0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : vampire --mode casc -t %d %s 0.03/0.23 % Computer : n146.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 05:42:55 CDT 2018 0.03/0.23 % CPUTime : 0.06/0.27 % dis-11_3_add=off:afp=40000:afq=1.0:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on_2 on theBenchmark 0.53/0.77 % Time limit reached! 0.53/0.77 % ------------------------------ 0.53/0.77 % Version: Vampire 4.2.2 (commit 552c234 on 2018-07-02 14:53:33 +0100) 0.53/0.77 % Termination reason: Time limit 0.53/0.77 % Termination phase: Saturation 0.53/0.77 0.53/0.77 % Memory used [KB]: 19189 0.53/0.77 % Time elapsed: 0.500 s 0.53/0.77 % ------------------------------ 0.53/0.77 % ------------------------------ 0.58/0.80 % lrs+10_12_add=off:afp=100000:afq=1.4:amm=sco:anc=none:cond=on:lma=on:nm=64:nwc=1.3:stl=30:sac=on:urr=on_2 on theBenchmark 1.02/1.30 % Time limit reached! 1.02/1.30 % ------------------------------ 1.02/1.30 % Version: Vampire 4.2.2 (commit 552c234 on 2018-07-02 14:53:33 +0100) 1.02/1.30 % Termination reason: Time limit 1.02/1.30 % Termination phase: Saturation 1.02/1.30 1.02/1.30 % Memory used [KB]: 18421 1.02/1.30 % Time elapsed: 0.500 s 1.02/1.30 % ------------------------------ 1.02/1.30 % ------------------------------ 1.10/1.34 % 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 1.62/1.84 % Time limit reached! 1.62/1.84 % ------------------------------ 1.62/1.84 % Version: Vampire 4.2.2 (commit 552c234 on 2018-07-02 14:53:33 +0100) 1.62/1.84 % Termination reason: Time limit 1.62/1.84 % Termination phase: Saturation 1.62/1.84 1.62/1.84 % Memory used [KB]: 12281 1.62/1.84 % Time elapsed: 0.500 s 1.62/1.84 % ------------------------------ 1.62/1.84 % ------------------------------ 1.62/1.87 % lrs+1_1_aac=none:acc=model:add=large:afp=100000:afq=1.2:anc=none:bd=off:bs=on:bsr=on:ccuc=first:cond=on:fde=unused:irw=on:nm=2:newcnf=on:nwc=1:stl=30:sd=3:ss=axioms:st=2.0:sos=on:sac=on:uhcvi=on_2 on theBenchmark 1.65/1.91 % Refutation found. Thanks to Tanya! 1.65/1.91 % SZS status Theorem for theBenchmark 1.65/1.91 % SZS output start Proof for theBenchmark 1.65/1.91 fof(f2,axiom,( 1.65/1.91 ! [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)))), 1.65/1.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn)). 1.65/1.91 fof(f4,axiom,( 1.65/1.91 ! [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)))), 1.65/1.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties)). 1.65/1.91 fof(f5,axiom,( 1.65/1.91 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))))), 1.65/1.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_properties)). 1.65/1.91 fof(f6,axiom,( 1.65/1.91 ! [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))), 1.65/1.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn)). 1.65/1.91 fof(f10,axiom,( 1.65/1.91 ! [X4] : (edge(X4) => (vertex(tail_of(X4)) & vertex(head_of(X4))))), 1.65/1.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices)). 1.65/1.91 fof(f11,axiom,( 1.65/1.91 ! [X4] : (edge(X4) => tail_of(X4) != head_of(X4))), 1.65/1.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops)). 1.65/1.91 fof(f12,axiom,( 1.65/1.91 ! [X5,X6] : (sequential(X5,X6) <=> (edge(X6) & X5 != X6 & tail_of(X6) = head_of(X5) & edge(X5)))), 1.65/1.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn)). 1.65/1.91 fof(f14,conjecture,( 1.65/1.91 complete => ! [X2,X0,X1] : (shortest_path(X0,X1,X2) => ! [X5,X6] : ((on_path(X6,X2) & sequential(X5,X6) & on_path(X5,X2)) => ? [X7] : triangle(X5,X6,X7)))), 1.65/1.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_path_means_stuff_means_triangles)). 1.65/1.91 fof(f15,negated_conjecture,( 1.65/1.91 ~(complete => ! [X2,X0,X1] : (shortest_path(X0,X1,X2) => ! [X5,X6] : ((on_path(X6,X2) & sequential(X5,X6) & on_path(X5,X2)) => ? [X7] : triangle(X5,X6,X7))))), 1.65/1.91 inference(negated_conjecture,[],[f14])). 1.65/1.91 fof(f18,axiom,( 1.65/1.91 ! [X5,X6,X7] : (triangle(X5,X6,X7) <=> (edge(X5) & edge(X6) & edge(X7) & sequential(X5,X6) & sequential(X6,X7) & sequential(X7,X5)))), 1.65/1.91 file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn)). 1.65/1.91 fof(f20,plain,( 1.65/1.91 ~(complete => ! [X0,X1,X2] : (shortest_path(X1,X2,X0) => ! [X3,X4] : ((on_path(X4,X0) & sequential(X3,X4) & on_path(X3,X0)) => ? [X5] : triangle(X3,X4,X5))))), 1.65/1.91 inference(rectify,[],[f15])). 1.65/1.91 fof(f21,plain,( 1.65/1.91 ! [X0,X1,X2] : (triangle(X0,X1,X2) <=> (edge(X0) & edge(X1) & edge(X2) & sequential(X0,X1) & sequential(X1,X2) & sequential(X2,X0)))), 1.65/1.91 inference(rectify,[],[f18])). 1.65/1.91 fof(f22,plain,( 1.65/1.91 ! [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)))), 1.65/1.91 inference(rectify,[],[f2])). 1.65/1.91 fof(f24,plain,( 1.65/1.91 ! [X0,X1] : (sequential(X0,X1) <=> (edge(X1) & X0 != X1 & tail_of(X1) = head_of(X0) & edge(X0)))), 1.65/1.91 inference(rectify,[],[f12])). 1.65/1.91 fof(f25,plain,( 1.65/1.91 ! [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)))), 1.65/1.91 inference(rectify,[],[f4])). 1.65/1.91 fof(f26,plain,( 1.65/1.91 ! [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))), 1.65/1.91 inference(rectify,[],[f6])). 