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 0.11/0.32 % Computer : n021.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 : 1440 0.11/0.32 % WCLimit : 180 0.11/0.32 % DateTime : Mon Jul 3 08:28:22 EDT 2023 0.11/0.33 % CPUTime : 0.41/0.97 ============================== Prover9 =============================== 0.41/0.97 Prover9 (32) version 2009-11A, November 2009. 0.41/0.97 Process 19777 was started by sandbox2 on n021.cluster.edu, 0.41/0.97 Mon Jul 3 08:28:23 2023 0.41/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_19542_n021.cluster.edu". 0.41/0.97 ============================== end of head =========================== 0.41/0.97 0.41/0.97 ============================== INPUT ================================= 0.41/0.97 0.41/0.97 % Reading from file /tmp/Prover9_19542_n021.cluster.edu 0.41/0.97 0.41/0.97 set(prolog_style_variables). 0.41/0.97 set(auto2). 0.41/0.97 % set(auto2) -> set(auto). 0.41/0.97 % set(auto) -> set(auto_inference). 0.41/0.97 % set(auto) -> set(auto_setup). 0.41/0.97 % set(auto_setup) -> set(predicate_elim). 0.41/0.97 % set(auto_setup) -> assign(eq_defs, unfold). 0.41/0.97 % set(auto) -> set(auto_limits). 0.41/0.97 % set(auto_limits) -> assign(max_weight, "100.000"). 0.41/0.97 % set(auto_limits) -> assign(sos_limit, 20000). 0.41/0.97 % set(auto) -> set(auto_denials). 0.41/0.97 % set(auto) -> set(auto_process). 0.41/0.97 % set(auto2) -> assign(new_constants, 1). 0.41/0.97 % set(auto2) -> assign(fold_denial_max, 3). 0.41/0.97 % set(auto2) -> assign(max_weight, "200.000"). 0.41/0.97 % set(auto2) -> assign(max_hours, 1). 0.41/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.41/0.97 % set(auto2) -> assign(max_seconds, 0). 0.41/0.97 % set(auto2) -> assign(max_minutes, 5). 0.41/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.41/0.97 % set(auto2) -> set(sort_initial_sos). 0.41/0.97 % set(auto2) -> assign(sos_limit, -1). 0.41/0.97 % set(auto2) -> assign(lrs_ticks, 3000). 0.41/0.97 % set(auto2) -> assign(max_megs, 400). 0.41/0.97 % set(auto2) -> assign(stats, some). 0.41/0.97 % set(auto2) -> clear(echo_input). 0.41/0.97 % set(auto2) -> set(quiet). 0.41/0.97 % set(auto2) -> clear(print_initial_clauses). 0.41/0.97 % set(auto2) -> clear(print_given). 0.41/0.97 assign(lrs_ticks,-1). 0.41/0.97 assign(sos_limit,10000). 0.41/0.97 assign(order,kbo). 0.41/0.97 set(lex_order_vars). 0.41/0.97 clear(print_given). 0.41/0.97 0.41/0.97 % formulas(sos). % not echoed (17 formulas) 0.41/0.97 0.41/0.97 ============================== end of input ========================== 0.41/0.97 0.41/0.97 % From the command line: assign(max_seconds, 1440). 0.41/0.97 0.41/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.41/0.97 0.41/0.97 % Formulas that are not ordinary clauses: 0.41/0.97 1 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.41/0.97 2 (all A all B (addition(A,B) = B <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.41/0.97 3 (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]. 0.41/0.97 4 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.41/0.97 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.41/0.97 6 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.41/0.97 7 (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]. 0.41/0.97 8 (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]. 