0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.31 % Computer : n016.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % DateTime : Thu Jul 2 07:39:20 EDT 2020 0.10/0.31 % CPUTime : 0.72/1.03 ============================== Prover9 =============================== 0.72/1.03 Prover9 (32) version 2009-11A, November 2009. 0.72/1.03 Process 6902 was started by sandbox2 on n016.cluster.edu, 0.72/1.03 Thu Jul 2 07:39:21 2020 0.72/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_6749_n016.cluster.edu". 0.72/1.03 ============================== end of head =========================== 0.72/1.03 0.72/1.03 ============================== INPUT ================================= 0.72/1.03 0.72/1.03 % Reading from file /tmp/Prover9_6749_n016.cluster.edu 0.72/1.03 0.72/1.03 set(prolog_style_variables). 0.72/1.03 set(auto2). 0.72/1.03 % set(auto2) -> set(auto). 0.72/1.03 % set(auto) -> set(auto_inference). 0.72/1.03 % set(auto) -> set(auto_setup). 0.72/1.03 % set(auto_setup) -> set(predicate_elim). 0.72/1.03 % set(auto_setup) -> assign(eq_defs, unfold). 0.72/1.03 % set(auto) -> set(auto_limits). 0.72/1.03 % set(auto_limits) -> assign(max_weight, "100.000"). 0.72/1.03 % set(auto_limits) -> assign(sos_limit, 20000). 0.72/1.03 % set(auto) -> set(auto_denials). 0.72/1.03 % set(auto) -> set(auto_process). 0.72/1.03 % set(auto2) -> assign(new_constants, 1). 0.72/1.03 % set(auto2) -> assign(fold_denial_max, 3). 0.72/1.03 % set(auto2) -> assign(max_weight, "200.000"). 0.72/1.03 % set(auto2) -> assign(max_hours, 1). 0.72/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.72/1.03 % set(auto2) -> assign(max_seconds, 0). 0.72/1.03 % set(auto2) -> assign(max_minutes, 5). 0.72/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.72/1.03 % set(auto2) -> set(sort_initial_sos). 0.72/1.03 % set(auto2) -> assign(sos_limit, -1). 0.72/1.03 % set(auto2) -> assign(lrs_ticks, 3000). 0.72/1.03 % set(auto2) -> assign(max_megs, 400). 0.72/1.03 % set(auto2) -> assign(stats, some). 0.72/1.03 % set(auto2) -> clear(echo_input). 0.72/1.03 % set(auto2) -> set(quiet). 0.72/1.03 % set(auto2) -> clear(print_initial_clauses). 0.72/1.03 % set(auto2) -> clear(print_given). 0.72/1.03 assign(lrs_ticks,-1). 0.72/1.03 assign(sos_limit,10000). 0.72/1.03 assign(order,kbo). 0.72/1.03 set(lex_order_vars). 0.72/1.03 clear(print_given). 0.72/1.03 0.72/1.03 % formulas(sos). % not echoed (28 formulas) 0.72/1.03 0.72/1.03 ============================== end of input ========================== 0.72/1.03 0.72/1.03 % From the command line: assign(max_seconds, 960). 0.72/1.03 0.72/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.72/1.03 0.72/1.03 % Formulas that are not ordinary clauses: 0.72/1.03 1 (all C all C1 ((all P (incident_c(P,C1) <-> incident_c(P,C))) -> C1 = C)) # label(c9) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 2 (all P all C all C1 (incident_c(P,C1) & (all Q (incident_c(Q,C1) & incident_c(Q,C) -> end_point(Q,C) & end_point(Q,C1))) & incident_c(P,C) <-> meet(P,C,C1))) # label(meet_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 3 (all C1 all C2 ((exists P meet(P,C1,C2)) -> (exists C C = sum(C1,C2)))) # label(c8) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 4 (all C all P (inner_point(P,C) -> (exists C1 exists C2 (sum(C1,C2) = C & meet(P,C1,C2))))) # label(c4) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 