1.65/1.91 fof(f27,plain,( 1.65/1.91 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))))), 1.65/1.91 inference(rectify,[],[f5])). 1.65/1.91 fof(f28,plain,( 1.65/1.91 ! [X0] : (edge(X0) => (vertex(tail_of(X0)) & vertex(head_of(X0))))), 1.65/1.91 inference(rectify,[],[f10])). 1.65/1.91 fof(f29,plain,( 1.65/1.91 ! [X0] : (edge(X0) => tail_of(X0) != head_of(X0))), 1.65/1.91 inference(rectify,[],[f11])). 1.65/1.91 fof(f31,plain,( 1.65/1.91 ! [X0,X1,X2] : ((edge(X0) & edge(X1) & edge(X2) & sequential(X0,X1) & sequential(X1,X2) & sequential(X2,X0)) => triangle(X0,X1,X2))), 1.65/1.91 inference(unused_predicate_definition_removal,[],[f21])). 1.65/1.91 fof(f32,plain,( 1.65/1.91 ? [X0,X1,X2] : (? [X3,X4] : (! [X5] : ~triangle(X3,X4,X5) & (on_path(X4,X0) & sequential(X3,X4) & on_path(X3,X0))) & shortest_path(X1,X2,X0)) & complete), 1.65/1.91 inference(ennf_transformation,[],[f20])). 1.65/1.91 fof(f33,plain,( 1.65/1.91 ? [X0,X1,X2] : (? [X3,X4] : (! [X5] : ~triangle(X3,X4,X5) & on_path(X4,X0) & sequential(X3,X4) & on_path(X3,X0)) & shortest_path(X1,X2,X0)) & complete), 1.65/1.91 inference(flattening,[],[f32])). 1.65/1.91 fof(f34,plain,( 1.65/1.91 ! [X0,X1,X2] : (triangle(X0,X1,X2) | (~edge(X0) | ~edge(X1) | ~edge(X2) | ~sequential(X0,X1) | ~sequential(X1,X2) | ~sequential(X2,X0)))), 1.65/1.91 inference(ennf_transformation,[],[f31])). 1.65/1.91 fof(f35,plain,( 1.65/1.91 ! [X0,X1,X2] : (triangle(X0,X1,X2) | ~edge(X0) | ~edge(X1) | ~edge(X2) | ~sequential(X0,X1) | ~sequential(X1,X2) | ~sequential(X2,X0))), 1.65/1.91 inference(flattening,[],[f34])). 1.65/1.91 fof(f36,plain,( 1.65/1.91 ! [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))), 1.65/1.91 inference(ennf_transformation,[],[f22])). 1.65/1.91 fof(f37,plain,( 1.65/1.91 ! [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))), 1.65/1.91 inference(flattening,[],[f36])). 1.65/1.91 fof(f39,plain,( 1.65/1.91 ! [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)))), 1.65/1.91 inference(ennf_transformation,[],[f25])). 1.65/1.91 fof(f40,plain,( 1.65/1.91 ! [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))), 1.65/1.91 inference(flattening,[],[f39])). 1.65/1.91 fof(f41,plain,( 1.65/1.91 ! [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))), 1.65/1.91 inference(ennf_transformation,[],[f26])). 1.65/1.91 fof(f42,plain,( 1.65/1.91 ! [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), 1.65/1.91 inference(ennf_transformation,[],[f27])). 1.65/1.91 fof(f43,plain,( 1.65/1.91 ! [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), 1.65/1.91 inference(flattening,[],[f42])). 1.65/1.91 fof(f44,plain,( 1.65/1.91 ! [X0] : ((vertex(tail_of(X0)) & vertex(head_of(X0))) | ~edge(X0))), 1.65/1.91 inference(ennf_transformation,[],[f28])). 1.65/1.91 fof(f45,plain,( 1.65/1.91 ! [X0] : (tail_of(X0) != head_of(X0) | ~edge(X0))), 1.65/1.91 inference(ennf_transformation,[],[f29])). 1.65/1.91 fof(f46,plain,( 1.65/1.91 on_path(sK3,sK0)), 1.65/1.91 inference(cnf_transformation,[],[f33])). 1.65/1.91 fof(f47,plain,( 1.65/1.91 sequential(sK3,sK4)), 1.65/1.91 inference(cnf_transformation,[],[f33])). 1.65/1.91 fof(f48,plain,( 1.65/1.91 on_path(sK4,sK0)), 1.65/1.91 inference(cnf_transformation,[],[f33])). 1.65/1.91 fof(f49,plain,( 1.65/1.91 ( ! [X5] : (~triangle(sK3,sK4,X5)) )), 1.65/1.91 inference(cnf_transformation,[],[f33])). 1.65/1.91 fof(f50,plain,( 1.65/1.91 shortest_path(sK1,sK2,sK0)), 1.65/1.91 inference(cnf_transformation,[],[f33])). 1.65/1.91 fof(f51,plain,( 1.65/1.91 complete), 1.65/1.91 inference(cnf_transformation,[],[f33])). 1.65/1.91 fof(f52,plain,( 1.65/1.91 ( ! [X2,X0,X1] : (~sequential(X2,X0) | ~sequential(X1,X2) | ~sequential(X0,X1) | ~edge(X2) | ~edge(X1) | ~edge(X0) | triangle(X0,X1,X2)) )), 1.65/1.91 inference(cnf_transformation,[],[f35])). 1.65/1.91 fof(f54,plain,( 1.65/1.91 ( ! [X4,X2,X0,X3,X1] : (~path(X1,X2,X0) | ~on_path(X4,X0) | ~sequential(X3,X4) | ~on_path(X3,X0) | precedes(X3,X4,X0)) )), 1.65/1.91 inference(cnf_transformation,[],[f37])). 1.65/1.91 fof(f60,plain,( 1.65/1.91 ( ! [X0,X1] : (~sequential(X0,X1) | edge(X0)) )), 1.65/1.91 inference(cnf_transformation,[],[f24])). 1.65/1.91 fof(f61,plain,( 1.65/1.91 ( ! [X0,X1] : (~sequential(X0,X1) | tail_of(X1) = head_of(X0)) )), 1.65/1.91 inference(cnf_transformation,[],[f24])). 1.65/1.91 fof(f63,plain,( 1.65/1.91 ( ! [X0,X1] : (~sequential(X0,X1) | edge(X1)) )), 1.65/1.91 inference(cnf_transformation,[],[f24])). 1.65/1.91 fof(f64,plain,( 1.65/1.91 ( ! [X0,X1] : (~edge(X0) | tail_of(X1) != head_of(X0) | X0 = X1 | ~edge(X1) | sequential(X0,X1)) )), 1.65/1.91 inference(cnf_transformation,[],[f24])). 1.65/1.91 fof(f65,plain,( 1.65/1.91 ( ! [X4,X2,X0,X5,X3,X1] : (~shortest_path(X0,X1,X4) | ~precedes(X2,X3,X4) | head_of(X3) != head_of(X5) | tail_of(X2) != tail_of(X5)) )), 1.65/1.91 inference(cnf_transformation,[],[f40])). 1.65/1.91 fof(f66,plain,( 1.65/1.91 ( ! [X4,X2,X0,X3,X1] : (~shortest_path(X0,X1,X4) | ~precedes(X2,X3,X4) | ~precedes(X3,X2,X4)) )), 1.65/1.91 inference(cnf_transformation,[],[f40])). 1.65/1.91 fof(f70,plain,( 1.65/1.91 ( ! [X2,X0,X1] : (~shortest_path(X0,X1,X2) | path(X0,X1,X2)) )), 1.65/1.91 inference(cnf_transformation,[],[f41])). 