0.41/0.97 9 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.41/0.97 10 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.41/0.97 11 (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]. 0.41/0.97 12 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.41/0.97 13 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 0.41/0.97 14 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 15 (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]. 2.95/3.26 16 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 2.95/3.26 ============================== end of process non-clausal formulas === 2.95/3.26 2.95/3.26 ============================== PROCESS INITIAL CLAUSES =============== 2.95/3.26 2.95/3.26 ============================== PREDICATE ELIMINATION ================= 2.95/3.26 2.95/3.26 ============================== end predicate elimination ============= 2.95/3.26 2.95/3.26 Auto_denials: 2.95/3.26 % copying label a to answer in negative clause 2.95/3.26 2.95/3.26 Term ordering decisions: 2.95/3.26 2.95/3.26 % Assigning unary symbol star kb_weight 0 and highest precedence (8). 2.95/3.26 Function symbol KB weights: zero=1. one=1. a=1. multiplication=1. addition=1. star=0. 2.95/3.26 2.95/3.26 ============================== end of process initial clauses ======== 2.95/3.26 2.95/3.26 ============================== CLAUSES FOR SEARCH ==================== 2.95/3.26 2.95/3.26 ============================== end of clauses for search ============= 2.95/3.26 2.95/3.26 ============================== SEARCH ================================ 2.95/3.26 2.95/3.26 % Starting search at 0.01 seconds. 2.95/3.26 2.95/3.26 Low Water (keep): wt=36.000, iters=3360 2.95/3.26 2.95/3.26 Low Water (keep): wt=35.000, iters=3344 2.95/3.26 2.95/3.26 Low Water (keep): wt=33.000, iters=3358 2.95/3.26 2.95/3.26 Low Water (keep): wt=32.000, iters=3465 2.95/3.26 2.95/3.26 Low Water (keep): wt=31.000, iters=3412 2.95/3.26 2.95/3.26 Low Water (keep): wt=29.000, iters=3355 2.95/3.26 2.95/3.26 Low Water (keep): wt=28.000, iters=3343 2.95/3.26 2.95/3.26 Low Water (keep): wt=27.000, iters=3344 2.95/3.26 2.95/3.26 Low Water (keep): wt=25.000, iters=3366 2.95/3.26 2.95/3.26 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 52 (0.00 of 0.83 sec). 2.95/3.26 2.95/3.26 Low Water (keep): wt=24.000, iters=3383 2.95/3.26 2.95/3.26 Low Water (keep): wt=23.000, iters=3363 2.95/3.26 2.95/3.26 Low Water (keep): wt=22.000, iters=3338 2.95/3.26 2.95/3.26 Low Water (keep): wt=21.000, iters=3361 2.95/3.26 2.95/3.26 Low Water (keep): wt=20.000, iters=3350 2.95/3.26 2.95/3.26 Low Water (keep): wt=19.000, iters=3356 2.95/3.26 2.95/3.26 Low Water (displace): id=5586, wt=46.000 2.95/3.26 2.95/3.26 Low Water (displace): id=5562, wt=44.000 2.95/3.26 2.95/3.26 Low Water (displace): id=6242, wt=43.000 2.95/3.26 2.95/3.26 Low Water (displace): id=5808, wt=42.000 2.95/3.26 2.95/3.26 Low Water (displace): id=6254, wt=41.000 2.95/3.26 2.95/3.26 Low Water (displace): id=6238, wt=40.000 2.95/3.26 2.95/3.26 Low Water (displace): id=6180, wt=39.000 2.95/3.26 2.95/3.26 Low Water (displace): id=6218, wt=38.000 2.95/3.26 2.95/3.26 Low Water (displace): id=6155, wt=37.000 2.95/3.26 2.95/3.26 Low Water (displace): id=11623, wt=18.000 2.95/3.26 2.95/3.26 Low Water (displace): id=11976, wt=17.000 2.95/3.26 2.95/3.26 Low Water (displace): id=11982, wt=16.000 2.95/3.26 2.95/3.26 Low Water (displace): id=12091, wt=15.000 2.95/3.26 2.95/3.26 Low Water (displace): id=12608, wt=14.000 2.95/3.26 