0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.24 % Computer : n165.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Fri Jul 13 15:56:57 CDT 2018 0.03/0.24 % CPUTime : 0.26/0.54 ============================== Prover9 =============================== 0.26/0.54 Prover9 (32) version 2009-11A, November 2009. 0.26/0.54 Process 18094 was started by sandbox2 on n165.star.cs.uiowa.edu, 0.26/0.54 Fri Jul 13 15:56:57 2018 0.26/0.54 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18062_n165.star.cs.uiowa.edu". 0.26/0.54 ============================== end of head =========================== 0.26/0.54 0.26/0.54 ============================== INPUT ================================= 0.26/0.54 0.26/0.54 % Reading from file /tmp/Prover9_18062_n165.star.cs.uiowa.edu 0.26/0.54 0.26/0.54 set(prolog_style_variables). 0.26/0.54 set(auto2). 0.26/0.54 % set(auto2) -> set(auto). 0.26/0.54 % set(auto) -> set(auto_inference). 0.26/0.54 % set(auto) -> set(auto_setup). 0.26/0.54 % set(auto_setup) -> set(predicate_elim). 0.26/0.54 % set(auto_setup) -> assign(eq_defs, unfold). 0.26/0.54 % set(auto) -> set(auto_limits). 0.26/0.54 % set(auto_limits) -> assign(max_weight, "100.000"). 0.26/0.54 % set(auto_limits) -> assign(sos_limit, 20000). 0.26/0.54 % set(auto) -> set(auto_denials). 0.26/0.54 % set(auto) -> set(auto_process). 0.26/0.54 % set(auto2) -> assign(new_constants, 1). 0.26/0.54 % set(auto2) -> assign(fold_denial_max, 3). 0.26/0.54 % set(auto2) -> assign(max_weight, "200.000"). 0.26/0.54 % set(auto2) -> assign(max_hours, 1). 0.26/0.54 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.26/0.54 % set(auto2) -> assign(max_seconds, 0). 0.26/0.54 % set(auto2) -> assign(max_minutes, 5). 0.26/0.54 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.26/0.54 % set(auto2) -> set(sort_initial_sos). 0.26/0.54 % set(auto2) -> assign(sos_limit, -1). 0.26/0.54 % set(auto2) -> assign(lrs_ticks, 3000). 0.26/0.54 % set(auto2) -> assign(max_megs, 400). 0.26/0.54 % set(auto2) -> assign(stats, some). 0.26/0.54 % set(auto2) -> clear(echo_input). 0.26/0.54 % set(auto2) -> set(quiet). 0.26/0.54 % set(auto2) -> clear(print_initial_clauses). 0.26/0.54 % set(auto2) -> clear(print_given). 0.26/0.54 assign(lrs_ticks,-1). 0.26/0.54 assign(sos_limit,10000). 0.26/0.54 assign(order,kbo). 0.26/0.54 set(lex_order_vars). 0.26/0.54 clear(print_given). 0.26/0.54 0.26/0.54 % formulas(sos). % not echoed (19 formulas) 0.26/0.54 0.26/0.54 ============================== end of input ========================== 0.26/0.54 0.26/0.54 % From the command line: assign(max_seconds, 300). 0.26/0.54 0.26/0.54 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.26/0.54 0.26/0.54 % Formulas that are not ordinary clauses: 0.26/0.54 1 (all V1 all V2 all P all V (in_path(V,P) & path(V1,V2,P) -> (exists E (on_path(E,P) & (V = tail_of(E) | V = head_of(E)))) & vertex(V))) # label(in_path_properties) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 2 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 (on_path(E2,P) & (sequential(E1,E2) | (exists