0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.18/0.50 % Computer : n029.cluster.edu 0.18/0.50 % Model : x86_64 x86_64 0.18/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.50 % Memory : 8046.5625MB 0.18/0.50 % OS : Linux 6.8.0-71-generic 0.18/0.50 % CPULimit : 1440 0.18/0.50 % WCLimit : 180 0.18/0.50 % DateTime : Mon Jul 27 09:13:17 UTC 2026 0.18/0.51 % CPUTime : 0.18/0.51 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.23/0.57 Running first-order theorem proving 0.23/0.57 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p 5.96/2.37 % (2654035)Detected formulas, will run a generic FOF schedule. 5.96/2.37 % (2654042)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=917884392:i=141695:sd=1:nm=32:gsp=on:ss=included_1799 on theBenchmark for (1799ds/141695Mi) 5.96/2.37 % (2654043)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2757454008:i=109:sd=1:ins=1:gsp=on:ss=axioms_1799 on theBenchmark for (1799ds/109Mi) 5.96/2.37 % (2654041)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=549267348:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_1799 on theBenchmark for (1799ds/134677Mi) 5.96/2.37 % (2654040)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1215548132:i=141193_1799 on theBenchmark for (1799ds/141193Mi) 5.96/2.37 % (2654043)First to succeed. 5.96/2.37 % (2654043)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2654035" 5.96/2.37 % (2654045)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3507367035:s2a=on:i=139:gtg=position_1799 on theBenchmark for (1799ds/139Mi) 5.96/2.37 % (2654044)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=979500009:i=119:av=off:ss=axioms_1799 on theBenchmark for (1799ds/119Mi) 5.96/2.37 % (2654044)Also succeeded, but the first one will report. 5.96/2.37 % (2654046)dis-21_1_sil=8000:lcm=predicate:random_seed=765401766:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_1799 on theBenchmark for (1799ds/129Mi) 5.96/2.37 % (2654045)Also succeeded, but the first one will report. 5.96/2.37 % (2654046)Also succeeded, but the first one will report. 5.96/2.37 % (2654043)Refutation found. Thanks to Tanya! 5.96/2.37 % SZS status Theorem for theBenchmark 5.96/2.37 % SZS output start Proof for theBenchmark 5.96/2.37 fof(f1,axiom,( 5.96/2.37 ! [X0,X1,X2,X3,X4] : ((shortest_path(X0,X1,X4) & precedes(X2,X3,X4)) => (~? [X5] : (head_of(X5) = head_of(X3) & tail_of(X2) = tail_of(X5)) & ~precedes(X3,X2,X4)))), 5.96/2.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_properties)). 5.96/2.37 fof(f16,conjecture,( 5.96/2.37 ! [X0,X1,X2,X3,X4] : ((precedes(X2,X3,X4) & shortest_path(X0,X1,X4)) => ~? [X5] : (head_of(X3) = head_of(X5) & tail_of(X5) = tail_of(X2) & edge(X5)))), 5.96/2.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_short_cut_edge)). 5.96/2.37 fof(f17,negated_conjecture,( 5.96/2.37 ~! [X0,X1,X2,X3,X4] : ((precedes(X2,X3,X4) & shortest_path(X0,X1,X4)) => ~? [X5] : (head_of(X3) = head_of(X5) & tail_of(X5) = tail_of(X2) & edge(X5)))), 5.96/2.37 inference(negated_conjecture,[status(cth)],[f16])). 5.96/2.37 fof(f22,plain,( 5.96/2.37 ? [X0,X1,X2,X3,X4] : (? [X5] : (head_of(X3) = head_of(X5) & tail_of(X5) = tail_of(X2) & edge(X5)) & (precedes(X2,X3,X4) & shortest_path(X0,X1,X4)))), 5.96/2.37 inference(ennf_transformation,[],[f17])). 