0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n025.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 960 0.12/0.33 % DateTime : Thu Jul 2 09:06:18 EDT 2020 0.12/0.33 % CPUTime : 0.72/1.00 ============================== Prover9 =============================== 0.72/1.00 Prover9 (32) version 2009-11A, November 2009. 0.72/1.00 Process 26854 was started by sandbox2 on n025.cluster.edu, 0.72/1.00 Thu Jul 2 09:06:18 2020 0.72/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_26701_n025.cluster.edu". 0.72/1.00 ============================== end of head =========================== 0.72/1.00 0.72/1.00 ============================== INPUT ================================= 0.72/1.00 0.72/1.00 % Reading from file /tmp/Prover9_26701_n025.cluster.edu 0.72/1.00 0.72/1.00 set(prolog_style_variables). 0.72/1.00 set(auto2). 0.72/1.00 % set(auto2) -> set(auto). 0.72/1.00 % set(auto) -> set(auto_inference). 0.72/1.00 % set(auto) -> set(auto_setup). 0.72/1.00 % set(auto_setup) -> set(predicate_elim). 0.72/1.00 % set(auto_setup) -> assign(eq_defs, unfold). 0.72/1.00 % set(auto) -> set(auto_limits). 0.72/1.00 % set(auto_limits) -> assign(max_weight, "100.000"). 0.72/1.00 % set(auto_limits) -> assign(sos_limit, 20000). 0.72/1.00 % set(auto) -> set(auto_denials). 0.72/1.00 % set(auto) -> set(auto_process). 0.72/1.00 % set(auto2) -> assign(new_constants, 1). 0.72/1.00 % set(auto2) -> assign(fold_denial_max, 3). 0.72/1.00 % set(auto2) -> assign(max_weight, "200.000"). 0.72/1.00 % set(auto2) -> assign(max_hours, 1). 0.72/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.72/1.00 % set(auto2) -> assign(max_seconds, 0). 0.72/1.00 % set(auto2) -> assign(max_minutes, 5). 0.72/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.72/1.00 % set(auto2) -> set(sort_initial_sos). 0.72/1.00 % set(auto2) -> assign(sos_limit, -1). 0.72/1.00 % set(auto2) -> assign(lrs_ticks, 3000). 0.72/1.00 % set(auto2) -> assign(max_megs, 400). 0.72/1.00 % set(auto2) -> assign(stats, some). 0.72/1.00 % set(auto2) -> clear(echo_input). 0.72/1.00 % set(auto2) -> set(quiet). 0.72/1.00 % set(auto2) -> clear(print_initial_clauses). 0.72/1.00 % set(auto2) -> clear(print_given). 0.72/1.00 assign(lrs_ticks,-1). 0.72/1.00 assign(sos_limit,10000). 0.72/1.00 assign(order,kbo). 0.72/1.00 set(lex_order_vars). 0.72/1.00 clear(print_given). 0.72/1.00 0.72/1.00 % formulas(sos). % not echoed (17 formulas) 0.72/1.00 0.72/1.00 ============================== end of input ========================== 0.72/1.00 0.72/1.00 % From the command line: assign(max_seconds, 960). 0.72/1.00 0.72/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.72/1.00 0.72/1.00 % Formulas that are not ordinary clauses: 0.72/1.00 1 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 2 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 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]. 0.72/1.00 4 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 5 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 6 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 7 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 8 (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]. 0.72/1.00 9 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 10 (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]. 