0.11/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.33 % Computer : n012.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 960 0.13/0.33 % DateTime : Thu Jul 2 08:21:06 EDT 2020 0.13/0.33 % CPUTime : 0.67/0.97 ============================== Prover9 =============================== 0.67/0.97 Prover9 (32) version 2009-11A, November 2009. 0.67/0.97 Process 23649 was started by sandbox2 on n012.cluster.edu, 0.67/0.97 Thu Jul 2 08:21:06 2020 0.67/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_23496_n012.cluster.edu". 0.67/0.97 ============================== end of head =========================== 0.67/0.97 0.67/0.97 ============================== INPUT ================================= 0.67/0.97 0.67/0.97 % Reading from file /tmp/Prover9_23496_n012.cluster.edu 0.67/0.97 0.67/0.97 set(prolog_style_variables). 0.67/0.97 set(auto2). 0.67/0.97 % set(auto2) -> set(auto). 0.67/0.97 % set(auto) -> set(auto_inference). 0.67/0.97 % set(auto) -> set(auto_setup). 0.67/0.97 % set(auto_setup) -> set(predicate_elim). 0.67/0.97 % set(auto_setup) -> assign(eq_defs, unfold). 0.67/0.97 % set(auto) -> set(auto_limits). 0.67/0.97 % set(auto_limits) -> assign(max_weight, "100.000"). 0.67/0.97 % set(auto_limits) -> assign(sos_limit, 20000). 0.67/0.97 % set(auto) -> set(auto_denials). 0.67/0.97 % set(auto) -> set(auto_process). 0.67/0.97 % set(auto2) -> assign(new_constants, 1). 0.67/0.97 % set(auto2) -> assign(fold_denial_max, 3). 0.67/0.97 % set(auto2) -> assign(max_weight, "200.000"). 0.67/0.97 % set(auto2) -> assign(max_hours, 1). 0.67/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.67/0.97 % set(auto2) -> assign(max_seconds, 0). 0.67/0.97 % set(auto2) -> assign(max_minutes, 5). 0.67/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.67/0.97 % set(auto2) -> set(sort_initial_sos). 0.67/0.97 % set(auto2) -> assign(sos_limit, -1). 0.67/0.97 % set(auto2) -> assign(lrs_ticks, 3000). 0.67/0.97 % set(auto2) -> assign(max_megs, 400). 0.67/0.97 % set(auto2) -> assign(stats, some). 0.67/0.97 % set(auto2) -> clear(echo_input). 0.67/0.97 % set(auto2) -> set(quiet). 0.67/0.97 % set(auto2) -> clear(print_initial_clauses). 0.67/0.97 % set(auto2) -> clear(print_given). 0.67/0.97 assign(lrs_ticks,-1). 0.67/0.97 assign(sos_limit,10000). 0.67/0.97 assign(order,kbo). 0.67/0.97 set(lex_order_vars). 0.67/0.97 clear(print_given). 0.67/0.97 0.67/0.97 % formulas(sos). % not echoed (10 formulas) 0.67/0.97 0.67/0.97 ============================== end of input ========================== 0.67/0.97 0.67/0.97 % From the command line: assign(max_seconds, 960). 0.67/0.97 0.67/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.67/0.97 0.67/0.97 % Formulas that are not ordinary clauses: 0.67/0.97 1 (all A all B all C (rewrite(a,A) & transitive_reflexive_rewrite(A,B) & transitive_reflexive_rewrite(A,C) -> (exists D (transitive_reflexive_rewrite(B,D) & transitive_reflexive_rewrite(C,D))))) # label(ih_cfl) # label(axiom) # label(non_clause). [assumption]. 