E3 (sequential(E1,E3) & precedes(E3,E2,P)))) & on_path(E1,P) -> precedes(E1,E2,P))))) # label(precedes_defn) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 3 (all V1 all V2 all P (path(V1,V2,P) -> (exists E (-(path_cons(E,empty) = P & V2 = head_of(E) <-> (exists TP (path(head_of(E),V2,TP) & path_cons(E,TP) = P))) & V1 = tail_of(E) & edge(E))) & vertex(V2) & vertex(V1))) # label(path_properties) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 4 (all V1 all V2 all E1 all E2 all P (shortest_path(V1,V2,P) & precedes(E1,E2,P) -> -precedes(E2,E1,P) & -(exists E3 (head_of(E3) = head_of(E2) & tail_of(E3) = tail_of(E1))))) # label(shortest_path_properties) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 5 complete -> (all V1 all V2 (V1 != V2 & vertex(V2) & vertex(V1) -> (exists E (-(head_of(E) = V1 & tail_of(E) = V2 <-> V2 = head_of(E) & V1 = tail_of(E)) & edge(E))))) # label(complete_properties) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 6 (all V1 all V2 all SP (path(V1,V2,SP) & V2 != V1 & (all P (path(V1,V2,P) -> less_or_equal(length_of(SP),length_of(P)))) <-> shortest_path(V1,V2,SP))) # label(shortest_path_defn) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 7 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 (precedes(E1,E2,P) -> -((exists E3 (sequential(E1,E3) & precedes(E3,E2,P))) <-> sequential(E1,E2)) & on_path(E2,P) & on_path(E1,P))))) # label(precedes_properties) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 8 (all V1 all V2 all P all E (path(V1,V2,P) & on_path(E,P) -> edge(E) & in_path(head_of(E),P) & in_path(tail_of(E),P))) # label(on_path_properties) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 9 (all V1 all V2 all P (vertex(V1) & vertex(V2) & (exists E (edge(E) & tail_of(E) = V1 & ((exists TP (path_cons(E,TP) = P & path(head_of(E),V2,TP))) | head_of(E) = V2 & P = path_cons(E,empty)))) -> path(V1,V2,P))) # label(path_defn) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 10 (all E (edge(E) -> vertex(head_of(E)) & vertex(tail_of(E)))) # label(edge_ends_are_vertices) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 11 (all E (edge(E) -> head_of(E) != tail_of(E))) # label(no_loops) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 12 (all E1 all E2 (sequential(E1,E2) <-> edge(E1) & head_of(E1) = tail_of(E2) & E1 != E2 & edge(E2))) # label(sequential_defn) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 13 (all Things all InThese less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph))) # label(graph_has_them_all) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 14 (all V1 all V2 all P (path(V1,V2,P) -> minus(length_of(P),n1) = number_of_in(sequential_pairs,P))) # label(path_length_sequential_pairs) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 15 (all V1 all V2 all P (path(V1,V2,P) -> length_of(P) = number_of_in(edges,P))) # label(length_defn) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 16 (all E1 all E2 all E3 (triangle(E1,E2,E3) <-> edge(E2) & sequential(E1,E2) & sequential(E3,E1) & sequential(E2,E3) & edge(E3) & edge(E1))) # label(triangle_defn) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 17 (all P all V1 all V2 (path(V1,V2,P) & (all E1 all E2 (on_path(E1,P) & sequential(E1,E2) & on_path(E2,P) -> (exists E3 triangle(E1,E2,E3)))) -> number_of_in(triangles,P) = number_of_in(sequential_pairs,P))) # label(sequential_pairs_and_triangles) # label(axiom) # label(non_clause). [assumption]. 