0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.32 % Computer : n009.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Aug 9 04:50:35 EDT 2022 0.11/0.34 % CPUTime : 0.70/1.29 ============================== Prover9 =============================== 0.70/1.29 Prover9 (32) version 2009-11A, November 2009. 0.70/1.29 Process 25001 was started by sandbox2 on n009.cluster.edu, 0.70/1.29 Tue Aug 9 04:50:36 2022 0.70/1.29 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_24845_n009.cluster.edu". 0.70/1.29 ============================== end of head =========================== 0.70/1.29 0.70/1.29 ============================== INPUT ================================= 0.70/1.29 0.70/1.29 % Reading from file /tmp/Prover9_24845_n009.cluster.edu 0.70/1.29 0.70/1.29 set(prolog_style_variables). 0.70/1.29 set(auto2). 0.70/1.29 % set(auto2) -> set(auto). 0.70/1.29 % set(auto) -> set(auto_inference). 0.70/1.29 % set(auto) -> set(auto_setup). 0.70/1.29 % set(auto_setup) -> set(predicate_elim). 0.70/1.29 % set(auto_setup) -> assign(eq_defs, unfold). 0.70/1.29 % set(auto) -> set(auto_limits). 0.70/1.29 % set(auto_limits) -> assign(max_weight, "100.000"). 0.70/1.29 % set(auto_limits) -> assign(sos_limit, 20000). 0.70/1.29 % set(auto) -> set(auto_denials). 0.70/1.29 % set(auto) -> set(auto_process). 0.70/1.29 % set(auto2) -> assign(new_constants, 1). 0.70/1.29 % set(auto2) -> assign(fold_denial_max, 3). 0.70/1.29 % set(auto2) -> assign(max_weight, "200.000"). 0.70/1.29 % set(auto2) -> assign(max_hours, 1). 0.70/1.29 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.70/1.29 % set(auto2) -> assign(max_seconds, 0). 0.70/1.29 % set(auto2) -> assign(max_minutes, 5). 0.70/1.29 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.70/1.29 % set(auto2) -> set(sort_initial_sos). 0.70/1.29 % set(auto2) -> assign(sos_limit, -1). 0.70/1.29 % set(auto2) -> assign(lrs_ticks, 3000). 0.70/1.29 % set(auto2) -> assign(max_megs, 400). 0.70/1.29 % set(auto2) -> assign(stats, some). 0.70/1.29 % set(auto2) -> clear(echo_input). 0.70/1.29 % set(auto2) -> set(quiet). 0.70/1.29 % set(auto2) -> clear(print_initial_clauses). 0.70/1.29 % set(auto2) -> clear(print_given). 0.70/1.29 assign(lrs_ticks,-1). 0.70/1.29 assign(sos_limit,10000). 0.70/1.29 assign(order,kbo). 0.70/1.29 set(lex_order_vars). 0.70/1.29 clear(print_given). 0.70/1.29 0.70/1.29 % formulas(sos). % not echoed (10 formulas) 0.70/1.29 0.70/1.29 ============================== end of input ========================== 0.70/1.29 0.70/1.29 % From the command line: assign(max_seconds, 960). 0.70/1.29 0.70/1.29 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.70/1.29 0.70/1.29 % Formulas that are not ordinary clauses: 0.70/1.29 1 (all A all B all C (transitive_reflexive_rewrite(A,B) & transitive_reflexive_rewrite(B,C) -> transitive_reflexive_rewrite(A,C))) # label(transitivity_of_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 0.70/1.29 2 (all A all B (rewrite(A,B) -> transitive_reflexive_rewrite(A,B))) # label(rewrite_in_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 0.70/1.29 3 (all A (transitive_reflexive_rewrite(b,A) & transitive_reflexive_rewrite(c,A) -> goal)) # label(found) # label(axiom) # label(non_clause). [assumption]. 