 fof(f76,plain,( 4.36/4.62 ! [X0,X1,X2] : ((sP3(X0,X1,X2) | tail_of(X1) != X0 | head_of(X1) != X2) & ((tail_of(X1) = X0 & head_of(X1) = X2) | ~sP3(X0,X1,X2)))), 4.36/4.62 inference(rectify,[],[f75])). 4.36/4.62 fof(f77,plain,( 4.36/4.62 ! [X1,X2,X0] : ((sP2(X1,X2,X0) | (tail_of(X2) != X1 | head_of(X2) != X0)) & ((tail_of(X2) = X1 & head_of(X2) = X0) | ~sP2(X1,X2,X0)))), 4.36/4.62 inference(nnf_transformation,[],[f52])). 4.36/4.62 fof(f78,plain,( 4.36/4.62 ! [X1,X2,X0] : ((sP2(X1,X2,X0) | tail_of(X2) != X1 | head_of(X2) != X0) & ((tail_of(X2) = X1 & head_of(X2) = X0) | ~sP2(X1,X2,X0)))), 4.36/4.62 inference(flattening,[],[f77])). 4.36/4.62 fof(f79,plain,( 4.36/4.62 ! [X0,X1,X2] : ((sP2(X0,X1,X2) | tail_of(X1) != X0 | head_of(X1) != X2) & ((tail_of(X1) = X0 & head_of(X1) = X2) | ~sP2(X0,X1,X2)))), 4.36/4.62 inference(rectify,[],[f78])). 4.36/4.62 fof(f80,plain,( 4.36/4.62 ! [X1,X0] : (? [X2] : (edge(X2) & sP4(X1,X2,X0)) => (edge(sK14(X0,X1)) & sP4(X1,sK14(X0,X1),X0)))), 4.36/4.62 introduced(choice_axiom,[])). 4.36/4.62 fof(f81,plain,( 4.36/4.62 ! [X0,X1] : ((edge(sK14(X0,X1)) & sP4(X1,sK14(X0,X1),X0)) | ~vertex(X0) | ~vertex(X1) | X0 = X1) | ~complete), 4.36/4.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f55,f80])). 4.36/4.62 fof(f82,plain,( 4.36/4.62 ! [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)))), 4.36/4.62 inference(nnf_transformation,[],[f26])). 4.36/4.62 fof(f83,plain,( 4.36/4.62 ! [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)))), 4.36/4.62 inference(flattening,[],[f82])). 4.36/4.62 fof(f92,plain,( 4.36/4.62 complete), 4.36/4.62 inference(cnf_transformation,[],[f61])). 4.36/4.62 fof(f93,plain,( 4.36/4.62 shortest_path(sK9,sK10,sK8)), 4.36/4.62 inference(cnf_transformation,[],[f61])). 4.36/4.62 fof(f94,plain,( 4.36/4.62 number_of_in(triangles,sK8) != number_of_in(sequential_pairs,sK8)), 4.36/4.62 inference(cnf_transformation,[],[f61])). 4.36/4.62 fof(f95,plain,( 4.36/4.62 ( ! [X0] : (tail_of(X0) != head_of(X0) | ~edge(X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f34])). 4.36/4.62 fof(f96,plain,( 4.36/4.62 ( ! [X0] : (~sP0(X0) | on_path(sK12(X0),X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f65])). 4.36/4.62 fof(f97,plain,( 4.36/4.62 ( ! [X0] : (~sP0(X0) | sequential(sK11(X0),sK12(X0))) )), 4.36/4.62 inference(cnf_transformation,[],[f65])). 4.36/4.62 fof(f98,plain,( 4.36/4.62 ( ! [X0] : (~sP0(X0) | on_path(sK11(X0),X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f65])). 4.36/4.62 fof(f99,plain,( 4.36/4.62 ( ! [X0,X3] : (~sP0(X0) | ~triangle(sK11(X0),sK12(X0),X3)) )), 4.36/4.62 inference(cnf_transformation,[],[f65])). 4.36/4.62 fof(f100,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~path(X1,X2,X0) | number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) | sP0(X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f49])). 4.36/4.62 fof(f101,plain,( 4.36/4.62 ( ! [X4,X2,X0,X3,X1] : (~shortest_path(X0,X1,X4) | ~precedes(X2,X3,X4) | ~precedes(X3,X2,X4)) )), 4.36/4.62 inference(cnf_transformation,[],[f38])). 4.36/4.62 fof(f102,plain,( 4.36/4.62 ( ! [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)) )), 4.36/4.62 inference(cnf_transformation,[],[f38])). 4.36/4.62 fof(f103,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~sP1(X0,X1,X2) | path(X2,X1,X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f70])). 4.36/4.62 fof(f109,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~shortest_path(X0,X1,X2) | sP1(X2,X1,X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f71])). 4.36/4.62 fof(f110,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~sP4(X0,X1,X2) | sP2(X0,X1,X2) | sP3(X2,X1,X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f73])). 4.36/4.62 fof(f112,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~sP3(X0,X1,X2) | head_of(X1) = X2) )), 4.36/4.62 inference(cnf_transformation,[],[f76])). 4.36/4.62 fof(f113,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~sP3(X0,X1,X2) | tail_of(X1) = X0) )), 4.36/4.62 inference(cnf_transformation,[],[f76])). 4.36/4.62 fof(f115,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~sP2(X0,X1,X2) | head_of(X1) = X2) )), 4.36/4.62 inference(cnf_transformation,[],[f79])). 