2.95/3.26 Low Water (displace): id=12613, wt=13.000 2.95/3.26 2.95/3.26 Low Water (keep): wt=18.000, iters=3420 2.95/3.26 2.95/3.26 Low Water (displace): id=14533, wt=12.000 2.95/3.26 2.95/3.26 Low Water (keep): wt=17.000, iters=3340 2.95/3.26 2.95/3.26 Low Water (keep): wt=16.000, iters=3345 2.95/3.26 2.95/3.26 ============================== PROOF ================================= 2.95/3.26 % SZS status Theorem 2.95/3.26 % SZS output start Refutation 2.95/3.26 2.95/3.26 % Proof 1 at 2.22 (+ 0.08) seconds: a. 2.95/3.26 % Length of proof is 120. 2.95/3.26 % Level of proof is 26. 2.95/3.26 % Maximum clause weight is 19.000. 2.95/3.26 % Given clauses 1484. 2.95/3.26 2.95/3.26 1 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 2 (all A all B (addition(A,B) = B <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 3 (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]. 2.95/3.26 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 7 (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]. 2.95/3.26 8 (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]. 2.95/3.26 9 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 10 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 11 (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]. 2.95/3.26 12 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 13 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 15 (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]. 2.95/3.26 16 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 2.95/3.26 18 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(5)]. 2.95/3.26 20 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(9)]. 2.95/3.26 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(10)]. 2.95/3.26 23 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(12)]. 2.95/3.26 24 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(13)]. 2.95/3.26 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(16)]. 2.95/3.26 26 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(3)]. 2.95/3.26 27 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(26),rewrite([23(2)]),flip(a)]. 2.95/3.26 28 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(15)]. 2.95/3.26 29 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(1)]. 2.95/3.26 30 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(29),flip(a)]. 2.95/3.26 31 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(8)]. 2.95/3.26 32 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(31),flip(a)]. 2.95/3.26 33 -leq(multiplication(a,multiplication(a,multiplication(a,multiplication(a,multiplication(a,a))))),star(a)) # label(a) # label(negated_conjecture) # answer(a). [assumption]. 2.95/3.26 34 addition(A,B) != B | leq(A,B) # label(order) # label(axiom). [clausify(2)]. 2.95/3.26 35 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom). [clausify(2)]. 2.95/3.26 36 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(7)]. 2.95/3.26 37 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(36),rewrite([23(2)])]. 2.95/3.26 38 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(11)]. 2.95/3.26 39 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(38),rewrite([23(2)])]. 2.95/3.26 42 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)])]. 2.95/3.26 44 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(18(a,1),30(a,1,1)),rewrite([23(4)]),flip(a)]. 