0.72/1.00 11 (all A A = addition(A,zero)) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 12 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 13 (all A zero = multiplication(A,zero)) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.72/1.00 14 (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]. 3.23/3.49 15 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 16 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 3.23/3.49 ============================== end of process non-clausal formulas === 3.23/3.49 3.23/3.49 ============================== PROCESS INITIAL CLAUSES =============== 3.23/3.49 3.23/3.49 ============================== PREDICATE ELIMINATION ================= 3.23/3.49 3.23/3.49 ============================== end predicate elimination ============= 3.23/3.49 3.23/3.49 Auto_denials: 3.23/3.49 % copying label a to answer in negative clause 3.23/3.49 3.23/3.49 Term ordering decisions: 3.23/3.49 3.23/3.49 % Assigning unary symbol star kb_weight 0 and highest precedence (8). 3.23/3.49 Function symbol KB weights: zero=1. one=1. a=1. multiplication=1. addition=1. star=0. 3.23/3.49 3.23/3.49 ============================== end of process initial clauses ======== 3.23/3.49 3.23/3.49 ============================== CLAUSES FOR SEARCH ==================== 3.23/3.49 3.23/3.49 ============================== end of clauses for search ============= 3.23/3.49 3.23/3.49 ============================== SEARCH ================================ 3.23/3.49 3.23/3.49 % Starting search at 0.01 seconds. 3.23/3.49 3.23/3.49 Low Water (keep): wt=34.000, iters=3342 3.23/3.49 3.23/3.49 Low Water (keep): wt=33.000, iters=3393 3.23/3.49 3.23/3.49 Low Water (keep): wt=32.000, iters=3543 3.23/3.49 3.23/3.49 Low Water (keep): wt=30.000, iters=3365 3.23/3.49 3.23/3.49 Low Water (keep): wt=29.000, iters=3335 3.23/3.49 3.23/3.49 Low Water (keep): wt=28.000, iters=3362 3.23/3.49 3.23/3.49 Low Water (keep): wt=27.000, iters=3376 3.23/3.49 3.23/3.49 Low Water (keep): wt=25.000, iters=3335 3.23/3.49 3.23/3.49 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 53 (0.00 of 0.89 sec). 3.23/3.49 3.23/3.49 Low Water (keep): wt=24.000, iters=3355 3.23/3.49 3.23/3.49 Low Water (keep): wt=23.000, iters=3340 3.23/3.49 3.23/3.49 Low Water (keep): wt=22.000, iters=3344 3.23/3.49 3.23/3.49 Low Water (keep): wt=21.000, iters=3357 3.23/3.49 3.23/3.49 Low Water (keep): wt=20.000, iters=3360 3.23/3.49 3.23/3.49 Low Water (keep): wt=19.000, iters=3338 3.23/3.49 3.23/3.49 Low Water (displace): id=5643, wt=46.000 3.23/3.49 3.23/3.49 Low Water (displace): id=5617, wt=44.000 3.23/3.49 3.23/3.49 Low Water (displace): id=6317, wt=43.000 3.23/3.49 3.23/3.49 Low Water (displace): id=5880, wt=42.000 3.23/3.49 3.23/3.49 Low Water (displace): id=6333, wt=41.000 3.23/3.49 3.23/3.49 Low Water (displace): id=6313, wt=40.000 3.23/3.49 3.23/3.49 Low Water (displace): id=6256, wt=39.000 3.23/3.49 3.23/3.49 Low Water (displace): id=6297, wt=38.000 3.23/3.49 3.23/3.49 Low Water (displace): id=6229, wt=37.000 3.23/3.49 3.23/3.49 Low Water (displace): id=11615, wt=18.000 3.23/3.49 3.23/3.49 Low Water (displace): id=11963, wt=15.000 3.23/3.49 3.23/3.49 Low Water (displace): id=12664, wt=14.000 3.23/3.49 3.23/3.49 Low Water (displace): id=12665, wt=13.000 3.23/3.49 3.23/3.49 Low Water (displace): id=12675, wt=12.000 3.23/3.49 3.23/3.49 Low Water (keep): wt=18.000, iters=3415 3.23/3.49 3.23/3.49 Low Water (displace): id=14599, wt=10.000 3.23/3.49 3.23/3.49 Low Water (keep): wt=17.000, iters=3428 3.23/3.49 3.23/3.49 ============================== PROOF ================================= 3.23/3.49 % SZS status Theorem 3.23/3.49 % SZS output start Refutation 3.23/3.49 3.23/3.49 % Proof 1 at 2.44 (+ 0.06) seconds: a. 3.23/3.49 % Length of proof is 118. 