0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.33 % Computer : n015.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 1200 0.11/0.33 % DateTime : Tue Jul 13 16:01:34 EDT 2021 0.11/0.33 % CPUTime : 0.70/1.04 ============================== Prover9 =============================== 0.70/1.04 Prover9 (32) version 2009-11A, November 2009. 0.70/1.04 Process 26623 was started by sandbox2 on n015.cluster.edu, 0.70/1.04 Tue Jul 13 16:01:35 2021 0.70/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_26339_n015.cluster.edu". 0.70/1.04 ============================== end of head =========================== 0.70/1.04 0.70/1.04 ============================== INPUT ================================= 0.70/1.04 0.70/1.04 % Reading from file /tmp/Prover9_26339_n015.cluster.edu 0.70/1.04 0.70/1.04 set(prolog_style_variables). 0.70/1.04 set(auto2). 0.70/1.04 % set(auto2) -> set(auto). 0.70/1.04 % set(auto) -> set(auto_inference). 0.70/1.04 % set(auto) -> set(auto_setup). 0.70/1.04 % set(auto_setup) -> set(predicate_elim). 0.70/1.04 % set(auto_setup) -> assign(eq_defs, unfold). 0.70/1.04 % set(auto) -> set(auto_limits). 0.70/1.04 % set(auto_limits) -> assign(max_weight, "100.000"). 0.70/1.04 % set(auto_limits) -> assign(sos_limit, 20000). 0.70/1.04 % set(auto) -> set(auto_denials). 0.70/1.04 % set(auto) -> set(auto_process). 0.70/1.04 % set(auto2) -> assign(new_constants, 1). 0.70/1.04 % set(auto2) -> assign(fold_denial_max, 3). 0.70/1.04 % set(auto2) -> assign(max_weight, "200.000"). 0.70/1.04 % set(auto2) -> assign(max_hours, 1). 0.70/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.70/1.04 % set(auto2) -> assign(max_seconds, 0). 0.70/1.04 % set(auto2) -> assign(max_minutes, 5). 0.70/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.70/1.04 % set(auto2) -> set(sort_initial_sos). 0.70/1.04 % set(auto2) -> assign(sos_limit, -1). 0.70/1.04 % set(auto2) -> assign(lrs_ticks, 3000). 0.70/1.04 % set(auto2) -> assign(max_megs, 400). 0.70/1.04 % set(auto2) -> assign(stats, some). 0.70/1.04 % set(auto2) -> clear(echo_input). 0.70/1.04 % set(auto2) -> set(quiet). 0.70/1.04 % set(auto2) -> clear(print_initial_clauses). 0.70/1.04 % set(auto2) -> clear(print_given). 0.70/1.04 assign(lrs_ticks,-1). 0.70/1.04 assign(sos_limit,10000). 0.70/1.04 assign(order,kbo). 0.70/1.04 set(lex_order_vars). 0.70/1.04 clear(print_given). 0.70/1.04 0.70/1.04 % formulas(sos). % not echoed (17 formulas) 0.70/1.04 0.70/1.04 ============================== end of input ========================== 0.70/1.04 0.70/1.04 % From the command line: assign(max_seconds, 1200). 0.70/1.04 0.70/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.70/1.04 0.70/1.04 % Formulas that are not ordinary clauses: 0.70/1.04 1 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 2 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 3 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 4 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 5 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 6 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 7 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 8 (all A all B all C multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C))) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 9 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 10 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 11 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 12 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 13 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption]. 