2.95/3.26 46 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(21(a,1),32(a,1,1)),rewrite([23(4)]),flip(a)]. 2.95/3.26 49 leq(A,A). [hyper(34,a,20,a)]. 2.95/3.26 53 addition(A,addition(B,C)) != addition(A,C) | leq(B,addition(A,C)). [para(27(a,1),34(a,1)),rewrite([23(3),23(5)])]. 2.95/3.26 54 addition(A,addition(B,C)) != addition(A,B) | leq(C,addition(A,B)). [para(27(a,2),34(a,1))]. 2.95/3.26 57 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(35,b,25,a),rewrite([23(6)])]. 2.95/3.26 58 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(35,b,24,a),rewrite([23(6)])]. 2.95/3.26 61 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A). [para(20(a,1),37(a,1)),rewrite([28(5)])]. 2.95/3.26 64 -leq(addition(A,multiplication(B,multiplication(C,D))),multiplication(B,C)) | leq(multiplication(A,star(D)),multiplication(B,C)). [para(28(a,1),37(a,1,2))]. 2.95/3.26 65 -leq(multiplication(A,addition(B,C)),A) | leq(multiplication(A,multiplication(B,star(C))),A). [para(30(a,1),37(a,1)),rewrite([28(6)])]. 2.95/3.26 66 -leq(multiplication(addition(A,B),C),B) | leq(multiplication(A,multiplication(C,star(C))),B). [para(32(a,1),37(a,1)),rewrite([28(6)])]. 2.95/3.26 69 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B). [para(20(a,1),39(a,1))]. 2.95/3.26 80 leq(A,addition(A,B)). [hyper(34,a,42,a)]. 2.95/3.26 81 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(30(a,1),80(a,2))]. 2.95/3.26 147 -leq(multiplication(addition(A,one),B),B) | leq(multiplication(star(A),B),B). [para(46(a,2),39(a,1))]. 2.95/3.26 200 leq(A,addition(B,A)). [para(20(a,1),53(a,1,2)),xx(a)]. 2.95/3.26 206 leq(A,addition(B,addition(A,C))). [para(42(a,1),53(a,1,2)),xx(a)]. 2.95/3.26 213 leq(addition(A,B),addition(A,addition(B,C))). [para(27(a,1),200(a,2)),rewrite([23(2),27(3,R),23(2)])]. 2.95/3.26 214 leq(multiplication(A,B),addition(C,multiplication(A,addition(B,D)))). [para(30(a,1),206(a,2,2))]. 2.95/3.26 215 leq(multiplication(A,B),addition(C,multiplication(addition(A,D),B))). [para(32(a,1),206(a,2,2))]. 2.95/3.26 217 leq(A,addition(B,multiplication(addition(C,one),A))). [para(46(a,2),206(a,2,2))]. 2.95/3.26 251 addition(A,addition(B,multiplication(addition(C,one),A))) = addition(B,multiplication(addition(C,one),A)). [hyper(35,b,217,a)]. 2.95/3.26 252 leq(A,multiplication(addition(B,one),addition(A,C))). [para(30(a,1),217(a,2)),rewrite([23(3)])]. 2.95/3.26 288 addition(one,multiplication(addition(A,one),star(addition(A,one)))) = star(addition(A,one)). [para(46(a,1),57(a,1,2,2)),rewrite([46(12,R),251(12)])]. 2.95/3.26 291 leq(one,star(A)). [para(57(a,1),206(a,2))]. 2.95/3.26 293 addition(star(A),one) != star(A) | leq(multiplication(A,star(A)),addition(star(A),one)). [para(57(a,1),54(a,1)),flip(a)]. 2.95/3.26 294 leq(addition(star(A),one),star(A)). [para(57(a,1),213(a,2))]. 2.95/3.26 297 addition(one,star(A)) = star(A). [hyper(35,b,291,a)]. 2.95/3.26 298 addition(star(A),one) = star(A). [hyper(35,b,294,a),rewrite([23(5),42(5)])]. 2.95/3.26 299 leq(multiplication(A,star(A)),star(A)). [back_rewrite(293),rewrite([298(3),298(8)]),xx(a)]. 2.95/3.26 300 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)). [para(297(a,1),30(a,2,2)),rewrite([18(2)])]. 2.95/3.26 303 leq(A,multiplication(A,star(B))). [para(297(a,1),81(a,2,2)),rewrite([18(2)])]. 2.95/3.26 309 leq(one,multiplication(addition(A,one),star(B))). [para(297(a,1),252(a,2,2))]. 2.95/3.26 310 leq(multiplication(A,B),multiplication(A,multiplication(B,star(C)))). [para(28(a,1),303(a,2))]. 