3.23/3.49 % Level of proof is 26. 3.23/3.49 % Maximum clause weight is 19.000. 3.23/3.49 % Given clauses 1480. 3.23/3.49 3.23/3.49 1 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 2 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 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]. 3.23/3.49 4 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 5 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 7 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 8 (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]. 3.23/3.49 9 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 10 (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]. 3.23/3.49 12 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 14 (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]. 3.23/3.49 15 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 16 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 3.23/3.49 17 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(2)]. 3.23/3.49 18 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(4)]. 3.23/3.49 20 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(7)]. 3.23/3.49 23 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(15)]. 3.23/3.49 24 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(1)]. 3.23/3.49 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(5)]. 3.23/3.49 26 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(3)]. 3.23/3.49 27 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(26),rewrite([23(2)]),flip(a)]. 3.23/3.49 28 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(9)]. 3.23/3.49 29 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom). [clausify(10)]. 3.23/3.49 30 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom). [clausify(12)]. 3.23/3.49 31 -leq(multiplication(a,multiplication(a,multiplication(a,multiplication(a,multiplication(a,a))))),star(a)) # label(a) # label(negated_conjecture) # answer(a). [assumption]. 3.23/3.49 32 addition(A,B) != B | leq(A,B) # label(order) # label(axiom). [clausify(16)]. 3.23/3.49 33 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom). [clausify(16)]. 3.23/3.49 34 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(8)]. 3.23/3.49 35 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(34),rewrite([23(2)])]. 3.23/3.49 36 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(14)]. 3.23/3.49 37 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(36),rewrite([23(2)])]. 3.23/3.49 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)])]. 3.23/3.49 42 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)). [para(18(a,1),29(a,1,1)),rewrite([23(4)])]. 3.23/3.49 44 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A). [para(17(a,1),30(a,1,1)),rewrite([23(4)])]. 3.23/3.49 48 leq(A,A). [hyper(32,a,20,a)]. 