0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.10 % Command : run_vampire %s %d 0.09/0.31 Computer : n010.cluster.edu 0.09/0.31 Model : x86_64 x86_64 0.09/0.31 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.31 RAMPerCPU : 8042.1875MB 0.09/0.31 OS : Linux 3.10.0-693.el7.x86_64 0.09/0.31 % CPULimit : 960 0.09/0.31 % WCLimit : 120 0.09/0.31 % DateTime : Tue Aug 9 04:50:50 EDT 2022 0.09/0.31 % CPUTime : 0.16/0.48 % (28063)dis-3_4_add=off:afp=40000:afq=1.1:amm=off:anc=none:bs=unit_only:cond=fast:fsr=off:gs=on:inw=on:lma=on:nm=64:nwc=1.5:nicw=on:sas=z3:sp=reverse_arity:tha=off:thf=on:uhcvi=on_13 on theBenchmark 0.16/0.48 % (28076)WARNING: option uwaf not known. 0.16/0.49 % (28086)lrs+10_8:1_aac=none:add=off:afr=on:afp=40000:afq=1.1:amm=off:anc=none:bd=off:cond=on:fsr=off:fde=none:gs=on:gsem=off:nm=0:nwc=1.2:sas=z3:stl=30:sos=all:sp=reverse_arity:tha=off:updr=off_68 on theBenchmark 0.16/0.49 % (28069)dis+10_3:2_afr=on:afp=1000:afq=1.2:bd=off:irw=on:lcm=predicate:lwlo=on:nm=0:newcnf=on:nwc=2:sos=on:tha=off:thf=on:urr=ec_only_11 on theBenchmark 0.16/0.49 % (28076)lrs-2_24_awrs=converge:awrsf=64:av=off:bd=off:bs=on:bsr=on:br=off:cond=on:fde=none:gsp=input_only:inw=on:lwlo=on:nm=6:nwc=4:stl=30:s2a=on:sos=all:sp=weighted_frequency:thf=on:uwa=one_side_interpreted:urr=on:updr=off:uhcvi=on:uwaf=on_21 on theBenchmark 0.16/0.50 % (28079)dis+1_3:1_acc=on:afp=100000:afq=1.1:amm=off:anc=none:bd=off:cond=on:fsr=off:gs=on:inw=on:lma=on:nm=32:nwc=1:urr=on_2 on theBenchmark 0.16/0.50 % (28072)lrs+1_2:3_afr=on:afp=1000:afq=1.1:amm=sco:anc=none:fsr=off:fde=none:gs=on:gsaa=full_model:gsem=on:lma=on:nm=64:nwc=1.3:sas=z3:stl=30:sac=on:tha=off:uwa=one_side_interpreted:updr=off_9 on theBenchmark 0.16/0.51 % (28060)dis+1011_5_aac=none:add=large:afp=40000:afq=1.2:amm=off:anc=none:bd=off:fsr=off:gsp=input_only:inw=on:irw=on:lma=on:nm=64:nwc=1:sas=z3:sos=on:sp=occurrence:tha=off:updr=off_26 on theBenchmark 0.16/0.51 % (28062)lrs-11_1_av=off:cond=on:gs=on:lcm=reverse:lma=on:lwlo=on:nm=16:nwc=5:stl=30:sp=reverse_arity:tha=off:thi=strong:uwa=interpreted_only_58 on theBenchmark 0.16/0.52 % (28064)lrs+1_5:4_aac=none:add=off:afr=on:afp=4000:afq=1.2:amm=sco:anc=none:gsp=input_only:gs=on:irw=on:nm=64:newcnf=on:nwc=1.3:nicw=on:sas=z3:stl=30:sp=occurrence:tha=off_3 on theBenchmark 0.16/0.53 % (28071)dis-10_4:1_aac=none:add=off:afp=1000:afq=1.4:amm=off:anc=none:cond=fast:ep=RSTC:gs=on:gsaa=from_current:gsem=on:inw=on:lma=on:nm=64:nwc=4:sas=z3:tha=off:thi=strong:uwa=interpreted_only:updr=off:uhcvi=on_6 on theBenchmark 0.16/0.53 % (28070)dis+1010_2:3_add=off:afr=on:afp=10000:afq=1.1:anc=none:fsr=off:gs=on:gsem=off:nwc=1:sas=z3:sos=all:sac=on:sp=reverse_arity:tha=off_5 on theBenchmark 0.16/0.53 % (28059)ott+1_3:1_av=off:bd=off:fsr=off:fde=none:gs=on:inw=on:nm=2:nwc=1.5:sp=frequency:uwa=one_side_interpreted_22 on theBenchmark 0.16/0.54 % (28066)dis+1_3_add=large:afp=4000:afq=1.0:anc=none:gs=on:gsem=off:inw=on:lcm=reverse:lwlo=on:nm=64:nwc=1:sas=z3:sos=all:sac=on:thi=all:uwa=all:updr=off:uhcvi=on_12 on theBenchmark 0.16/0.54 % (28087)dis+1002_4_add=off:afp=10000:afq=2.0:amm=off:anc=none:fsr=off:gsp=input_only:gs=on:gsem=on:irw=on:lwlo=on:nm=2:newcnf=on:nwc=1:sos=on:sac=on:sp=occurrence:tha=off:updr=off_2 on theBenchmark 0.16/0.54 % (28068)dis+11_6_add=large:afr=on:afp=100000:afq=1.2:amm=off:anc=none:cond=fast:gs=on:gsaa=from_current:gsem=off:irw=on:lma=on:lwlo=on:nm=64:nwc=1:sas=z3:sos=on:sp=occurrence:tha=off:thi=strong:updr=off_2 on theBenchmark 0.16/0.55 % (28061)lrs+1_3_awrs=decay:awrsf=4:afp=10000:afq=1.0:amm=off:anc=none:bd=off:cond=on:fsr=off:fde=unused:gs=on:lwlo=on:nm=16:nwc=1:sas=z3:stl=30:ss=axioms:s2a=on:st=1.2:sos=theory:sp=frequency_29 on theBenchmark 0.16/0.55 % (28077)ott+10_8_add=large:afp=100000:afq=1.4:amm=sco:cond=fast:fsr=off:fde=none:lcm=predicate:lma=on:nm=32:nwc=1:sos=on:sac=on:tha=off:updr=off_29 on theBenchmark 0.16/0.55 % (28082)dis+11_3_add=large:afr=on:afp=4000:afq=1.2:amm=off:anc=none:gs=on:gsem=on:lwlo=on:nm=64:nwc=1:sas=z3:sac=on:sp=reverse_arity:tha=off:thf=on:updr=off_92 on theBenchmark 0.16/0.55 % (28074)lrs+1011_1_add=off:afp=100000:afq=1.0:anc=none:cond=on:gs=on:gsaa=from_current:gsem=on:inw=on:lma=on:nm=64:newcnf=on:nwc=1:sas=z3:stl=30:sos=on:sp=occurrence:tha=off:uwa=ground_3 on theBenchmark 0.16/0.56 % (28065)dis+1002_8:1_awrs=converge:awrsf=256:anc=all_dependent:br=off:fsr=off:fde=none:gs=on:gsaa=from_current:gsem=on:irw=on:nm=64:nwc=1:sas=z3:s2a=on:sp=frequency:thf=on:uwa=interpreted_only:urr=on_7 on theBenchmark 0.16/0.56 % (28078)dis-2_2:3_add=large:afp=40000:afq=1.4:amm=off:anc=none:gsp=input_only:gs=on:gsem=on:inw=on:lcm=reverse:lma=on:nm=2:nwc=1:nicw=on:sas=z3:sos=all:sp=reverse_arity:tha=off:urr=on_5 on theBenchmark 0.16/0.56 % (28073)lrs+10_2_add=off:afr=on:afp=4000:afq=2.0:amm=off:anc=none:cond=fast:fsr=off:fde=unused:gs=on:gsaa=full_model:gsem=on:inw=on:nm=64:nwc=1:sas=z3:stl=30:sos=all:sp=occurrence:tha=off:thf=on:urr=on:updr=off:uhcvi=on_6 on theBenchmark 0.16/0.57 % (28075)dis+1010_4_add=off:afp=100000:afq=1.0:anc=none:fsr=off:gs=on:gsem=off:inw=on:irw=on:lma=on:nm=64:nwc=1:sas=z3:sos=on:sac=on:tha=off:thf=on_179 on theBenchmark 0.16/0.57 % (28058)ott+10_3:2_aac=none:add=large:afp=10000:afq=2.0:amm=off:fsr=off:fde=none:gs=on:gsaa=from_current:gsem=off:lcm=reverse:lma=on:nm=0:nwc=4:sas=z3:updr=off_22 on theBenchmark 0.16/0.57 % (28083)lrs+1003_2_awrs=converge:awrsf=512:add=large:afp=10000:afq=1.1:amm=sco:anc=none:cond=fast:fde=unused:lma=on:nm=64:nwc=1.2:stl=30:s2a=on:sac=on:sp=reverse_arity:tha=some:thi=new:urr=on:updr=off_80 on theBenchmark 0.16/0.57 % (28085)dis+10_6_afr=on:afp=1000:afq=1.2:anc=none:bsr=on:fsr=off:gs=on:lcm=reverse:nm=64:newcnf=on:nwc=1.7:sas=z3:tha=off_4 on theBenchmark 1.84/0.58 % (28080)dis+1011_2:3_add=off:afr=on:afp=4000:afq=1.4:anc=none:bs=unit_only:fsr=off:gs=on:gsem=on:lwlo=on:nm=16:nwc=1.3:nicw=on:sas=z3:sac=on:tha=off_260 on theBenchmark 1.84/0.58 % (28084)ott+10_4_awrs=converge:awrsf=128:afp=100000:afq=1.4:amm=sco:anc=none:fsr=off:fde=unused:gs=on:gsaa=from_current:gsem=on:irw=on:nm=64:nwc=1:s2a=on:sac=on:sp=frequency:tha=off_3 on theBenchmark 1.84/0.58 % (28067)lrs+3_128_awrs=converge:awrsf=2:av=off:bs=on:cond=fast:fsr=off:fde=unused:gsp=input_only:irw=on:lma=on:nm=64:nwc=1.5:stl=30:sp=frequency:tha=some:updr=off_148 on theBenchmark 1.84/0.59 % (28081)dis+1010_24_aac=none:afr=on:anc=none:cond=on:fsr=off:gs=on:gsem=on:nm=6:nwc=1:sas=z3:sos=on:sp=reverse_arity:tha=off_9 on theBenchmark 1.99/0.63 % (28076)Refutation found. Thanks to Tanya! 1.99/0.63 % SZS status Theorem for theBenchmark 1.99/0.64 % SZS output start Proof for theBenchmark 1.99/0.64 tff(type_def_5, type, uni: $tType). 1.99/0.64 tff(type_def_6, type, ty: $tType). 1.99/0.64 tff(type_def_7, type, bool1: $tType). 1.99/0.64 tff(type_def_8, type, tuple02: $tType). 1.99/0.64 tff(type_def_9, type, vertex1: $tType). 1.99/0.64 tff(type_def_10, type, set_vertex: $tType). 1.99/0.64 tff(func_def_0, type, witness1: ty > uni). 1.99/0.64 tff(func_def_1, type, int: ty). 1.99/0.64 tff(func_def_2, type, real: ty). 1.99/0.64 tff(func_def_3, type, bool: ty). 1.99/0.64 tff(func_def_4, type, true1: bool1). 1.99/0.64 tff(func_def_5, type, false1: bool1). 1.99/0.64 tff(func_def_6, type, match_bool1: (ty * bool1 * uni * uni) > uni). 1.99/0.64 tff(func_def_7, type, tuple0: ty). 1.99/0.64 tff(func_def_8, type, tuple03: tuple02). 1.99/0.64 tff(func_def_9, type, qtmark: ty). 1.99/0.64 tff(func_def_10, type, set: ty > ty). 1.99/0.64 tff(func_def_11, type, empty: ty > uni). 1.99/0.64 tff(func_def_12, type, add: (ty * uni * uni) > uni). 1.99/0.64 tff(func_def_13, type, remove: (ty * uni * uni) > uni). 1.99/0.64 tff(func_def_14, type, union: (ty * uni * uni) > uni). 1.99/0.64 tff(func_def_15, type, inter: (ty * uni * uni) > uni). 1.99/0.64 tff(func_def_16, type, diff: (ty * uni * uni) > uni). 1.99/0.64 tff(func_def_17, type, choose: (ty * uni) > uni). 1.99/0.64 tff(func_def_18, type, cardinal1: (ty * uni) > $int). 1.99/0.64 tff(func_def_19, type, vertex: ty). 1.99/0.64 tff(func_def_20, type, succ1: vertex1 > set_vertex). 1.99/0.64 tff(func_def_21, type, t2tb: set_vertex > uni). 1.99/0.64 tff(func_def_22, type, tb2t: uni > set_vertex). 1.99/0.64 tff(func_def_23, type, t2tb1: vertex1 > uni). 1.99/0.64 tff(func_def_24, type, tb2t1: uni > vertex1). 1.99/0.64 tff(func_def_25, type, ref: ty > ty). 1.99/0.64 tff(func_def_26, type, mk_ref: (ty * uni) > uni). 1.99/0.64 tff(func_def_27, type, contents: (ty * uni) > uni). 1.99/0.64 tff(func_def_33, type, sK7: vertex1). 1.99/0.64 tff(func_def_34, type, sK8: vertex1). 1.99/0.64 tff(func_def_35, type, sK9: $int). 1.99/0.64 tff(func_def_36, type, sK10: set_vertex). 1.99/0.64 tff(func_def_37, type, sK11: set_vertex). 1.99/0.64 tff(func_def_38, type, sK12: set_vertex). 1.99/0.64 tff(func_def_39, type, sK13: bool1). 1.99/0.64 tff(func_def_40, type, sK14: set_vertex). 1.99/0.64 tff(func_def_41, type, sK15: vertex1). 1.99/0.64 tff(func_def_42, type, sK16: set_vertex). 1.99/0.64 tff(func_def_43, type, sK17: set_vertex). 1.99/0.64 tff(func_def_44, type, sK18: bool1). 1.99/0.64 tff(func_def_45, type, sK19: set_vertex). 1.99/0.64 tff(func_def_46, type, sK20: set_vertex). 1.99/0.64 tff(func_def_47, type, sK21: $int). 1.99/0.64 tff(func_def_48, type, sK22: vertex1). 1.99/0.64 tff(func_def_49, type, sK23: set_vertex > vertex1). 1.99/0.64 tff(func_def_50, type, sK24: set_vertex > vertex1). 1.99/0.64 tff(func_def_51, type, sK25: (ty * uni) > uni). 1.99/0.64 tff(func_def_52, type, sK26: (ty * uni * uni) > uni). 1.99/0.64 tff(func_def_53, type, sK27: (ty * uni * uni) > uni). 1.99/0.64 tff(func_def_54, type, sK28: (vertex1 * vertex1 * $int) > vertex1). 1.99/0.64 tff(func_def_55, type, sK29: (vertex1 * vertex1 * $int) > vertex1). 1.99/0.64 tff(func_def_56, type, sK30: (vertex1 * vertex1 * $int) > vertex1). 1.99/0.64 tff(func_def_57, type, sK31: (vertex1 * vertex1 * $int) > vertex1). 1.99/0.64 tff(func_def_58, type, sK32: (vertex1 * vertex1 * $int) > $int). 1.99/0.64 tff(func_def_59, type, sK33: (vertex1 * vertex1 * $int) > vertex1). 1.99/0.64 tff(func_def_60, type, sK34: (vertex1 * vertex1 * $int) > $int). 1.99/0.64 tff(func_def_61, type, sK35: (set_vertex * vertex1) > vertex1). 1.99/0.64 tff(func_def_62, type, sK36: (set_vertex * $int * vertex1) > vertex1). 1.99/0.64 tff(func_def_63, type, sK37: (vertex1 * $int * set_vertex) > vertex1). 1.99/0.64 tff(func_def_64, type, sK38: (vertex1 * $int * vertex1) > $int). 