0.70/1.04 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 15 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 16 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 2.65/3.04 ============================== end of process non-clausal formulas === 2.65/3.04 2.65/3.04 ============================== PROCESS INITIAL CLAUSES =============== 2.65/3.04 2.65/3.04 ============================== PREDICATE ELIMINATION ================= 2.65/3.04 2.65/3.04 ============================== end predicate elimination ============= 2.65/3.04 2.65/3.04 Auto_denials: 2.65/3.04 % copying label a to answer in negative clause 2.65/3.04 2.65/3.04 Term ordering decisions: 2.65/3.04 2.65/3.04 % Assigning unary symbol star kb_weight 0 and highest precedence (8). 2.65/3.04 Function symbol KB weights: zero=1. one=1. a=1. multiplication=1. addition=1. star=0. 2.65/3.04 2.65/3.04 ============================== end of process initial clauses ======== 2.65/3.04 2.65/3.04 ============================== CLAUSES FOR SEARCH ==================== 2.65/3.04 2.65/3.04 ============================== end of clauses for search ============= 2.65/3.04 2.65/3.04 ============================== SEARCH ================================ 2.65/3.04 2.65/3.04 % Starting search at 0.01 seconds. 2.65/3.04 2.65/3.04 Low Water (keep): wt=35.000, iters=3344 2.65/3.04 2.65/3.04 Low Water (keep): wt=33.000, iters=3360 2.65/3.04 2.65/3.04 Low Water (keep): wt=30.000, iters=3357 2.65/3.04 2.65/3.04 Low Water (keep): wt=29.000, iters=3366 2.65/3.04 2.65/3.04 Low Water (keep): wt=28.000, iters=3333 2.65/3.04 2.65/3.04 Low Water (keep): wt=27.000, iters=3378 2.65/3.04 2.65/3.04 Low Water (keep): wt=26.000, iters=3334 2.65/3.04 2.65/3.04 Low Water (keep): wt=25.000, iters=3344 2.65/3.04 2.65/3.04 Low Water (keep): wt=24.000, iters=3340 2.65/3.04 2.65/3.04 Low Water (keep): wt=23.000, iters=3347 2.65/3.04 2.65/3.04 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 64 (0.00 of 0.86 sec). 2.65/3.04 2.65/3.04 Low Water (keep): wt=22.000, iters=3335 2.65/3.04 2.65/3.04 Low Water (keep): wt=21.000, iters=3352 2.65/3.04 2.65/3.04 Low Water (keep): wt=20.000, iters=3336 2.65/3.04 2.65/3.04 Low Water (keep): wt=19.000, iters=3333 2.65/3.04 2.65/3.04 Low Water (displace): id=1249, wt=42.000 2.65/3.04 2.65/3.04 Low Water (displace): id=5016, wt=40.000 2.65/3.04 2.65/3.04 Low Water (displace): id=5397, wt=39.000 2.65/3.04 2.65/3.04 Low Water (displace): id=5858, wt=38.000 2.65/3.04 2.65/3.04 Low Water (displace): id=5908, wt=37.000 2.65/3.04 2.65/3.04 Low Water (displace): id=6184, wt=36.000 2.65/3.04 2.65/3.04 Low Water (displace): id=6103, wt=35.000 2.65/3.04 2.65/3.04 Low Water (displace): id=5745, wt=34.000 2.65/3.04 2.65/3.04 Low Water (displace): id=11430, wt=18.000 2.65/3.04 2.65/3.04 Low Water (displace): id=11445, wt=16.000 2.65/3.04 2.65/3.04 Low Water (displace): id=11653, wt=15.000 2.65/3.04 2.65/3.04 Low Water (displace): id=12264, wt=13.000 2.65/3.04 2.65/3.04 Low Water (keep): wt=18.000, iters=3348 2.65/3.04 2.65/3.04 Low Water (displace): id=13096, wt=12.000 2.65/3.04 2.65/3.04 ============================== PROOF ================================= 2.65/3.04 % SZS status Theorem 2.65/3.04 % SZS output start Refutation 2.65/3.04 2.65/3.04 % Proof 1 at 1.96 (+ 0.05) seconds: a. 2.65/3.04 % Length of proof is 96. 2.65/3.04 % Level of proof is 22. 