5 (all P all C ((all C1 all C2 (part_of(C1,C) & incident_c(P,C2) & part_of(C2,C) & incident_c(P,C1) -> part_of(C2,C1) | part_of(C1,C2))) & incident_c(P,C) <-> end_point(P,C))) # label(end_point_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 6 (all C all C1 all C2 all C3 ((exists P (end_point(P,C1) & end_point(P,C2) & end_point(P,C3))) & part_of(C3,C) & part_of(C2,C) & part_of(C1,C) -> part_of(C1,C2) | part_of(C1,C3) | part_of(C3,C1) | part_of(C2,C1) | part_of(C3,C2) | part_of(C2,C3))) # label(c2) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 7 (all C all P all Q all R (end_point(P,C) & end_point(Q,C) & end_point(R,C) -> Q = R | P = R | Q = P)) # label(c5) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 8 (all C all C1 (part_of(C1,C) & C1 != C -> open(C1))) # label(c1) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 9 (all C all C1 all C2 all P (closed(C) & meet(P,C1,C2) & sum(C1,C2) = C -> (all Q (end_point(Q,C1) -> meet(Q,C1,C2))))) # label(c7) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 10 (all C all P (end_point(P,C) -> (exists Q (Q != P & end_point(Q,C))))) # label(c6) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 11 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 12 (all C all C1 ((all P (incident_c(P,C1) -> incident_c(P,C))) <-> part_of(C1,C))) # label(part_of_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 13 (all C all C1 all C2 ((all Q (incident_c(Q,C1) | incident_c(Q,C2) <-> incident_c(Q,C))) <-> sum(C1,C2) = C)) # label(sum_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 14 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 15 (all C ((exists P end_point(P,C)) <-> open(C))) # label(open_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 16 (all P all C (inner_point(P,C) <-> incident_c(P,C) & -end_point(P,C))) # label(inner_point_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 17 (all C all P all Q all R (R != P & (exists Cpp (end_point(P,Cpp) & inner_point(Q,Cpp) & end_point(R,Cpp) & part_of(Cpp,C))) <-> between_c(C,P,Q,R))) # label(between_c_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 18 (all P all O (incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,P,Q))) <-> start_point(P,O))) # label(start_point_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 19 (all O exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & open(C))) # label(o2) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 20 (all O1 all O2 ((all P all Q (ordered_by(O1,P,Q) <-> ordered_by(O2,P,Q))) -> O1 = O2)) # label(o6) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 21 (all P all Q all R all O (between_o(O,P,Q,R) <-> (exists C ((all P (incident_c(P,C) <-> incident_o(P,O))) & between_c(C,P,Q,R))))) # label(o3) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 22 (all O all P all Q (ordered_by(O,P,Q) -> incident_o(P,O) & incident_o(Q,O))) # label(o1) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 23 (all C all O ((all P (incident_o(P,O) <-> incident_c(P,C))) <-> C = underlying_curve(O))) # label(underlying_curve_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 24 (all P all O (finish_point(P,O) <-> (all Q (incident_o(Q,O) & P != Q -> ordered_by(O,Q,P))) & incident_o(P,O))) # label(finish_point_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 25 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 26 (all P all Q all C (open(C) & incident_c(Q,C) & incident_c(P,C) & P != Q -> (exists O ((all R (incident_o(R,O) <-> incident_c(R,C))) & ordered_by(O,P,Q))))) # label(o5) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 27 (all O all P all Q all R (between_o(O,P,Q,R) <-> ordered_by(O,R,Q) & ordered_by(O,Q,P) | ordered_by(O,P,Q) & ordered_by(O,Q,R))) # label(between_o_defn) # label(axiom) # label(non_clause). [assumption]. 