1.65/1.91 fof(f72,plain,( 1.65/1.91 ( ! [X2,X0,X1] : (head_of(X2) != X1 | tail_of(X2) != X0 | sP8(X2,X1,X0)) )), 1.65/1.91 inference(cnf_transformation,[],[f43])). 1.65/1.91 fof(f73,plain,( 1.65/1.91 ( ! [X2,X0,X1] : (~sP8(X2,X1,X0) | head_of(X2) = X1) )), 1.65/1.91 inference(cnf_transformation,[],[f43])). 1.65/1.91 fof(f74,plain,( 1.65/1.91 ( ! [X2,X0,X1] : (~sP8(X2,X1,X0) | tail_of(X2) = X0) )), 1.65/1.91 inference(cnf_transformation,[],[f43])). 1.65/1.91 fof(f76,plain,( 1.65/1.91 ( ! [X0,X1] : (~vertex(X1) | X0 = X1 | ~complete | ~vertex(X0) | sP8(sK7(X0,X1),X1,X0) | head_of(sK7(X0,X1)) = X0) )), 1.65/1.91 inference(cnf_transformation,[],[f43])). 1.65/1.91 fof(f77,plain,( 1.65/1.91 ( ! [X0,X1] : (~vertex(X1) | X0 = X1 | ~complete | ~vertex(X0) | sP8(sK7(X0,X1),X1,X0) | tail_of(sK7(X0,X1)) = X1) )), 1.65/1.91 inference(cnf_transformation,[],[f43])). 1.65/1.91 fof(f78,plain,( 1.65/1.91 ( ! [X0,X1] : (~vertex(X1) | X0 = X1 | ~complete | ~vertex(X0) | edge(sK7(X0,X1))) )), 1.65/1.91 inference(cnf_transformation,[],[f43])). 1.65/1.91 fof(f79,plain,( 1.65/1.91 ( ! [X0] : (~edge(X0) | vertex(head_of(X0))) )), 1.65/1.91 inference(cnf_transformation,[],[f44])). 1.65/1.91 fof(f80,plain,( 1.65/1.91 ( ! [X0] : (~edge(X0) | vertex(tail_of(X0))) )), 1.65/1.91 inference(cnf_transformation,[],[f44])). 1.65/1.91 fof(f81,plain,( 1.65/1.91 ( ! [X0] : (~edge(X0) | tail_of(X0) != head_of(X0)) )), 1.65/1.91 inference(cnf_transformation,[],[f45])). 1.65/1.91 fof(f85,plain,( 1.65/1.91 ( ! [X2,X0] : (tail_of(X2) != X0 | sP8(X2,head_of(X2),X0)) )), 1.65/1.91 inference(equality_resolution,[],[f72])). 1.65/1.91 fof(f86,plain,( 1.65/1.91 ( ! [X2] : (sP8(X2,head_of(X2),tail_of(X2))) )), 1.65/1.91 inference(equality_resolution,[],[f85])). 1.65/1.91 fof(f88,plain,( 1.65/1.91 ( ! [X0,X1] : (~vertex(X1) | X0 = X1 | ~vertex(X0) | sP8(sK7(X0,X1),X1,X0) | head_of(sK7(X0,X1)) = X0) )), 1.65/1.91 inference(subsumption_resolution,[],[f76,f51])). 1.65/1.91 fof(f89,plain,( 1.65/1.91 ( ! [X0,X1] : (~vertex(X1) | X0 = X1 | ~vertex(X0) | sP8(sK7(X0,X1),X1,X0) | tail_of(sK7(X0,X1)) = X1) )), 1.65/1.91 inference(subsumption_resolution,[],[f77,f51])). 1.65/1.91 fof(f90,plain,( 1.65/1.91 ( ! [X0,X1] : (~vertex(X1) | X0 = X1 | ~vertex(X0) | edge(sK7(X0,X1))) )), 1.65/1.91 inference(subsumption_resolution,[],[f78,f51])). 1.65/1.91 fof(f96,plain,( 1.65/1.91 spl9_2 <=> on_path(sK3,sK0)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_2])])). 1.65/1.91 fof(f97,plain,( 1.65/1.91 on_path(sK3,sK0) | ~spl9_2), 1.65/1.91 inference(avatar_component_clause,[],[f96])). 1.65/1.91 fof(f98,plain,( 1.65/1.91 spl9_2), 1.65/1.91 inference(avatar_split_clause,[],[f46,f96])). 1.65/1.91 fof(f100,plain,( 1.65/1.91 spl9_4 <=> sequential(sK3,sK4)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_4])])). 1.65/1.91 fof(f101,plain,( 1.65/1.91 sequential(sK3,sK4) | ~spl9_4), 1.65/1.91 inference(avatar_component_clause,[],[f100])). 1.65/1.91 fof(f102,plain,( 1.65/1.91 spl9_4), 1.65/1.91 inference(avatar_split_clause,[],[f47,f100])). 1.65/1.91 fof(f104,plain,( 1.65/1.91 spl9_6 <=> on_path(sK4,sK0)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_6])])). 1.65/1.91 fof(f105,plain,( 1.65/1.91 on_path(sK4,sK0) | ~spl9_6), 1.65/1.91 inference(avatar_component_clause,[],[f104])). 1.65/1.91 fof(f106,plain,( 1.65/1.91 spl9_6), 1.65/1.91 inference(avatar_split_clause,[],[f48,f104])). 1.65/1.91 fof(f107,plain,( 1.65/1.91 edge(sK3) | ~spl9_4), 1.65/1.91 inference(resolution,[],[f101,f60])). 1.65/1.91 fof(f108,plain,( 1.65/1.91 tail_of(sK4) = head_of(sK3) | ~spl9_4), 1.65/1.91 inference(resolution,[],[f101,f61])). 1.65/1.91 fof(f109,plain,( 1.65/1.91 edge(sK4) | ~spl9_4), 1.65/1.91 inference(resolution,[],[f101,f63])). 1.65/1.91 fof(f115,plain,( 1.65/1.91 spl9_8 <=> edge(sK3)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_8])])). 1.65/1.91 fof(f116,plain,( 1.65/1.91 edge(sK3) | ~spl9_8), 1.65/1.91 inference(avatar_component_clause,[],[f115])). 1.65/1.91 fof(f117,plain,( 1.65/1.91 spl9_8 | ~spl9_4), 1.65/1.91 inference(avatar_split_clause,[],[f107,f100,f115])). 1.65/1.91 fof(f119,plain,( 1.65/1.91 spl9_10 <=> edge(sK4)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_10])])). 1.65/1.91 fof(f120,plain,( 1.65/1.91 edge(sK4) | ~spl9_10), 1.65/1.91 inference(avatar_component_clause,[],[f119])). 1.65/1.91 fof(f121,plain,( 1.65/1.91 spl9_10 | ~spl9_4), 1.65/1.91 inference(avatar_split_clause,[],[f109,f100,f119])). 1.65/1.91 fof(f123,plain,( 1.65/1.91 spl9_12 <=> shortest_path(sK1,sK2,sK0)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_12])])). 1.65/1.91 fof(f124,plain,( 1.65/1.91 shortest_path(sK1,sK2,sK0) | ~spl9_12), 1.65/1.91 inference(avatar_component_clause,[],[f123])). 1.65/1.91 fof(f125,plain,( 1.65/1.91 spl9_12), 1.65/1.91 inference(avatar_split_clause,[],[f50,f123])). 1.65/1.91 fof(f126,plain,( 1.65/1.91 tail_of(sK3) != head_of(sK3) | ~spl9_8), 1.65/1.91 inference(resolution,[],[f116,f81])). 1.65/1.91 fof(f127,plain,( 1.65/1.91 vertex(head_of(sK3)) | ~spl9_8), 1.65/1.91 inference(resolution,[],[f116,f79])). 1.65/1.91 fof(f128,plain,( 1.65/1.91 vertex(tail_of(sK3)) | ~spl9_8), 1.65/1.91 inference(resolution,[],[f116,f80])). 1.65/1.91 fof(f130,plain,( 1.65/1.91 vertex(tail_of(sK4)) | (~spl9_4 | ~spl9_8)), 1.65/1.91 inference(forward_demodulation,[],[f127,f108])). 