0.67/0.97 2 (all A (transitive_reflexive_rewrite(b,A) & transitive_reflexive_rewrite(c,A) -> goal)) # label(found) # label(axiom) # label(non_clause). [assumption]. 0.67/0.97 3 (all A all B (rewrite(A,B) -> transitive_reflexive_rewrite(A,B))) # label(rewrite_in_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 0.67/0.97 4 (all A all B (B = A -> transitive_reflexive_rewrite(A,B))) # label(equality_in_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 0.67/0.97 5 (all A all B all C (transitive_reflexive_rewrite(B,C) & transitive_reflexive_rewrite(A,B) -> transitive_reflexive_rewrite(A,C))) # label(transitivity_of_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 0.67/0.97 6 (all A all B (transitive_reflexive_rewrite(A,B) -> A = B | (exists C (transitive_reflexive_rewrite(C,B) & rewrite(A,C))))) # label(equal_or_rewrite) # label(axiom) # label(non_clause). [assumption]. 0.67/0.97 7 (all A all B all C (rewrite(A,B) & rewrite(A,C) -> (exists D (transitive_reflexive_rewrite(C,D) & transitive_reflexive_rewrite(B,D))))) # label(lo_cfl) # label(axiom) # label(non_clause). [assumption]. 0.67/0.97 0.67/0.97 ============================== end of process non-clausal formulas === 0.67/0.97 0.67/0.97 ============================== PROCESS INITIAL CLAUSES =============== 0.67/0.97 0.67/0.97 ============================== PREDICATE ELIMINATION ================= 0.67/0.97 0.67/0.97 ============================== end predicate elimination ============= 0.67/0.97 0.67/0.97 Auto_denials: (non-Horn, no changes). 0.67/0.97 0.67/0.97 Term ordering decisions: 0.67/0.97 Function symbol KB weights: a=1. b=1. c=1. f2=1. f1=1. f3=1. 0.67/0.97 0.67/0.97 ============================== end of process initial clauses ======== 0.67/0.97 0.67/0.97 ============================== CLAUSES FOR SEARCH ==================== 0.67/0.97 0.67/0.97 ============================== end of clauses for search ============= 18.82/19.17 18.82/19.17 ============================== SEARCH ================================ 18.82/19.17 18.82/19.17 % Starting search at 0.01 seconds. 18.82/19.17 18.82/19.17 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.24 sec). 18.82/19.17 18.82/19.17 Low Water (keep): wt=67.000, iters=3503 18.82/19.17 18.82/19.17 Low Water (keep): wt=63.000, iters=3498 18.82/19.17 18.82/19.17 Low Water (keep): wt=48.000, iters=3380 18.82/19.17 18.82/19.17 Low Water (keep): wt=43.000, iters=3340 18.82/19.17 18.82/19.17 Low Water (keep): wt=42.000, iters=3415 18.82/19.17 18.82/19.17 Low Water (keep): wt=41.000, iters=3463 18.82/19.17 18.82/19.17 Low Water (keep): wt=39.000, iters=3340 18.82/19.17 18.82/19.17 Low Water (keep): wt=38.000, iters=3351 18.82/19.17 18.82/19.17 Low Water (keep): wt=37.000, iters=3400 18.82/19.17 18.82/19.17 Low Water (keep): wt=36.000, iters=3342 18.82/19.17 18.82/19.17 Low Water (keep): wt=35.000, iters=3566 18.82/19.17 18.82/19.17 Low Water (keep): wt=34.000, iters=3487 18.82/19.17 18.82/19.17 Low Water (keep): wt=33.000, iters=3348 18.82/19.17 18.82/19.17 Low Water (keep): wt=32.000, iters=3333 18.82/19.17 