2.65/3.04 % Maximum clause weight is 20.000. 2.65/3.04 % Given clauses 1290. 2.65/3.04 2.65/3.04 2 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 3 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 5 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 6 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 7 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 8 (all A all B all C multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C))) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 10 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 11 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 12 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 15 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 16 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 2.65/3.04 18 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(2)]. 2.65/3.04 20 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(5)]. 2.65/3.04 22 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(11)]. 2.65/3.04 23 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(12)]. 2.65/3.04 24 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(6)]. 2.65/3.04 25 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)]. 2.65/3.04 26 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(7)]. 2.65/3.04 27 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(26),rewrite([23(2)]),flip(a)]. 2.65/3.04 28 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(8)]. 2.65/3.04 29 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom). [clausify(3)]. 2.65/3.04 30 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom). [clausify(15)]. 2.65/3.04 31 -leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)) # label(a) # label(negated_conjecture) # answer(a). [assumption]. 2.65/3.04 32 addition(A,B) != B | leq(A,B) # label(order) # label(axiom). [clausify(16)]. 2.65/3.04 33 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom). [clausify(16)]. 2.65/3.04 34 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(10)]. 2.65/3.04 35 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(34),rewrite([23(2)])]. 2.65/3.04 40 addition(A,addition(A,B)) = addition(A,B). [para(27(a,1),20(a,1)),rewrite([23(1),23(2),27(2,R),20(1),23(3)])]. 2.65/3.04 43 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A). [para(22(a,1),29(a,1,1)),rewrite([23(4)])]. 2.65/3.04 46 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)). [para(18(a,1),30(a,1,1)),rewrite([23(4)])]. 2.65/3.04 48 leq(A,A). [hyper(32,a,20,a)]. 2.65/3.04 52 addition(A,addition(B,C)) != addition(A,C) | leq(B,addition(A,C)). [para(27(a,1),32(a,1)),rewrite([23(3),23(5)])]. 2.65/3.04 53 addition(A,addition(B,C)) != addition(A,B) | leq(C,addition(A,B)). [para(27(a,2),32(a,1))]. 2.65/3.04 56 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(33,b,25,a),rewrite([23(6)])]. 2.65/3.04 57 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(33,b,24,a),rewrite([23(6)])]. 2.65/3.04 63 -leq(addition(A,multiplication(B,multiplication(C,D))),multiplication(B,C)) | leq(multiplication(A,star(D)),multiplication(B,C)). [para(28(a,1),35(a,1,2))]. 2.65/3.04 64 -leq(multiplication(addition(A,B),C),B) | leq(multiplication(A,multiplication(C,star(C))),B). [para(29(a,1),35(a,1)),rewrite([28(6)])]. 2.65/3.04 65 -leq(multiplication(A,addition(B,C)),A) | leq(multiplication(A,multiplication(B,star(C))),A). [para(30(a,1),35(a,1)),rewrite([28(6)])]. 2.65/3.04 79 leq(A,addition(A,B)). [hyper(32,a,40,a)]. 