1.65/1.91 fof(f133,plain,( 1.65/1.91 path(sK1,sK2,sK0) | ~spl9_12), 1.65/1.91 inference(resolution,[],[f124,f70])). 1.65/1.91 fof(f134,plain,( 1.65/1.91 ( ! [X2,X3,X1] : (~precedes(X1,X2,sK0) | head_of(X2) != head_of(X3) | tail_of(X1) != tail_of(X3)) ) | ~spl9_12), 1.65/1.91 inference(resolution,[],[f124,f65])). 1.65/1.91 fof(f135,plain,( 1.65/1.91 ( ! [X4,X5] : (~precedes(X4,X5,sK0) | ~precedes(X5,X4,sK0)) ) | ~spl9_12), 1.65/1.91 inference(resolution,[],[f124,f66])). 1.65/1.91 fof(f137,plain,( 1.65/1.91 vertex(head_of(sK4)) | ~spl9_10), 1.65/1.91 inference(resolution,[],[f120,f79])). 1.65/1.91 fof(f139,plain,( 1.65/1.91 ( ! [X0] : (~edge(X0) | sK4 = X0 | tail_of(X0) != head_of(sK4) | sequential(sK4,X0)) ) | ~spl9_10), 1.65/1.91 inference(resolution,[],[f120,f64])). 1.65/1.91 fof(f141,plain,( 1.65/1.91 spl9_14 <=> vertex(tail_of(sK3))), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_14])])). 1.65/1.91 fof(f142,plain,( 1.65/1.91 vertex(tail_of(sK3)) | ~spl9_14), 1.65/1.91 inference(avatar_component_clause,[],[f141])). 1.65/1.91 fof(f143,plain,( 1.65/1.91 spl9_14 | ~spl9_8), 1.65/1.91 inference(avatar_split_clause,[],[f128,f115,f141])). 1.65/1.91 fof(f145,plain,( 1.65/1.91 spl9_16 <=> vertex(tail_of(sK4))), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_16])])). 1.65/1.91 fof(f146,plain,( 1.65/1.91 vertex(tail_of(sK4)) | ~spl9_16), 1.65/1.91 inference(avatar_component_clause,[],[f145])). 1.65/1.91 fof(f147,plain,( 1.65/1.91 spl9_16 | ~spl9_4 | ~spl9_8), 1.65/1.91 inference(avatar_split_clause,[],[f130,f115,f100,f145])). 1.65/1.91 fof(f149,plain,( 1.65/1.91 spl9_18 <=> vertex(head_of(sK4))), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_18])])). 1.65/1.91 fof(f150,plain,( 1.65/1.91 vertex(head_of(sK4)) | ~spl9_18), 1.65/1.91 inference(avatar_component_clause,[],[f149])). 1.65/1.91 fof(f151,plain,( 1.65/1.91 spl9_18 | ~spl9_10), 1.65/1.91 inference(avatar_split_clause,[],[f137,f119,f149])). 1.65/1.91 fof(f152,plain,( 1.65/1.91 ( ! [X0] : (~vertex(X0) | tail_of(sK3) = X0 | sP8(sK7(X0,tail_of(sK3)),tail_of(sK3),X0) | tail_of(sK3) = tail_of(sK7(X0,tail_of(sK3)))) ) | ~spl9_14), 1.65/1.91 inference(resolution,[],[f142,f89])). 1.65/1.91 fof(f153,plain,( 1.65/1.91 ( ! [X1] : (~vertex(X1) | tail_of(sK3) = X1 | sP8(sK7(X1,tail_of(sK3)),tail_of(sK3),X1) | head_of(sK7(X1,tail_of(sK3))) = X1) ) | ~spl9_14), 1.65/1.91 inference(resolution,[],[f142,f88])). 1.65/1.91 fof(f156,plain,( 1.65/1.91 spl9_20 <=> path(sK1,sK2,sK0)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_20])])). 1.65/1.91 fof(f157,plain,( 1.65/1.91 path(sK1,sK2,sK0) | ~spl9_20), 1.65/1.91 inference(avatar_component_clause,[],[f156])). 1.65/1.91 fof(f158,plain,( 1.65/1.91 spl9_20 | ~spl9_12), 1.65/1.91 inference(avatar_split_clause,[],[f133,f123,f156])). 1.65/1.91 fof(f163,plain,( 1.65/1.91 ( ! [X4,X3] : (~sequential(X4,X3) | ~on_path(X3,sK0) | ~on_path(X4,sK0) | precedes(X4,X3,sK0)) ) | ~spl9_20), 1.65/1.91 inference(resolution,[],[f157,f54])). 1.65/1.91 fof(f170,plain,( 1.65/1.91 ( ! [X0] : (~vertex(X0) | head_of(sK4) = X0 | sP8(sK7(X0,head_of(sK4)),head_of(sK4),X0) | tail_of(sK7(X0,head_of(sK4))) = head_of(sK4)) ) | ~spl9_18), 1.65/1.91 inference(resolution,[],[f150,f89])). 1.65/1.91 fof(f171,plain,( 1.65/1.91 ( ! [X1] : (~vertex(X1) | head_of(sK4) = X1 | sP8(sK7(X1,head_of(sK4)),head_of(sK4),X1) | head_of(sK7(X1,head_of(sK4))) = X1) ) | ~spl9_18), 1.65/1.91 inference(resolution,[],[f150,f88])). 1.65/1.91 fof(f172,plain,( 1.65/1.91 ( ! [X2] : (~vertex(X2) | head_of(sK4) = X2 | edge(sK7(X2,head_of(sK4)))) ) | ~spl9_18), 1.65/1.91 inference(resolution,[],[f150,f90])). 1.65/1.91 fof(f174,plain,( 1.65/1.91 spl9_22 <=> tail_of(sK4) = head_of(sK3)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_22])])). 1.65/1.91 fof(f175,plain,( 1.65/1.91 tail_of(sK4) = head_of(sK3) | ~spl9_22), 1.65/1.91 inference(avatar_component_clause,[],[f174])). 1.65/1.91 fof(f176,plain,( 1.65/1.91 spl9_22 | ~spl9_4), 1.65/1.91 inference(avatar_split_clause,[],[f108,f100,f174])). 1.65/1.91 fof(f179,plain,( 1.65/1.91 spl9_25 <=> tail_of(sK3) != head_of(sK3)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_25])])). 1.65/1.91 fof(f180,plain,( 1.65/1.91 tail_of(sK3) != head_of(sK3) | ~spl9_25), 1.65/1.91 inference(avatar_component_clause,[],[f179])). 1.65/1.91 fof(f181,plain,( 1.65/1.91 ~spl9_25 | ~spl9_8), 1.65/1.91 inference(avatar_split_clause,[],[f126,f115,f179])). 1.65/1.91 fof(f187,plain,( 1.65/1.91 tail_of(sK3) != tail_of(sK4) | (~spl9_22 | ~spl9_25)), 1.65/1.91 inference(superposition,[],[f180,f175])). 1.65/1.91 fof(f197,plain,( 1.65/1.91 spl9_33 <=> tail_of(sK3) != tail_of(sK4)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_33])])). 1.65/1.91 fof(f198,plain,( 1.65/1.91 tail_of(sK3) != tail_of(sK4) | ~spl9_33), 1.65/1.91 inference(avatar_component_clause,[],[f197])). 1.65/1.91 fof(f199,plain,( 1.65/1.91 ~spl9_33 | ~spl9_22 | spl9_25), 1.65/1.91 inference(avatar_split_clause,[],[f187,f179,f174,f197])). 1.65/1.91 fof(f209,plain,( 1.65/1.91 sK3 = sK4 | tail_of(sK3) != head_of(sK4) | sequential(sK4,sK3) | (~spl9_8 | ~spl9_10)), 1.65/1.91 inference(resolution,[],[f139,f116])). 