3.23/3.49 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)])]. 3.23/3.49 53 addition(A,addition(B,C)) != addition(A,B) | leq(C,addition(A,B)). [para(27(a,2),32(a,1))]. 3.23/3.49 56 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(33,b,25,a),rewrite([23(6)])]. 3.23/3.49 57 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(33,b,24,a),rewrite([23(6)])]. 3.23/3.49 61 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A). [para(20(a,1),35(a,1)),rewrite([28(5)])]. 3.23/3.49 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))]. 3.23/3.49 64 -leq(multiplication(A,addition(B,C)),A) | leq(multiplication(A,multiplication(B,star(C))),A). [para(29(a,1),35(a,1)),rewrite([28(6)])]. 3.23/3.49 65 -leq(multiplication(addition(A,B),C),B) | leq(multiplication(A,multiplication(C,star(C))),B). [para(30(a,1),35(a,1)),rewrite([28(6)])]. 3.23/3.49 69 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B). [para(20(a,1),37(a,1))]. 3.23/3.49 79 leq(A,addition(A,B)). [hyper(32,a,40,a)]. 3.23/3.49 80 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(29(a,1),79(a,2))]. 3.23/3.49 145 -leq(multiplication(addition(A,one),B),B) | leq(multiplication(star(A),B),B). [para(44(a,1),37(a,1))]. 3.23/3.49 199 leq(A,addition(B,A)). [para(20(a,1),52(a,1,2)),xx(a)]. 3.23/3.49 205 leq(A,addition(B,addition(A,C))). [para(40(a,1),52(a,1,2)),xx(a)]. 3.23/3.49 212 leq(addition(A,B),addition(A,addition(B,C))). [para(27(a,1),199(a,2)),rewrite([23(2),27(3,R),23(2)])]. 3.23/3.49 213 leq(multiplication(A,B),addition(C,multiplication(A,addition(B,D)))). [para(29(a,1),205(a,2,2))]. 3.23/3.49 214 leq(multiplication(A,B),addition(C,multiplication(addition(A,D),B))). [para(30(a,1),205(a,2,2))]. 3.23/3.49 216 leq(A,addition(B,multiplication(addition(C,one),A))). [para(44(a,1),205(a,2,2))]. 3.23/3.49 250 addition(A,addition(B,multiplication(addition(C,one),A))) = addition(B,multiplication(addition(C,one),A)). [hyper(33,b,216,a)]. 3.23/3.49 251 leq(A,multiplication(addition(B,one),addition(A,C))). [para(29(a,1),216(a,2)),rewrite([23(3)])]. 3.23/3.49 287 addition(one,multiplication(addition(A,one),star(addition(A,one)))) = star(addition(A,one)). [para(44(a,2),56(a,1,2,2)),rewrite([44(12),250(12)])]. 3.23/3.49 290 leq(one,star(A)). [para(56(a,1),205(a,2))]. 3.23/3.49 292 addition(star(A),one) != star(A) | leq(multiplication(A,star(A)),addition(star(A),one)). [para(56(a,1),53(a,1)),flip(a)]. 3.23/3.49 293 leq(addition(star(A),one),star(A)). [para(56(a,1),212(a,2))]. 3.23/3.49 296 addition(one,star(A)) = star(A). [hyper(33,b,290,a)]. 3.23/3.49 297 addition(star(A),one) = star(A). [hyper(33,b,293,a),rewrite([23(5),40(5)])]. 3.23/3.49 298 leq(multiplication(A,star(A)),star(A)). [back_rewrite(292),rewrite([297(3),297(8)]),xx(a)]. 3.23/3.49 299 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)). [para(296(a,1),29(a,2,2)),rewrite([18(2)])]. 3.23/3.49 302 leq(A,multiplication(A,star(B))). [para(296(a,1),80(a,2,2)),rewrite([18(2)])]. 3.23/3.49 308 leq(one,multiplication(addition(A,one),star(B))). [para(296(a,1),251(a,2,2))]. 3.23/3.49 309 leq(multiplication(A,B),multiplication(A,multiplication(B,star(C)))). [para(28(a,1),302(a,2))]. 3.23/3.49 311 addition(star(A),multiplication(star(A),A)) = star(A). [para(57(a,1),27(a,1)),rewrite([297(6),23(5)]),flip(a)]. 