0.72/1.03 28 -(all O exists P exists Q (Q != P & ordered_by(O,P,Q))) # label(theorem_4_11) # label(negated_conjecture) # label(non_clause). [assumption]. 0.72/1.03 0.72/1.03 ============================== end of process non-clausal formulas === 0.72/1.03 0.72/1.03 ============================== PROCESS INITIAL CLAUSES =============== 0.72/1.03 0.72/1.03 ============================== PREDICATE ELIMINATION ================= 0.72/1.03 29 end_point(f13(A),A) | -open(A) # label(open_defn) # label(axiom). [clausify(15)]. 0.72/1.03 30 open(f16(A)) # label(o2) # label(axiom). [clausify(19)]. 0.72/1.03 31 -end_point(A,B) | open(B) # label(open_defn) # label(axiom). [clausify(15)]. 0.72/1.03 Derived: end_point(f13(f16(A)),f16(A)). [resolve(29,b,30,a)]. 0.72/1.03 Derived: end_point(f13(A),A) | -end_point(B,A). [resolve(29,b,31,b)]. 0.72/1.03 32 -part_of(A,B) | A = B | open(A) # label(c1) # label(axiom). [clausify(8)]. 0.72/1.03 Derived: -part_of(A,B) | A = B | end_point(f13(A),A). [resolve(32,c,29,b)]. 0.72/1.03 33 -open(A) | -incident_c(B,A) | -incident_c(C,A) | B = C | ordered_by(f24(C,B,A),C,B) # label(o5) # label(axiom). [clausify(26)]. 0.72/1.03 Derived: -incident_c(A,f16(B)) | -incident_c(C,f16(B)) | A = C | ordered_by(f24(C,A,f16(B)),C,A). [resolve(33,a,30,a)]. 0.72/1.03 Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | ordered_by(f24(C,A,B),C,A) | -end_point(D,B). [resolve(33,a,31,b)]. 0.72/1.03 Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | ordered_by(f24(C,A,B),C,A) | -part_of(B,D) | B = D. [resolve(33,a,32,c)]. 0.72/1.03 34 -open(A) | -incident_c(B,A) | -incident_c(C,A) | B = C | -incident_o(D,f24(C,B,A)) | incident_c(D,A) # label(o5) # label(axiom). [clausify(26)]. 0.72/1.03 Derived: -incident_c(A,f16(B)) | -incident_c(C,f16(B)) | A = C | -incident_o(D,f24(C,A,f16(B))) | incident_c(D,f16(B)). [resolve(34,a,30,a)]. 0.72/1.03 Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | -incident_o(D,f24(C,A,B)) | incident_c(D,B) | -end_point(E,B). [resolve(34,a,31,b)]. 0.72/1.03 Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | -incident_o(D,f24(C,A,B)) | incident_c(D,B) | -part_of(B,E) | B = E. [resolve(34,a,32,c)]. 0.72/1.03 35 -open(A) | -incident_c(B,A) | -incident_c(C,A) | B = C | incident_o(D,f24(C,B,A)) | -incident_c(D,A) # label(o5) # label(axiom). [clausify(26)]. 0.72/1.03 Derived: -incident_c(A,f16(B)) | -incident_c(C,f16(B)) | A = C | incident_o(D,f24(C,A,f16(B))) | -incident_c(D,f16(B)). [resolve(35,a,30,a)]. 0.72/1.03 Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | incident_o(D,f24(C,A,B)) | -incident_c(D,B) | -end_point(E,B). [resolve(35,a,31,b)]. 0.72/1.03 Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | incident_o(D,f24(C,A,B)) | -incident_c(D,B) | -part_of(B,E) | B = E. [resolve(35,a,32,c)]. 0.72/1.03 36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(16)]. 