1.65/1.91 fof(f215,plain,( 1.65/1.91 ~on_path(sK4,sK0) | ~on_path(sK3,sK0) | precedes(sK3,sK4,sK0) | (~spl9_4 | ~spl9_20)), 1.65/1.91 inference(resolution,[],[f163,f101])). 1.65/1.91 fof(f216,plain,( 1.65/1.91 ~on_path(sK3,sK0) | precedes(sK3,sK4,sK0) | (~spl9_4 | ~spl9_6 | ~spl9_20)), 1.65/1.91 inference(subsumption_resolution,[],[f215,f105])). 1.65/1.91 fof(f217,plain,( 1.65/1.91 precedes(sK3,sK4,sK0) | (~spl9_2 | ~spl9_4 | ~spl9_6 | ~spl9_20)), 1.65/1.91 inference(subsumption_resolution,[],[f216,f97])). 1.65/1.91 fof(f219,plain,( 1.65/1.91 spl9_36 <=> precedes(sK3,sK4,sK0)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_36])])). 1.65/1.91 fof(f220,plain,( 1.65/1.91 precedes(sK3,sK4,sK0) | ~spl9_36), 1.65/1.91 inference(avatar_component_clause,[],[f219])). 1.65/1.91 fof(f221,plain,( 1.65/1.91 spl9_36 | ~spl9_2 | ~spl9_4 | ~spl9_6 | ~spl9_20), 1.65/1.91 inference(avatar_split_clause,[],[f217,f156,f104,f100,f96,f219])). 1.65/1.91 fof(f225,plain,( 1.65/1.91 ( ! [X0] : (head_of(sK4) != head_of(X0) | tail_of(sK3) != tail_of(X0)) ) | (~spl9_12 | ~spl9_36)), 1.65/1.91 inference(resolution,[],[f220,f134])). 1.65/1.91 fof(f226,plain,( 1.65/1.91 ~precedes(sK4,sK3,sK0) | (~spl9_12 | ~spl9_36)), 1.65/1.91 inference(resolution,[],[f220,f135])). 1.65/1.91 fof(f230,plain,( 1.65/1.91 spl9_39 <=> ~precedes(sK4,sK3,sK0)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_39])])). 1.65/1.91 fof(f231,plain,( 1.65/1.91 ~precedes(sK4,sK3,sK0) | ~spl9_39), 1.65/1.91 inference(avatar_component_clause,[],[f230])). 1.65/1.91 fof(f232,plain,( 1.65/1.91 ~spl9_39 | ~spl9_12 | ~spl9_36), 1.65/1.91 inference(avatar_split_clause,[],[f226,f219,f123,f230])). 1.65/1.91 fof(f253,plain,( 1.65/1.91 tail_of(sK3) = head_of(sK4) | edge(sK7(tail_of(sK3),head_of(sK4))) | (~spl9_14 | ~spl9_18)), 1.65/1.91 inference(resolution,[],[f172,f142])). 1.65/1.91 fof(f262,plain,( 1.65/1.91 spl9_44 <=> sequential(sK4,sK3)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_44])])). 1.65/1.91 fof(f263,plain,( 1.65/1.91 sequential(sK4,sK3) | ~spl9_44), 1.65/1.91 inference(avatar_component_clause,[],[f262])). 1.65/1.91 fof(f265,plain,( 1.65/1.91 spl9_47 <=> tail_of(sK3) != head_of(sK4)), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_47])])). 1.65/1.91 fof(f266,plain,( 1.65/1.91 tail_of(sK3) != head_of(sK4) | ~spl9_47), 1.65/1.91 inference(avatar_component_clause,[],[f265])). 1.65/1.91 fof(f268,plain,( 1.65/1.91 spl9_48 <=> sK3 = sK4), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_48])])). 1.65/1.91 fof(f270,plain,( 1.65/1.91 spl9_44 | ~spl9_47 | spl9_48 | ~spl9_8 | ~spl9_10), 1.65/1.91 inference(avatar_split_clause,[],[f209,f119,f115,f268,f265,f262])). 1.65/1.91 fof(f271,plain,( 1.65/1.91 edge(sK7(tail_of(sK3),head_of(sK4))) | (~spl9_14 | ~spl9_18 | ~spl9_47)), 1.65/1.91 inference(subsumption_resolution,[],[f253,f266])). 1.65/1.91 fof(f274,plain,( 1.65/1.91 tail_of(sK3) = tail_of(sK4) | sP8(sK7(tail_of(sK4),tail_of(sK3)),tail_of(sK3),tail_of(sK4)) | tail_of(sK4) = head_of(sK7(tail_of(sK4),tail_of(sK3))) | (~spl9_14 | ~spl9_16)), 1.65/1.91 inference(resolution,[],[f153,f146])). 1.65/1.91 fof(f275,plain,( 1.65/1.91 tail_of(sK3) = head_of(sK4) | sP8(sK7(head_of(sK4),tail_of(sK3)),tail_of(sK3),head_of(sK4)) | head_of(sK4) = head_of(sK7(head_of(sK4),tail_of(sK3))) | (~spl9_14 | ~spl9_18)), 1.65/1.91 inference(resolution,[],[f153,f150])). 1.65/1.91 fof(f276,plain,( 1.65/1.91 sP8(sK7(tail_of(sK4),tail_of(sK3)),tail_of(sK3),tail_of(sK4)) | tail_of(sK4) = head_of(sK7(tail_of(sK4),tail_of(sK3))) | (~spl9_14 | ~spl9_16 | ~spl9_33)), 1.65/1.91 inference(subsumption_resolution,[],[f274,f198])). 1.65/1.91 fof(f293,plain,( 1.65/1.91 tail_of(sK3) = head_of(sK4) | sP8(sK7(tail_of(sK3),head_of(sK4)),head_of(sK4),tail_of(sK3)) | tail_of(sK3) = head_of(sK7(tail_of(sK3),head_of(sK4))) | (~spl9_14 | ~spl9_18)), 1.65/1.91 inference(resolution,[],[f171,f142])). 1.65/1.91 fof(f306,plain,( 1.65/1.91 tail_of(sK3) = head_of(sK4) | sP8(sK7(head_of(sK4),tail_of(sK3)),tail_of(sK3),head_of(sK4)) | tail_of(sK3) = tail_of(sK7(head_of(sK4),tail_of(sK3))) | (~spl9_14 | ~spl9_18)), 1.65/1.91 inference(resolution,[],[f152,f150])). 1.65/1.91 fof(f310,plain,( 1.65/1.91 spl9_52 <=> edge(sK7(tail_of(sK3),head_of(sK4)))), 1.65/1.91 introduced(avatar_definition,[new_symbols(naming,[spl9_52])])). 1.65/1.91 fof(f311,plain,( 1.65/1.91 edge(sK7(tail_of(sK3),head_of(sK4))) | ~spl9_52), 1.65/1.91 inference(avatar_component_clause,[],[f310])). 1.65/1.91 fof(f312,plain,( 1.65/1.91 spl9_52 | ~spl9_14 | ~spl9_18 | spl9_47), 1.65/1.91 inference(avatar_split_clause,[],[f271,f265,f149,f141,f310])). 1.65/1.91 fof(f331,plain,( 1.65/1.91 ~on_path(sK3,sK0) | ~on_path(sK4,sK0) | precedes(sK4,sK3,sK0) | (~spl9_20 | ~spl9_44)), 1.65/1.91 inference(resolution,[],[f263,f163])). 1.65/1.91 fof(f338,plain,( 1.65/1.91 ~on_path(sK4,sK0) | precedes(sK4,sK3,sK0) | (~spl9_2 | ~spl9_20 | ~spl9_44)), 1.65/1.91 inference(subsumption_resolution,[],[f331,f97])). 1.65/1.91 fof(f339,plain,( 1.65/1.91 precedes(sK4,sK3,sK0) | (~spl9_2 | ~spl9_6 | ~spl9_20 | ~spl9_44)), 1.65/1.92 inference(subsumption_resolution,[],[f338,f105])). 