18.82/19.17 Low Water (keep): wt=31.000, iters=3350 18.82/19.17 18.82/19.17 Low Water (keep): wt=30.000, iters=3369 18.82/19.17 18.82/19.17 Low Water (keep): wt=29.000, iters=3335 18.82/19.17 18.82/19.17 Low Water (displace): id=10751, wt=35.000 18.82/19.17 18.82/19.17 Low Water (displace): id=10897, wt=34.000 18.82/19.17 18.82/19.17 Low Water (displace): id=9274, wt=33.000 18.82/19.17 18.82/19.17 Low Water (displace): id=11170, wt=32.000 18.82/19.17 18.82/19.17 Low Water (displace): id=11427, wt=31.000 18.82/19.17 18.82/19.17 Low Water (displace): id=11477, wt=30.000 18.82/19.17 18.82/19.17 Low Water (keep): wt=27.000, iters=3333 18.82/19.17 18.82/19.17 Low Water (displace): id=12862, wt=29.000 18.82/19.17 18.82/19.17 Low Water (displace): id=14285, wt=28.000 18.82/19.17 18.82/19.17 Low Water (displace): id=14982, wt=27.000 18.82/19.17 18.82/19.17 ============================== PROOF ================================= 18.82/19.17 % SZS status Theorem 18.82/19.17 % SZS output start Refutation 18.82/19.17 18.82/19.17 % Proof 1 at 18.15 (+ 0.04) seconds. 18.82/19.17 % Length of proof is 55. 18.82/19.17 % Level of proof is 13. 18.82/19.17 % Maximum clause weight is 32.000. 18.82/19.17 % Given clauses 4532. 18.82/19.17 18.82/19.17 1 (all A all B all C (rewrite(a,A) & transitive_reflexive_rewrite(A,B) & transitive_reflexive_rewrite(A,C) -> (exists D (transitive_reflexive_rewrite(B,D) & transitive_reflexive_rewrite(C,D))))) # label(ih_cfl) # label(axiom) # label(non_clause). [assumption]. 18.82/19.17 2 (all A (transitive_reflexive_rewrite(b,A) & transitive_reflexive_rewrite(c,A) -> goal)) # label(found) # label(axiom) # label(non_clause). [assumption]. 18.82/19.17 4 (all A all B (B = A -> transitive_reflexive_rewrite(A,B))) # label(equality_in_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 18.82/19.17 5 (all A all B all C (transitive_reflexive_rewrite(B,C) & transitive_reflexive_rewrite(A,B) -> transitive_reflexive_rewrite(A,C))) # label(transitivity_of_transitive_reflexive_rewrite) # label(axiom) # label(non_clause). [assumption]. 18.82/19.17 6 (all A all B (transitive_reflexive_rewrite(A,B) -> A = B | (exists C (transitive_reflexive_rewrite(C,B) & rewrite(A,C))))) # label(equal_or_rewrite) # label(axiom) # label(non_clause). [assumption]. 18.82/19.17 7 (all A all B all C (rewrite(A,B) & rewrite(A,C) -> (exists D (transitive_reflexive_rewrite(C,D) & transitive_reflexive_rewrite(B,D))))) # label(lo_cfl) # label(axiom) # label(non_clause). [assumption]. 18.82/19.17 8 transitive_reflexive_rewrite(a,c) # label(assumption_AndLHS) # label(axiom). [assumption]. 18.82/19.17 9 transitive_reflexive_rewrite(a,b) # label(assumption_AndRHS) # label(axiom). [assumption]. 18.82/19.17 10 -goal # label(goal_to_be_proved) # label(negated_conjecture). [assumption]. 18.82/19.17 12 A != B | transitive_reflexive_rewrite(B,A) # label(equality_in_transitive_reflexive_rewrite) # label(axiom). [clausify(4)]. 18.82/19.17 13 -transitive_reflexive_rewrite(b,A) | -transitive_reflexive_rewrite(c,A) | goal # label(found) # label(axiom). [clausify(2)]. 