0.72/1.03 37 inner_point(f12(A),A) # label(c3) # label(axiom). [clausify(14)]. 0.72/1.03 Derived: -end_point(f12(A),A). [resolve(36,a,37,a)]. 0.72/1.03 38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom). [clausify(16)]. 0.72/1.03 Derived: incident_c(f12(A),A). [resolve(38,a,37,a)]. 0.72/1.03 39 inner_point(A,B) | -incident_c(A,B) | end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(16)]. 0.72/1.03 40 -inner_point(A,B) | meet(A,f4(B,A),f5(B,A)) # label(c4) # label(axiom). [clausify(4)]. 0.72/1.03 Derived: meet(f12(A),f4(A,f12(A)),f5(A,f12(A))). [resolve(40,a,37,a)]. 0.72/1.03 Derived: meet(A,f4(B,A),f5(B,A)) | -incident_c(A,B) | end_point(A,B). [resolve(40,a,39,a)]. 0.72/1.03 41 -inner_point(A,B) | sum(f4(B,A),f5(B,A)) = B # label(c4) # label(axiom). [clausify(4)]. 0.72/1.03 Derived: sum(f4(A,f12(A)),f5(A,f12(A))) = A. [resolve(41,a,37,a)]. 0.72/1.03 Derived: sum(f4(A,B),f5(A,B)) = A | -incident_c(B,A) | end_point(B,A). [resolve(41,a,39,a)]. 0.72/1.03 42 inner_point(A,f14(B,C,A,D)) | -between_c(B,C,A,D) # label(between_c_defn) # label(axiom). [clausify(17)]. 0.72/1.03 Derived: -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)). [resolve(42,a,36,a)]. 0.72/1.03 Derived: -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)). [resolve(42,a,38,a)]. 0.72/1.03 Derived: -between_c(A,B,C,D) | meet(C,f4(f14(A,B,C,D),C),f5(f14(A,B,C,D),C)). [resolve(42,a,40,a)]. 0.72/1.03 Derived: -between_c(A,B,C,D) | sum(f4(f14(A,B,C,D),C),f5(f14(A,B,C,D),C)) = f14(A,B,C,D). [resolve(42,a,41,a)]. 0.72/1.03 43 A = B | -end_point(B,C) | -inner_point(D,C) | -end_point(A,C) | -part_of(C,E) | between_c(E,B,D,A) # label(between_c_defn) # label(axiom). [clausify(17)]. 0.72/1.03 Derived: A = B | -end_point(B,C) | -end_point(A,C) | -part_of(C,D) | between_c(D,B,f12(C),A). [resolve(43,c,37,a)]. 0.72/1.03 Derived: A = B | -end_point(B,C) | -end_point(A,C) | -part_of(C,D) | between_c(D,B,E,A) | -incident_c(E,C) | end_point(E,C). [resolve(43,c,39,a)]. 0.72/1.03 Derived: A = B | -end_point(B,f14(C,D,E,F)) | -end_point(A,f14(C,D,E,F)) | -part_of(f14(C,D,E,F),V6) | between_c(V6,B,E,A) | -between_c(C,D,E,F). [resolve(43,c,42,a)]. 0.72/1.03 44 incident_o(A,B) | -start_point(A,B) # label(start_point_defn) # label(axiom). [clausify(18)]. 0.72/1.03 45 start_point(f23(A),A) # label(o4) # label(axiom). [clausify(25)]. 0.72/1.03 Derived: incident_o(f23(A),A). [resolve(44,b,45,a)]. 0.72/1.03 46 -incident_o(A,B) | f15(A,B) != A | start_point(A,B) # label(start_point_defn) # label(axiom). [clausify(18)]. 0.72/1.03 47 -incident_o(A,B) | incident_o(f15(A,B),B) | start_point(A,B) # label(start_point_defn) # label(axiom). [clausify(18)]. 0.72/1.03 48 -incident_o(A,B) | -ordered_by(B,A,f15(A,B)) | start_point(A,B) # label(start_point_defn) # label(axiom). [clausify(18)]. 0.72/1.03 49 A = B | -incident_o(A,C) | ordered_by(C,B,A) | -start_point(B,C) # label(start_point_defn) # label(axiom). [clausify(18)]. 0.72/1.03 Derived: A = f23(B) | -incident_o(A,B) | ordered_by(B,f23(B),A). [resolve(49,d,45,a)]. 0.72/1.03 Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | f15(B,C) != B. [resolve(49,d,46,c)]. 0.72/1.03 Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | incident_o(f15(B,C),C). [resolve(49,d,47,c)]. 0.72/1.03 Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | -ordered_by(C,B,f15(B,C)). [resolve(49,d,48,c)]. 