0.26/0.54 18 complete -> (all V1 all V2 all E1 all E2 all P (shortest_path(V1,V2,P) & precedes(E1,E2,P) -> (exists E3 (head_of(E3) = tail_of(E1) & tail_of(E3) = head_of(E2) & edge(E3))))) # label(back_edge) # label(lemma) # label(non_clause). [assumption]. 0.26/0.54 19 -(complete -> (all V1 all V2 all E1 all E2 all P (precedes(E1,E2,P) & sequential(E1,E2) & shortest_path(V1,V2,P) -> (exists E3 triangle(E1,E2,E3))))) # label(sequential_is_triangle) # label(negated_conjecture) # label(non_clause). [assumption]. 0.26/0.54 0.26/0.54 ============================== end of process non-clausal formulas === 0.26/0.54 0.26/0.54 ============================== PROCESS INITIAL CLAUSES =============== 0.26/0.54 0.26/0.54 ============================== PREDICATE ELIMINATION ================= 0.26/0.54 20 A != B | -shortest_path(B,A,C) # label(shortest_path_defn) # label(axiom). [clausify(6)]. 0.26/0.54 21 shortest_path(c1,c2,c5) # label(sequential_is_triangle) # label(negated_conjecture). [clausify(19)]. 0.26/0.54 Derived: c2 != c1. [resolve(20,b,21,a)]. 0.26/0.54 22 -shortest_path(A,B,C) | -precedes(D,E,C) | -precedes(E,D,C) # label(shortest_path_properties) # label(axiom). [clausify(4)]. 0.26/0.54 Derived: -precedes(A,B,c5) | -precedes(B,A,c5). [resolve(22,a,21,a)]. 0.26/0.54 23 -shortest_path(A,B,C) | -precedes(D,E,C) | head_of(F) != head_of(E) | tail_of(F) != tail_of(D) # label(shortest_path_properties) # label(axiom). [clausify(4)]. 0.26/0.54 Derived: -precedes(A,B,c5) | head_of(C) != head_of(B) | tail_of(C) != tail_of(A). [resolve(23,a,21,a)]. 0.26/0.54 24 path(A,B,C) | -shortest_path(A,B,C) # label(shortest_path_defn) # label(axiom). [clausify(6)]. 0.26/0.54 Derived: path(c1,c2,c5). [resolve(24,b,21,a)]. 0.26/0.54 25 -path(A,B,C) | less_or_equal(length_of(D),length_of(C)) | -shortest_path(A,B,D) # label(shortest_path_defn) # label(axiom). [clausify(6)]. 0.26/0.54 Derived: -path(c1,c2,A) | less_or_equal(length_of(c5),length_of(A)). [resolve(25,c,21,a)]. 0.26/0.54 26 -complete | -shortest_path(A,B,C) | -precedes(D,E,C) | edge(f9(A,B,D,E,C)) # label(back_edge) # label(lemma). [clausify(18)]. 0.26/0.54 Derived: -complete | -precedes(A,B,c5) | edge(f9(c1,c2,A,B,c5)). [resolve(26,b,21,a)]. 0.26/0.54 27 -path(A,B,C) | B = A | path(A,B,f5(A,B,C)) | shortest_path(A,B,C) # label(shortest_path_defn) # label(axiom). [clausify(6)]. 0.26/0.54 Derived: -path(A,B,C) | B = A | path(A,B,f5(A,B,C)) | -precedes(D,E,C) | -precedes(E,D,C). [resolve(27,d,22,a)]. 0.26/0.54 Derived: -path(A,B,C) | B = A | path(A,B,f5(A,B,C)) | -precedes(D,E,C) | head_of(F) != head_of(E) | tail_of(F) != tail_of(D). [resolve(27,d,23,a)]. 