0.70/1.29 4 (all A all B (A = B -> transitive_reflexive_rewrite(A,B))) # label(equality_in_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 0.70/1.29 5 (all A all B all C (rewrite(A,C) & rewrite(A,B) -> (exists D (transitive_reflexive_rewrite(B,D) & transitive_reflexive_rewrite(C,D))))) # label(lo_cfl) # label(axiom) # label(non_clause). [assumption]. 0.70/1.29 6 (all A all B all C (transitive_reflexive_rewrite(A,B) & transitive_reflexive_rewrite(A,C) & rewrite(a,A) -> (exists D (transitive_reflexive_rewrite(C,D) & transitive_reflexive_rewrite(B,D))))) # label(ih_cfl) # label(axiom) # label(non_clause). [assumption]. 0.70/1.29 7 (all A all B (transitive_reflexive_rewrite(A,B) -> B = A | (exists C (rewrite(A,C) & transitive_reflexive_rewrite(C,B))))) # label(equal_or_rewrite) # label(axiom) # label(non_clause). [assumption]. 0.70/1.29 0.70/1.29 ============================== end of process non-clausal formulas === 0.70/1.29 0.70/1.29 ============================== PROCESS INITIAL CLAUSES =============== 0.70/1.29 0.70/1.29 ============================== PREDICATE ELIMINATION ================= 0.70/1.29 0.70/1.29 ============================== end predicate elimination ============= 0.70/1.29 0.70/1.29 Auto_denials: (non-Horn, no changes). 0.70/1.29 0.70/1.29 Term ordering decisions: 0.70/1.29 Function symbol KB weights: a=1. b=1. c=1. f3=1. f1=1. f2=1. 0.70/1.29 0.70/1.29 ============================== end of process initial clauses ======== 0.70/1.29 0.70/1.29 ============================== CLAUSES FOR SEARCH ==================== 0.70/1.29 0.70/1.29 ============================== end of clauses for search ============= 24.10/24.73 24.10/24.73 ============================== SEARCH ================================ 24.10/24.73 24.10/24.73 % Starting search at 0.01 seconds. 24.10/24.73 24.10/24.73 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.25 sec). 24.10/24.73 24.10/24.73 Low Water (keep): wt=63.000, iters=3350 24.10/24.73 24.10/24.73 Low Water (keep): wt=53.000, iters=3345 24.10/24.73 24.10/24.73 Low Water (keep): wt=48.000, iters=3366 24.10/24.73 24.10/24.73 Low Water (keep): wt=43.000, iters=3358 24.10/24.73 24.10/24.73 Low Water (keep): wt=42.000, iters=3418 24.10/24.73 24.10/24.73 Low Water (keep): wt=41.000, iters=3471 24.10/24.73 24.10/24.73 Low Water (keep): wt=40.000, iters=3344 24.10/24.73 24.10/24.73 Low Water (keep): wt=39.000, iters=3505 24.10/24.73 24.10/24.73 Low Water (keep): wt=38.000, iters=3355 24.10/24.73 24.10/24.73 Low Water (keep): wt=36.000, iters=3353 24.10/24.73 24.10/24.73 Low Water (keep): wt=35.000, iters=3436 24.10/24.73 24.10/24.73 Low Water (keep): wt=34.000, iters=3357 24.10/24.73 24.10/24.73 Low Water (keep): wt=33.000, iters=3333 24.10/24.73 24.10/24.73 Low Water (keep): wt=32.000, iters=3346 24.10/24.73 24.10/24.73 Low Water (keep): wt=31.000, iters=3343 24.10/24.73 24.10/24.73 Low Water (keep): wt=30.000, iters=3349 24.10/24.73 24.10/24.73 Low Water (displace): id=10825, wt=35.000 24.10/24.73 24.10/24.73 Low Water (keep): wt=29.000, iters=3344 24.10/24.73 24.10/24.73 Low Water (displace): id=10869, wt=34.000 24.10/24.73 24.10/24.73 Low Water (displace): id=9921, wt=33.000 24.10/24.73 24.10/24.73 Low Water (displace): id=10879, wt=32.000 24.10/24.73 24.10/24.73 Low Water (displace): id=12116, wt=31.000 24.10/24.73 24.10/24.73 Low Water (keep): wt=28.000, iters=3364 24.10/24.73 24.10/24.73 Low Water (displace): id=10882, wt=30.000 24.10/24.73 24.10/24.73 Low Water (keep): wt=27.000, iters=3337 24.10/24.73 24.10/24.73 Low Water (displace): id=13035, wt=29.000 24.10/24.73 24.10/24.73 Low Water (displace): id=13992, wt=28.000 24.10/24.73 24.10/24.73 Low Water (displace): id=14917, wt=27.000 24.10/24.73 24.10/24.73 ============================== PROOF ================================= 24.10/24.73 % SZS status Theorem 24.10/24.73 % SZS output start Refutation 24.10/24.73 24.10/24.73 % Proof 1 at 23.37 (+ 0.08) seconds. 24.10/24.73 % Length of proof is 55. 24.10/24.73 % Level of proof is 13. 24.10/24.73 % Maximum clause weight is 32.000. 24.10/24.73 % Given clauses 4557. 24.10/24.73 24.10/24.73 1 (all A all B all C (transitive_reflexive_rewrite(A,B) & transitive_reflexive_rewrite(B,C) -> transitive_reflexive_rewrite(A,C))) # label(transitivity_of_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 24.10/24.73 3 (all A (transitive_reflexive_rewrite(b,A) & transitive_reflexive_rewrite(c,A) -> goal)) # label(found) # label(axiom) # label(non_clause). [assumption]. 24.10/24.73 4 (all A all B (A = B -> transitive_reflexive_rewrite(A,B))) # label(equality_in_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 24.10/24.73 5 (all A all B all C (rewrite(A,C) & rewrite(A,B) -> (exists D (transitive_reflexive_rewrite(B,D) & transitive_reflexive_rewrite(C,D))))) # label(lo_cfl) # label(axiom) # label(non_clause). [assumption]. 24.10/24.73 6 (all A all B all C (transitive_reflexive_rewrite(A,B) & transitive_reflexive_rewrite(A,C) & rewrite(a,A) -> (exists D (transitive_reflexive_rewrite(C,D) & transitive_reflexive_rewrite(B,D))))) # label(ih_cfl) # label(axiom) # label(non_clause). [assumption]. 24.10/24.73 7 (all A all B (transitive_reflexive_rewrite(A,B) -> B = A | (exists C (rewrite(A,C) & transitive_reflexive_rewrite(C,B))))) # label(equal_or_rewrite) # label(axiom) # label(non_clause). [assumption]. 24.10/24.73 8 transitive_reflexive_rewrite(a,c) # label(assumption_AndLHS) # label(axiom). [assumption]. 24.10/24.73 9 transitive_reflexive_rewrite(a,b) # label(assumption_AndRHS) # label(axiom). [assumption]. 24.10/24.73 10 -goal # label(goal_to_be_proved) # label(negated_conjecture). [assumption]. 24.10/24.73 12 A != B | transitive_reflexive_rewrite(B,A) # label(equality_in_transitive_reflexive_rewrite) # label(axiom). [clausify(4)]. 