0.72/1.03 50 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom). [clausify(11)]. 0.72/1.03 51 closed(A) | end_point(f9(A),A) # label(closed_defn) # label(axiom). [clausify(11)]. 0.72/1.03 Derived: -end_point(A,B) | end_point(f9(B),B). [resolve(50,a,51,a)]. 0.72/1.03 52 -closed(A) | -meet(B,C,D) | sum(C,D) != A | -end_point(E,C) | meet(E,C,D) # label(c7) # label(axiom). [clausify(9)]. 0.72/1.03 Derived: -meet(A,B,C) | sum(B,C) != D | -end_point(E,B) | meet(E,B,C) | end_point(f9(D),D). [resolve(52,a,51,a)]. 0.72/1.03 53 finish_point(A,B) | incident_o(f22(A,B),B) | -incident_o(A,B) # label(finish_point_defn) # label(axiom). [clausify(24)]. 0.72/1.03 54 -finish_point(A,B) | incident_o(A,B) # label(finish_point_defn) # label(axiom). [clausify(24)]. 0.72/1.03 55 finish_point(A,B) | f22(A,B) != A | -incident_o(A,B) # label(finish_point_defn) # label(axiom). [clausify(24)]. 0.72/1.03 56 finish_point(A,B) | -ordered_by(B,f22(A,B),A) | -incident_o(A,B) # label(finish_point_defn) # label(axiom). [clausify(24)]. 0.72/1.03 57 -finish_point(A,B) | -incident_o(C,B) | C = A | ordered_by(B,C,A) # label(finish_point_defn) # label(axiom). [clausify(24)]. 0.72/1.03 Derived: -incident_o(A,B) | A = C | ordered_by(B,A,C) | incident_o(f22(C,B),B) | -incident_o(C,B). [resolve(57,a,53,a)]. 0.72/1.03 Derived: -incident_o(A,B) | A = C | ordered_by(B,A,C) | f22(C,B) != C | -incident_o(C,B). [resolve(57,a,55,a)]. 0.72/1.03 Derived: -incident_o(A,B) | A = C | ordered_by(B,A,C) | -ordered_by(B,f22(C,B),C) | -incident_o(C,B). [resolve(57,a,56,a)]. 0.72/1.03 58 between_o(A,B,C,D) | -ordered_by(A,D,C) | -ordered_by(A,C,B) # label(between_o_defn) # label(axiom). [clausify(27)]. 0.72/1.03 59 -between_o(A,B,C,D) | ordered_by(A,D,C) | ordered_by(A,B,C) # label(between_o_defn) # label(axiom). [clausify(27)]. 0.72/1.03 60 -between_o(A,B,C,D) | ordered_by(A,D,C) | ordered_by(A,C,D) # label(between_o_defn) # label(axiom). [clausify(27)]. 0.72/1.03 61 -between_o(A,B,C,D) | ordered_by(A,C,B) | ordered_by(A,B,C) # label(between_o_defn) # label(axiom). [clausify(27)]. 0.72/1.03 62 -between_o(A,B,C,D) | ordered_by(A,C,B) | ordered_by(A,C,D) # label(between_o_defn) # label(axiom). [clausify(27)]. 0.72/1.03 63 between_o(A,B,C,D) | -ordered_by(A,B,C) | -ordered_by(A,C,D) # label(between_o_defn) # label(axiom). [clausify(27)]. 0.72/1.03 64 -between_o(A,B,C,D) | between_c(f19(B,C,D,A),B,C,D) # label(o3) # label(axiom). [clausify(21)]. 0.72/1.03 Derived: between_c(f19(A,B,C,D),A,B,C) | -ordered_by(D,C,B) | -ordered_by(D,B,A). [resolve(64,a,58,a)]. 0.72/1.03 Derived: between_c(f19(A,B,C,D),A,B,C) | -ordered_by(D,A,B) | -ordered_by(D,B,C). [resolve(64,a,63,a)]. 0.72/1.03 65 -between_o(A,B,C,D) | -incident_c(E,f19(B,C,D,A)) | incident_o(E,A) # label(o3) # label(axiom). [clausify(21)]. 0.72/1.03 Derived: -incident_c(A,f19(B,C,D,E)) | incident_o(A,E) | -ordered_by(E,D,C) | -ordered_by(E,C,B). [resolve(65,a,58,a)]. 0.72/1.03 Derived: -incident_c(A,f19(B,C,D,E)) | incident_o(A,E) | -ordered_by(E,B,C) | -ordered_by(E,C,D). [resolve(65,a,63,a)]. 0.72/1.03 66 -between_o(A,B,C,D) | incident_c(E,f19(B,C,D,A)) | -incident_o(E,A) # label(o3) # label(axiom). [clausify(21)]. 0.72/1.03 Derived: incident_c(A,f19(B,C,D,E)) | -incident_o(A,E) | -ordered_by(E,D,C) | -ordered_by(E,C,B). [resolve(66,a,58,a)]. 