0.26/0.55 Derived: -path(A,B,C) | B = A | path(A,B,f5(A,B,C)) | -path(A,B,D) | less_or_equal(length_of(C),length_of(D)). [resolve(27,d,25,c)]. 0.26/0.55 Derived: -path(A,B,C) | B = A | path(A,B,f5(A,B,C)) | -complete | -precedes(D,E,C) | edge(f9(A,B,D,E,C)). [resolve(27,d,26,b)]. 0.26/0.55 28 -path(A,B,C) | B = A | -less_or_equal(length_of(C),length_of(f5(A,B,C))) | shortest_path(A,B,C) # label(shortest_path_defn) # label(axiom). [clausify(6)]. 0.26/0.55 Derived: -path(A,B,C) | B = A | -less_or_equal(length_of(C),length_of(f5(A,B,C))) | -precedes(D,E,C) | -precedes(E,D,C). [resolve(28,d,22,a)]. 0.26/0.55 Derived: -path(A,B,C) | B = A | -less_or_equal(length_of(C),length_of(f5(A,B,C))) | -precedes(D,E,C) | head_of(F) != head_of(E) | tail_of(F) != tail_of(D). [resolve(28,d,23,a)]. 0.26/0.55 Derived: -path(A,B,C) | B = A | -less_or_equal(length_of(C),length_of(f5(A,B,C))) | -path(A,B,D) | less_or_equal(length_of(C),length_of(D)). [resolve(28,d,25,c)]. 0.26/0.55 Derived: -path(A,B,C) | B = A | -less_or_equal(length_of(C),length_of(f5(A,B,C))) | -complete | -precedes(D,E,C) | edge(f9(A,B,D,E,C)). [resolve(28,d,26,b)]. 0.26/0.55 29 -complete | -shortest_path(A,B,C) | -precedes(D,E,C) | head_of(f9(A,B,D,E,C)) = tail_of(D) # label(back_edge) # label(lemma). [clausify(18)]. 0.26/0.55 Derived: -complete | -precedes(A,B,c5) | head_of(f9(c1,c2,A,B,c5)) = tail_of(A). [resolve(29,b,21,a)]. 0.26/0.55 Derived: -complete | -precedes(A,B,C) | head_of(f9(D,E,A,B,C)) = tail_of(A) | -path(D,E,C) | E = D | path(D,E,f5(D,E,C)). [resolve(29,b,27,d)]. 0.26/0.55 Derived: -complete | -precedes(A,B,C) | head_of(f9(D,E,A,B,C)) = tail_of(A) | -path(D,E,C) | E = D | -less_or_equal(length_of(C),length_of(f5(D,E,C))). [resolve(29,b,28,d)]. 0.26/0.55 30 -complete | -shortest_path(A,B,C) | -precedes(D,E,C) | head_of(E) = tail_of(f9(A,B,D,E,C)) # label(back_edge) # label(lemma). [clausify(18)]. 0.26/0.55 Derived: -complete | -precedes(A,B,c5) | head_of(B) = tail_of(f9(c1,c2,A,B,c5)). [resolve(30,b,21,a)]. 0.26/0.55 Derived: -complete | -precedes(A,B,C) | head_of(B) = tail_of(f9(D,E,A,B,C)) | -path(D,E,C) | E = D | path(D,E,f5(D,E,C)). [resolve(30,b,27,d)]. 0.26/0.55 Derived: -complete | -precedes(A,B,C) | head_of(B) = tail_of(f9(D,E,A,B,C)) | -path(D,E,C) | E = D | -less_or_equal(length_of(C),length_of(f5(D,E,C))). [resolve(30,b,28,d)]. 0.26/0.55 31 -path(A,B,C) | -on_path(D,C) | in_path(head_of(D),C) # label(on_path_properties) # label(axiom). [clausify(8)]. 0.26/0.55 32 -in_path(A,B) | -path(C,D,B) | vertex(A) # label(in_path_properties) # label(axiom). [clausify(1)]. 0.26/0.55 Derived: -path(A,B,C) | -on_path(D,C) | -path(E,F,C) | vertex(head_of(D)). [resolve(31,c,32,a)]. 0.26/0.55 33 -path(A,B,C) | -on_path(D,C) | in_path(tail_of(D),C) # label(on_path_properties) # label(axiom). [clausify(8)]. 0.26/0.55 Derived: -path(A,B,C) | -on_path(D,C) | -path(E,F,C) | vertex(tail_of(D)). [resolve(33,c,32,a)]. 0.26/0.55 34 -in_path(A,B) | -path(C,D,B) | on_path(f1(C,D,B,A),B) # label(in_path_properties) # label(axiom). [clausify(1)]. 