2.65/3.04 81 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(30(a,1),79(a,2))]. 2.65/3.04 110 addition(addition(A,multiplication(B,A)),multiplication(addition(B,one),C)) = multiplication(addition(B,one),addition(A,C)). [para(43(a,2),30(a,1,1))]. 2.65/3.04 165 -leq(multiplication(A,addition(B,one)),A) | leq(multiplication(A,star(B)),A). [para(46(a,1),35(a,1))]. 2.65/3.04 197 leq(A,addition(B,A)). [para(20(a,1),52(a,1,2)),xx(a)]. 2.65/3.04 203 leq(A,addition(B,addition(A,C))). [para(40(a,1),52(a,1,2)),xx(a)]. 2.65/3.04 204 addition(A,multiplication(addition(B,one),C)) != addition(A,multiplication(B,C)) | leq(C,addition(A,multiplication(B,C))). [para(43(a,1),52(a,1,2))]. 2.65/3.04 210 leq(addition(A,B),addition(A,addition(B,C))). [para(27(a,1),197(a,2)),rewrite([23(2),27(3,R),23(2)])]. 2.65/3.04 212 leq(multiplication(A,B),addition(C,multiplication(addition(A,D),B))). [para(29(a,1),203(a,2,2))]. 2.65/3.04 216 leq(A,addition(B,multiplication(A,addition(C,one)))). [para(46(a,1),203(a,2,2))]. 2.65/3.04 289 leq(one,star(A)). [para(56(a,1),203(a,2))]. 2.65/3.04 291 addition(star(A),one) != star(A) | leq(multiplication(star(A),A),addition(star(A),one)). [para(56(a,1),53(a,1)),flip(a)]. 2.65/3.04 292 leq(addition(star(A),one),star(A)). [para(56(a,1),210(a,2))]. 2.65/3.04 295 addition(one,star(A)) = star(A). [hyper(33,b,289,a)]. 2.65/3.04 296 addition(star(A),one) = star(A). [hyper(33,b,292,a),rewrite([23(5),40(5)])]. 2.65/3.04 297 leq(multiplication(star(A),A),star(A)). [back_rewrite(291),rewrite([296(3),296(8)]),xx(a)]. 2.65/3.04 299 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)). [para(295(a,1),30(a,2,2)),rewrite([18(2)])]. 2.65/3.04 302 leq(A,multiplication(A,star(B))). [para(295(a,1),81(a,2,2)),rewrite([18(2)])]. 2.65/3.04 309 addition(star(A),multiplication(A,star(A))) = star(A). [para(57(a,1),27(a,1)),rewrite([296(6),23(5)]),flip(a)]. 2.65/3.04 317 leq(multiplication(A,B),multiplication(A,multiplication(B,star(C)))). [para(28(a,1),302(a,2))]. 2.65/3.04 321 leq(A,addition(B,multiplication(A,star(C)))). [para(296(a,1),216(a,2,2,2))]. 2.65/3.04 327 addition(star(A),multiplication(star(A),A)) = star(A). [hyper(33,b,297,a),rewrite([23(4)])]. 2.65/3.04 399 -leq(multiplication(A,addition(one,multiplication(B,C))),multiplication(A,B)) | leq(multiplication(A,star(C)),multiplication(A,B)). [para(46(a,1),63(a,1)),rewrite([23(3)])]. 2.65/3.04 429 -leq(multiplication(star(A),B),star(A)) | leq(multiplication(B,star(B)),star(A)). [para(295(a,1),64(a,1,1)),rewrite([22(8)])]. 2.65/3.04 441 leq(multiplication(star(addition(A,B)),multiplication(A,star(B))),star(addition(A,B))). [hyper(65,a,297,a)]. 2.65/3.04 483 multiplication(addition(A,one),star(A)) = star(A). [para(309(a,1),43(a,1)),flip(a)]. 2.65/3.04 488 leq(A,star(A)). [para(309(a,1),321(a,2))]. 2.65/3.04 493 addition(A,star(A)) = star(A). [hyper(33,b,488,a)]. 2.65/3.04 576 multiplication(star(A),star(star(A))) = star(star(A)). [para(296(a,1),483(a,1,1))]. 2.65/3.04 650 leq(multiplication(A,addition(B,one)),multiplication(A,star(B))). [para(483(a,1),317(a,2,2))]. 2.65/3.04 653 multiplication(star(A),addition(A,one)) = star(A). [para(327(a,1),46(a,1)),flip(a)]. 2.65/3.04 690 multiplication(star(star(A)),star(A)) = star(star(A)). [para(296(a,1),653(a,1,2))]. 2.65/3.04 1359 multiplication(star(star(A)),multiplication(star(A),B)) = multiplication(star(star(A)),B). [para(690(a,1),28(a,1,1)),flip(a)]. 2.65/3.04 1375 leq(multiplication(star(star(A)),addition(A,one)),star(star(A))). [para(690(a,1),650(a,2))]. 