1.99/0.64 tff(func_def_65, type, sK39: ($int * vertex1 * set_vertex) > vertex1). 1.99/0.64 tff(func_def_66, type, sK40: (set_vertex * $int * vertex1) > vertex1). 1.99/0.64 tff(func_def_67, type, sK41: (set_vertex * $int * vertex1) > $int). 1.99/0.64 tff(func_def_68, type, sK42: (set_vertex * set_vertex * $int * vertex1) > vertex1). 1.99/0.64 tff(pred_def_1, type, sort1: (ty * uni) > $o). 1.99/0.64 tff(pred_def_2, type, mem: (ty * uni * uni) > $o). 1.99/0.64 tff(pred_def_3, type, infix_eqeq: (ty * uni * uni) > $o). 1.99/0.64 tff(pred_def_4, type, subset: (ty * uni * uni) > $o). 1.99/0.64 tff(pred_def_5, type, is_empty: (ty * uni) > $o). 1.99/0.64 tff(pred_def_6, type, path1: (vertex1 * vertex1 * $int) > $o). 1.99/0.64 tff(pred_def_7, type, shortest_path1: (vertex1 * vertex1 * $int) > $o). 1.99/0.64 tff(pred_def_8, type, inv1: (vertex1 * vertex1 * set_vertex * set_vertex * set_vertex * $int) > $o). 1.99/0.64 tff(pred_def_9, type, closure1: (set_vertex * set_vertex * set_vertex * vertex1) > $o). 1.99/0.64 tff(pred_def_12, type, sP0: (vertex1 * vertex1 * $int) > $o). 1.99/0.64 tff(pred_def_13, type, sP1: (set_vertex * vertex1 * set_vertex * set_vertex) > $o). 1.99/0.64 tff(pred_def_14, type, sP2: (set_vertex * set_vertex * $int * vertex1) > $o). 1.99/0.64 tff(pred_def_15, type, sP3: (set_vertex * $int * vertex1) > $o). 1.99/0.64 tff(pred_def_16, type, sP4: ($int * vertex1 * set_vertex) > $o). 1.99/0.64 tff(pred_def_17, type, sP5: (vertex1 * $int * set_vertex) > $o). 1.99/0.64 tff(pred_def_18, type, sP6: (set_vertex * set_vertex * $int * vertex1 * set_vertex * vertex1) > $o). 1.99/0.64 tff(pred_def_19, type, sP43: (vertex1 * vertex1) > $o). 1.99/0.64 tff(pred_def_20, type, sP44: (vertex1 * vertex1) > $o). 1.99/0.64 tff(pred_def_21, type, sP45: (vertex1 * vertex1) > $o). 1.99/0.64 tff(pred_def_22, type, sP46: (vertex1 * set_vertex) > $o). 1.99/0.64 tff(pred_def_23, type, sP47: (vertex1 * $int * set_vertex) > $o). 1.99/0.64 tff(pred_def_24, type, sP48: (vertex1 * vertex1 * $int) > $o). 1.99/0.64 tff(f1464,plain,( 1.99/0.64 $false), 1.99/0.64 inference(subsumption_resolution,[],[f1413,f500])). 1.99/0.64 tff(f500,plain,( 1.99/0.64 mem(vertex,t2tb1(sK35(sK17,sK22)),t2tb(succ1(sK22)))), 1.99/0.64 inference(unit_resulting_resolution,[],[f302,f387])). 1.99/0.64 tff(f387,plain,( 1.99/0.64 ( ! [X2:set_vertex,X0:set_vertex,X3:vertex1,X1:set_vertex] : (closure1(X0,X1,X2,X3) | mem(vertex,t2tb1(sK35(X0,X3)),t2tb(succ1(X3)))) )), 1.99/0.64 inference(cnf_transformation,[],[f246])). 1.99/0.64 tff(f246,plain,( 1.99/0.64 ! [X0 : set_vertex,X1 : set_vertex,X2 : set_vertex,X3 : vertex1] : ((closure1(X0,X1,X2,X3) | ((~mem(vertex,t2tb1(sK35(X0,X3)),t2tb(X0)) & mem(vertex,t2tb1(sK35(X0,X3)),t2tb(succ1(X3)))) & ~mem(vertex,t2tb1(X3),t2tb(X2)) & ~mem(vertex,t2tb1(X3),t2tb(X1)) & mem(vertex,t2tb1(X3),t2tb(X0)))) & (! [X5 : vertex1] : (mem(vertex,t2tb1(X5),t2tb(X0)) | ~mem(vertex,t2tb1(X5),t2tb(succ1(X3)))) | mem(vertex,t2tb1(X3),t2tb(X2)) | mem(vertex,t2tb1(X3),t2tb(X1)) | ~mem(vertex,t2tb1(X3),t2tb(X0)) | ~closure1(X0,X1,X2,X3)))), 1.99/0.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f244,f245])). 1.99/0.64 tff(f245,plain,( 1.99/0.64 ! [X3 : vertex1,X0 : set_vertex] : (? [X4 : vertex1] : (~mem(vertex,t2tb1(X4),t2tb(X0)) & mem(vertex,t2tb1(X4),t2tb(succ1(X3)))) => (~mem(vertex,t2tb1(sK35(X0,X3)),t2tb(X0)) & mem(vertex,t2tb1(sK35(X0,X3)),t2tb(succ1(X3)))))), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f244,plain,( 1.99/0.64 ! [X0 : set_vertex,X1 : set_vertex,X2 : set_vertex,X3 : vertex1] : ((closure1(X0,X1,X2,X3) | (? [X4 : vertex1] : (~mem(vertex,t2tb1(X4),t2tb(X0)) & mem(vertex,t2tb1(X4),t2tb(succ1(X3)))) & ~mem(vertex,t2tb1(X3),t2tb(X2)) & ~mem(vertex,t2tb1(X3),t2tb(X1)) & mem(vertex,t2tb1(X3),t2tb(X0)))) & (! [X5 : vertex1] : (mem(vertex,t2tb1(X5),t2tb(X0)) | ~mem(vertex,t2tb1(X5),t2tb(succ1(X3)))) | mem(vertex,t2tb1(X3),t2tb(X2)) | mem(vertex,t2tb1(X3),t2tb(X1)) | ~mem(vertex,t2tb1(X3),t2tb(X0)) | ~closure1(X0,X1,X2,X3)))), 1.99/0.64 inference(rectify,[],[f243])). 1.99/0.64 tff(f243,plain,( 1.99/0.64 ! [X0 : set_vertex,X1 : set_vertex,X2 : set_vertex,X3 : vertex1] : ((closure1(X0,X1,X2,X3) | (? [X4 : vertex1] : (~mem(vertex,t2tb1(X4),t2tb(X0)) & mem(vertex,t2tb1(X4),t2tb(succ1(X3)))) & ~mem(vertex,t2tb1(X3),t2tb(X2)) & ~mem(vertex,t2tb1(X3),t2tb(X1)) & mem(vertex,t2tb1(X3),t2tb(X0)))) & (! [X4 : vertex1] : (mem(vertex,t2tb1(X4),t2tb(X0)) | ~mem(vertex,t2tb1(X4),t2tb(succ1(X3)))) | mem(vertex,t2tb1(X3),t2tb(X2)) | mem(vertex,t2tb1(X3),t2tb(X1)) | ~mem(vertex,t2tb1(X3),t2tb(X0)) | ~closure1(X0,X1,X2,X3)))), 1.99/0.64 inference(flattening,[],[f242])). 1.99/0.64 tff(f242,plain,( 1.99/0.64 ! [X0 : set_vertex,X1 : set_vertex,X2 : set_vertex,X3 : vertex1] : ((closure1(X0,X1,X2,X3) | (? [X4 : vertex1] : (~mem(vertex,t2tb1(X4),t2tb(X0)) & mem(vertex,t2tb1(X4),t2tb(succ1(X3)))) & ~mem(vertex,t2tb1(X3),t2tb(X2)) & ~mem(vertex,t2tb1(X3),t2tb(X1)) & mem(vertex,t2tb1(X3),t2tb(X0)))) & ((! [X4 : vertex1] : (mem(vertex,t2tb1(X4),t2tb(X0)) | ~mem(vertex,t2tb1(X4),t2tb(succ1(X3)))) | mem(vertex,t2tb1(X3),t2tb(X2)) | mem(vertex,t2tb1(X3),t2tb(X1)) | ~mem(vertex,t2tb1(X3),t2tb(X0))) | ~closure1(X0,X1,X2,X3)))), 1.99/0.64 inference(nnf_transformation,[],[f187])). 