0.26/0.55 Derived: -path(A,B,C) | on_path(f1(A,B,C,head_of(D)),C) | -path(E,F,C) | -on_path(D,C). [resolve(34,a,31,c)]. 0.26/0.55 Derived: -path(A,B,C) | on_path(f1(A,B,C,tail_of(D)),C) | -path(E,F,C) | -on_path(D,C). [resolve(34,a,33,c)]. 0.26/0.55 35 -in_path(A,B) | -path(C,D,B) | tail_of(f1(C,D,B,A)) = A | head_of(f1(C,D,B,A)) = A # label(in_path_properties) # label(axiom). [clausify(1)]. 0.26/0.55 Derived: -path(A,B,C) | tail_of(f1(A,B,C,head_of(D))) = head_of(D) | head_of(f1(A,B,C,head_of(D))) = head_of(D) | -path(E,F,C) | -on_path(D,C). [resolve(35,a,31,c)]. 0.26/0.55 Derived: -path(A,B,C) | tail_of(f1(A,B,C,tail_of(D))) = tail_of(D) | head_of(f1(A,B,C,tail_of(D))) = tail_of(D) | -path(E,F,C) | -on_path(D,C). [resolve(35,a,33,c)]. 0.26/0.55 0.26/0.55 ============================== end predicate elimination ============= 0.26/0.55 0.26/0.55 Auto_denials: (non-Horn, no changes). 0.26/0.55 0.26/0.55 Term ordering decisions: 0.26/0.55 Function symbol KB weights: sequential_pairs=1. triangles=1. empty=1. edges=1. graph=1. n1=1. c1=1. c2=1. c3=1. c4=1. c5=1. number_of_in=1. path_cons=1. minus=1. f4=1. head_of=1. tail_of=1. length_of=1. f2=1. f3=1. f5=1. f7=1. f8=1. f1=1. f6=1. f9=1. 0.26/0.55 0.26/0.55 ============================== end of process initial clauses ======== 38.05/38.35 38.05/38.35 ============================== CLAUSES FOR SEARCH ==================== 38.05/38.35 38.05/38.35 ============================== end of clauses for search ============= 38.05/38.35 38.05/38.35 ============================== SEARCH ================================ 38.05/38.35 38.05/38.35 % Starting search at 0.01 seconds. 38.05/38.35 38.05/38.35 Low Water (keep): wt=111.000, iters=3363 38.05/38.35 38.05/38.35 Low Water (keep): wt=82.000, iters=3358 38.05/38.35 38.05/38.35 Low Water (keep): wt=77.000, iters=3345 38.05/38.35 38.05/38.35 Low Water (keep): wt=63.000, iters=5700 38.05/38.35 38.05/38.35 Low Water (keep): wt=49.000, iters=4956 38.05/38.35 38.05/38.35 Low Water (keep): wt=39.000, iters=3813 38.05/38.35 38.05/38.35 Low Water (keep): wt=37.000, iters=3735 38.05/38.35 38.05/38.35 Low Water (keep): wt=36.000, iters=3341 38.05/38.35 38.05/38.35 Low Water (keep): wt=35.000, iters=3840 38.05/38.35 38.05/38.35 Low Water (keep): wt=34.000, iters=3611 38.05/38.35 38.05/38.35 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 383 (0.00 of 15.70 sec). 38.05/38.35 38.05/38.35 Low Water (keep): wt=32.000, iters=4025 38.05/38.35 38.05/38.35 Low Water (keep): wt=31.000, iters=3822 38.05/38.35 38.05/38.35 Low Water (displace): id=5558, wt=111.000 38.05/38.35 38.05/38.35 Low Water (displace): id=3797, wt=106.000 38.05/38.35 38.05/38.35 Low Water (displace): id=3789, wt=104.000 38.05/38.35 38.05/38.35 Low Water (displace): id=5919, wt=83.000 38.05/38.35 38.05/38.35 Low Water (displace): id=5867, wt=82.000 38.05/38.35 38.05/38.35 Low Water (displace): id=10865, wt=30.000 38.05/38.35 38.05/38.35 Low Water (displace): id=10867, wt=28.000 38.05/38.35 38.05/38.35 Low Water (displace): id=10958, wt=21.000 38.05/38.35 38.05/38.35 Low Water (displace): id=11066, wt=19.000 38.05/38.35 38.05/38.35 ============================== PROOF ================================= 38.05/38.35 % SZS status Theorem 38.05/38.35 % SZS output start Refutation 38.05/38.35 38.05/38.35 % Proof 1 at 37.79 (+ 0.02) seconds. 