24.10/24.73 13 -transitive_reflexive_rewrite(b,A) | -transitive_reflexive_rewrite(c,A) | goal # label(found) # label(axiom). [clausify(3)]. 24.10/24.73 14 -transitive_reflexive_rewrite(b,A) | -transitive_reflexive_rewrite(c,A). [copy(13),unit_del(c,10)]. 24.10/24.73 15 -transitive_reflexive_rewrite(A,B) | -transitive_reflexive_rewrite(B,C) | transitive_reflexive_rewrite(A,C) # label(transitivity_of_transitive_reflexive_rewrite) # label(axiom). [clausify(1)]. 24.10/24.73 16 -transitive_reflexive_rewrite(A,B) | B = A | rewrite(A,f3(A,B)) # label(equal_or_rewrite) # label(axiom). [clausify(7)]. 24.10/24.73 17 -transitive_reflexive_rewrite(A,B) | B = A | transitive_reflexive_rewrite(f3(A,B),B) # label(equal_or_rewrite) # label(axiom). [clausify(7)]. 24.10/24.73 18 -rewrite(A,B) | -rewrite(A,C) | transitive_reflexive_rewrite(C,f1(A,C,B)) # label(lo_cfl) # label(axiom). [clausify(5)]. 24.10/24.73 19 -rewrite(A,B) | -rewrite(A,C) | transitive_reflexive_rewrite(B,f1(A,C,B)) # label(lo_cfl) # label(axiom). [clausify(5)]. 24.10/24.73 20 -transitive_reflexive_rewrite(A,B) | -transitive_reflexive_rewrite(A,C) | -rewrite(a,A) | transitive_reflexive_rewrite(C,f2(A,B,C)) # label(ih_cfl) # label(axiom). [clausify(6)]. 24.10/24.73 21 -transitive_reflexive_rewrite(A,B) | -transitive_reflexive_rewrite(A,C) | -rewrite(a,A) | transitive_reflexive_rewrite(B,f2(A,B,C)) # label(ih_cfl) # label(axiom). [clausify(6)]. 24.10/24.73 24 transitive_reflexive_rewrite(A,A). [xx_res(12,a)]. 24.10/24.73 29 b = a | rewrite(a,f3(a,b)). [resolve(16,a,9,a)]. 24.10/24.73 30 c = a | rewrite(a,f3(a,c)). [resolve(16,a,8,a)]. 24.10/24.73 31 b = a | transitive_reflexive_rewrite(f3(a,b),b). [resolve(17,a,9,a)]. 24.10/24.73 32 c = a | transitive_reflexive_rewrite(f3(a,c),c). [resolve(17,a,8,a)]. 24.10/24.73 33 -transitive_reflexive_rewrite(b,c). [resolve(24,a,14,b)]. 24.10/24.73 34 -transitive_reflexive_rewrite(c,b). [ur(14,a,24,a)]. 24.10/24.73 35 -transitive_reflexive_rewrite(b,a). [ur(15,b,8,a,c,33,a)]. 24.10/24.73 38 -transitive_reflexive_rewrite(c,a). [ur(15,b,9,a,c,34,a)]. 24.10/24.73 40 b != a. [ur(12,b,35,a),flip(a)]. 24.10/24.73 42 transitive_reflexive_rewrite(f3(a,b),b). [back_unit_del(31),unit_del(a,40)]. 24.10/24.73 43 rewrite(a,f3(a,b)). [back_unit_del(29),unit_del(a,40)]. 24.10/24.73 51 -transitive_reflexive_rewrite(f3(a,b),A) | -transitive_reflexive_rewrite(f3(a,b),B) | transitive_reflexive_rewrite(A,f2(f3(a,b),A,B)). [resolve(43,a,21,c)]. 24.10/24.73 52 -transitive_reflexive_rewrite(f3(a,b),A) | -transitive_reflexive_rewrite(f3(a,b),B) | transitive_reflexive_rewrite(B,f2(f3(a,b),A,B)). [resolve(43,a,20,c)]. 24.10/24.73 53 -rewrite(a,A) | transitive_reflexive_rewrite(A,f1(a,f3(a,b),A)). [resolve(43,a,19,b)]. 24.10/24.73 62 c != a. [ur(12,b,38,a),flip(a)]. 24.10/24.73 64 transitive_reflexive_rewrite(f3(a,c),c). [back_unit_del(32),unit_del(a,62)]. 24.10/24.73 65 rewrite(a,f3(a,c)). [back_unit_del(30),unit_del(a,62)]. 24.10/24.73 73 -transitive_reflexive_rewrite(f3(a,c),A) | -transitive_reflexive_rewrite(f3(a,c),B) | transitive_reflexive_rewrite(A,f2(f3(a,c),A,B)). [resolve(65,a,21,c)]. 