1.99/0.64 tff(f187,plain,( 1.99/0.64 ! [X0 : set_vertex,X1 : set_vertex,X2 : set_vertex,X3 : vertex1] : (closure1(X0,X1,X2,X3) <=> (! [X4 : vertex1] : (mem(vertex,t2tb1(X4),t2tb(X0)) | ~mem(vertex,t2tb1(X4),t2tb(succ1(X3)))) | mem(vertex,t2tb1(X3),t2tb(X2)) | mem(vertex,t2tb1(X3),t2tb(X1)) | ~mem(vertex,t2tb1(X3),t2tb(X0))))), 1.99/0.64 inference(flattening,[],[f186])). 1.99/0.64 tff(f186,plain,( 1.99/0.64 ! [X0 : set_vertex,X1 : set_vertex,X2 : set_vertex,X3 : vertex1] : (closure1(X0,X1,X2,X3) <=> (((! [X4 : vertex1] : (mem(vertex,t2tb1(X4),t2tb(X0)) | ~mem(vertex,t2tb1(X4),t2tb(succ1(X3)))) | mem(vertex,t2tb1(X3),t2tb(X2))) | mem(vertex,t2tb1(X3),t2tb(X1))) | ~mem(vertex,t2tb1(X3),t2tb(X0))))), 1.99/0.64 inference(ennf_transformation,[],[f141])). 1.99/0.64 tff(f141,plain,( 1.99/0.64 ! [X0 : set_vertex,X1 : set_vertex,X2 : set_vertex,X3 : vertex1] : (closure1(X0,X1,X2,X3) <=> (mem(vertex,t2tb1(X3),t2tb(X0)) => (~mem(vertex,t2tb1(X3),t2tb(X1)) => (~mem(vertex,t2tb1(X3),t2tb(X2)) => ! [X4 : vertex1] : (mem(vertex,t2tb1(X4),t2tb(succ1(X3))) => mem(vertex,t2tb1(X4),t2tb(X0)))))))), 1.99/0.64 inference(rectify,[],[f48])). 1.99/0.64 tff(f48,axiom,( 1.99/0.64 ! [X15 : set_vertex,X16 : set_vertex,X17 : set_vertex,X11 : vertex1] : (closure1(X15,X16,X17,X11) <=> (mem(vertex,t2tb1(X11),t2tb(X15)) => (~mem(vertex,t2tb1(X11),t2tb(X16)) => (~mem(vertex,t2tb1(X11),t2tb(X17)) => ! [X20 : vertex1] : (mem(vertex,t2tb1(X20),t2tb(succ1(X11))) => mem(vertex,t2tb1(X20),t2tb(X15)))))))), 1.99/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_def)). 1.99/0.64 tff(f302,plain,( 1.99/0.64 ~closure1(sK17,sK19,sK20,sK22)), 1.99/0.64 inference(cnf_transformation,[],[f211])). 1.99/0.64 tff(f211,plain,( 1.99/0.64 (((((((~closure1(sK17,sK19,sK20,sK22) & $sum(sK9,1) = sK21) & tb2t(empty(vertex)) = sK20) & sK16 = sK19) & true1 = sK18 & (is_empty(vertex,t2tb(sK14)) | true1 != sK18) & (true1 = sK18 | ~is_empty(vertex,t2tb(sK14)))) & subset(vertex,t2tb(succ1(sK15)),t2tb(sK17)) & ! [X16 : vertex1] : closure1(sK17,sK14,sK16,X16) & inv1(sK7,sK8,sK17,sK14,sK16,sK9)) & ! [X17 : vertex1] : (closure1(sK12,sK14,sK10,X17) | sK15 = X17) & shortest_path1(sK7,sK15,sK9) & inv1(sK7,sK8,sK12,sK14,sK10,sK9) & sK8 != sK15 & sK14 = tb2t(remove(vertex,t2tb1(sK15),t2tb(sK11))) & mem(vertex,t2tb1(sK15),t2tb(sK11))) & ~is_empty(vertex,t2tb(sK11)) & true1 != sK13 & (is_empty(vertex,t2tb(sK11)) | true1 != sK13) & (true1 = sK13 | ~is_empty(vertex,t2tb(sK11)))) & inv1(sK7,sK8,sK12,sK11,sK10,sK9) & ~$less(sK9,0) & ! [X18 : vertex1] : closure1(sK12,sK11,sK10,X18) & (is_empty(vertex,t2tb(sK10)) | ~is_empty(vertex,t2tb(sK11)))), 1.99/0.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22])],[f201,f210,f209,f208,f207,f206,f205,f204,f203,f202])). 1.99/0.64 tff(f202,plain,( 1.99/0.64 ? [X0 : vertex1,X1 : vertex1,X2 : $int,X3 : set_vertex,X4 : set_vertex,X5 : set_vertex] : (? [X6 : bool1] : (? [X7 : set_vertex,X8 : vertex1] : (? [X9 : set_vertex,X10 : set_vertex] : (? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(X10,X12,X13,X15) & $sum(X2,1) = X14) & tb2t(empty(vertex)) = X13) & X9 = X12) & true1 = X11 & (is_empty(vertex,t2tb(X7)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(X7)))) & subset(vertex,t2tb(succ1(X8)),t2tb(X10)) & ! [X16 : vertex1] : closure1(X10,X7,X9,X16) & inv1(X0,X1,X10,X7,X9,X2)) & ! [X17 : vertex1] : (closure1(X5,X7,X3,X17) | X8 = X17) & shortest_path1(X0,X8,X2) & inv1(X0,X1,X5,X7,X3,X2) & X1 != X8 & tb2t(remove(vertex,t2tb1(X8),t2tb(X4))) = X7 & mem(vertex,t2tb1(X8),t2tb(X4))) & ~is_empty(vertex,t2tb(X4)) & true1 != X6 & (is_empty(vertex,t2tb(X4)) | true1 != X6) & (true1 = X6 | ~is_empty(vertex,t2tb(X4)))) & inv1(X0,X1,X5,X4,X3,X2) & ~$less(X2,0) & ! [X18 : vertex1] : closure1(X5,X4,X3,X18) & (is_empty(vertex,t2tb(X3)) | ~is_empty(vertex,t2tb(X4)))) => (? [X6 : bool1] : (? [X8 : vertex1,X7 : set_vertex] : (? [X10 : set_vertex,X9 : set_vertex] : (? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(X10,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & X9 = X12) & true1 = X11 & (is_empty(vertex,t2tb(X7)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(X7)))) & subset(vertex,t2tb(succ1(X8)),t2tb(X10)) & ! [X16 : vertex1] : closure1(X10,X7,X9,X16) & inv1(sK7,sK8,X10,X7,X9,sK9)) & ! [X17 : vertex1] : (closure1(sK12,X7,sK10,X17) | X8 = X17) & shortest_path1(sK7,X8,sK9) & inv1(sK7,sK8,sK12,X7,sK10,sK9) & sK8 != X8 & tb2t(remove(vertex,t2tb1(X8),t2tb(sK11))) = X7 & mem(vertex,t2tb1(X8),t2tb(sK11))) & ~is_empty(vertex,t2tb(sK11)) & true1 != X6 & (is_empty(vertex,t2tb(sK11)) | true1 != X6) & (true1 = X6 | ~is_empty(vertex,t2tb(sK11)))) & inv1(sK7,sK8,sK12,sK11,sK10,sK9) & ~$less(sK9,0) & ! [X18 : vertex1] : closure1(sK12,sK11,sK10,X18) & (is_empty(vertex,t2tb(sK10)) | ~is_empty(vertex,t2tb(sK11))))), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f203,plain,( 1.99/0.64 ? [X6 : bool1] : (? [X8 : vertex1,X7 : set_vertex] : (? [X10 : set_vertex,X9 : set_vertex] : (? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(X10,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & X9 = X12) & true1 = X11 & (is_empty(vertex,t2tb(X7)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(X7)))) & subset(vertex,t2tb(succ1(X8)),t2tb(X10)) & ! [X16 : vertex1] : closure1(X10,X7,X9,X16) & inv1(sK7,sK8,X10,X7,X9,sK9)) & ! [X17 : vertex1] : (closure1(sK12,X7,sK10,X17) | X8 = X17) & shortest_path1(sK7,X8,sK9) & inv1(sK7,sK8,sK12,X7,sK10,sK9) & sK8 != X8 & tb2t(remove(vertex,t2tb1(X8),t2tb(sK11))) = X7 & mem(vertex,t2tb1(X8),t2tb(sK11))) & ~is_empty(vertex,t2tb(sK11)) & true1 != X6 & (is_empty(vertex,t2tb(sK11)) | true1 != X6) & (true1 = X6 | ~is_empty(vertex,t2tb(sK11)))) => (? [X8 : vertex1,X7 : set_vertex] : (? [X10 : set_vertex,X9 : set_vertex] : (? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(X10,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & X9 = X12) & true1 = X11 & (is_empty(vertex,t2tb(X7)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(X7)))) & subset(vertex,t2tb(succ1(X8)),t2tb(X10)) & ! [X16 : vertex1] : closure1(X10,X7,X9,X16) & inv1(sK7,sK8,X10,X7,X9,sK9)) & ! [X17 : vertex1] : (closure1(sK12,X7,sK10,X17) | X8 = X17) & shortest_path1(sK7,X8,sK9) & inv1(sK7,sK8,sK12,X7,sK10,sK9) & sK8 != X8 & tb2t(remove(vertex,t2tb1(X8),t2tb(sK11))) = X7 & mem(vertex,t2tb1(X8),t2tb(sK11))) & ~is_empty(vertex,t2tb(sK11)) & true1 != sK13 & (is_empty(vertex,t2tb(sK11)) | true1 != sK13) & (true1 = sK13 | ~is_empty(vertex,t2tb(sK11))))), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f204,plain,( 1.99/0.64 ? [X8 : vertex1,X7 : set_vertex] : (? [X10 : set_vertex,X9 : set_vertex] : (? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(X10,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & X9 = X12) & true1 = X11 & (is_empty(vertex,t2tb(X7)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(X7)))) & subset(vertex,t2tb(succ1(X8)),t2tb(X10)) & ! [X16 : vertex1] : closure1(X10,X7,X9,X16) & inv1(sK7,sK8,X10,X7,X9,sK9)) & ! [X17 : vertex1] : (closure1(sK12,X7,sK10,X17) | X8 = X17) & shortest_path1(sK7,X8,sK9) & inv1(sK7,sK8,sK12,X7,sK10,sK9) & sK8 != X8 & tb2t(remove(vertex,t2tb1(X8),t2tb(sK11))) = X7 & mem(vertex,t2tb1(X8),t2tb(sK11))) => (? [X10 : set_vertex,X9 : set_vertex] : (? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(X10,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & X9 = X12) & true1 = X11 & (is_empty(vertex,t2tb(sK14)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(sK14)))) & subset(vertex,t2tb(succ1(sK15)),t2tb(X10)) & ! [X16 : vertex1] : closure1(X10,sK14,X9,X16) & inv1(sK7,sK8,X10,sK14,X9,sK9)) & ! [X17 : vertex1] : (closure1(sK12,sK14,sK10,X17) | sK15 = X17) & shortest_path1(sK7,sK15,sK9) & inv1(sK7,sK8,sK12,sK14,sK10,sK9) & sK8 != sK15 & sK14 = tb2t(remove(vertex,t2tb1(sK15),t2tb(sK11))) & mem(vertex,t2tb1(sK15),t2tb(sK11)))), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f205,plain,( 1.99/0.64 ? [X10 : set_vertex,X9 : set_vertex] : (? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(X10,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & X9 = X12) & true1 = X11 & (is_empty(vertex,t2tb(sK14)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(sK14)))) & subset(vertex,t2tb(succ1(sK15)),t2tb(X10)) & ! [X16 : vertex1] : closure1(X10,sK14,X9,X16) & inv1(sK7,sK8,X10,sK14,X9,sK9)) => (? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(sK17,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & sK16 = X12) & true1 = X11 & (is_empty(vertex,t2tb(sK14)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(sK14)))) & subset(vertex,t2tb(succ1(sK15)),t2tb(sK17)) & ! [X16 : vertex1] : closure1(sK17,sK14,sK16,X16) & inv1(sK7,sK8,sK17,sK14,sK16,sK9))), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f206,plain,( 1.99/0.64 ? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(sK17,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & sK16 = X12) & true1 = X11 & (is_empty(vertex,t2tb(sK14)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(sK14)))) => (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(sK17,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & sK16 = X12) & true1 = sK18 & (is_empty(vertex,t2tb(sK14)) | true1 != sK18) & (true1 = sK18 | ~is_empty(vertex,t2tb(sK14))))), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f207,plain,( 1.99/0.64 ? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(sK17,X12,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & sK16 = X12) => (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(sK17,sK19,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) & sK16 = sK19)), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f208,plain,( 1.99/0.64 ? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(sK17,sK19,X13,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = X13) => (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(sK17,sK19,sK20,X15) & $sum(sK9,1) = X14) & tb2t(empty(vertex)) = sK20)), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f209,plain,( 1.99/0.64 ? [X14 : $int] : (? [X15 : vertex1] : ~closure1(sK17,sK19,sK20,X15) & $sum(sK9,1) = X14) => (? [X15 : vertex1] : ~closure1(sK17,sK19,sK20,X15) & $sum(sK9,1) = sK21)), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f210,plain,( 1.99/0.64 ? [X15 : vertex1] : ~closure1(sK17,sK19,sK20,X15) => ~closure1(sK17,sK19,sK20,sK22)), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f201,plain,( 1.99/0.64 ? [X0 : vertex1,X1 : vertex1,X2 : $int,X3 : set_vertex,X4 : set_vertex,X5 : set_vertex] : (? [X6 : bool1] : (? [X7 : set_vertex,X8 : vertex1] : (? [X9 : set_vertex,X10 : set_vertex] : (? [X11 : bool1] : (? [X12 : set_vertex] : (? [X13 : set_vertex] : (? [X14 : $int] : (? [X15 : vertex1] : ~closure1(X10,X12,X13,X15) & $sum(X2,1) = X14) & tb2t(empty(vertex)) = X13) & X9 = X12) & true1 = X11 & (is_empty(vertex,t2tb(X7)) | true1 != X11) & (true1 = X11 | ~is_empty(vertex,t2tb(X7)))) & subset(vertex,t2tb(succ1(X8)),t2tb(X10)) & ! [X16 : vertex1] : closure1(X10,X7,X9,X16) & inv1(X0,X1,X10,X7,X9,X2)) & ! [X17 : vertex1] : (closure1(X5,X7,X3,X17) | X8 = X17) & shortest_path1(X0,X8,X2) & inv1(X0,X1,X5,X7,X3,X2) & X1 != X8 & tb2t(remove(vertex,t2tb1(X8),t2tb(X4))) = X7 & mem(vertex,t2tb1(X8),t2tb(X4))) & ~is_empty(vertex,t2tb(X4)) & true1 != X6 & (is_empty(vertex,t2tb(X4)) | true1 != X6) & (true1 = X6 | ~is_empty(vertex,t2tb(X4)))) & inv1(X0,X1,X5,X4,X3,X2) & ~$less(X2,0) & ! [X18 : vertex1] : closure1(X5,X4,X3,X18) & (is_empty(vertex,t2tb(X3)) | ~is_empty(vertex,t2tb(X4))))), 1.99/0.64 inference(rectify,[],[f200])). 1.99/0.64 tff(f200,plain,( 1.99/0.64 ? [X0 : vertex1,X1 : vertex1,X2 : $int,X3 : set_vertex,X4 : set_vertex,X5 : set_vertex] : (? [X7 : bool1] : (? [X8 : set_vertex,X9 : vertex1] : (? [X11 : set_vertex,X12 : set_vertex] : (? [X14 : bool1] : (? [X15 : set_vertex] : (? [X16 : set_vertex] : (? [X17 : $int] : (? [X18 : vertex1] : ~closure1(X12,X15,X16,X18) & $sum(X2,1) = X17) & tb2t(empty(vertex)) = X16) & X11 = X15) & true1 = X14 & (is_empty(vertex,t2tb(X8)) | true1 != X14) & (true1 = X14 | ~is_empty(vertex,t2tb(X8)))) & subset(vertex,t2tb(succ1(X9)),t2tb(X12)) & ! [X13 : vertex1] : closure1(X12,X8,X11,X13) & inv1(X0,X1,X12,X8,X11,X2)) & ! [X10 : vertex1] : (closure1(X5,X8,X3,X10) | X9 = X10) & shortest_path1(X0,X9,X2) & inv1(X0,X1,X5,X8,X3,X2) & X1 != X9 & tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 & mem(vertex,t2tb1(X9),t2tb(X4))) & ~is_empty(vertex,t2tb(X4)) & true1 != X7 & (is_empty(vertex,t2tb(X4)) | true1 != X7) & (true1 = X7 | ~is_empty(vertex,t2tb(X4)))) & inv1(X0,X1,X5,X4,X3,X2) & ~$less(X2,0) & ! [X6 : vertex1] : closure1(X5,X4,X3,X6) & (is_empty(vertex,t2tb(X3)) | ~is_empty(vertex,t2tb(X4))))), 1.99/0.64 inference(flattening,[],[f199])). 1.99/0.64 tff(f199,plain,( 1.99/0.64 ? [X0 : vertex1,X1 : vertex1,X2 : $int,X3 : set_vertex,X4 : set_vertex,X5 : set_vertex] : (? [X7 : bool1] : (? [X8 : set_vertex,X9 : vertex1] : (? [X11 : set_vertex,X12 : set_vertex] : (? [X14 : bool1] : (? [X15 : set_vertex] : (? [X16 : set_vertex] : (? [X17 : $int] : (? [X18 : vertex1] : ~closure1(X12,X15,X16,X18) & $sum(X2,1) = X17) & tb2t(empty(vertex)) = X16) & X11 = X15) & true1 = X14 & ((is_empty(vertex,t2tb(X8)) | true1 != X14) & (true1 = X14 | ~is_empty(vertex,t2tb(X8))))) & subset(vertex,t2tb(succ1(X9)),t2tb(X12)) & ! [X13 : vertex1] : closure1(X12,X8,X11,X13) & inv1(X0,X1,X12,X8,X11,X2)) & ! [X10 : vertex1] : (closure1(X5,X8,X3,X10) | X9 = X10) & shortest_path1(X0,X9,X2) & inv1(X0,X1,X5,X8,X3,X2) & X1 != X9 & tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 & mem(vertex,t2tb1(X9),t2tb(X4))) & ~is_empty(vertex,t2tb(X4)) & true1 != X7 & ((is_empty(vertex,t2tb(X4)) | true1 != X7) & (true1 = X7 | ~is_empty(vertex,t2tb(X4))))) & inv1(X0,X1,X5,X4,X3,X2) & ~$less(X2,0) & ! [X6 : vertex1] : closure1(X5,X4,X3,X6) & (is_empty(vertex,t2tb(X3)) | ~is_empty(vertex,t2tb(X4))))), 1.99/0.64 inference(nnf_transformation,[],[f147])). 1.99/0.64 tff(f147,plain,( 1.99/0.64 ? [X0 : vertex1,X1 : vertex1,X2 : $int,X3 : set_vertex,X4 : set_vertex,X5 : set_vertex] : (? [X7 : bool1] : (? [X8 : set_vertex,X9 : vertex1] : (? [X11 : set_vertex,X12 : set_vertex] : (? [X14 : bool1] : (? [X15 : set_vertex] : (? [X16 : set_vertex] : (? [X17 : $int] : (? [X18 : vertex1] : ~closure1(X12,X15,X16,X18) & $sum(X2,1) = X17) & tb2t(empty(vertex)) = X16) & X11 = X15) & true1 = X14 & (is_empty(vertex,t2tb(X8)) <=> true1 = X14)) & subset(vertex,t2tb(succ1(X9)),t2tb(X12)) & ! [X13 : vertex1] : closure1(X12,X8,X11,X13) & inv1(X0,X1,X12,X8,X11,X2)) & ! [X10 : vertex1] : (closure1(X5,X8,X3,X10) | X9 = X10) & shortest_path1(X0,X9,X2) & inv1(X0,X1,X5,X8,X3,X2) & X1 != X9 & tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 & mem(vertex,t2tb1(X9),t2tb(X4))) & ~is_empty(vertex,t2tb(X4)) & true1 != X7 & (is_empty(vertex,t2tb(X4)) <=> true1 = X7)) & inv1(X0,X1,X5,X4,X3,X2) & ~$less(X2,0) & ! [X6 : vertex1] : closure1(X5,X4,X3,X6) & (is_empty(vertex,t2tb(X3)) | ~is_empty(vertex,t2tb(X4))))), 1.99/0.64 inference(flattening,[],[f146])). 1.99/0.64 tff(f146,plain,( 1.99/0.64 ? [X0 : vertex1,X1 : vertex1,X2 : $int,X3 : set_vertex,X4 : set_vertex,X5 : set_vertex] : (? [X7 : bool1] : (((? [X8 : set_vertex,X9 : vertex1] : (((? [X11 : set_vertex,X12 : set_vertex] : (? [X14 : bool1] : ((? [X15 : set_vertex] : (? [X16 : set_vertex] : (? [X17 : $int] : (? [X18 : vertex1] : ~closure1(X12,X15,X16,X18) & $sum(X2,1) = X17) & tb2t(empty(vertex)) = X16) & X11 = X15) & true1 = X14) & (is_empty(vertex,t2tb(X8)) <=> true1 = X14)) & (subset(vertex,t2tb(succ1(X9)),t2tb(X12)) & ! [X13 : vertex1] : closure1(X12,X8,X11,X13) & inv1(X0,X1,X12,X8,X11,X2))) & (! [X10 : vertex1] : (closure1(X5,X8,X3,X10) | X9 = X10) & shortest_path1(X0,X9,X2) & inv1(X0,X1,X5,X8,X3,X2))) & X1 != X9) & (tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 & mem(vertex,t2tb1(X9),t2tb(X4)))) & ~is_empty(vertex,t2tb(X4))) & true1 != X7) & (is_empty(vertex,t2tb(X4)) <=> true1 = X7)) & (inv1(X0,X1,X5,X4,X3,X2) & ~$less(X2,0) & ! [X6 : vertex1] : closure1(X5,X4,X3,X6) & (is_empty(vertex,t2tb(X3)) | ~is_empty(vertex,t2tb(X4)))))), 1.99/0.64 inference(ennf_transformation,[],[f86])). 