38.05/38.35 % Length of proof is 63. 38.05/38.35 % Level of proof is 9. 38.05/38.35 % Maximum clause weight is 25.000. 38.05/38.35 % Given clauses 672. 38.05/38.35 38.05/38.35 2 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 (on_path(E2,P) & (sequential(E1,E2) | (exists E3 (sequential(E1,E3) & precedes(E3,E2,P)))) & on_path(E1,P) -> precedes(E1,E2,P))))) # label(precedes_defn) # label(axiom) # label(non_clause). [assumption]. 38.05/38.35 4 (all V1 all V2 all E1 all E2 all P (shortest_path(V1,V2,P) & precedes(E1,E2,P) -> -precedes(E2,E1,P) & -(exists E3 (head_of(E3) = head_of(E2) & tail_of(E3) = tail_of(E1))))) # label(shortest_path_properties) # label(axiom) # label(non_clause). [assumption]. 38.05/38.35 6 (all V1 all V2 all SP (path(V1,V2,SP) & V2 != V1 & (all P (path(V1,V2,P) -> less_or_equal(length_of(SP),length_of(P)))) <-> shortest_path(V1,V2,SP))) # label(shortest_path_defn) # label(axiom) # label(non_clause). [assumption]. 38.05/38.35 7 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 (precedes(E1,E2,P) -> -((exists E3 (sequential(E1,E3) & precedes(E3,E2,P))) <-> sequential(E1,E2)) & on_path(E2,P) & on_path(E1,P))))) # label(precedes_properties) # label(axiom) # label(non_clause). [assumption]. 38.05/38.35 12 (all E1 all E2 (sequential(E1,E2) <-> edge(E1) & head_of(E1) = tail_of(E2) & E1 != E2 & edge(E2))) # label(sequential_defn) # label(axiom) # label(non_clause). [assumption]. 38.05/38.35 16 (all E1 all E2 all E3 (triangle(E1,E2,E3) <-> edge(E2) & sequential(E1,E2) & sequential(E3,E1) & sequential(E2,E3) & edge(E3) & edge(E1))) # label(triangle_defn) # label(axiom) # label(non_clause). [assumption]. 38.05/38.35 18 complete -> (all V1 all V2 all E1 all E2 all P (shortest_path(V1,V2,P) & precedes(E1,E2,P) -> (exists E3 (head_of(E3) = tail_of(E1) & tail_of(E3) = head_of(E2) & edge(E3))))) # label(back_edge) # label(lemma) # label(non_clause). [assumption]. 38.05/38.35 19 -(complete -> (all V1 all V2 all E1 all E2 all P (precedes(E1,E2,P) & sequential(E1,E2) & shortest_path(V1,V2,P) -> (exists E3 triangle(E1,E2,E3))))) # label(sequential_is_triangle) # label(negated_conjecture) # label(non_clause). [assumption]. 38.05/38.35 21 shortest_path(c1,c2,c5) # label(sequential_is_triangle) # label(negated_conjecture). [clausify(19)]. 38.05/38.35 22 -shortest_path(A,B,C) | -precedes(D,E,C) | -precedes(E,D,C) # label(shortest_path_properties) # label(axiom). [clausify(4)]. 38.05/38.35 24 path(A,B,C) | -shortest_path(A,B,C) # label(shortest_path_defn) # label(axiom). [clausify(6)]. 38.05/38.35 26 -complete | -shortest_path(A,B,C) | -precedes(D,E,C) | edge(f9(A,B,D,E,C)) # label(back_edge) # label(lemma). [clausify(18)]. 