3.23/3.49 316 leq(multiplication(star(A),A),star(A)). [para(57(a,1),53(a,1)),rewrite([297(4),297(8)]),xx(a)]. 3.23/3.49 322 leq(A,addition(B,multiplication(star(C),A))). [para(297(a,1),216(a,2,2,1))]. 3.23/3.49 328 addition(star(A),multiplication(A,star(A))) = star(A). [hyper(33,b,298,a),rewrite([23(4)])]. 3.23/3.49 364 addition(one,multiplication(addition(A,one),star(B))) = multiplication(addition(A,one),star(B)). [hyper(33,b,308,a)]. 3.23/3.49 366 multiplication(addition(A,one),star(addition(A,one))) = star(addition(A,one)). [back_rewrite(287),rewrite([364(8)])]. 3.23/3.49 374 leq(multiplication(star(A),multiplication(A,star(A))),star(A)). [hyper(61,a,316,a)]. 3.23/3.49 396 -leq(multiplication(A,addition(one,multiplication(B,C))),multiplication(A,B)) | leq(multiplication(A,star(C)),multiplication(A,B)). [para(42(a,1),63(a,1)),rewrite([23(3)])]. 3.23/3.49 423 leq(multiplication(star(addition(A,B)),multiplication(A,star(B))),star(addition(A,B))). [hyper(64,a,316,a)]. 3.23/3.49 452 -leq(multiplication(star(A),B),star(A)) | leq(multiplication(B,star(B)),star(A)). [para(296(a,1),65(a,1,1)),rewrite([17(8)])]. 3.23/3.49 471 multiplication(star(A),addition(A,one)) = star(A). [para(311(a,1),42(a,1)),flip(a)]. 3.23/3.49 477 leq(A,star(A)). [para(311(a,1),322(a,2))]. 3.23/3.49 495 addition(A,star(A)) = star(A). [hyper(33,b,477,a)]. 3.23/3.49 584 multiplication(star(star(A)),star(A)) = star(star(A)). [para(297(a,1),471(a,1,2))]. 3.23/3.49 652 multiplication(addition(A,one),star(A)) = star(A). [para(328(a,1),44(a,1)),flip(a)]. 3.23/3.49 675 multiplication(star(A),star(star(A))) = star(star(A)). [para(297(a,1),652(a,1,1))]. 3.23/3.49 678 leq(multiplication(A,addition(B,one)),multiplication(A,star(B))). [para(652(a,1),309(a,2,2))]. 3.23/3.49 805 multiplication(star(star(A)),multiplication(star(A),B)) = multiplication(star(star(A)),B). [para(584(a,1),28(a,1,1)),flip(a)]. 3.23/3.49 1255 leq(multiplication(star(star(A)),star(star(A))),star(star(A))). [para(675(a,1),374(a,1,2))]. 3.23/3.49 1372 leq(multiplication(star(star(A)),addition(A,one)),star(star(A))). [para(584(a,1),678(a,2))]. 3.23/3.49 1896 leq(multiplication(A,B),addition(C,multiplication(A,star(B)))). [para(495(a,1),213(a,2,2,2))]. 3.23/3.49 1922 leq(multiplication(A,B),multiplication(addition(A,C),star(B))). [para(30(a,1),1896(a,2)),rewrite([23(2)])]. 3.23/3.49 1926 leq(multiplication(A,A),star(A)). [para(328(a,1),1896(a,2))]. 3.23/3.49 1942 addition(star(A),multiplication(A,A)) = star(A). [hyper(33,b,1926,a),rewrite([23(3)])]. 3.23/3.49 2032 leq(multiplication(A,B),multiplication(star(A),star(B))). [para(495(a,1),1922(a,2,1))]. 3.23/3.49 2318 leq(multiplication(A,star(addition(A,B))),star(addition(A,B))). [para(328(a,1),214(a,2))]. 3.23/3.49 4020 leq(multiplication(star(A),star(addition(A,one))),star(addition(A,one))). [hyper(145,a,298,a)]. 3.23/3.49 6987 multiplication(star(star(A)),star(star(A))) = star(star(A)). [hyper(33,b,1255,a),rewrite([23(8),299(8)])]. 3.23/3.49 7364 leq(multiplication(star(star(A)),star(addition(A,one))),star(star(A))). [hyper(61,a,1372,a),rewrite([366(8)])]. 3.23/3.49 7982 multiplication(addition(A,one),star(addition(A,B))) = star(addition(A,B)). [hyper(33,b,2318,a),rewrite([23(6),44(6)])]. 3.23/3.49 13733 -leq(addition(one,multiplication(A,B)),A) | leq(star(B),A). [para(17(a,1),396(a,1)),rewrite([17(5),17(7),17(7)])]. 