1.99/0.64 tff(f86,plain,( 1.99/0.64 ~! [X0 : vertex1,X1 : vertex1,X2 : $int,X3 : set_vertex,X4 : set_vertex,X5 : set_vertex] : ((inv1(X0,X1,X5,X4,X3,X2) & ~$less(X2,0) & ! [X6 : vertex1] : closure1(X5,X4,X3,X6) & (is_empty(vertex,t2tb(X4)) => is_empty(vertex,t2tb(X3)))) => ! [X7 : bool1] : ((is_empty(vertex,t2tb(X4)) <=> true1 = X7) => (true1 != X7 => (~is_empty(vertex,t2tb(X4)) => ! [X8 : set_vertex,X9 : vertex1] : ((tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 & mem(vertex,t2tb1(X9),t2tb(X4))) => (X1 != X9 => ((! [X10 : vertex1] : (X9 != X10 => closure1(X5,X8,X3,X10)) & shortest_path1(X0,X9,X2) & inv1(X0,X1,X5,X8,X3,X2)) => ! [X11 : set_vertex,X12 : set_vertex] : ((subset(vertex,t2tb(succ1(X9)),t2tb(X12)) & ! [X13 : vertex1] : closure1(X12,X8,X11,X13) & inv1(X0,X1,X12,X8,X11,X2)) => ! [X14 : bool1] : ((is_empty(vertex,t2tb(X8)) <=> true1 = X14) => (true1 = X14 => ! [X15 : set_vertex] : (X11 = X15 => ! [X16 : set_vertex] : (tb2t(empty(vertex)) = X16 => ! [X17 : $int] : ($sum(X2,1) = X17 => ! [X18 : vertex1] : closure1(X12,X15,X16,X18))))))))))))))), 1.99/0.64 inference(rectify,[],[f61])). 1.99/0.64 tff(f61,plain,( 1.99/0.64 ~! [X13 : vertex1,X14 : vertex1,X18 : $int,X17 : set_vertex,X16 : set_vertex,X15 : set_vertex] : ((inv1(X13,X14,X15,X16,X17,X18) & ~$less(X18,0) & ! [X11 : vertex1] : closure1(X15,X16,X17,X11) & (is_empty(vertex,t2tb(X16)) => is_empty(vertex,t2tb(X17)))) => ! [X24 : bool1] : ((is_empty(vertex,t2tb(X16)) <=> true1 = X24) => (true1 != X24 => (~is_empty(vertex,t2tb(X16)) => ! [X25 : set_vertex,X3 : vertex1] : ((tb2t(remove(vertex,t2tb1(X3),t2tb(X16))) = X25 & mem(vertex,t2tb1(X3),t2tb(X16))) => (X3 != X14 => ((! [X11 : vertex1] : (X3 != X11 => closure1(X15,X25,X17,X11)) & shortest_path1(X13,X3,X18) & inv1(X13,X14,X15,X25,X17,X18)) => ! [X26 : set_vertex,X27 : set_vertex] : ((subset(vertex,t2tb(succ1(X3)),t2tb(X27)) & ! [X11 : vertex1] : closure1(X27,X25,X26,X11) & inv1(X13,X14,X27,X25,X26,X18)) => ! [X28 : bool1] : ((is_empty(vertex,t2tb(X25)) <=> true1 = X28) => (true1 = X28 => ! [X29 : set_vertex] : (X26 = X29 => ! [X30 : set_vertex] : (tb2t(empty(vertex)) = X30 => ! [X31 : $int] : ($sum(X18,1) = X31 => ! [X11 : vertex1] : closure1(X27,X29,X30,X11))))))))))))))), 1.99/0.64 inference(theory_normalization,[],[f40])). 1.99/0.64 tff(f40,negated_conjecture,( 1.99/0.64 ~! [X13 : vertex1,X14 : vertex1,X18 : $int,X17 : set_vertex,X16 : set_vertex,X15 : set_vertex] : ((inv1(X13,X14,X15,X16,X17,X18) & $lesseq(0,X18) & ! [X11 : vertex1] : closure1(X15,X16,X17,X11) & (is_empty(vertex,t2tb(X16)) => is_empty(vertex,t2tb(X17)))) => ! [X24 : bool1] : ((is_empty(vertex,t2tb(X16)) <=> true1 = X24) => (true1 != X24 => (~is_empty(vertex,t2tb(X16)) => ! [X25 : set_vertex,X3 : vertex1] : ((tb2t(remove(vertex,t2tb1(X3),t2tb(X16))) = X25 & mem(vertex,t2tb1(X3),t2tb(X16))) => (X3 != X14 => ((! [X11 : vertex1] : (X3 != X11 => closure1(X15,X25,X17,X11)) & shortest_path1(X13,X3,X18) & inv1(X13,X14,X15,X25,X17,X18)) => ! [X26 : set_vertex,X27 : set_vertex] : ((subset(vertex,t2tb(succ1(X3)),t2tb(X27)) & ! [X11 : vertex1] : closure1(X27,X25,X26,X11) & inv1(X13,X14,X27,X25,X26,X18)) => ! [X28 : bool1] : ((is_empty(vertex,t2tb(X25)) <=> true1 = X28) => (true1 = X28 => ! [X29 : set_vertex] : (X26 = X29 => ! [X30 : set_vertex] : (tb2t(empty(vertex)) = X30 => ! [X31 : $int] : ($sum(X18,1) = X31 => ! [X11 : vertex1] : closure1(X27,X29,X30,X11))))))))))))))), 1.99/0.64 inference(negated_conjecture,[],[f39])). 1.99/0.64 tff(f39,conjecture,( 1.99/0.64 ! [X13 : vertex1,X14 : vertex1,X18 : $int,X17 : set_vertex,X16 : set_vertex,X15 : set_vertex] : ((inv1(X13,X14,X15,X16,X17,X18) & $lesseq(0,X18) & ! [X11 : vertex1] : closure1(X15,X16,X17,X11) & (is_empty(vertex,t2tb(X16)) => is_empty(vertex,t2tb(X17)))) => ! [X24 : bool1] : ((is_empty(vertex,t2tb(X16)) <=> true1 = X24) => (true1 != X24 => (~is_empty(vertex,t2tb(X16)) => ! [X25 : set_vertex,X3 : vertex1] : ((tb2t(remove(vertex,t2tb1(X3),t2tb(X16))) = X25 & mem(vertex,t2tb1(X3),t2tb(X16))) => (X3 != X14 => ((! [X11 : vertex1] : (X3 != X11 => closure1(X15,X25,X17,X11)) & shortest_path1(X13,X3,X18) & inv1(X13,X14,X15,X25,X17,X18)) => ! [X26 : set_vertex,X27 : set_vertex] : ((subset(vertex,t2tb(succ1(X3)),t2tb(X27)) & ! [X11 : vertex1] : closure1(X27,X25,X26,X11) & inv1(X13,X14,X27,X25,X26,X18)) => ! [X28 : bool1] : ((is_empty(vertex,t2tb(X25)) <=> true1 = X28) => (true1 = X28 => ! [X29 : set_vertex] : (X26 = X29 => ! [X30 : set_vertex] : (tb2t(empty(vertex)) = X30 => ! [X31 : $int] : ($sum(X18,1) = X31 => ! [X11 : vertex1] : closure1(X27,X29,X30,X11))))))))))))))), 1.99/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_bfs)). 