4.36/4.62 fof(f116,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~sP2(X0,X1,X2) | tail_of(X1) = X0) )), 4.36/4.62 inference(cnf_transformation,[],[f79])). 4.36/4.62 fof(f118,plain,( 4.36/4.62 ( ! [X0,X1] : (sP4(X1,sK14(X0,X1),X0) | ~vertex(X0) | ~vertex(X1) | X0 = X1 | ~complete) )), 4.36/4.62 inference(cnf_transformation,[],[f81])). 4.36/4.62 fof(f119,plain,( 4.36/4.62 ( ! [X0,X1] : (edge(sK14(X0,X1)) | ~vertex(X0) | ~vertex(X1) | X0 = X1 | ~complete) )), 4.36/4.62 inference(cnf_transformation,[],[f81])). 4.36/4.62 fof(f120,plain,( 4.36/4.62 ( ! [X0,X1] : (~sequential(X0,X1) | edge(X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f83])). 4.36/4.62 fof(f121,plain,( 4.36/4.62 ( ! [X0,X1] : (~sequential(X0,X1) | tail_of(X1) = head_of(X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f83])). 4.36/4.62 fof(f122,plain,( 4.36/4.62 ( ! [X0,X1] : (X0 != X1 | ~sequential(X0,X1)) )), 4.36/4.62 inference(cnf_transformation,[],[f83])). 4.36/4.62 fof(f123,plain,( 4.36/4.62 ( ! [X0,X1] : (~sequential(X0,X1) | edge(X1)) )), 4.36/4.62 inference(cnf_transformation,[],[f83])). 4.36/4.62 fof(f124,plain,( 4.36/4.62 ( ! [X0,X1] : (tail_of(X1) != head_of(X0) | ~edge(X1) | X0 = X1 | sequential(X0,X1) | ~edge(X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f83])). 4.36/4.62 fof(f125,plain,( 4.36/4.62 ( ! [X0] : (vertex(head_of(X0)) | ~edge(X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f42])). 4.36/4.62 fof(f126,plain,( 4.36/4.62 ( ! [X0] : (vertex(tail_of(X0)) | ~edge(X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f42])). 4.36/4.62 fof(f127,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (triangle(X0,X1,X2) | ~edge(X1) | ~edge(X2) | ~sequential(X2,X0) | ~sequential(X1,X2) | ~sequential(X0,X1) | ~edge(X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f44])). 4.36/4.62 fof(f128,plain,( 4.36/4.62 ( ! [X4,X2,X0,X3,X1] : (~sequential(X3,X4) | ~on_path(X3,X0) | precedes(X3,X4,X0) | ~on_path(X4,X0) | ~path(X1,X2,X0)) )), 4.36/4.62 inference(cnf_transformation,[],[f46])). 4.36/4.62 fof(f145,plain,( 4.36/4.62 ( ! [X1] : (~sequential(X1,X1)) )), 4.36/4.62 inference(equality_resolution,[],[f122])). 4.36/4.62 fof(f146,plain,( 4.36/4.62 ( ! [X0,X1] : (edge(sK14(X0,X1)) | ~vertex(X0) | ~vertex(X1) | X0 = X1) )), 4.36/4.62 inference(subsumption_resolution,[],[f119,f92])). 4.36/4.62 fof(f147,plain,( 4.36/4.62 ( ! [X0,X1] : (sP4(X1,sK14(X0,X1),X0) | ~vertex(X0) | ~vertex(X1) | X0 = X1) )), 4.36/4.62 inference(subsumption_resolution,[],[f118,f92])). 4.36/4.62 fof(f148,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (triangle(X0,X1,X2) | ~edge(X2) | ~sequential(X2,X0) | ~sequential(X1,X2) | ~sequential(X0,X1) | ~edge(X0)) )), 4.36/4.62 inference(subsumption_resolution,[],[f127,f123])). 4.36/4.62 fof(f149,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (triangle(X0,X1,X2) | ~sequential(X2,X0) | ~sequential(X1,X2) | ~sequential(X0,X1) | ~edge(X0)) )), 4.36/4.62 inference(subsumption_resolution,[],[f148,f123])). 4.36/4.62 fof(f150,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~sequential(X2,X0) | triangle(X0,X1,X2) | ~sequential(X1,X2) | ~sequential(X0,X1)) )), 4.36/4.62 inference(subsumption_resolution,[],[f149,f123])). 4.36/4.62 fof(f151,plain,( 4.36/4.62 sP1(sK8,sK10,sK9)), 4.36/4.62 inference(resolution,[],[f109,f93])). 4.36/4.62 fof(f153,plain,( 4.36/4.62 path(sK9,sK10,sK8)), 4.36/4.62 inference(resolution,[],[f151,f103])). 4.36/4.62 fof(f158,plain,( 4.36/4.62 ( ! [X0,X1] : (~precedes(X1,X0,sK8) | ~precedes(X0,X1,sK8)) )), 4.36/4.62 inference(resolution,[],[f101,f93])). 4.36/4.62 fof(f160,plain,( 4.36/4.62 ( ! [X0,X1] : (sP3(X1,sK14(X1,X0),X0) | sP2(X0,sK14(X1,X0),X1) | ~vertex(X1) | ~vertex(X0) | X0 = X1) )), 4.36/4.62 inference(resolution,[],[f110,f147])). 4.36/4.62 fof(f163,plain,( 4.36/4.62 number_of_in(triangles,sK8) = number_of_in(sequential_pairs,sK8) | sP0(sK8)), 4.36/4.62 inference(resolution,[],[f100,f153])). 4.36/4.62 fof(f164,plain,( 4.36/4.62 sP0(sK8)), 4.36/4.62 inference(subsumption_resolution,[],[f163,f94])). 4.36/4.62 fof(f165,plain,( 4.36/4.62 ( ! [X0] : (~triangle(sK11(sK8),sK12(sK8),X0)) )), 4.36/4.62 inference(resolution,[],[f164,f99])). 