3.23/3.49 13760 -leq(star(A),star(A)) | leq(star(addition(A,one)),star(A)). [para(471(a,1),13733(a,1,2)),rewrite([296(3)])]. 3.23/3.49 13936 leq(multiplication(star(star(A)),star(multiplication(A,A))),star(star(A))). [para(1942(a,1),423(a,1,1,1)),rewrite([805(7),1942(8)])]. 3.23/3.49 14167 leq(multiplication(star(star(A)),star(addition(A,one))),star(addition(A,one))). [hyper(69,a,4020,a),rewrite([805(8)])]. 3.23/3.49 14576 leq(star(addition(A,one)),star(star(A))). [hyper(452,a,1372,a),rewrite([7982(6)])]. 3.23/3.49 14581 addition(star(star(A)),star(addition(A,one))) = star(star(A)). [hyper(33,b,14576,a),rewrite([23(6)])]. 3.23/3.49 14780 multiplication(star(star(A)),star(addition(A,one))) = star(star(A)). [hyper(33,b,7364,a),rewrite([23(9),299(9)])]. 3.23/3.49 14781 leq(star(star(A)),star(addition(A,one))). [back_rewrite(14167),rewrite([14780(6)])]. 3.23/3.49 14782 star(addition(A,one)) = star(star(A)). [hyper(33,b,14781,a),rewrite([14581(6)]),flip(a)]. 3.23/3.49 14825 -leq(star(A),star(A)) | leq(star(star(A)),star(A)). [back_rewrite(13760),rewrite([14782(6)])]. 3.23/3.49 15208 leq(star(star(A)),star(A)). [hyper(14825,a,48,a)]. 3.23/3.49 15210 star(star(A)) = star(A). [hyper(33,b,15208,a),rewrite([23(4),495(4)])]. 3.23/3.49 15394 leq(multiplication(star(A),star(multiplication(A,A))),star(A)). [back_rewrite(13936),rewrite([15210(2),15210(6)])]. 3.23/3.49 15495 multiplication(star(A),star(A)) = star(A). [back_rewrite(6987),rewrite([15210(2),15210(3),15210(5)])]. 3.23/3.49 15896 leq(star(multiplication(A,A)),star(A)). [hyper(452,a,15394,a),rewrite([15210(5),15495(5)])]. 3.23/3.49 15897 multiplication(star(A),star(multiplication(A,A))) = star(A). [hyper(33,b,15394,a),rewrite([23(6),299(6)])]. 3.23/3.49 15900 addition(star(A),star(multiplication(A,A))) = star(A). [hyper(33,b,15896,a),rewrite([23(4)])]. 3.23/3.49 15924 leq(multiplication(A,multiplication(A,A)),star(A)). [para(15897(a,1),2032(a,2))]. 3.23/3.49 15985 addition(star(A),multiplication(A,multiplication(A,A))) = star(A). [hyper(33,b,15924,a),rewrite([23(4)])]. 3.23/3.49 18123 leq(multiplication(A,multiplication(A,A)),addition(B,star(A))). [para(15985(a,1),53(a,1,2)),xx(a)]. 3.23/3.49 18152 leq(multiplication(A,multiplication(A,multiplication(A,multiplication(A,multiplication(A,A))))),star(A)). [para(15900(a,1),18123(a,2)),rewrite([28(4),28(5)])]. 3.23/3.49 18153 $F # answer(a). [resolve(18152,a,31,a)]. 3.23/3.49 3.23/3.49 % SZS output end Refutation 3.23/3.49 ============================== end of proof ========================== 3.23/3.49 3.23/3.49 ============================== STATISTICS ============================ 3.23/3.49 3.23/3.49 Given=1480. Generated=119626. Kept=18133. proofs=1. 3.23/3.49 Usable=1086. Sos=9999. Demods=491. Limbo=1, Disabled=7064. Hints=0. 3.23/3.49 Megabytes=12.64. 3.23/3.49 User_CPU=2.44, System_CPU=0.06, Wall_clock=3. 3.23/3.49 3.23/3.49 ============================== end of statistics ===================== 3.23/3.49 3.23/3.49 ============================== end of search ========================= 3.23/3.49 3.23/3.49 THEOREM PROVED 3.23/3.49 % SZS status Theorem 3.23/3.49 3.23/3.49 Exiting with 1 proof. 3.23/3.49 3.23/3.49 Process 26854 exit (max_proofs) Thu Jul 2 09:06:21 2020 3.23/3.49 Prover9 interrupted 3.23/3.49 EOF