18.82/19.17 14 -transitive_reflexive_rewrite(b,A) | -transitive_reflexive_rewrite(c,A). [copy(13),unit_del(c,10)]. 18.82/19.17 15 -transitive_reflexive_rewrite(A,B) | -transitive_reflexive_rewrite(C,A) | transitive_reflexive_rewrite(C,B) # label(transitivity_of_transitive_reflexive_rewrite) # label(axiom). [clausify(5)]. 18.82/19.17 16 -transitive_reflexive_rewrite(A,B) | B = A | transitive_reflexive_rewrite(f2(A,B),B) # label(equal_or_rewrite) # label(axiom). [clausify(6)]. 18.82/19.17 17 -transitive_reflexive_rewrite(A,B) | B = A | rewrite(A,f2(A,B)) # label(equal_or_rewrite) # label(axiom). [clausify(6)]. 18.82/19.17 18 -rewrite(A,B) | -rewrite(A,C) | transitive_reflexive_rewrite(C,f3(A,B,C)) # label(lo_cfl) # label(axiom). [clausify(7)]. 18.82/19.17 19 -rewrite(A,B) | -rewrite(A,C) | transitive_reflexive_rewrite(B,f3(A,B,C)) # label(lo_cfl) # label(axiom). [clausify(7)]. 18.82/19.17 20 -rewrite(a,A) | -transitive_reflexive_rewrite(A,B) | -transitive_reflexive_rewrite(A,C) | transitive_reflexive_rewrite(B,f1(A,B,C)) # label(ih_cfl) # label(axiom). [clausify(1)]. 18.82/19.17 21 -rewrite(a,A) | -transitive_reflexive_rewrite(A,B) | -transitive_reflexive_rewrite(A,C) | transitive_reflexive_rewrite(C,f1(A,B,C)) # label(ih_cfl) # label(axiom). [clausify(1)]. 18.82/19.17 24 transitive_reflexive_rewrite(A,A). [xx_res(12,a)]. 18.82/19.17 29 b = a | transitive_reflexive_rewrite(f2(a,b),b). [resolve(16,a,9,a)]. 18.82/19.17 30 c = a | transitive_reflexive_rewrite(f2(a,c),c). [resolve(16,a,8,a)]. 18.82/19.17 31 b = a | rewrite(a,f2(a,b)). [resolve(17,a,9,a)]. 18.82/19.17 32 c = a | rewrite(a,f2(a,c)). [resolve(17,a,8,a)]. 18.82/19.17 33 -transitive_reflexive_rewrite(b,c). [resolve(24,a,14,b)]. 18.82/19.17 34 -transitive_reflexive_rewrite(c,b). [ur(14,a,24,a)]. 18.82/19.17 35 -transitive_reflexive_rewrite(b,a). [ur(15,a,8,a,c,33,a)]. 18.82/19.17 38 -transitive_reflexive_rewrite(c,a). [ur(15,a,9,a,c,34,a)]. 18.82/19.17 40 b != a. [ur(12,b,35,a),flip(a)]. 18.82/19.17 42 rewrite(a,f2(a,b)). [back_unit_del(31),unit_del(a,40)]. 18.82/19.17 43 transitive_reflexive_rewrite(f2(a,b),b). [back_unit_del(29),unit_del(a,40)]. 18.82/19.17 46 -transitive_reflexive_rewrite(f2(a,b),A) | -transitive_reflexive_rewrite(f2(a,b),B) | transitive_reflexive_rewrite(B,f1(f2(a,b),A,B)). [resolve(42,a,21,a)]. 18.82/19.17 47 -transitive_reflexive_rewrite(f2(a,b),A) | -transitive_reflexive_rewrite(f2(a,b),B) | transitive_reflexive_rewrite(A,f1(f2(a,b),A,B)). [resolve(42,a,20,a)]. 18.82/19.17 48 -rewrite(a,A) | transitive_reflexive_rewrite(A,f3(a,A,f2(a,b))). [resolve(42,a,19,b)]. 18.82/19.17 62 c != a. [ur(12,b,38,a),flip(a)]. 18.82/19.17 64 rewrite(a,f2(a,c)). [back_unit_del(32),unit_del(a,62)]. 18.82/19.17 65 transitive_reflexive_rewrite(f2(a,c),c). [back_unit_del(30),unit_del(a,62)]. 18.82/19.17 68 -transitive_reflexive_rewrite(f2(a,c),A) | -transitive_reflexive_rewrite(f2(a,c),B) | transitive_reflexive_rewrite(B,f1(f2(a,c),A,B)). [resolve(64,a,21,a)]. 