24.10/24.73 74 -transitive_reflexive_rewrite(f3(a,c),A) | -transitive_reflexive_rewrite(f3(a,c),B) | transitive_reflexive_rewrite(B,f2(f3(a,c),A,B)). [resolve(65,a,20,c)]. 24.10/24.73 78 -rewrite(a,A) | transitive_reflexive_rewrite(A,f1(a,A,f3(a,c))). [resolve(65,a,18,a)]. 24.10/24.73 98 transitive_reflexive_rewrite(f3(a,c),f1(a,f3(a,b),f3(a,c))). [resolve(53,a,65,a)]. 24.10/24.73 101 transitive_reflexive_rewrite(f3(a,b),f1(a,f3(a,b),f3(a,c))). [resolve(78,a,43,a)]. 24.10/24.73 164 -transitive_reflexive_rewrite(f3(a,b),A) | transitive_reflexive_rewrite(A,f2(f3(a,b),A,b)). [resolve(51,b,42,a)]. 24.10/24.73 189 -transitive_reflexive_rewrite(f3(a,b),A) | transitive_reflexive_rewrite(b,f2(f3(a,b),A,b)). [resolve(52,b,42,a)]. 24.10/24.73 219 -transitive_reflexive_rewrite(f1(a,f3(a,b),f3(a,c)),A) | transitive_reflexive_rewrite(f3(a,c),A). [resolve(98,a,15,a)]. 24.10/24.73 339 -transitive_reflexive_rewrite(f3(a,c),A) | transitive_reflexive_rewrite(A,f2(f3(a,c),A,c)). [resolve(73,b,64,a)]. 24.10/24.73 364 -transitive_reflexive_rewrite(f3(a,c),A) | transitive_reflexive_rewrite(c,f2(f3(a,c),A,c)). [resolve(74,b,64,a)]. 24.10/24.73 418 transitive_reflexive_rewrite(f1(a,f3(a,b),f3(a,c)),f2(f3(a,b),f1(a,f3(a,b),f3(a,c)),b)). [resolve(164,a,101,a)]. 24.10/24.73 482 transitive_reflexive_rewrite(b,f2(f3(a,b),f1(a,f3(a,b),f3(a,c)),b)). [resolve(189,a,101,a)]. 24.10/24.73 1212 -transitive_reflexive_rewrite(f2(f3(a,b),f1(a,f3(a,b),f3(a,c)),b),A) | transitive_reflexive_rewrite(b,A). [resolve(482,a,15,a)]. 24.10/24.73 8066 transitive_reflexive_rewrite(f3(a,c),f2(f3(a,b),f1(a,f3(a,b),f3(a,c)),b)). [resolve(418,a,219,a)]. 24.10/24.73 8832 transitive_reflexive_rewrite(c,f2(f3(a,c),f2(f3(a,b),f1(a,f3(a,b),f3(a,c)),b),c)). [resolve(8066,a,364,a)]. 24.10/24.73 8835 transitive_reflexive_rewrite(f2(f3(a,b),f1(a,f3(a,b),f3(a,c)),b),f2(f3(a,c),f2(f3(a,b),f1(a,f3(a,b),f3(a,c)),b),c)). [resolve(8066,a,339,a)]. 24.10/24.73 14632 -transitive_reflexive_rewrite(b,f2(f3(a,c),f2(f3(a,b),f1(a,f3(a,b),f3(a,c)),b),c)). [resolve(8832,a,14,b)]. 24.10/24.73 17015 $F. [ur(1212,b,14632,a),unit_del(a,8835)]. 24.10/24.73 24.10/24.73 % SZS output end Refutation 24.10/24.73 ============================== end of proof ========================== 24.10/24.73 24.10/24.73 ============================== STATISTICS ============================ 24.10/24.74 24.10/24.74 Given=4557. Generated=61884. Kept=17006. proofs=1. 24.10/24.74 Usable=4472. Sos=9999. Demods=0. Limbo=0, Disabled=2548. Hints=0. 24.10/24.74 Megabytes=19.39. 24.10/24.74 User_CPU=23.37, System_CPU=0.08, Wall_clock=24. 24.10/24.74 24.10/24.74 ============================== end of statistics ===================== 24.10/24.74 24.10/24.74 ============================== end of search ========================= 24.10/24.74 24.10/24.74 THEOREM PROVED 24.10/24.74 % SZS status Theorem 24.10/24.74 24.10/24.74 Exiting with 1 proof. 24.10/24.74 24.10/24.74 Process 25001 exit (max_proofs) Tue Aug 9 04:51:00 2022 24.10/24.74 Prover9 interrupted 24.19/24.74 EOF