2.95/3.26 312 addition(star(A),multiplication(star(A),A)) = star(A). [para(58(a,1),27(a,1)),rewrite([298(6),23(5)]),flip(a)]. 2.95/3.26 317 leq(multiplication(star(A),A),star(A)). [para(58(a,1),54(a,1)),rewrite([298(4),298(8)]),xx(a)]. 2.95/3.26 323 leq(A,addition(B,multiplication(star(C),A))). [para(298(a,1),217(a,2,2,1))]. 2.95/3.26 329 addition(star(A),multiplication(A,star(A))) = star(A). [hyper(35,b,299,a),rewrite([23(4)])]. 2.95/3.26 350 leq(multiplication(star(A),multiplication(A,star(A))),star(A)). [hyper(61,a,317,a)]. 2.95/3.26 356 addition(one,multiplication(addition(A,one),star(B))) = multiplication(addition(A,one),star(B)). [hyper(35,b,309,a)]. 2.95/3.26 358 multiplication(addition(A,one),star(addition(A,one))) = star(addition(A,one)). [back_rewrite(288),rewrite([356(8)])]. 2.95/3.26 400 -leq(multiplication(A,addition(one,multiplication(B,C))),multiplication(A,B)) | leq(multiplication(A,star(C)),multiplication(A,B)). [para(44(a,2),64(a,1)),rewrite([23(3)])]. 2.95/3.26 421 leq(multiplication(star(addition(A,B)),multiplication(A,star(B))),star(addition(A,B))). [hyper(65,a,317,a)]. 2.95/3.26 455 -leq(multiplication(star(A),B),star(A)) | leq(multiplication(B,star(B)),star(A)). [para(297(a,1),66(a,1,1)),rewrite([21(8)])]. 2.95/3.26 489 multiplication(star(A),addition(A,one)) = star(A). [para(312(a,1),44(a,2))]. 2.95/3.26 494 leq(A,star(A)). [para(312(a,1),323(a,2))]. 2.95/3.26 500 addition(A,star(A)) = star(A). [hyper(35,b,494,a)]. 2.95/3.26 602 multiplication(star(star(A)),star(A)) = star(star(A)). [para(298(a,1),489(a,1,2))]. 2.95/3.26 657 multiplication(addition(A,one),star(A)) = star(A). [para(329(a,1),46(a,2))]. 2.95/3.26 693 multiplication(star(A),star(star(A))) = star(star(A)). [para(298(a,1),657(a,1,1))]. 2.95/3.26 696 leq(multiplication(A,addition(B,one)),multiplication(A,star(B))). [para(657(a,1),310(a,2,2))]. 2.95/3.26 810 multiplication(star(star(A)),multiplication(star(A),B)) = multiplication(star(star(A)),B). [para(602(a,1),28(a,1,1)),flip(a)]. 2.95/3.26 1362 leq(multiplication(star(star(A)),star(star(A))),star(star(A))). [para(693(a,1),350(a,1,2))]. 2.95/3.26 1374 leq(multiplication(star(star(A)),addition(A,one)),star(star(A))). [para(602(a,1),696(a,2))]. 2.95/3.26 1894 leq(multiplication(A,B),addition(C,multiplication(A,star(B)))). [para(500(a,1),214(a,2,2,2))]. 2.95/3.26 1930 leq(multiplication(A,B),multiplication(addition(A,C),star(B))). [para(32(a,1),1894(a,2)),rewrite([23(2)])]. 2.95/3.26 1934 leq(multiplication(A,A),star(A)). [para(329(a,1),1894(a,2))]. 2.95/3.26 1950 addition(star(A),multiplication(A,A)) = star(A). [hyper(35,b,1934,a),rewrite([23(3)])]. 2.95/3.26 2030 leq(multiplication(A,B),multiplication(star(A),star(B))). [para(500(a,1),1930(a,2,1))]. 2.95/3.26 2327 leq(multiplication(A,star(addition(A,B))),star(addition(A,B))). [para(329(a,1),215(a,2))]. 2.95/3.26 3998 leq(multiplication(star(A),star(addition(A,one))),star(addition(A,one))). [hyper(147,a,299,a)]. 2.95/3.26 6992 multiplication(star(star(A)),star(star(A))) = star(star(A)). [hyper(35,b,1362,a),rewrite([23(8),300(8)])]. 2.95/3.26 7327 leq(multiplication(star(star(A)),star(addition(A,one))),star(star(A))). [hyper(61,a,1374,a),rewrite([358(8)])]. 2.95/3.26 7918 multiplication(addition(A,one),star(addition(A,B))) = star(addition(A,B)). [hyper(35,b,2327,a),rewrite([23(6),46(6,R)])]. 