4.36/4.62 fof(f166,plain,( 4.36/4.62 sequential(sK11(sK8),sK12(sK8))), 4.36/4.62 inference(resolution,[],[f164,f97])). 4.36/4.62 fof(f167,plain,( 4.36/4.62 on_path(sK11(sK8),sK8)), 4.36/4.62 inference(resolution,[],[f164,f98])). 4.36/4.62 fof(f168,plain,( 4.36/4.62 on_path(sK12(sK8),sK8)), 4.36/4.62 inference(resolution,[],[f164,f96])). 4.36/4.62 fof(f172,plain,( 4.36/4.62 tail_of(sK12(sK8)) = head_of(sK11(sK8))), 4.36/4.62 inference(resolution,[],[f166,f121])). 4.36/4.62 fof(f173,plain,( 4.36/4.62 edge(sK12(sK8))), 4.36/4.62 inference(resolution,[],[f166,f123])). 4.36/4.62 fof(f174,plain,( 4.36/4.62 edge(sK11(sK8))), 4.36/4.62 inference(resolution,[],[f166,f120])). 4.36/4.62 fof(f175,plain,( 4.36/4.62 tail_of(sK11(sK8)) != tail_of(sK12(sK8)) | ~edge(sK11(sK8))), 4.36/4.62 inference(superposition,[],[f95,f172])). 4.36/4.62 fof(f179,plain,( 4.36/4.62 tail_of(sK11(sK8)) != tail_of(sK12(sK8))), 4.36/4.62 inference(subsumption_resolution,[],[f175,f174])). 4.36/4.62 fof(f189,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~on_path(sK12(sK8),X0) | precedes(sK11(sK8),sK12(sK8),X0) | ~on_path(sK11(sK8),X0) | ~path(X1,X2,X0)) )), 4.36/4.62 inference(resolution,[],[f128,f166])). 4.36/4.62 fof(f190,plain,( 4.36/4.62 ( ! [X0,X1] : (precedes(sK11(sK8),sK12(sK8),sK8) | ~on_path(sK11(sK8),sK8) | ~path(X0,X1,sK8)) )), 4.36/4.62 inference(resolution,[],[f189,f168])). 4.36/4.62 fof(f191,plain,( 4.36/4.62 ( ! [X0,X1] : (precedes(sK11(sK8),sK12(sK8),sK8) | ~path(X0,X1,sK8)) )), 4.36/4.62 inference(subsumption_resolution,[],[f190,f167])). 4.36/4.62 fof(f193,plain,( 4.36/4.62 spl16_0 <=> ! [X1,X0] : ~path(X0,X1,sK8)), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_0])])). 4.36/4.62 fof(f194,plain,( 4.36/4.62 ( ! [X0,X1] : (~path(X0,X1,sK8)) ) | ~spl16_0), 4.36/4.62 inference(avatar_component_clause,[],[f193])). 4.36/4.62 fof(f199,plain,( 4.36/4.62 spl16_2 <=> precedes(sK11(sK8),sK12(sK8),sK8)), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_2])])). 4.36/4.62 fof(f200,plain,( 4.36/4.62 precedes(sK11(sK8),sK12(sK8),sK8) | ~spl16_2), 4.36/4.62 inference(avatar_component_clause,[],[f199])). 4.36/4.62 fof(f201,plain,( 4.36/4.62 spl16_0 | spl16_2), 4.36/4.62 inference(avatar_split_clause,[],[f191,f199,f193])). 4.36/4.62 fof(f202,plain,( 4.36/4.62 ~precedes(sK12(sK8),sK11(sK8),sK8) | ~spl16_2), 4.36/4.62 inference(resolution,[],[f200,f158])). 4.36/4.62 fof(f211,plain,( 4.36/4.62 $false | ~spl16_0), 4.36/4.62 inference(subsumption_resolution,[],[f153,f194])). 4.36/4.62 fof(f212,plain,( 4.36/4.62 ~spl16_0), 4.36/4.62 inference(avatar_contradiction_clause,[],[f211])). 4.36/4.62 fof(f224,plain,( 4.36/4.62 ( ! [X0,X1] : (~vertex(X0) | ~vertex(X1) | sP2(X0,sK14(X1,X0),X1) | X0 = X1 | tail_of(sK14(X1,X0)) = X1) )), 4.36/4.62 inference(resolution,[],[f160,f113])). 4.36/4.62 fof(f225,plain,( 4.36/4.62 ( ! [X2,X3] : (~vertex(X2) | ~vertex(X3) | sP2(X2,sK14(X3,X2),X3) | X2 = X3 | head_of(sK14(X3,X2)) = X2) )), 4.36/4.62 inference(resolution,[],[f160,f112])). 4.36/4.62 fof(f227,plain,( 4.36/4.62 ( ! [X0,X1] : (~edge(X1) | sP2(head_of(X1),sK14(X0,head_of(X1)),X0) | head_of(X1) = X0 | tail_of(sK14(X0,head_of(X1))) = X0 | ~vertex(X0)) )), 4.36/4.62 inference(resolution,[],[f224,f125])). 4.36/4.62 fof(f230,plain,( 4.36/4.62 ( ! [X0,X1] : (~edge(X1) | sP2(head_of(X1),sK14(X0,head_of(X1)),X0) | head_of(X1) = X0 | head_of(X1) = head_of(sK14(X0,head_of(X1))) | ~vertex(X0)) )), 4.36/4.62 inference(resolution,[],[f225,f125])). 4.36/4.62 fof(f237,plain,( 4.36/4.62 ( ! [X3] : (sP2(head_of(sK12(sK8)),sK14(X3,head_of(sK12(sK8))),X3) | head_of(sK12(sK8)) = X3 | tail_of(sK14(X3,head_of(sK12(sK8)))) = X3 | ~vertex(X3)) )), 4.36/4.62 inference(resolution,[],[f227,f173])). 4.36/4.62 fof(f250,plain,( 4.36/4.62 ( ! [X3] : (sP2(head_of(sK12(sK8)),sK14(X3,head_of(sK12(sK8))),X3) | head_of(sK12(sK8)) = X3 | head_of(sK12(sK8)) = head_of(sK14(X3,head_of(sK12(sK8)))) | ~vertex(X3)) )), 4.36/4.62 inference(resolution,[],[f230,f173])). 4.36/4.62 fof(f259,plain,( 4.36/4.62 ( ! [X1] : (~vertex(X1) | tail_of(sK14(X1,head_of(sK12(sK8)))) = X1 | head_of(sK12(sK8)) = X1 | tail_of(sK14(X1,head_of(sK12(sK8)))) = head_of(sK12(sK8))) )), 4.36/4.62 inference(resolution,[],[f237,f116])). 