5.96/2.37 fof(f23,plain,( 5.96/2.37 ? [X0,X1,X2,X3,X4] : (? [X5] : (head_of(X3) = head_of(X5) & tail_of(X5) = tail_of(X2) & edge(X5)) & precedes(X2,X3,X4) & shortest_path(X0,X1,X4))), 5.96/2.37 inference(flattening,[],[f22])). 5.96/2.37 fof(f24,plain,( 5.96/2.37 ! [X0,X1,X2,X3,X4] : ((! [X5] : (head_of(X5) != head_of(X3) | tail_of(X2) != tail_of(X5)) & ~precedes(X3,X2,X4)) | (~shortest_path(X0,X1,X4) | ~precedes(X2,X3,X4)))), 5.96/2.37 inference(ennf_transformation,[],[f1])). 5.96/2.37 fof(f25,plain,( 5.96/2.37 ! [X0,X1,X2,X3,X4] : ((! [X5] : (head_of(X5) != head_of(X3) | tail_of(X2) != tail_of(X5)) & ~precedes(X3,X2,X4)) | ~shortest_path(X0,X1,X4) | ~precedes(X2,X3,X4))), 5.96/2.37 inference(flattening,[],[f24])). 5.96/2.37 fof(f27,plain,( 5.96/2.37 (head_of(sK5) = head_of(sK3) & tail_of(sK2) = tail_of(sK5) & edge(sK5)) & precedes(sK2,sK3,sK4) & shortest_path(sK0,sK1,sK4)), 5.96/2.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f23])). 5.96/2.37 fof(f28,plain,( 5.96/2.37 shortest_path(sK0,sK1,sK4)), 5.96/2.37 inference(cnf_transformation,[],[f27])). 5.96/2.37 fof(f29,plain,( 5.96/2.37 precedes(sK2,sK3,sK4)), 5.96/2.37 inference(cnf_transformation,[],[f27])). 5.96/2.37 fof(f31,plain,( 5.96/2.37 tail_of(sK2) = tail_of(sK5)), 5.96/2.37 inference(cnf_transformation,[],[f27])). 5.96/2.37 fof(f32,plain,( 5.96/2.37 head_of(sK5) = head_of(sK3)), 5.96/2.37 inference(cnf_transformation,[],[f27])). 5.96/2.37 fof(f34,plain,( 5.96/2.37 ( ! [X2,X3,X0,X1,X4,X5] : (head_of(X5) != head_of(X3) | tail_of(X2) != tail_of(X5) | ~shortest_path(X0,X1,X4) | ~precedes(X2,X3,X4)) )), 5.96/2.37 inference(cnf_transformation,[],[f25])). 5.96/2.37 fof(f36,plain,( 5.96/2.37 ( ! [X0,X1,X4] : (~shortest_path(X0,X1,X4) | sP6(X4,X1)) )), 5.96/2.37 inference(cnf_transformation,[],[f36_D])). 5.96/2.37 fof(f36_D,definition,( 5.96/2.37 ( ! [X1,X4] : (( ! [X0] : ~shortest_path(X0,X1,X4) ) <=> ~sP6(X4,X1)) )), 5.96/2.37 introduced(definition,[new_symbols(definition,[sP6])],[general_splitting_component_introduction])). 5.96/2.37 fof(f37,plain,( 5.96/2.37 ( ! [X2,X3,X1,X4,X5] : (head_of(X5) != head_of(X3) | tail_of(X2) != tail_of(X5) | ~precedes(X2,X3,X4) | ~sP6(X4,X1)) )), 5.96/2.37 inference(general_splitting,[],[f34,f36_D])). 5.96/2.37 fof(f38,plain,( 5.96/2.37 ( ! [X1,X4] : (~sP6(X4,X1) | sP7(X4)) )), 5.96/2.37 inference(cnf_transformation,[],[f38_D])). 5.96/2.37 fof(f38_D,definition,( 5.96/2.37 ( ! [X4] : (( ! [X1] : ~sP6(X4,X1) ) <=> ~sP7(X4)) )), 5.96/2.37 introduced(definition,[new_symbols(definition,[sP7])],[general_splitting_component_introduction])). 5.96/2.37 fof(f39,plain,( 5.96/2.37 ( ! [X2,X3,X4,X5] : (head_of(X5) != head_of(X3) | tail_of(X2) != tail_of(X5) | ~precedes(X2,X3,X4) | ~sP7(X4)) )), 5.96/2.37 inference(general_splitting,[],[f37,f38_D])). 5.96/2.37 fof(f40,plain,( 5.96/2.37 ( ! [X2,X3,X4] : (~precedes(X2,X3,X4) | ~sP7(X4) | sP8(X3,X2)) )), 5.96/2.37 inference(cnf_transformation,[],[f40_D])). 5.96/2.37 fof(f40_D,definition,( 5.96/2.37 ( ! [X2,X3] : (( ! [X4] : (~precedes(X2,X3,X4) | ~sP7(X4)) ) <=> ~sP8(X3,X2)) )), 5.96/2.37 introduced(definition,[new_symbols(definition,[sP8])],[general_splitting_component_introduction])). 