0.72/1.03 Derived: incident_c(A,f19(B,C,D,E)) | -incident_o(A,E) | -ordered_by(E,B,C) | -ordered_by(E,C,D). [resolve(66,a,63,a)]. 0.72/1.03 67 between_o(A,B,C,D) | incident_c(f20(B,C,D,A,E),E) | incident_o(f20(B,C,D,A,E),A) | -between_c(E,B,C,D) # label(o3) # label(axiom). [clausify(21)]. 0.72/1.03 Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,A,B). [resolve(67,a,59,a)]. 0.72/1.03 Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,B,C). [resolve(67,a,60,a)]. 0.72/1.03 Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,A,B). [resolve(67,a,61,a)]. 0.72/1.03 Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,B,C). [resolve(67,a,62,a)]. 1.53/1.86 Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_c(f19(A,B,C,D),A,B,C). [resolve(67,a,64,a)]. 1.53/1.86 Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | -incident_c(F,f19(A,B,C,D)) | incident_o(F,D). [resolve(67,a,65,a)]. 1.53/1.86 Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | incident_c(F,f19(A,B,C,D)) | -incident_o(F,D). [resolve(67,a,66,a)]. 1.53/1.86 68 between_o(A,B,C,D) | -incident_c(f20(B,C,D,A,E),E) | -incident_o(f20(B,C,D,A,E),A) | -between_c(E,B,C,D) # label(o3) # label(axiom). [clausify(21)]. 1.53/1.86 Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,A,B). [resolve(68,a,59,a)]. 1.53/1.86 Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,B,C). [resolve(68,a,60,a)]. 1.53/1.86 Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,A,B). [resolve(68,a,61,a)]. 1.53/1.86 Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,B,C). [resolve(68,a,62,a)]. 1.53/1.86 Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_c(f19(A,B,C,D),A,B,C). [resolve(68,a,64,a)]. 1.53/1.86 Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | -incident_c(F,f19(A,B,C,D)) | incident_o(F,D). [resolve(68,a,65,a)]. 1.53/1.86 Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | incident_c(F,f19(A,B,C,D)) | -incident_o(F,D). [resolve(68,a,66,a)]. 1.53/1.86 1.53/1.86 ============================== end predicate elimination ============= 1.53/1.86 1.53/1.86 Auto_denials: (non-Horn, no changes). 1.53/1.86 1.53/1.86 Term ordering decisions: 1.53/1.86 Function symbol KB weights: c10=1. sum=1. f1=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f10=1. f15=1. f17=1. f18=1. f21=1. f22=1. underlying_curve=1. f9=1. f12=1. f13=1. f16=1. f23=1. f2=1. f11=1. f24=1. f14=1. f19=1. f20=1. 1.53/1.86 1.53/1.86 ============================== end of process initial clauses ======== 1.53/1.86 1.53/1.86 ============================== CLAUSES FOR SEARCH ==================== 1.53/1.86 1.53/1.86 ============================== end of clauses for search ============= 1.53/1.86 1.53/1.86 ============================== SEARCH ================================ 1.53/1.86 1.53/1.86 % Starting search at 0.02 seconds. 1.53/1.86 1.53/1.86 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 0.50 sec). 1.53/1.86 1.53/1.86 Low Water (keep): wt=46.000, iters=3442 1.53/1.86 1.53/1.86 Low Water (keep): wt=43.000, iters=3335 1.53/1.86 1.53/1.86 Low Water (keep): wt=42.000, iters=3410 1.53/1.86 1.53/1.86 Low Water (keep): wt=41.000, iters=3338 1.53/1.86 1.53/1.86 Low Water (keep): wt=40.000, iters=3375 1.53/1.86 1.53/1.86 Low Water (keep): wt=39.000, iters=3340 1.53/1.86 1.53/1.86 ============================== PROOF ================================= 1.53/1.86 % SZS status Theorem 1.53/1.86 % SZS output start Refutation 1.53/1.86 1.53/1.86 % Proof 1 at 0.82 (+ 0.02) seconds. 