2.65/3.04 1740 leq(multiplication(A,star(addition(A,B))),star(addition(A,B))). [para(309(a,1),212(a,2))]. 2.65/3.04 1741 leq(multiplication(A,B),addition(C,multiplication(star(A),B))). [para(493(a,1),212(a,2,2,1))]. 2.65/3.04 1770 leq(multiplication(A,A),star(A)). [para(327(a,1),1741(a,2))]. 2.65/3.04 1783 addition(star(A),multiplication(A,A)) = star(A). [hyper(33,b,1770,a),rewrite([23(3)])]. 2.65/3.04 5900 leq(multiplication(star(addition(A,one)),star(A)),star(addition(A,one))). [hyper(165,a,297,a)]. 2.65/3.04 6750 multiplication(addition(A,one),star(addition(A,B))) = star(addition(A,B)). [hyper(33,b,1740,a),rewrite([23(6),43(6)])]. 2.65/3.04 8866 leq(A,multiplication(addition(B,one),addition(C,A))). [para(110(a,1),204(a,2)),rewrite([23(6),27(6,R),20(5),110(6),110(15)]),xx(a)]. 2.65/3.04 8876 leq(multiplication(A,A),multiplication(addition(B,one),star(A))). [para(1783(a,1),8866(a,2,2))]. 2.65/3.04 9352 leq(multiplication(A,A),multiplication(star(B),star(A))). [para(296(a,1),8876(a,2,1))]. 2.65/3.04 13395 -leq(addition(one,multiplication(A,B)),A) | leq(star(B),A). [para(22(a,1),399(a,1)),rewrite([22(5),22(7),22(7)])]. 2.65/3.04 13400 -leq(star(A),star(A)) | leq(star(addition(A,one)),star(A)). [para(653(a,1),13395(a,1,2)),rewrite([295(3)])]. 2.65/3.04 13763 leq(star(addition(A,one)),star(star(A))). [hyper(429,a,1375,a),rewrite([6750(6)])]. 2.65/3.04 13766 addition(star(star(A)),star(addition(A,one))) = star(star(A)). [hyper(33,b,13763,a),rewrite([23(6)])]. 2.65/3.04 13895 leq(multiplication(star(star(A)),star(multiplication(A,A))),star(star(A))). [para(1783(a,1),441(a,1,1,1)),rewrite([1359(7),1783(8)])]. 2.65/3.04 14097 leq(star(star(A)),star(addition(A,one))). [hyper(429,a,5900,a),rewrite([576(4)])]. 2.65/3.04 14100 star(addition(A,one)) = star(star(A)). [hyper(33,b,14097,a),rewrite([13766(6)]),flip(a)]. 2.65/3.04 14143 -leq(star(A),star(A)) | leq(star(star(A)),star(A)). [back_rewrite(13400),rewrite([14100(6)])]. 2.65/3.04 14415 leq(star(star(A)),star(A)). [hyper(14143,a,48,a)]. 2.65/3.04 14416 star(star(A)) = star(A). [hyper(33,b,14415,a),rewrite([23(4),493(4)])]. 2.65/3.04 14579 leq(multiplication(star(A),star(multiplication(A,A))),star(A)). [back_rewrite(13895),rewrite([14416(2),14416(6)])]. 2.65/3.04 15068 multiplication(star(A),star(multiplication(A,A))) = star(A). [hyper(33,b,14579,a),rewrite([23(6),299(6)])]. 2.65/3.04 15105 leq(multiplication(A,multiplication(A,multiplication(A,A))),star(A)). [para(15068(a,1),9352(a,2)),rewrite([28(3)])]. 2.65/3.04 15106 $F # answer(a). [resolve(15105,a,31,a)]. 2.65/3.04 2.65/3.04 % SZS output end Refutation 2.65/3.04 ============================== end of proof ========================== 2.65/3.04 2.65/3.04 ============================== STATISTICS ============================ 2.65/3.04 2.65/3.04 Given=1290. Generated=95599. Kept=15086. proofs=1. 2.65/3.04 Usable=945. Sos=8040. Demods=402. Limbo=29, Disabled=6089. Hints=0. 2.65/3.04 Megabytes=11.26. 2.65/3.04 User_CPU=1.96, System_CPU=0.05, Wall_clock=2. 2.65/3.04 2.65/3.04 ============================== end of statistics ===================== 2.65/3.04 2.65/3.04 ============================== end of search ========================= 2.65/3.04 2.65/3.04 THEOREM PROVED 2.65/3.04 % SZS status Theorem 2.65/3.04 2.65/3.04 Exiting with 1 proof. 2.65/3.04 2.65/3.04 Process 26623 exit (max_proofs) Tue Jul 13 16:01:37 2021 2.65/3.04 Prover9 interrupted 2.65/3.04 EOF