4.36/4.62 fof(f260,plain,( 4.36/4.62 ( ! [X2] : (~vertex(X2) | tail_of(sK14(X2,head_of(sK12(sK8)))) = X2 | head_of(sK12(sK8)) = X2 | head_of(sK14(X2,head_of(sK12(sK8)))) = X2) )), 4.36/4.62 inference(resolution,[],[f237,f115])). 4.36/4.62 fof(f263,plain,( 4.36/4.62 ( ! [X1] : (~edge(X1) | tail_of(X1) = head_of(sK12(sK8)) | tail_of(X1) = head_of(sK14(tail_of(X1),head_of(sK12(sK8)))) | tail_of(X1) = tail_of(sK14(tail_of(X1),head_of(sK12(sK8))))) )), 4.36/4.62 inference(resolution,[],[f260,f126])). 4.36/4.62 fof(f362,plain,( 4.36/4.62 spl16_17 <=> ~vertex(tail_of(sK11(sK8)))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_17])])). 4.36/4.62 fof(f363,plain,( 4.36/4.62 ~vertex(tail_of(sK11(sK8))) | ~spl16_17), 4.36/4.62 inference(avatar_component_clause,[],[f362])). 4.36/4.62 fof(f365,plain,( 4.36/4.62 spl16_16 <=> vertex(tail_of(sK11(sK8)))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_16])])). 4.36/4.62 fof(f366,plain,( 4.36/4.62 vertex(tail_of(sK11(sK8))) | ~spl16_16), 4.36/4.62 inference(avatar_component_clause,[],[f365])). 4.36/4.62 fof(f368,plain,( 4.36/4.62 ~edge(sK11(sK8)) | ~spl16_17), 4.36/4.62 inference(resolution,[],[f363,f126])). 4.36/4.62 fof(f369,plain,( 4.36/4.62 $false | ~spl16_17), 4.36/4.62 inference(subsumption_resolution,[],[f368,f174])). 4.36/4.62 fof(f370,plain,( 4.36/4.62 spl16_17), 4.36/4.62 inference(avatar_contradiction_clause,[],[f369])). 4.36/4.62 fof(f373,plain,( 4.36/4.62 tail_of(sK11(sK8)) = tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | tail_of(sK11(sK8)) = head_of(sK12(sK8)) | tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) = head_of(sK12(sK8)) | ~spl16_16), 4.36/4.62 inference(resolution,[],[f366,f259])). 4.36/4.62 fof(f524,plain,( 4.36/4.62 ( ! [X1] : (~vertex(X1) | head_of(sK12(sK8)) = head_of(sK14(X1,head_of(sK12(sK8)))) | head_of(sK12(sK8)) = X1 | tail_of(sK14(X1,head_of(sK12(sK8)))) = head_of(sK12(sK8))) )), 4.36/4.62 inference(resolution,[],[f250,f116])). 4.36/4.62 fof(f555,plain,( 4.36/4.62 spl16_29 <=> ~vertex(head_of(sK12(sK8)))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_29])])). 4.36/4.62 fof(f556,plain,( 4.36/4.62 ~vertex(head_of(sK12(sK8))) | ~spl16_29), 4.36/4.62 inference(avatar_component_clause,[],[f555])). 4.36/4.62 fof(f558,plain,( 4.36/4.62 spl16_28 <=> vertex(head_of(sK12(sK8)))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_28])])). 4.36/4.62 fof(f559,plain,( 4.36/4.62 vertex(head_of(sK12(sK8))) | ~spl16_28), 4.36/4.62 inference(avatar_component_clause,[],[f558])). 4.36/4.62 fof(f561,plain,( 4.36/4.62 ~edge(sK12(sK8)) | ~spl16_29), 4.36/4.62 inference(resolution,[],[f556,f125])). 4.36/4.62 fof(f562,plain,( 4.36/4.62 $false | ~spl16_29), 4.36/4.62 inference(subsumption_resolution,[],[f561,f173])). 4.36/4.62 fof(f563,plain,( 4.36/4.62 spl16_29), 4.36/4.62 inference(avatar_contradiction_clause,[],[f562])). 4.36/4.62 fof(f928,plain,( 4.36/4.62 ( ! [X1] : (~edge(X1) | tail_of(X1) = head_of(sK12(sK8)) | tail_of(sK14(tail_of(X1),head_of(sK12(sK8)))) = head_of(sK12(sK8)) | head_of(sK12(sK8)) = head_of(sK14(tail_of(X1),head_of(sK12(sK8))))) )), 4.36/4.62 inference(resolution,[],[f524,f126])). 4.36/4.62 fof(f1141,plain,( 4.36/4.62 spl16_52 <=> tail_of(sK11(sK8)) = head_of(sK12(sK8))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_52])])). 4.36/4.62 fof(f1142,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK12(sK8)) | ~spl16_52), 4.36/4.62 inference(avatar_component_clause,[],[f1141])). 4.36/4.62 fof(f1144,plain,( 4.36/4.62 spl16_53 <=> tail_of(sK11(sK8)) != head_of(sK12(sK8))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_53])])). 4.36/4.62 fof(f1145,plain,( 4.36/4.62 tail_of(sK11(sK8)) != head_of(sK12(sK8)) | ~spl16_53), 4.36/4.62 inference(avatar_component_clause,[],[f1144])). 4.36/4.62 fof(f1147,plain,( 4.36/4.62 tail_of(sK11(sK8)) = tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) = head_of(sK12(sK8)) | (~spl16_16 | ~spl16_53)), 4.36/4.62 inference(subsumption_resolution,[],[f373,f1145])). 4.36/4.62 fof(f1187,plain,( 4.36/4.62 spl16_54 <=> tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) = head_of(sK12(sK8))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_54])])). 