1.53/1.86 % Length of proof is 53. 1.53/1.86 % Level of proof is 9. 1.53/1.86 % Maximum clause weight is 15.000. 1.53/1.86 % Given clauses 802. 1.53/1.86 1.53/1.86 4 (all C all P (inner_point(P,C) -> (exists C1 exists C2 (sum(C1,C2) = C & meet(P,C1,C2))))) # label(c4) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 5 (all P all C ((all C1 all C2 (part_of(C1,C) & incident_c(P,C2) & part_of(C2,C) & incident_c(P,C1) -> part_of(C2,C1) | part_of(C1,C2))) & incident_c(P,C) <-> end_point(P,C))) # label(end_point_defn) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 11 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 14 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 15 (all C ((exists P end_point(P,C)) <-> open(C))) # label(open_defn) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 16 (all P all C (inner_point(P,C) <-> incident_c(P,C) & -end_point(P,C))) # label(inner_point_defn) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 18 (all P all O (incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,P,Q))) <-> start_point(P,O))) # label(start_point_defn) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 19 (all O exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & open(C))) # label(o2) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 23 (all C all O ((all P (incident_o(P,O) <-> incident_c(P,C))) <-> C = underlying_curve(O))) # label(underlying_curve_defn) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 25 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause). [assumption]. 1.53/1.86 28 -(all O exists P exists Q (Q != P & ordered_by(O,P,Q))) # label(theorem_4_11) # label(negated_conjecture) # label(non_clause). [assumption]. 1.53/1.86 29 end_point(f13(A),A) | -open(A) # label(open_defn) # label(axiom). [clausify(15)]. 1.53/1.86 30 open(f16(A)) # label(o2) # label(axiom). [clausify(19)]. 1.53/1.86 36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(16)]. 1.53/1.86 37 inner_point(f12(A),A) # label(c3) # label(axiom). [clausify(14)]. 1.53/1.86 38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom). [clausify(16)]. 1.53/1.86 41 -inner_point(A,B) | sum(f4(B,A),f5(B,A)) = B # label(c4) # label(axiom). [clausify(4)]. 1.53/1.86 45 start_point(f23(A),A) # label(o4) # label(axiom). [clausify(25)]. 1.53/1.86 49 A = B | -incident_o(A,C) | ordered_by(C,B,A) | -start_point(B,C) # label(start_point_defn) # label(axiom). [clausify(18)]. 1.53/1.86 50 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom). [clausify(11)]. 1.53/1.86 51 closed(A) | end_point(f9(A),A) # label(closed_defn) # label(axiom). [clausify(11)]. 1.53/1.86 71 incident_o(f21(A,B),B) | incident_c(f21(A,B),A) | underlying_curve(B) = A # label(underlying_curve_defn) # label(axiom). [clausify(23)]. 1.53/1.86 76 incident_c(A,B) | -end_point(A,B) # label(end_point_defn) # label(axiom). [clausify(5)]. 1.53/1.86 79 -incident_o(A,B) | incident_c(A,f16(B)) # label(o2) # label(axiom). [clausify(19)]. 1.53/1.86 80 incident_o(A,B) | -incident_c(A,f16(B)) # label(o2) # label(axiom). [clausify(19)]. 1.53/1.86 83 A = B | -ordered_by(c10,B,A) # label(theorem_4_11) # label(negated_conjecture). [clausify(28)]. 