38.05/38.35 29 -complete | -shortest_path(A,B,C) | -precedes(D,E,C) | head_of(f9(A,B,D,E,C)) = tail_of(D) # label(back_edge) # label(lemma). [clausify(18)]. 38.05/38.35 30 -complete | -shortest_path(A,B,C) | -precedes(D,E,C) | head_of(E) = tail_of(f9(A,B,D,E,C)) # label(back_edge) # label(lemma). [clausify(18)]. 38.05/38.35 36 complete # label(sequential_is_triangle) # label(negated_conjecture). [clausify(19)]. 38.05/38.35 37 sequential(c3,c4) # label(sequential_is_triangle) # label(negated_conjecture). [clausify(19)]. 38.05/38.35 38 precedes(c3,c4,c5) # label(sequential_is_triangle) # label(negated_conjecture). [clausify(19)]. 38.05/38.35 40 -triangle(c3,c4,A) # label(sequential_is_triangle) # label(negated_conjecture). [clausify(19)]. 38.05/38.35 41 -sequential(A,B) | B != A # label(sequential_defn) # label(axiom). [clausify(12)]. 38.05/38.35 48 -sequential(A,B) | edge(A) # label(sequential_defn) # label(axiom). [clausify(12)]. 38.05/38.35 49 -sequential(A,B) | edge(B) # label(sequential_defn) # label(axiom). [clausify(12)]. 38.05/38.35 63 -path(A,B,C) | -precedes(D,E,C) | on_path(E,C) # label(precedes_properties) # label(axiom). [clausify(7)]. 38.05/38.35 64 -path(A,B,C) | -precedes(D,E,C) | on_path(D,C) # label(precedes_properties) # label(axiom). [clausify(7)]. 38.05/38.35 68 sequential(A,B) | -edge(A) | head_of(A) != tail_of(B) | B = A | -edge(B) # label(sequential_defn) # label(axiom). [clausify(12)]. 38.05/38.35 69 -path(A,B,C) | -on_path(D,C) | -sequential(E,D) | -on_path(E,C) | precedes(E,D,C) # label(precedes_defn) # label(axiom). [clausify(2)]. 38.05/38.35 73 triangle(A,B,C) | -edge(B) | -sequential(A,B) | -sequential(C,A) | -sequential(B,C) | -edge(C) | -edge(A) # label(triangle_defn) # label(axiom). [clausify(16)]. 38.05/38.35 84 -path(A,B,C) | -on_path(D,C) | -sequential(E,F) | -precedes(F,D,C) | -on_path(E,C) | precedes(E,D,C) # label(precedes_defn) # label(axiom). [clausify(2)]. 38.05/38.35 95 -precedes(A,B,c5) | -precedes(B,A,c5). [resolve(22,a,21,a)]. 38.05/38.35 97 path(c1,c2,c5). [resolve(24,b,21,a)]. 38.05/38.35 99 -complete | -precedes(A,B,c5) | edge(f9(c1,c2,A,B,c5)). [resolve(26,b,21,a)]. 38.05/38.35 100 -precedes(A,B,c5) | edge(f9(c1,c2,A,B,c5)). [copy(99),unit_del(a,36)]. 38.05/38.35 111 -complete | -precedes(A,B,c5) | head_of(f9(c1,c2,A,B,c5)) = tail_of(A). [resolve(29,b,21,a)]. 38.05/38.35 112 -precedes(A,B,c5) | head_of(f9(c1,c2,A,B,c5)) = tail_of(A). [copy(111),unit_del(a,36)]. 38.05/38.35 117 -complete | -precedes(A,B,c5) | head_of(B) = tail_of(f9(c1,c2,A,B,c5)). [resolve(30,b,21,a)]. 38.05/38.35 118 -precedes(A,B,c5) | tail_of(f9(c1,c2,A,B,c5)) = head_of(B). [copy(117),flip(c),unit_del(a,36)]. 38.05/38.35 140 -precedes(A,A,c5). [factor(95,a,b)]. 38.05/38.35 152 c4 != c3. [resolve(41,a,37,a)]. 38.05/38.35 156 edge(c3). [resolve(48,a,37,a)]. 38.05/38.35 157 edge(c4). [resolve(49,a,37,a)]. 38.05/38.35 159 -path(A,B,c5) | on_path(c4,c5). [resolve(63,b,38,a)]. 38.05/38.35 160 -path(A,B,c5) | on_path(c3,c5). [resolve(64,b,38,a)]. 38.05/38.35 161 -sequential(A,c3) | -sequential(c4,A) | -edge(A). [resolve(73,c,37,a),unit_del(a,40),unit_del(b,157),unit_del(f,156)]. 