5.96/2.37 fof(f41,plain,( 5.96/2.37 ( ! [X2,X3,X5] : (tail_of(X2) != tail_of(X5) | head_of(X5) != head_of(X3) | ~sP8(X3,X2)) )), 5.96/2.37 inference(general_splitting,[],[f39,f40_D])). 5.96/2.37 fof(f46,plain,( 5.96/2.37 sP6(sK4,sK1)), 5.96/2.37 inference(resolution,[],[f28,f36])). 5.96/2.37 fof(f48,plain,( 5.96/2.37 ~sP7(sK4) | sP8(sK3,sK2)), 5.96/2.37 inference(resolution,[],[f29,f40])). 5.96/2.37 fof(f60,definition,( 5.96/2.37 spl11_3 <=> sP8(sK3,sK2)), 5.96/2.37 introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition])). 5.96/2.37 fof(f62,plain,( 5.96/2.37 sP8(sK3,sK2) | ~spl11_3), 5.96/2.37 inference(avatar_component_clause,[],[f60])). 5.96/2.37 fof(f64,definition,( 5.96/2.37 spl11_4 <=> sP7(sK4)), 5.96/2.37 introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition])). 5.96/2.37 fof(f66,plain,( 5.96/2.37 ~sP7(sK4) | spl11_4), 5.96/2.37 inference(avatar_component_clause,[],[f64])). 5.96/2.37 fof(f67,plain,( 5.96/2.37 spl11_3 | ~spl11_4), 5.96/2.37 inference(avatar_split_clause,[],[f48,f64,f60])). 5.96/2.37 fof(f70,plain,( 5.96/2.37 ( ! [X0,X1] : (tail_of(X0) != tail_of(sK5) | head_of(X0) != head_of(X1) | ~sP8(X1,sK2)) )), 5.96/2.37 inference(superposition,[],[f41,f31])). 5.96/2.37 fof(f80,plain,( 5.96/2.37 sP7(sK4)), 5.96/2.37 inference(resolution,[],[f46,f38])). 5.96/2.37 fof(f81,plain,( 5.96/2.37 $false | spl11_4), 5.96/2.37 inference(forward_subsumption_resolution,[],[f80,f66])). 5.96/2.37 fof(f82,plain,( 5.96/2.37 spl11_4), 5.96/2.37 inference(avatar_contradiction_clause,[],[f81])). 5.96/2.37 fof(f87,plain,( 5.96/2.37 ( ! [X0] : (head_of(X0) != head_of(sK5) | ~sP8(X0,sK2)) )), 5.96/2.37 inference(equality_resolution,[],[f70])). 5.96/2.37 fof(f104,plain,( 5.96/2.37 head_of(sK5) != head_of(sK5) | ~sP8(sK3,sK2)), 5.96/2.37 inference(superposition,[],[f87,f32])). 5.96/2.37 fof(f106,plain,( 5.96/2.37 ~sP8(sK3,sK2)), 5.96/2.37 inference(trivial_inequality_removal,[],[f104])). 5.96/2.37 fof(f107,plain,( 5.96/2.37 $false | ~spl11_3), 5.96/2.37 inference(forward_subsumption_resolution,[],[f106,f62])). 5.96/2.37 fof(f108,plain,( 5.96/2.37 ~spl11_3), 5.96/2.37 inference(avatar_contradiction_clause,[],[f107])). 5.96/2.37 cnf(s2, plain, spl11_3 | ~spl11_4, inference(sat_conversion,[],[f67])). 5.96/2.37 cnf(s4, plain, spl11_4, inference(sat_conversion,[],[f82])). 5.96/2.37 cnf(s7, plain, ~spl11_3, inference(sat_conversion,[],[f108])). 5.96/2.37 cnf(s8, plain, $false, inference(rat,[],[s2,s4,s7])). 5.96/2.37 fof(f109,plain,( 5.96/2.37 $false), 5.96/2.37 inference(avatar_sat_refutation,[],[s8])). 5.96/2.37 % SZS output end Proof for theBenchmark 5.96/2.37 % (2654043)------------------------------ 5.96/2.37 % (2654043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 5.96/2.37 % (2654043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.96/2.37 % (2654043)CaDiCaL version: 2.1.3 5.96/2.37 % (2654043)Termination reason: Refutation 5.96/2.37 % (2654043)Time elapsed: 0.006 s 5.96/2.37 % (2654043)Peak memory usage: 89 MB 5.96/2.37 % (2654043)Instructions burned: 3 (million) 5.96/2.37 % (2654043)------------------------------ 5.96/2.37 % (2654043)------------------------------ 5.96/2.37 % (2654035)Success in time 0.703 s 5.96/2.37 % Vampire exiting 5.96/2.38 EOF