1.53/1.86 88 incident_o(A,B) | -incident_c(A,C) | underlying_curve(B) != C # label(underlying_curve_defn) # label(axiom). [clausify(23)]. 1.53/1.86 106 -incident_o(f21(A,B),B) | -incident_c(f21(A,B),A) | underlying_curve(B) = A # label(underlying_curve_defn) # label(axiom). [clausify(23)]. 1.53/1.86 116 end_point(f13(f16(A)),f16(A)). [resolve(29,b,30,a)]. 1.53/1.86 128 -end_point(f12(A),A). [resolve(36,a,37,a)]. 1.53/1.86 129 incident_c(f12(A),A). [resolve(38,a,37,a)]. 1.53/1.86 132 sum(f4(A,f12(A)),f5(A,f12(A))) = A. [resolve(41,a,37,a)]. 1.53/1.86 142 A = f23(B) | -incident_o(A,B) | ordered_by(B,f23(B),A). [resolve(49,d,45,a)]. 1.53/1.86 143 f23(A) = B | -incident_o(B,A) | ordered_by(A,f23(A),B). [copy(142),flip(a)]. 1.53/1.86 147 -end_point(A,B) | end_point(f9(B),B). [resolve(50,a,51,a)]. 1.53/1.86 209 incident_c(f21(A,B),f16(B)) | incident_c(f21(A,B),A) | underlying_curve(B) = A. [resolve(79,a,71,a)]. 1.53/1.86 210 incident_c(f21(f16(A),A),f16(A)) | f16(A) = underlying_curve(A). [factor(209,a,b),flip(b)]. 1.53/1.86 493 incident_o(f12(A),B) | underlying_curve(B) != A. [resolve(129,a,88,b)]. 1.53/1.86 531 end_point(f9(f16(A)),f16(A)). [resolve(147,a,116,a)]. 1.53/1.86 841 f16(A) = underlying_curve(A) | incident_o(f21(f16(A),A),A). [resolve(210,a,80,b)]. 1.53/1.86 881 incident_c(f9(f16(A)),f16(A)). [resolve(531,a,76,b)]. 1.53/1.86 902 incident_o(f9(f16(A)),A). [resolve(881,a,80,b)]. 1.53/1.86 941 f9(f16(A)) = f23(A) | ordered_by(A,f23(A),f9(f16(A))). [resolve(902,a,143,b),flip(a)]. 1.53/1.86 1036 incident_o(f12(underlying_curve(A)),A). [resolve(493,b,132,a(flip)),rewrite([132(9)])]. 1.53/1.86 1045 f12(underlying_curve(A)) = f23(A) | ordered_by(A,f23(A),f12(underlying_curve(A))). [resolve(1036,a,143,b),flip(a)]. 1.53/1.86 2238 f16(A) = underlying_curve(A) | -incident_c(f21(f16(A),A),f16(A)). [resolve(841,b,106,a),flip(c),merge(c)]. 1.53/1.86 4065 f16(A) = underlying_curve(A). [resolve(2238,b,210,a),merge(b)]. 1.53/1.86 4623 f9(underlying_curve(A)) = f23(A) | ordered_by(A,f23(A),f9(underlying_curve(A))). [back_rewrite(941),rewrite([4065(1),4065(6)])]. 1.53/1.86 4762 end_point(f9(underlying_curve(A)),underlying_curve(A)). [back_rewrite(531),rewrite([4065(1),4065(3)])]. 1.53/1.86 5687 f12(underlying_curve(c10)) = f23(c10). [resolve(1045,b,83,b),merge(b)]. 1.53/1.86 5688 -end_point(f23(c10),underlying_curve(c10)). [para(5687(a,1),128(a,1))]. 1.53/1.86 9426 f9(underlying_curve(c10)) = f23(c10). [resolve(4623,b,83,b),merge(b)]. 1.53/1.86 9429 $F. [para(9426(a,1),4762(a,1)),unit_del(a,5688)]. 1.53/1.86 1.53/1.86 % SZS output end Refutation 1.53/1.86 ============================== end of proof ========================== 1.53/1.86 1.53/1.86 ============================== STATISTICS ============================ 1.53/1.86 1.53/1.86 Given=802. Generated=18020. Kept=9358. proofs=1. 1.53/1.86 Usable=662. Sos=6885. Demods=8. Limbo=2, Disabled=1950. Hints=0. 1.53/1.86 Megabytes=12.11. 1.53/1.86 User_CPU=0.82, System_CPU=0.02, Wall_clock=1. 1.53/1.86 1.53/1.86 ============================== end of statistics ===================== 1.53/1.86 1.53/1.86 ============================== end of search ========================= 1.53/1.86 1.53/1.86 THEOREM PROVED 1.53/1.86 % SZS status Theorem 1.53/1.86 1.53/1.86 Exiting with 1 proof. 1.53/1.86 1.53/1.86 Process 6902 exit (max_proofs) Thu Jul 2 07:39:22 2020 1.53/1.86 Prover9 interrupted 1.53/1.87 EOF