38.05/38.35 162 -path(A,B,c5) | -on_path(c4,c5) | -sequential(C,c3) | -on_path(C,c5) | precedes(C,c4,c5). [resolve(84,d,38,a)]. 38.05/38.35 163 -path(A,B,c5) | -on_path(c4,c5) | -sequential(c4,c3). [factor(162,b,d),unit_del(d,140)]. 38.05/38.35 164 -precedes(c4,c3,c5). [resolve(95,a,38,a)]. 38.05/38.35 175 -on_path(A,c5) | -sequential(B,A) | -on_path(B,c5) | precedes(B,A,c5). [resolve(97,a,69,a)]. 38.05/38.35 184 edge(f9(c1,c2,c3,c4,c5)). [resolve(100,a,38,a)]. 38.05/38.35 189 head_of(f9(c1,c2,c3,c4,c5)) = tail_of(c3). [resolve(112,a,38,a)]. 38.05/38.35 192 tail_of(f9(c1,c2,c3,c4,c5)) = head_of(c4). [resolve(118,a,38,a)]. 38.05/38.35 206 sequential(A,c3) | -edge(A) | head_of(A) != tail_of(c3) | c3 = A. [resolve(156,a,68,e)]. 38.05/38.35 213 sequential(c4,A) | head_of(c4) != tail_of(A) | c4 = A | -edge(A). [resolve(157,a,68,b),flip(c)]. 38.05/38.35 275 -on_path(c4,c5) | -sequential(c4,c3). [resolve(163,a,97,a)]. 38.05/38.35 283 on_path(c4,c5). [resolve(159,a,97,a)]. 38.05/38.35 284 -sequential(c4,c3). [back_unit_del(275),unit_del(a,283)]. 38.05/38.35 286 tail_of(c3) != head_of(c4). [ur(68,a,284,a,b,157,a,d,152,a(flip),e,156,a),flip(a)]. 38.05/38.35 302 on_path(c3,c5). [resolve(160,a,97,a)]. 38.05/38.35 1644 sequential(f9(c1,c2,c3,c4,c5),c3) | f9(c1,c2,c3,c4,c5) = c3. [resolve(206,b,184,a),rewrite([189(15)]),flip(c),xx(b)]. 38.05/38.35 2044 sequential(c4,f9(c1,c2,c3,c4,c5)) | f9(c1,c2,c3,c4,c5) = c4. [resolve(213,d,184,a),rewrite([192(17)]),flip(c),xx(b)]. 38.05/38.35 9538 f9(c1,c2,c3,c4,c5) = c3 | -sequential(c4,f9(c1,c2,c3,c4,c5)). [resolve(1644,a,161,a),unit_del(c,184)]. 38.05/38.35 9570 f9(c1,c2,c3,c4,c5) = c4 | -on_path(f9(c1,c2,c3,c4,c5),c5) | precedes(c4,f9(c1,c2,c3,c4,c5),c5). [resolve(2044,a,175,b),unit_del(c,283)]. 38.05/38.35 11533 f9(c1,c2,c3,c4,c5) = c3 | f9(c1,c2,c3,c4,c5) = c4. [resolve(9538,b,2044,a)]. 38.05/38.35 11534 f9(c1,c2,c3,c4,c5) = c3. [para(11533(b,1),189(a,1,1)),flip(b),unit_del(b,286)]. 38.05/38.35 11547 $F. [back_rewrite(9570),rewrite([11534(6),11534(9),11534(13)]),flip(a),unit_del(a,152),unit_del(b,302),unit_del(c,164)]. 38.05/38.35 38.05/38.35 % SZS output end Refutation 38.05/38.35 ============================== end of proof ========================== 38.05/38.35 38.05/38.35 ============================== STATISTICS ============================ 38.05/38.35 38.05/38.35 Given=672. Generated=25179. Kept=11495. proofs=1. 38.05/38.35 Usable=665. Sos=9983. Demods=13. Limbo=13, Disabled=927. Hints=0. 38.05/38.35 Megabytes=18.66. 38.05/38.35 User_CPU=37.79, System_CPU=0.02, Wall_clock=38. 38.05/38.35 38.05/38.35 ============================== end of statistics ===================== 38.05/38.35 38.05/38.35 ============================== end of search ========================= 38.05/38.35 38.05/38.35 THEOREM PROVED 38.05/38.35 % SZS status Theorem 38.05/38.35 38.05/38.35 Exiting with 1 proof. 38.05/38.35 38.05/38.35 Process 18094 exit (max_proofs) Fri Jul 13 15:57:35 2018 38.05/38.35 Prover9 interrupted 38.05/38.36 EOF