4.36/4.62 fof(f1188,plain,( 4.36/4.62 tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) = head_of(sK12(sK8)) | ~spl16_54), 4.36/4.62 inference(avatar_component_clause,[],[f1187])). 4.36/4.62 fof(f1190,plain,( 4.36/4.62 spl16_57 <=> tail_of(sK11(sK8)) != tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_57])])). 4.36/4.62 fof(f1191,plain,( 4.36/4.62 tail_of(sK11(sK8)) != tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~spl16_57), 4.36/4.62 inference(avatar_component_clause,[],[f1190])). 4.36/4.62 fof(f1193,plain,( 4.36/4.62 spl16_56 <=> tail_of(sK11(sK8)) = tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_56])])). 4.36/4.62 fof(f1194,plain,( 4.36/4.62 tail_of(sK11(sK8)) = tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~spl16_56), 4.36/4.62 inference(avatar_component_clause,[],[f1193])). 4.36/4.62 fof(f1195,plain,( 4.36/4.62 spl16_54 | spl16_56 | ~spl16_16 | spl16_53), 4.36/4.62 inference(avatar_split_clause,[],[f1147,f1144,f365,f1193,f1187])). 4.36/4.62 fof(f2385,plain,( 4.36/4.62 ( ! [X10] : (head_of(X10) != head_of(sK12(sK8)) | ~edge(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) = X10 | sequential(X10,sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~edge(X10)) ) | ~spl16_54), 4.36/4.62 inference(superposition,[],[f124,f1188])). 4.36/4.62 fof(f2522,plain,( 4.36/4.62 tail_of(sK11(sK8)) = tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | tail_of(sK11(sK8)) = head_of(sK12(sK8)) | tail_of(sK11(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~spl16_16), 4.36/4.62 inference(resolution,[],[f260,f366])). 4.36/4.62 fof(f2540,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK12(sK8)) | tail_of(sK11(sK8)) = head_of(sK12(sK8)) | tail_of(sK11(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | (~spl16_16 | ~spl16_54)), 4.36/4.62 inference(forward_demodulation,[],[f2522,f1188])). 4.36/4.62 fof(f2541,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK12(sK8)) | tail_of(sK11(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | (~spl16_16 | ~spl16_54)), 4.36/4.62 inference(duplicate_literal_removal,[],[f2540])). 4.36/4.62 fof(f2965,plain,( 4.36/4.62 ( ! [X0] : (tail_of(X0) != tail_of(sK11(sK8)) | ~edge(X0) | sK12(sK8) = X0 | sequential(sK12(sK8),X0) | ~edge(sK12(sK8))) ) | ~spl16_52), 4.36/4.62 inference(superposition,[],[f124,f1142])). 4.36/4.62 fof(f2970,plain,( 4.36/4.62 ( ! [X0] : (tail_of(X0) != tail_of(sK11(sK8)) | ~edge(X0) | sK12(sK8) = X0 | sequential(sK12(sK8),X0)) ) | ~spl16_52), 4.36/4.62 inference(subsumption_resolution,[],[f2965,f173])). 4.36/4.62 fof(f2976,plain,( 4.36/4.62 ~edge(sK11(sK8)) | sK11(sK8) = sK12(sK8) | sequential(sK12(sK8),sK11(sK8)) | ~spl16_52), 4.36/4.62 inference(equality_resolution,[],[f2970])). 4.36/4.62 fof(f2977,plain,( 4.36/4.62 sK11(sK8) = sK12(sK8) | sequential(sK12(sK8),sK11(sK8)) | ~spl16_52), 4.36/4.62 inference(subsumption_resolution,[],[f2976,f174])). 4.36/4.62 fof(f2982,plain,( 4.36/4.62 spl16_62 <=> sequential(sK12(sK8),sK11(sK8))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_62])])). 4.36/4.62 fof(f2983,plain,( 4.36/4.62 sequential(sK12(sK8),sK11(sK8)) | ~spl16_62), 4.36/4.62 inference(avatar_component_clause,[],[f2982])). 4.36/4.62 fof(f2988,plain,( 4.36/4.62 spl16_64 <=> sK11(sK8) = sK12(sK8)), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_64])])). 4.36/4.62 fof(f2989,plain,( 4.36/4.62 sK11(sK8) = sK12(sK8) | ~spl16_64), 4.36/4.62 inference(avatar_component_clause,[],[f2988])). 4.36/4.62 fof(f2990,plain,( 4.36/4.62 spl16_62 | spl16_64 | ~spl16_52), 4.36/4.62 inference(avatar_split_clause,[],[f2977,f1141,f2988,f2982])). 4.36/4.62 fof(f3439,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | (~spl16_16 | ~spl16_53 | ~spl16_54)), 4.36/4.62 inference(subsumption_resolution,[],[f2541,f1145])). 4.36/4.62 fof(f3525,plain,( 4.36/4.62 ( ! [X0] : (tail_of(X0) != tail_of(sK11(sK8)) | ~edge(X0) | sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) = X0 | sequential(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))),X0) | ~edge(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))))) ) | (~spl16_16 | ~spl16_53 | ~spl16_54)), 4.36/4.62 inference(superposition,[],[f124,f3439])). 