1.65/1.92 fof(f340,plain,( 1.65/1.92 $false | (~spl9_2 | ~spl9_6 | ~spl9_20 | ~spl9_39 | ~spl9_44)), 1.65/1.92 inference(subsumption_resolution,[],[f339,f231])). 1.65/1.92 fof(f341,plain,( 1.65/1.92 ~spl9_2 | ~spl9_6 | ~spl9_20 | spl9_39 | ~spl9_44), 1.65/1.92 inference(avatar_contradiction_clause,[],[f340])). 1.65/1.92 fof(f345,plain,( 1.65/1.92 sK3 != sK4 | sequential(sK4,sK3) | ~sequential(sK3,sK4)), 1.65/1.92 introduced(theory_axiom,[])). 1.65/1.92 fof(f346,plain,( 1.65/1.92 sP8(sK7(head_of(sK4),tail_of(sK3)),tail_of(sK3),head_of(sK4)) | tail_of(sK3) = tail_of(sK7(head_of(sK4),tail_of(sK3))) | (~spl9_14 | ~spl9_18 | ~spl9_47)), 1.65/1.92 inference(subsumption_resolution,[],[f306,f266])). 1.65/1.92 fof(f347,plain,( 1.65/1.92 sP8(sK7(tail_of(sK3),head_of(sK4)),head_of(sK4),tail_of(sK3)) | tail_of(sK3) = head_of(sK7(tail_of(sK3),head_of(sK4))) | (~spl9_14 | ~spl9_18 | ~spl9_47)), 1.65/1.92 inference(subsumption_resolution,[],[f293,f266])). 1.65/1.92 fof(f348,plain,( 1.65/1.92 sP8(sK7(head_of(sK4),tail_of(sK3)),tail_of(sK3),head_of(sK4)) | head_of(sK4) = head_of(sK7(head_of(sK4),tail_of(sK3))) | (~spl9_14 | ~spl9_18 | ~spl9_47)), 1.65/1.92 inference(subsumption_resolution,[],[f275,f266])). 1.65/1.92 fof(f355,plain,( 1.65/1.92 tail_of(sK3) = head_of(sK4) | sP8(sK7(tail_of(sK3),head_of(sK4)),head_of(sK4),tail_of(sK3)) | tail_of(sK7(tail_of(sK3),head_of(sK4))) = head_of(sK4) | (~spl9_14 | ~spl9_18)), 1.65/1.92 inference(resolution,[],[f170,f142])). 1.65/1.92 fof(f358,plain,( 1.65/1.92 sP8(sK7(tail_of(sK3),head_of(sK4)),head_of(sK4),tail_of(sK3)) | tail_of(sK7(tail_of(sK3),head_of(sK4))) = head_of(sK4) | (~spl9_14 | ~spl9_18 | ~spl9_47)), 1.65/1.92 inference(subsumption_resolution,[],[f355,f266])). 1.65/1.92 fof(f360,plain,( 1.65/1.92 sK4 = sK7(tail_of(sK3),head_of(sK4)) | tail_of(sK7(tail_of(sK3),head_of(sK4))) != head_of(sK4) | sequential(sK4,sK7(tail_of(sK3),head_of(sK4))) | (~spl9_10 | ~spl9_52)), 1.65/1.92 inference(resolution,[],[f311,f139])). 1.65/1.92 fof(f365,plain,( 1.65/1.92 ( ! [X0] : (~edge(X0) | sK7(tail_of(sK3),head_of(sK4)) = X0 | tail_of(X0) != head_of(sK7(tail_of(sK3),head_of(sK4))) | sequential(sK7(tail_of(sK3),head_of(sK4)),X0)) ) | ~spl9_52), 1.65/1.92 inference(resolution,[],[f311,f64])). 1.65/1.92 fof(f382,plain,( 1.65/1.92 spl9_60 <=> tail_of(sK4) = head_of(sK7(tail_of(sK4),tail_of(sK3)))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_60])])). 1.65/1.92 fof(f385,plain,( 1.65/1.92 spl9_62 <=> sP8(sK7(tail_of(sK4),tail_of(sK3)),tail_of(sK3),tail_of(sK4))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_62])])). 1.65/1.92 fof(f386,plain,( 1.65/1.92 sP8(sK7(tail_of(sK4),tail_of(sK3)),tail_of(sK3),tail_of(sK4)) | ~spl9_62), 1.65/1.92 inference(avatar_component_clause,[],[f385])). 1.65/1.92 fof(f387,plain,( 1.65/1.92 spl9_60 | spl9_62 | ~spl9_14 | ~spl9_16 | spl9_33), 1.65/1.92 inference(avatar_split_clause,[],[f276,f197,f145,f141,f385,f382])). 1.65/1.92 fof(f393,plain,( 1.65/1.92 tail_of(sK3) = head_of(sK7(tail_of(sK4),tail_of(sK3))) | ~spl9_62), 1.65/1.92 inference(resolution,[],[f386,f73])). 1.65/1.92 fof(f618,plain,( 1.65/1.92 spl9_100 <=> tail_of(sK3) = tail_of(sK7(head_of(sK4),tail_of(sK3)))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_100])])). 1.65/1.92 fof(f619,plain,( 1.65/1.92 tail_of(sK3) = tail_of(sK7(head_of(sK4),tail_of(sK3))) | ~spl9_100), 1.65/1.92 inference(avatar_component_clause,[],[f618])). 1.65/1.92 fof(f621,plain,( 1.65/1.92 spl9_102 <=> sP8(sK7(head_of(sK4),tail_of(sK3)),tail_of(sK3),head_of(sK4))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_102])])). 1.65/1.92 fof(f622,plain,( 1.65/1.92 sP8(sK7(head_of(sK4),tail_of(sK3)),tail_of(sK3),head_of(sK4)) | ~spl9_102), 1.65/1.92 inference(avatar_component_clause,[],[f621])). 1.65/1.92 fof(f623,plain,( 1.65/1.92 spl9_100 | spl9_102 | ~spl9_14 | ~spl9_18 | spl9_47), 1.65/1.92 inference(avatar_split_clause,[],[f346,f265,f149,f141,f621,f618])). 1.65/1.92 fof(f699,plain,( 1.65/1.92 spl9_104 <=> tail_of(sK3) = head_of(sK7(tail_of(sK3),head_of(sK4)))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_104])])). 1.65/1.92 fof(f700,plain,( 1.65/1.92 tail_of(sK3) = head_of(sK7(tail_of(sK3),head_of(sK4))) | ~spl9_104), 1.65/1.92 inference(avatar_component_clause,[],[f699])). 1.65/1.92 fof(f702,plain,( 1.65/1.92 spl9_106 <=> sP8(sK7(tail_of(sK3),head_of(sK4)),head_of(sK4),tail_of(sK3))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_106])])). 1.65/1.92 fof(f703,plain,( 1.65/1.92 sP8(sK7(tail_of(sK3),head_of(sK4)),head_of(sK4),tail_of(sK3)) | ~spl9_106), 1.65/1.92 inference(avatar_component_clause,[],[f702])). 1.65/1.92 fof(f704,plain,( 1.65/1.92 spl9_104 | spl9_106 | ~spl9_14 | ~spl9_18 | spl9_47), 1.65/1.92 inference(avatar_split_clause,[],[f347,f265,f149,f141,f702,f699])). 1.65/1.92 fof(f783,plain,( 1.65/1.92 spl9_108 <=> head_of(sK4) = head_of(sK7(head_of(sK4),tail_of(sK3)))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_108])])). 1.65/1.92 fof(f784,plain,( 1.65/1.92 head_of(sK4) = head_of(sK7(head_of(sK4),tail_of(sK3))) | ~spl9_108), 1.65/1.92 inference(avatar_component_clause,[],[f783])). 1.65/1.92 fof(f785,plain,( 1.65/1.92 spl9_108 | spl9_102 | ~spl9_14 | ~spl9_18 | spl9_47), 1.65/1.92 inference(avatar_split_clause,[],[f348,f265,f149,f141,f621,f783])). 