18.82/19.17 69 -transitive_reflexive_rewrite(f2(a,c),A) | -transitive_reflexive_rewrite(f2(a,c),B) | transitive_reflexive_rewrite(A,f1(f2(a,c),A,B)). [resolve(64,a,20,a)]. 18.82/19.17 73 -rewrite(a,A) | transitive_reflexive_rewrite(A,f3(a,f2(a,c),A)). [resolve(64,a,18,a)]. 18.82/19.17 121 -transitive_reflexive_rewrite(f2(a,b),A) | transitive_reflexive_rewrite(A,f1(f2(a,b),b,A)). [resolve(46,a,43,a)]. 18.82/19.17 148 transitive_reflexive_rewrite(f2(a,c),f3(a,f2(a,c),f2(a,b))). [resolve(48,a,64,a)]. 18.82/19.17 153 -transitive_reflexive_rewrite(f2(a,b),A) | transitive_reflexive_rewrite(b,f1(f2(a,b),b,A)). [resolve(47,a,43,a)]. 18.82/19.17 162 transitive_reflexive_rewrite(f2(a,b),f3(a,f2(a,c),f2(a,b))). [resolve(73,a,42,a)]. 18.82/19.17 224 -transitive_reflexive_rewrite(f3(a,f2(a,c),f2(a,b)),A) | transitive_reflexive_rewrite(f2(a,c),A). [resolve(148,a,15,b)]. 18.82/19.17 299 -transitive_reflexive_rewrite(f2(a,c),A) | transitive_reflexive_rewrite(A,f1(f2(a,c),c,A)). [resolve(68,a,65,a)]. 18.82/19.17 339 -transitive_reflexive_rewrite(f2(a,c),A) | transitive_reflexive_rewrite(c,f1(f2(a,c),c,A)). [resolve(69,a,65,a)]. 18.82/19.17 381 transitive_reflexive_rewrite(f3(a,f2(a,c),f2(a,b)),f1(f2(a,b),b,f3(a,f2(a,c),f2(a,b)))). [resolve(121,a,162,a)]. 18.82/19.17 491 transitive_reflexive_rewrite(b,f1(f2(a,b),b,f3(a,f2(a,c),f2(a,b)))). [resolve(153,a,162,a)]. 18.82/19.17 1255 -transitive_reflexive_rewrite(f1(f2(a,b),b,f3(a,f2(a,c),f2(a,b))),A) | transitive_reflexive_rewrite(b,A). [resolve(491,a,15,b)]. 18.82/19.17 7492 transitive_reflexive_rewrite(f2(a,c),f1(f2(a,b),b,f3(a,f2(a,c),f2(a,b)))). [resolve(381,a,224,a)]. 18.82/19.17 8262 transitive_reflexive_rewrite(c,f1(f2(a,c),c,f1(f2(a,b),b,f3(a,f2(a,c),f2(a,b))))). [resolve(7492,a,339,a)]. 18.82/19.17 8267 transitive_reflexive_rewrite(f1(f2(a,b),b,f3(a,f2(a,c),f2(a,b))),f1(f2(a,c),c,f1(f2(a,b),b,f3(a,f2(a,c),f2(a,b))))). [resolve(7492,a,299,a)]. 18.82/19.17 14340 -transitive_reflexive_rewrite(b,f1(f2(a,c),c,f1(f2(a,b),b,f3(a,f2(a,c),f2(a,b))))). [resolve(8262,a,14,b)]. 18.82/19.17 17119 $F. [ur(1255,b,14340,a),unit_del(a,8267)]. 18.82/19.17 18.82/19.17 % SZS output end Refutation 18.82/19.17 ============================== end of proof ========================== 18.82/19.17 18.82/19.17 ============================== STATISTICS ============================ 18.82/19.17 18.82/19.17 Given=4532. Generated=62712. Kept=17110. proofs=1. 18.82/19.17 Usable=4464. Sos=9999. Demods=0. Limbo=0, Disabled=2660. Hints=0. 18.82/19.17 Megabytes=19.41. 18.82/19.17 User_CPU=18.15, System_CPU=0.04, Wall_clock=19. 18.82/19.17 18.82/19.17 ============================== end of statistics ===================== 18.82/19.17 18.82/19.17 ============================== end of search ========================= 18.82/19.17 18.82/19.17 THEOREM PROVED 18.82/19.17 % SZS status Theorem 18.82/19.17 18.82/19.17 Exiting with 1 proof. 18.82/19.17 18.82/19.17 Process 23649 exit (max_proofs) Thu Jul 2 08:21:25 2020 18.82/19.17 Prover9 interrupted 18.82/19.17 EOF