4.36/4.62 fof(f4623,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK12(sK8)) | tail_of(sK11(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | tail_of(sK11(sK8)) = tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))))), 4.36/4.62 inference(resolution,[],[f263,f174])). 4.36/4.62 fof(f5308,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK12(sK8)) | tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) = head_of(sK12(sK8)) | head_of(sK12(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))))), 4.36/4.62 inference(resolution,[],[f928,f174])). 4.36/4.62 fof(f5437,plain,( 4.36/4.62 spl16_92 <=> edge(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_92])])). 4.36/4.62 fof(f5438,plain,( 4.36/4.62 edge(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~spl16_92), 4.36/4.62 inference(avatar_component_clause,[],[f5437])). 4.36/4.62 fof(f5440,plain,( 4.36/4.62 spl16_93 <=> ~edge(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_93])])). 4.36/4.62 fof(f5441,plain,( 4.36/4.62 ~edge(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~spl16_93), 4.36/4.62 inference(avatar_component_clause,[],[f5440])). 4.36/4.62 fof(f5443,plain,( 4.36/4.62 spl16_94 <=> ! [X10] : (head_of(X10) != head_of(sK12(sK8)) | ~edge(X10) | sequential(X10,sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) = X10)), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_94])])). 4.36/4.62 fof(f5444,plain,( 4.36/4.62 ( ! [X10] : (head_of(X10) != head_of(sK12(sK8)) | ~edge(X10) | sequential(X10,sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) = X10) ) | ~spl16_94), 4.36/4.62 inference(avatar_component_clause,[],[f5443])). 4.36/4.62 fof(f5445,plain,( 4.36/4.62 ~spl16_93 | spl16_94 | ~spl16_54), 4.36/4.62 inference(avatar_split_clause,[],[f2385,f1187,f5443,f5440])). 4.36/4.62 fof(f5446,plain,( 4.36/4.62 ~vertex(tail_of(sK11(sK8))) | ~vertex(head_of(sK12(sK8))) | tail_of(sK11(sK8)) = head_of(sK12(sK8)) | ~spl16_93), 4.36/4.62 inference(resolution,[],[f5441,f146])). 4.36/4.62 fof(f5447,plain,( 4.36/4.62 ~vertex(head_of(sK12(sK8))) | tail_of(sK11(sK8)) = head_of(sK12(sK8)) | (~spl16_16 | ~spl16_93)), 4.36/4.62 inference(subsumption_resolution,[],[f5446,f366])). 4.36/4.62 fof(f5448,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK12(sK8)) | (~spl16_16 | ~spl16_28 | ~spl16_93)), 4.36/4.62 inference(subsumption_resolution,[],[f5447,f559])). 4.36/4.62 fof(f5449,plain,( 4.36/4.62 $false | (~spl16_16 | ~spl16_28 | ~spl16_53 | ~spl16_93)), 4.36/4.62 inference(subsumption_resolution,[],[f5448,f1145])). 4.36/4.62 fof(f5450,plain,( 4.36/4.62 ~spl16_16 | ~spl16_28 | spl16_53 | spl16_93), 4.36/4.62 inference(avatar_contradiction_clause,[],[f5449])). 4.36/4.62 fof(f5451,plain,( 4.36/4.62 ( ! [X0] : (tail_of(X0) != tail_of(sK11(sK8)) | ~edge(X0) | sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) = X0 | sequential(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))),X0)) ) | (~spl16_16 | ~spl16_53 | ~spl16_54 | ~spl16_92)), 4.36/4.62 inference(subsumption_resolution,[],[f3525,f5438])). 4.36/4.62 fof(f5609,plain,( 4.36/4.62 ~edge(sK12(sK8)) | sequential(sK12(sK8),sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | sK12(sK8) = sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) | ~spl16_94), 4.36/4.62 inference(equality_resolution,[],[f5444])). 4.36/4.62 fof(f5612,plain,( 4.36/4.62 sequential(sK12(sK8),sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | sK12(sK8) = sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) | ~spl16_94), 4.36/4.62 inference(subsumption_resolution,[],[f5609,f173])). 4.36/4.62 fof(f5617,plain,( 4.36/4.62 spl16_96 <=> sK12(sK8) = sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_96])])). 4.36/4.62 fof(f5618,plain,( 4.36/4.62 sK12(sK8) = sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) | ~spl16_96), 4.36/4.62 inference(avatar_component_clause,[],[f5617])). 4.36/4.62 fof(f5623,plain,( 4.36/4.62 spl16_98 <=> sequential(sK12(sK8),sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_98])])). 