2.95/3.26 13709 -leq(addition(one,multiplication(A,B)),A) | leq(star(B),A). [para(21(a,1),400(a,1)),rewrite([21(5),21(7),21(7)])]. 2.95/3.26 13728 -leq(star(A),star(A)) | leq(star(addition(A,one)),star(A)). [para(489(a,1),13709(a,1,2)),rewrite([297(3)])]. 2.95/3.26 13864 leq(multiplication(star(star(A)),star(multiplication(A,A))),star(star(A))). [para(1950(a,1),421(a,1,1,1)),rewrite([810(7),1950(8)])]. 2.95/3.26 14123 leq(multiplication(star(star(A)),star(addition(A,one))),star(addition(A,one))). [hyper(69,a,3998,a),rewrite([810(8)])]. 2.95/3.26 14506 leq(star(addition(A,one)),star(star(A))). [hyper(455,a,1374,a),rewrite([7918(6)])]. 2.95/3.26 14511 addition(star(star(A)),star(addition(A,one))) = star(star(A)). [hyper(35,b,14506,a),rewrite([23(6)])]. 2.95/3.26 14781 multiplication(star(star(A)),star(addition(A,one))) = star(star(A)). [hyper(35,b,7327,a),rewrite([23(9),300(9)])]. 2.95/3.26 14782 leq(star(star(A)),star(addition(A,one))). [back_rewrite(14123),rewrite([14781(6)])]. 2.95/3.26 14783 star(addition(A,one)) = star(star(A)). [hyper(35,b,14782,a),rewrite([14511(6)]),flip(a)]. 2.95/3.26 14822 -leq(star(A),star(A)) | leq(star(star(A)),star(A)). [back_rewrite(13728),rewrite([14783(6)])]. 2.95/3.26 15087 leq(star(star(A)),star(A)). [hyper(14822,a,49,a)]. 2.95/3.26 15088 star(star(A)) = star(A). [hyper(35,b,15087,a),rewrite([23(4),500(4)])]. 2.95/3.26 15267 leq(multiplication(star(A),star(multiplication(A,A))),star(A)). [back_rewrite(13864),rewrite([15088(2),15088(6)])]. 2.95/3.26 15359 multiplication(star(A),star(A)) = star(A). [back_rewrite(6992),rewrite([15088(2),15088(3),15088(5)])]. 2.95/3.26 15773 leq(star(multiplication(A,A)),star(A)). [hyper(455,a,15267,a),rewrite([15088(5),15359(5)])]. 2.95/3.26 15774 multiplication(star(A),star(multiplication(A,A))) = star(A). [hyper(35,b,15267,a),rewrite([23(6),300(6)])]. 2.95/3.26 15777 addition(star(A),star(multiplication(A,A))) = star(A). [hyper(35,b,15773,a),rewrite([23(4)])]. 2.95/3.26 15792 leq(multiplication(A,multiplication(A,A)),star(A)). [para(15774(a,1),2030(a,2))]. 2.95/3.26 15852 addition(star(A),multiplication(A,multiplication(A,A))) = star(A). [hyper(35,b,15792,a),rewrite([23(4)])]. 2.95/3.26 17954 leq(multiplication(A,multiplication(A,A)),addition(B,star(A))). [para(15852(a,1),54(a,1,2)),xx(a)]. 2.95/3.26 17978 leq(multiplication(A,multiplication(A,multiplication(A,multiplication(A,multiplication(A,A))))),star(A)). [para(15777(a,1),17954(a,2)),rewrite([28(4),28(5)])]. 2.95/3.26 17979 $F # answer(a). [resolve(17978,a,33,a)]. 2.95/3.26 2.95/3.26 % SZS output end Refutation 2.95/3.26 ============================== end of proof ========================== 2.95/3.26 2.95/3.26 ============================== STATISTICS ============================ 2.95/3.26 2.95/3.26 Given=1484. Generated=119314. Kept=17957. proofs=1. 2.95/3.26 Usable=1088. Sos=9999. Demods=490. Limbo=0, Disabled=6887. Hints=0. 2.95/3.26 Megabytes=12.53. 2.95/3.26 User_CPU=2.22, System_CPU=0.08, Wall_clock=2. 2.95/3.26 2.95/3.26 ============================== end of statistics ===================== 2.95/3.26 2.95/3.26 ============================== end of search ========================= 2.95/3.26 2.95/3.26 THEOREM PROVED 2.95/3.26 % SZS status Theorem 2.95/3.26 2.95/3.26 Exiting with 1 proof. 2.95/3.26 2.95/3.26 Process 19777 exit (max_proofs) Mon Jul 3 08:28:25 2023 2.95/3.26 Prover9 interrupted 2.95/3.27 EOF