1.65/1.92 fof(f799,plain,( 1.65/1.92 tail_of(sK3) = head_of(sK7(head_of(sK4),tail_of(sK3))) | ~spl9_102), 1.65/1.92 inference(resolution,[],[f622,f73])). 1.65/1.92 fof(f849,plain,( 1.65/1.92 spl9_110 <=> tail_of(sK7(tail_of(sK3),head_of(sK4))) = head_of(sK4)), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_110])])). 1.65/1.92 fof(f850,plain,( 1.65/1.92 tail_of(sK7(tail_of(sK3),head_of(sK4))) = head_of(sK4) | ~spl9_110), 1.65/1.92 inference(avatar_component_clause,[],[f849])). 1.65/1.92 fof(f851,plain,( 1.65/1.92 spl9_110 | spl9_106 | ~spl9_14 | ~spl9_18 | spl9_47), 1.65/1.92 inference(avatar_split_clause,[],[f358,f265,f149,f141,f702,f849])). 1.65/1.92 fof(f865,plain,( 1.65/1.92 head_of(sK4) = head_of(sK7(tail_of(sK3),head_of(sK4))) | ~spl9_106), 1.65/1.92 inference(resolution,[],[f703,f73])). 1.65/1.92 fof(f866,plain,( 1.65/1.92 tail_of(sK3) = tail_of(sK7(tail_of(sK3),head_of(sK4))) | ~spl9_106), 1.65/1.92 inference(resolution,[],[f703,f74])). 1.65/1.92 fof(f1048,plain,( 1.65/1.92 spl9_114 <=> tail_of(sK3) = head_of(sK7(tail_of(sK4),tail_of(sK3)))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_114])])). 1.65/1.92 fof(f1050,plain,( 1.65/1.92 spl9_114 | ~spl9_62), 1.65/1.92 inference(avatar_split_clause,[],[f393,f385,f1048])). 1.65/1.92 fof(f1086,plain,( 1.65/1.92 spl9_120 <=> tail_of(sK3) = head_of(sK7(head_of(sK4),tail_of(sK3)))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_120])])). 1.65/1.92 fof(f1088,plain,( 1.65/1.92 spl9_120 | ~spl9_102), 1.65/1.92 inference(avatar_split_clause,[],[f799,f621,f1086])). 1.65/1.92 fof(f1102,plain,( 1.65/1.92 head_of(sK4) != head_of(sK4) | tail_of(sK3) != tail_of(sK7(head_of(sK4),tail_of(sK3))) | (~spl9_12 | ~spl9_36 | ~spl9_108)), 1.65/1.92 inference(superposition,[],[f225,f784])). 1.65/1.92 fof(f1104,plain,( 1.65/1.92 tail_of(sK3) != tail_of(sK7(head_of(sK4),tail_of(sK3))) | (~spl9_12 | ~spl9_36 | ~spl9_108)), 1.65/1.92 inference(trivial_inequality_removal,[],[f1102])). 1.65/1.92 fof(f1105,plain,( 1.65/1.92 $false | (~spl9_12 | ~spl9_36 | ~spl9_100 | ~spl9_108)), 1.65/1.92 inference(subsumption_resolution,[],[f1104,f619])). 1.65/1.92 fof(f1106,plain,( 1.65/1.92 ~spl9_12 | ~spl9_36 | ~spl9_100 | ~spl9_108), 1.65/1.92 inference(avatar_contradiction_clause,[],[f1105])). 1.65/1.92 fof(f1113,plain,( 1.65/1.92 sK4 = sK7(tail_of(sK3),head_of(sK4)) | sequential(sK4,sK7(tail_of(sK3),head_of(sK4))) | (~spl9_10 | ~spl9_52 | ~spl9_110)), 1.65/1.92 inference(subsumption_resolution,[],[f360,f850])). 1.65/1.92 fof(f1117,plain,( 1.65/1.92 sP8(sK7(tail_of(sK3),head_of(sK4)),tail_of(sK3),tail_of(sK7(tail_of(sK3),head_of(sK4)))) | ~spl9_104), 1.65/1.92 inference(superposition,[],[f86,f700])). 1.65/1.92 fof(f1118,plain,( 1.65/1.92 sP8(sK7(tail_of(sK3),head_of(sK4)),tail_of(sK3),head_of(sK4)) | (~spl9_104 | ~spl9_110)), 1.65/1.92 inference(forward_demodulation,[],[f1117,f850])). 1.65/1.92 fof(f1187,plain,( 1.65/1.92 spl9_136 <=> sP8(sK7(tail_of(sK3),head_of(sK4)),tail_of(sK3),head_of(sK4))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_136])])). 1.65/1.92 fof(f1189,plain,( 1.65/1.92 spl9_136 | ~spl9_104 | ~spl9_110), 1.65/1.92 inference(avatar_split_clause,[],[f1118,f849,f699,f1187])). 1.65/1.92 fof(f1501,plain,( 1.65/1.92 spl9_178 <=> sequential(sK4,sK7(tail_of(sK3),head_of(sK4)))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_178])])). 1.65/1.92 fof(f1502,plain,( 1.65/1.92 sequential(sK4,sK7(tail_of(sK3),head_of(sK4))) | ~spl9_178), 1.65/1.92 inference(avatar_component_clause,[],[f1501])). 1.65/1.92 fof(f1504,plain,( 1.65/1.92 spl9_180 <=> sK4 = sK7(tail_of(sK3),head_of(sK4))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_180])])). 1.65/1.92 fof(f1506,plain,( 1.65/1.92 spl9_178 | spl9_180 | ~spl9_10 | ~spl9_52 | ~spl9_110), 1.65/1.92 inference(avatar_split_clause,[],[f1113,f849,f310,f119,f1504,f1501])). 1.65/1.92 fof(f1586,plain,( 1.65/1.92 spl9_208 <=> sK3 = sK7(tail_of(sK3),head_of(sK4))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_208])])). 1.65/1.92 fof(f1734,plain,( 1.65/1.92 sK3 = sK7(tail_of(sK3),head_of(sK4)) | tail_of(sK3) != head_of(sK7(tail_of(sK3),head_of(sK4))) | sequential(sK7(tail_of(sK3),head_of(sK4)),sK3) | (~spl9_8 | ~spl9_52)), 1.65/1.92 inference(resolution,[],[f365,f116])). 1.65/1.92 fof(f1742,plain,( 1.65/1.92 sK3 = sK7(tail_of(sK3),head_of(sK4)) | sequential(sK7(tail_of(sK3),head_of(sK4)),sK3) | (~spl9_8 | ~spl9_52 | ~spl9_104)), 1.65/1.92 inference(subsumption_resolution,[],[f1734,f700])). 1.65/1.92 fof(f1773,plain,( 1.65/1.92 spl9_222 <=> sequential(sK7(tail_of(sK3),head_of(sK4)),sK3)), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_222])])). 1.65/1.92 fof(f1774,plain,( 1.65/1.92 sequential(sK7(tail_of(sK3),head_of(sK4)),sK3) | ~spl9_222), 1.65/1.92 inference(avatar_component_clause,[],[f1773])). 1.65/1.92 fof(f1775,plain,( 1.65/1.92 spl9_222 | spl9_208 | ~spl9_8 | ~spl9_52 | ~spl9_104), 1.65/1.92 inference(avatar_split_clause,[],[f1742,f699,f310,f115,f1586,f1773])). 1.65/1.92 fof(f1783,plain,( 1.65/1.92 ( ! [X1] : (~sequential(X1,sK7(tail_of(sK3),head_of(sK4))) | ~sequential(sK3,X1) | ~edge(sK7(tail_of(sK3),head_of(sK4))) | ~edge(X1) | ~edge(sK3) | triangle(sK3,X1,sK7(tail_of(sK3),head_of(sK4)))) ) | ~spl9_222), 1.65/1.92 inference(resolution,[],[f1774,f52])). 