4.36/4.62 fof(f5624,plain,( 4.36/4.62 sequential(sK12(sK8),sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~spl16_98), 4.36/4.62 inference(avatar_component_clause,[],[f5623])). 4.36/4.62 fof(f5625,plain,( 4.36/4.62 spl16_96 | spl16_98 | ~spl16_94), 4.36/4.62 inference(avatar_split_clause,[],[f5612,f5443,f5623,f5617])). 4.36/4.62 fof(f5641,plain,( 4.36/4.62 ~edge(sK11(sK8)) | sK11(sK8) = sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) | sequential(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))),sK11(sK8)) | (~spl16_16 | ~spl16_53 | ~spl16_54 | ~spl16_92)), 4.36/4.62 inference(equality_resolution,[],[f5451])). 4.36/4.62 fof(f5644,plain,( 4.36/4.62 sK11(sK8) = sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) | sequential(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))),sK11(sK8)) | (~spl16_16 | ~spl16_53 | ~spl16_54 | ~spl16_92)), 4.36/4.62 inference(subsumption_resolution,[],[f5641,f174])). 4.36/4.62 fof(f5655,plain,( 4.36/4.62 spl16_100 <=> sequential(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))),sK11(sK8))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_100])])). 4.36/4.62 fof(f5656,plain,( 4.36/4.62 sequential(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))),sK11(sK8)) | ~spl16_100), 4.36/4.62 inference(avatar_component_clause,[],[f5655])). 4.36/4.62 fof(f5661,plain,( 4.36/4.62 spl16_102 <=> sK11(sK8) = sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))), 4.36/4.62 introduced(avatar_definition,[new_symbols(naming,[spl16_102])])). 4.36/4.62 fof(f5662,plain,( 4.36/4.62 sK11(sK8) = sK14(tail_of(sK11(sK8)),head_of(sK12(sK8))) | ~spl16_102), 4.36/4.62 inference(avatar_component_clause,[],[f5661])). 4.36/4.62 fof(f5663,plain,( 4.36/4.62 spl16_100 | spl16_102 | ~spl16_16 | spl16_53 | ~spl16_54 | ~spl16_92), 4.36/4.62 inference(avatar_split_clause,[],[f5644,f5437,f1187,f1144,f365,f5661,f5655])). 4.36/4.62 fof(f5665,plain,( 4.36/4.62 tail_of(sK11(sK8)) != tail_of(sK11(sK8)) | (~spl16_57 | ~spl16_102)), 4.36/4.62 inference(backward_demodulation,[],[f5662,f1191])). 4.36/4.62 fof(f5685,plain,( 4.36/4.62 $false | (~spl16_57 | ~spl16_102)), 4.36/4.62 inference(trivial_inequality_removal,[],[f5665])). 4.36/4.62 fof(f5686,plain,( 4.36/4.62 spl16_57 | ~spl16_102), 4.36/4.62 inference(avatar_contradiction_clause,[],[f5685])). 4.36/4.62 fof(f5860,plain,( 4.36/4.62 ( ! [X10] : (triangle(sK11(sK8),X10,sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~sequential(X10,sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~sequential(sK11(sK8),X10)) ) | ~spl16_100), 4.36/4.62 inference(resolution,[],[f5656,f150])). 4.36/4.62 fof(f6038,plain,( 4.36/4.62 ~sequential(sK12(sK8),sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~sequential(sK11(sK8),sK12(sK8)) | ~spl16_100), 4.36/4.62 inference(resolution,[],[f5860,f165])). 4.36/4.62 fof(f6039,plain,( 4.36/4.62 ~sequential(sK11(sK8),sK12(sK8)) | (~spl16_98 | ~spl16_100)), 4.36/4.62 inference(subsumption_resolution,[],[f6038,f5624])). 4.36/4.62 fof(f6040,plain,( 4.36/4.62 $false | (~spl16_98 | ~spl16_100)), 4.36/4.62 inference(subsumption_resolution,[],[f6039,f166])). 4.36/4.62 fof(f6041,plain,( 4.36/4.62 ~spl16_98 | ~spl16_100), 4.36/4.62 inference(avatar_contradiction_clause,[],[f6040])). 4.36/4.62 fof(f6578,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | tail_of(sK11(sK8)) = tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~spl16_53), 4.36/4.62 inference(subsumption_resolution,[],[f4623,f1145])). 4.36/4.62 fof(f6579,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK12(sK8)) | tail_of(sK11(sK8)) = tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | (~spl16_53 | ~spl16_96)), 4.36/4.62 inference(forward_demodulation,[],[f6578,f5618])). 4.36/4.62 fof(f6580,plain,( 4.36/4.62 tail_of(sK11(sK8)) = tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | (~spl16_53 | ~spl16_96)), 4.36/4.62 inference(subsumption_resolution,[],[f6579,f1145])). 4.36/4.62 fof(f6581,plain,( 4.36/4.62 tail_of(sK11(sK8)) = tail_of(sK12(sK8)) | (~spl16_53 | ~spl16_96)), 4.36/4.62 inference(forward_demodulation,[],[f6580,f5618])). 4.36/4.62 fof(f6582,plain,( 4.36/4.62 $false | (~spl16_53 | ~spl16_96)), 4.36/4.62 inference(subsumption_resolution,[],[f6581,f179])). 