1.99/0.64 tff(f1413,plain,( 1.99/0.64 ~mem(vertex,t2tb1(sK35(sK17,sK22)),t2tb(succ1(sK22)))), 1.99/0.64 inference(unit_resulting_resolution,[],[f1263,f501,f438])). 1.99/0.64 tff(f438,plain,( 1.99/0.64 ( ! [X0:set_vertex,X5:vertex1,X3:vertex1] : (mem(vertex,t2tb1(X5),t2tb(X0)) | ~mem(vertex,t2tb1(X5),t2tb(succ1(X3))) | sP46(X3,X0)) )), 1.99/0.64 inference(cnf_transformation,[],[f438_D])). 1.99/0.64 tff(f438_D,plain,( 1.99/0.64 ( ! [X0,X3] : (( ! [X5] : (mem(vertex,t2tb1(X5),t2tb(X0)) | ~mem(vertex,t2tb1(X5),t2tb(succ1(X3)))) ) <=> ~sP46(X3,X0)) )), 1.99/0.64 introduced(general_splitting_component_introduction,[new_symbols(naming,[sP46])])). 1.99/0.64 tff(f501,plain,( 1.99/0.64 ~mem(vertex,t2tb1(sK35(sK17,sK22)),t2tb(sK17))), 1.99/0.64 inference(unit_resulting_resolution,[],[f302,f388])). 1.99/0.64 tff(f388,plain,( 1.99/0.64 ( ! [X2:set_vertex,X0:set_vertex,X3:vertex1,X1:set_vertex] : (closure1(X0,X1,X2,X3) | ~mem(vertex,t2tb1(sK35(X0,X3)),t2tb(X0))) )), 1.99/0.64 inference(cnf_transformation,[],[f246])). 1.99/0.64 tff(f1263,plain,( 1.99/0.64 ~sP46(sK22,sK17)), 1.99/0.64 inference(unit_resulting_resolution,[],[f294,f497,f477,f503,f439])). 1.99/0.64 tff(f439,plain,( 1.99/0.64 ( ! [X2:set_vertex,X0:set_vertex,X3:vertex1,X1:set_vertex] : (mem(vertex,t2tb1(X3),t2tb(X2)) | mem(vertex,t2tb1(X3),t2tb(X1)) | ~mem(vertex,t2tb1(X3),t2tb(X0)) | ~closure1(X0,X1,X2,X3) | ~sP46(X3,X0)) )), 1.99/0.64 inference(general_splitting,[],[f383,f438_D])). 1.99/0.64 tff(f383,plain,( 1.99/0.64 ( ! [X2:set_vertex,X0:set_vertex,X5:vertex1,X3:vertex1,X1:set_vertex] : (mem(vertex,t2tb1(X5),t2tb(X0)) | ~mem(vertex,t2tb1(X5),t2tb(succ1(X3))) | mem(vertex,t2tb1(X3),t2tb(X2)) | mem(vertex,t2tb1(X3),t2tb(X1)) | ~mem(vertex,t2tb1(X3),t2tb(X0)) | ~closure1(X0,X1,X2,X3)) )), 1.99/0.64 inference(cnf_transformation,[],[f246])). 1.99/0.64 tff(f503,plain,( 1.99/0.64 ~mem(vertex,t2tb1(sK22),t2tb(sK16))), 1.99/0.64 inference(forward_demodulation,[],[f498,f299])). 1.99/0.64 tff(f299,plain,( 1.99/0.64 sK16 = sK19), 1.99/0.64 inference(cnf_transformation,[],[f211])). 1.99/0.64 tff(f498,plain,( 1.99/0.64 ~mem(vertex,t2tb1(sK22),t2tb(sK19))), 1.99/0.64 inference(unit_resulting_resolution,[],[f302,f385])). 1.99/0.64 tff(f385,plain,( 1.99/0.64 ( ! [X2:set_vertex,X0:set_vertex,X3:vertex1,X1:set_vertex] : (closure1(X0,X1,X2,X3) | ~mem(vertex,t2tb1(X3),t2tb(X1))) )), 1.99/0.64 inference(cnf_transformation,[],[f246])). 1.99/0.64 tff(f477,plain,( 1.99/0.64 ( ! [X0:uni] : (~mem(vertex,X0,t2tb(sK14))) )), 1.99/0.64 inference(unit_resulting_resolution,[],[f463,f324])). 1.99/0.64 tff(f324,plain,( 1.99/0.64 ( ! [X0:ty,X3:uni,X1:uni] : (~mem(X0,X3,X1) | ~is_empty(X0,X1)) )), 1.99/0.64 inference(cnf_transformation,[],[f217])). 1.99/0.64 tff(f217,plain,( 1.99/0.64 ! [X0 : ty,X1 : uni] : ((is_empty(X0,X1) | (mem(X0,sK25(X0,X1),X1) & sort1(X0,sK25(X0,X1)))) & (! [X3 : uni] : ~mem(X0,X3,X1) | ~is_empty(X0,X1)))), 1.99/0.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f152,f216])). 1.99/0.64 tff(f216,plain,( 1.99/0.64 ! [X1 : uni,X0 : ty] : (? [X2 : uni] : (mem(X0,X2,X1) & sort1(X0,X2)) => (mem(X0,sK25(X0,X1),X1) & sort1(X0,sK25(X0,X1))))), 1.99/0.64 introduced(choice_axiom,[])). 1.99/0.64 tff(f152,plain,( 1.99/0.64 ! [X0 : ty,X1 : uni] : ((is_empty(X0,X1) | ? [X2 : uni] : (mem(X0,X2,X1) & sort1(X0,X2))) & (! [X3 : uni] : ~mem(X0,X3,X1) | ~is_empty(X0,X1)))), 1.99/0.64 inference(ennf_transformation,[],[f105])). 1.99/0.64 tff(f105,plain,( 1.99/0.64 ! [X0 : ty,X1 : uni] : ((! [X2 : uni] : (sort1(X0,X2) => ~mem(X0,X2,X1)) => is_empty(X0,X1)) & (is_empty(X0,X1) => ! [X3 : uni] : ~mem(X0,X3,X1)))), 1.99/0.64 inference(rectify,[],[f38])). 1.99/0.64 tff(f38,axiom,( 1.99/0.64 ! [X8 : ty,X13 : uni] : ((! [X11 : uni] : (sort1(X8,X11) => ~mem(X8,X11,X13)) => is_empty(X8,X13)) & (is_empty(X8,X13) => ! [X11 : uni] : ~mem(X8,X11,X13)))), 1.99/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',is_empty_def)). 1.99/0.64 tff(f463,plain,( 1.99/0.64 is_empty(vertex,t2tb(sK14))), 1.99/0.64 inference(subsumption_resolution,[],[f297,f298])). 1.99/0.64 tff(f298,plain,( 1.99/0.64 true1 = sK18), 1.99/0.64 inference(cnf_transformation,[],[f211])). 1.99/0.64 tff(f297,plain,( 1.99/0.64 is_empty(vertex,t2tb(sK14)) | true1 != sK18), 1.99/0.64 inference(cnf_transformation,[],[f211])). 1.99/0.64 tff(f497,plain,( 1.99/0.64 mem(vertex,t2tb1(sK22),t2tb(sK17))), 1.99/0.64 inference(unit_resulting_resolution,[],[f302,f384])). 1.99/0.64 tff(f384,plain,( 1.99/0.64 ( ! [X2:set_vertex,X0:set_vertex,X3:vertex1,X1:set_vertex] : (closure1(X0,X1,X2,X3) | mem(vertex,t2tb1(X3),t2tb(X0))) )), 1.99/0.64 inference(cnf_transformation,[],[f246])). 1.99/0.64 tff(f294,plain,( 1.99/0.64 ( ! [X16:vertex1] : (closure1(sK17,sK14,sK16,X16)) )), 1.99/0.64 inference(cnf_transformation,[],[f211])). 1.99/0.64 % SZS output end Proof for theBenchmark 1.99/0.64 % (28076)------------------------------ 1.99/0.64 % (28076)Version: Vampire 4.5.0 (commit 2ee491ce on 2020-06-19 13:55:12 +0100) 1.99/0.64 % (28076)Termination reason: Refutation 1.99/0.64 1.99/0.64 % (28076)Memory used [KB]: 3326 1.99/0.64 % (28076)Time elapsed: 0.243 s 1.99/0.64 % (28076)------------------------------ 1.99/0.64 % (28076)------------------------------ 2.40/0.65 % (28057)Success in time 0.325 s 2.40/0.66 EOF