1.65/1.92 fof(f1787,plain,( 1.65/1.92 ( ! [X1] : (~sequential(X1,sK7(tail_of(sK3),head_of(sK4))) | ~sequential(sK3,X1) | ~edge(X1) | ~edge(sK3) | triangle(sK3,X1,sK7(tail_of(sK3),head_of(sK4)))) ) | (~spl9_52 | ~spl9_222)), 1.65/1.92 inference(subsumption_resolution,[],[f1783,f311])). 1.65/1.92 fof(f1788,plain,( 1.65/1.92 ( ! [X1] : (~sequential(X1,sK7(tail_of(sK3),head_of(sK4))) | ~sequential(sK3,X1) | ~edge(X1) | triangle(sK3,X1,sK7(tail_of(sK3),head_of(sK4)))) ) | (~spl9_8 | ~spl9_52 | ~spl9_222)), 1.65/1.92 inference(subsumption_resolution,[],[f1787,f116])). 1.65/1.92 fof(f1789,plain,( 1.65/1.92 ( ! [X1] : (~sequential(X1,sK7(tail_of(sK3),head_of(sK4))) | ~sequential(sK3,X1) | triangle(sK3,X1,sK7(tail_of(sK3),head_of(sK4)))) ) | (~spl9_8 | ~spl9_52 | ~spl9_222)), 1.65/1.92 inference(subsumption_resolution,[],[f1788,f63])). 1.65/1.92 fof(f2065,plain,( 1.65/1.92 ~sequential(sK3,sK4) | triangle(sK3,sK4,sK7(tail_of(sK3),head_of(sK4))) | (~spl9_8 | ~spl9_52 | ~spl9_178 | ~spl9_222)), 1.65/1.92 inference(resolution,[],[f1789,f1502])). 1.65/1.92 fof(f2066,plain,( 1.65/1.92 triangle(sK3,sK4,sK7(tail_of(sK3),head_of(sK4))) | (~spl9_4 | ~spl9_8 | ~spl9_52 | ~spl9_178 | ~spl9_222)), 1.65/1.92 inference(subsumption_resolution,[],[f2065,f101])). 1.65/1.92 fof(f2067,plain,( 1.65/1.92 $false | (~spl9_4 | ~spl9_8 | ~spl9_52 | ~spl9_178 | ~spl9_222)), 1.65/1.92 inference(subsumption_resolution,[],[f2066,f49])). 1.65/1.92 fof(f2068,plain,( 1.65/1.92 ~spl9_4 | ~spl9_8 | ~spl9_52 | ~spl9_178 | ~spl9_222), 1.65/1.92 inference(avatar_contradiction_clause,[],[f2067])). 1.65/1.92 fof(f2156,plain,( 1.65/1.92 spl9_154 <=> tail_of(sK3) = tail_of(sK7(tail_of(sK3),head_of(sK4)))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_154])])). 1.65/1.92 fof(f2157,plain,( 1.65/1.92 tail_of(sK3) = tail_of(sK7(tail_of(sK3),head_of(sK4))) | ~spl9_154), 1.65/1.92 inference(avatar_component_clause,[],[f2156])). 1.65/1.92 fof(f2242,plain,( 1.65/1.92 spl9_260 <=> head_of(sK4) = head_of(sK7(tail_of(sK3),head_of(sK4)))), 1.65/1.92 introduced(avatar_definition,[new_symbols(naming,[spl9_260])])). 1.65/1.92 fof(f2243,plain,( 1.65/1.92 head_of(sK4) = head_of(sK7(tail_of(sK3),head_of(sK4))) | ~spl9_260), 1.65/1.92 inference(avatar_component_clause,[],[f2242])). 1.65/1.92 fof(f2244,plain,( 1.65/1.92 spl9_260 | ~spl9_106), 1.65/1.92 inference(avatar_split_clause,[],[f865,f702,f2242])). 1.65/1.92 fof(f2252,plain,( 1.65/1.92 spl9_154 | ~spl9_106), 1.65/1.92 inference(avatar_split_clause,[],[f866,f702,f2156])). 1.65/1.92 fof(f2258,plain,( 1.65/1.92 head_of(sK4) != head_of(sK4) | tail_of(sK3) != tail_of(sK7(tail_of(sK3),head_of(sK4))) | (~spl9_12 | ~spl9_36 | ~spl9_260)), 1.65/1.92 inference(superposition,[],[f225,f2243])). 1.65/1.92 fof(f2260,plain,( 1.65/1.92 tail_of(sK3) != tail_of(sK7(tail_of(sK3),head_of(sK4))) | (~spl9_12 | ~spl9_36 | ~spl9_260)), 1.65/1.92 inference(trivial_inequality_removal,[],[f2258])). 1.65/1.92 fof(f2261,plain,( 1.65/1.92 $false | (~spl9_12 | ~spl9_36 | ~spl9_154 | ~spl9_260)), 1.65/1.92 inference(subsumption_resolution,[],[f2260,f2157])). 1.65/1.92 fof(f2262,plain,( 1.65/1.92 ~spl9_12 | ~spl9_36 | ~spl9_154 | ~spl9_260), 1.65/1.92 inference(avatar_contradiction_clause,[],[f2261])). 1.65/1.92 fof(f2270,plain,( 1.65/1.92 sK3 != sK7(tail_of(sK3),head_of(sK4)) | tail_of(sK7(tail_of(sK3),head_of(sK4))) != head_of(sK4) | sP8(sK7(tail_of(sK3),head_of(sK4)),head_of(sK4),tail_of(sK3)) | ~sP8(sK7(tail_of(sK3),head_of(sK4)),tail_of(sK3),head_of(sK4))), 1.65/1.92 introduced(theory_axiom,[])). 1.65/1.92 fof(f2278,plain,( 1.65/1.92 sK4 != sK7(tail_of(sK3),head_of(sK4)) | tail_of(sK3) != head_of(sK7(head_of(sK4),tail_of(sK3))) | tail_of(sK7(tail_of(sK3),head_of(sK4))) != head_of(sK4) | tail_of(sK4) != head_of(sK7(tail_of(sK4),tail_of(sK3))) | sP8(sK7(tail_of(sK3),head_of(sK4)),head_of(sK4),tail_of(sK3)) | ~sP8(sK7(tail_of(sK3),head_of(sK4)),tail_of(sK3),head_of(sK4))), 1.65/1.92 introduced(theory_axiom,[])). 1.65/1.92 fof(f2281,plain,( 1.65/1.92 tail_of(sK3) != head_of(sK7(tail_of(sK4),tail_of(sK3))) | tail_of(sK7(tail_of(sK3),head_of(sK4))) != head_of(sK4) | sK4 != sK7(tail_of(sK3),head_of(sK4)) | tail_of(sK3) != head_of(sK7(tail_of(sK3),head_of(sK4))) | sP8(sK7(tail_of(sK3),head_of(sK4)),head_of(sK4),tail_of(sK3)) | ~sP8(sK7(tail_of(sK3),head_of(sK4)),tail_of(sK3),head_of(sK4))), 1.65/1.92 introduced(theory_axiom,[])). 1.65/1.92 fof(f2282,plain,( 1.65/1.92 $false), 1.65/1.92 inference(avatar_sat_refutation,[],[f98,f102,f106,f117,f121,f125,f143,f147,f151,f158,f176,f181,f199,f221,f232,f270,f312,f341,f345,f387,f623,f704,f785,f851,f1050,f1088,f1106,f1189,f1506,f1775,f2068,f2244,f2252,f2262,f2270,f2278,f2281])). 1.65/1.92 % SZS output end Proof for theBenchmark 1.65/1.92 % ------------------------------ 1.65/1.92 % Version: Vampire 4.2.2 (commit 552c234 on 2018-07-02 14:53:33 +0100) 1.65/1.92 % Termination reason: Refutation 1.65/1.92 1.65/1.92 % Memory used [KB]: 6396 1.65/1.92 % Time elapsed: 0.045 s 1.65/1.92 % ------------------------------ 1.65/1.92 % ------------------------------ 1.65/1.92 % Success in time 1.681 s 1.65/1.92 EOF