4.36/4.62 fof(f6583,plain,( 4.36/4.62 spl16_53 | ~spl16_96), 4.36/4.62 inference(avatar_contradiction_clause,[],[f6582])). 4.36/4.62 fof(f10067,plain,( 4.36/4.62 sequential(sK11(sK8),sK11(sK8)) | ~spl16_64), 4.36/4.62 inference(forward_demodulation,[],[f166,f2989])). 4.36/4.62 fof(f10068,plain,( 4.36/4.62 $false | ~spl16_64), 4.36/4.62 inference(subsumption_resolution,[],[f10067,f145])). 4.36/4.62 fof(f10069,plain,( 4.36/4.62 ~spl16_64), 4.36/4.62 inference(avatar_contradiction_clause,[],[f10068])). 4.36/4.62 fof(f12511,plain,( 4.36/4.62 ( ! [X2,X0,X1] : (~on_path(sK12(sK8),X0) | precedes(sK12(sK8),sK11(sK8),X0) | ~on_path(sK11(sK8),X0) | ~path(X1,X2,X0)) ) | ~spl16_62), 4.36/4.62 inference(resolution,[],[f2983,f128])). 4.36/4.62 fof(f12787,plain,( 4.36/4.62 ( ! [X0,X1] : (precedes(sK12(sK8),sK11(sK8),sK8) | ~on_path(sK11(sK8),sK8) | ~path(X0,X1,sK8)) ) | ~spl16_62), 4.36/4.62 inference(resolution,[],[f12511,f168])). 4.36/4.62 fof(f12788,plain,( 4.36/4.62 ( ! [X0,X1] : (~on_path(sK11(sK8),sK8) | ~path(X0,X1,sK8)) ) | (~spl16_2 | ~spl16_62)), 4.36/4.62 inference(subsumption_resolution,[],[f12787,f202])). 4.36/4.62 fof(f12789,plain,( 4.36/4.62 ( ! [X0,X1] : (~path(X0,X1,sK8)) ) | (~spl16_2 | ~spl16_62)), 4.36/4.62 inference(subsumption_resolution,[],[f12788,f167])). 4.36/4.62 fof(f12790,plain,( 4.36/4.62 $false | (~spl16_2 | ~spl16_62)), 4.36/4.62 inference(subsumption_resolution,[],[f153,f12789])). 4.36/4.62 fof(f12791,plain,( 4.36/4.62 ~spl16_2 | ~spl16_62), 4.36/4.62 inference(avatar_contradiction_clause,[],[f12790])). 4.36/4.62 fof(f14047,plain,( 4.36/4.62 tail_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) = head_of(sK12(sK8)) | head_of(sK12(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~spl16_53), 4.36/4.62 inference(subsumption_resolution,[],[f5308,f1145])). 4.36/4.62 fof(f14048,plain,( 4.36/4.62 tail_of(sK11(sK8)) = head_of(sK12(sK8)) | head_of(sK12(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | (~spl16_53 | ~spl16_56)), 4.36/4.62 inference(forward_demodulation,[],[f14047,f1194])). 4.36/4.62 fof(f14049,plain,( 4.36/4.62 head_of(sK12(sK8)) = head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | (~spl16_53 | ~spl16_56)), 4.36/4.62 inference(subsumption_resolution,[],[f14048,f1145])). 4.36/4.62 fof(f14833,plain,( 4.36/4.62 ( ! [X4,X2,X0,X3,X1] : (tail_of(X0) != tail_of(sK11(sK8)) | head_of(X1) != head_of(sK14(tail_of(sK11(sK8)),head_of(sK12(sK8)))) | ~precedes(X0,X1,X2) | ~shortest_path(X3,X4,X2)) ) | ~spl16_56), 4.36/4.62 inference(superposition,[],[f102,f1194])). 4.36/4.62 fof(f15096,plain,( 4.36/4.62 ( ! [X4,X2,X0,X3,X1] : (~shortest_path(X3,X4,X2) | tail_of(X0) != tail_of(sK11(sK8)) | ~precedes(X0,X1,X2) | head_of(X1) != head_of(sK12(sK8))) ) | (~spl16_53 | ~spl16_56)), 4.36/4.62 inference(backward_demodulation,[],[f14049,f14833])). 4.36/4.62 fof(f15444,plain,( 4.36/4.62 ( ! [X0,X1] : (~precedes(X0,X1,sK8) | tail_of(X0) != tail_of(sK11(sK8)) | head_of(X1) != head_of(sK12(sK8))) ) | (~spl16_53 | ~spl16_56)), 4.36/4.62 inference(resolution,[],[f15096,f93])). 4.36/4.62 fof(f15446,plain,( 4.36/4.62 tail_of(sK11(sK8)) != tail_of(sK11(sK8)) | head_of(sK12(sK8)) != head_of(sK12(sK8)) | (~spl16_2 | ~spl16_53 | ~spl16_56)), 4.36/4.62 inference(resolution,[],[f15444,f200])). 4.36/4.62 fof(f15447,plain,( 4.36/4.62 $false | (~spl16_2 | ~spl16_53 | ~spl16_56)), 4.36/4.62 inference(trivial_inequality_removal,[],[f15446])). 4.36/4.62 fof(f15448,plain,( 4.36/4.62 ~spl16_2 | spl16_53 | ~spl16_56), 4.36/4.62 inference(avatar_contradiction_clause,[],[f15447])). 4.36/4.62 fof(f15449,plain,( 4.36/4.62 $false), 4.36/4.62 inference(avatar_sat_refutation,[],[f201,f212,f370,f563,f1195,f2990,f5445,f5450,f5625,f5663,f5686,f6041,f6583,f10069,f12791,f15448])). 4.36/4.62 % SZS output end Proof for theBenchmark 4.36/4.62 % ------------------------------ 4.36/4.62 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 4.36/4.62 % Termination reason: Refutation 4.36/4.62 4.36/4.62 % Memory used [KB]: 12537 4.36/4.62 % Time elapsed: 0.648 s 4.36/4.62 % ------------------------------ 4.36/4.62 % ------------------------------ 4.36/4.62 % Success in time 4.386 s 4.36/4.62 EOF