0.03/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.30 % Computer : n012.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 1440 0.10/0.30 % WCLimit : 180 0.10/0.30 % DateTime : Mon Jul 3 07:53:22 EDT 2023 0.10/0.31 % CPUTime : 0.72/1.07 ============================== Prover9 =============================== 0.72/1.07 Prover9 (32) version 2009-11A, November 2009. 0.72/1.07 Process 26159 was started by sandbox on n012.cluster.edu, 0.72/1.07 Mon Jul 3 07:53:23 2023 0.72/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_26006_n012.cluster.edu". 0.72/1.07 ============================== end of head =========================== 0.72/1.07 0.72/1.07 ============================== INPUT ================================= 0.72/1.07 0.72/1.07 % Reading from file /tmp/Prover9_26006_n012.cluster.edu 0.72/1.07 0.72/1.07 set(prolog_style_variables). 0.72/1.07 set(auto2). 0.72/1.07 % set(auto2) -> set(auto). 0.72/1.07 % set(auto) -> set(auto_inference). 0.72/1.07 % set(auto) -> set(auto_setup). 0.72/1.07 % set(auto_setup) -> set(predicate_elim). 0.72/1.07 % set(auto_setup) -> assign(eq_defs, unfold). 0.72/1.07 % set(auto) -> set(auto_limits). 0.72/1.07 % set(auto_limits) -> assign(max_weight, "100.000"). 0.72/1.07 % set(auto_limits) -> assign(sos_limit, 20000). 0.72/1.07 % set(auto) -> set(auto_denials). 0.72/1.07 % set(auto) -> set(auto_process). 0.72/1.07 % set(auto2) -> assign(new_constants, 1). 0.72/1.07 % set(auto2) -> assign(fold_denial_max, 3). 0.72/1.07 % set(auto2) -> assign(max_weight, "200.000"). 0.72/1.07 % set(auto2) -> assign(max_hours, 1). 0.72/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.72/1.07 % set(auto2) -> assign(max_seconds, 0). 0.72/1.07 % set(auto2) -> assign(max_minutes, 5). 0.72/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.72/1.07 % set(auto2) -> set(sort_initial_sos). 0.72/1.07 % set(auto2) -> assign(sos_limit, -1). 0.72/1.07 % set(auto2) -> assign(lrs_ticks, 3000). 0.72/1.07 % set(auto2) -> assign(max_megs, 400). 0.72/1.07 % set(auto2) -> assign(stats, some). 0.72/1.07 % set(auto2) -> clear(echo_input). 0.72/1.07 % set(auto2) -> set(quiet). 0.72/1.07 % set(auto2) -> clear(print_initial_clauses). 0.72/1.07 % set(auto2) -> clear(print_given). 0.72/1.07 assign(lrs_ticks,-1). 0.72/1.07 assign(sos_limit,10000). 0.72/1.07 assign(order,kbo). 0.72/1.07 set(lex_order_vars). 0.72/1.07 clear(print_given). 0.72/1.07 0.72/1.07 % formulas(sos). % not echoed (17 formulas) 0.72/1.07 0.72/1.07 ============================== end of input ========================== 0.72/1.07 0.72/1.07 % From the command line: assign(max_seconds, 1440). 0.72/1.07 0.72/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.72/1.07 0.72/1.07 % Formulas that are not ordinary clauses: 0.72/1.07 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]. 0.72/1.07 2 (all A all B (addition(A,B) = B <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.72/1.07 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]. 0.72/1.07 4 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.72/1.07 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.07 6 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.07 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]. 0.72/1.07 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]. 0.72/1.07 9 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.72/1.07 10 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.07 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]. 0.72/1.07 12 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.07 13 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 0.72/1.07 14 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 4.82/5.30 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]. 4.82/5.30 16 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 4.82/5.30 4.82/5.30 ============================== end of process non-clausal formulas === 4.82/5.30 4.82/5.30 ============================== PROCESS INITIAL CLAUSES =============== 4.82/5.30 4.82/5.30 ============================== PREDICATE ELIMINATION ================= 4.82/5.30 4.82/5.30 ============================== end predicate elimination ============= 4.82/5.30 4.82/5.30 Auto_denials: 4.82/5.30 % copying label a to answer in negative clause 4.82/5.30 4.82/5.30 Term ordering decisions: 4.82/5.30 4.82/5.30 % Assigning unary symbol star kb_weight 0 and highest precedence (8). 4.82/5.30 Function symbol KB weights: zero=1. one=1. a=1. multiplication=1. addition=1. star=0. 4.82/5.30 4.82/5.30 ============================== end of process initial clauses ======== 4.82/5.30 4.82/5.30 ============================== CLAUSES FOR SEARCH ==================== 4.82/5.30 4.82/5.30 ============================== end of clauses for search ============= 4.82/5.30 4.82/5.30 ============================== SEARCH ================================ 4.82/5.30 4.82/5.30 % Starting search at 0.01 seconds. 4.82/5.30 4.82/5.30 Low Water (keep): wt=36.000, iters=3360 4.82/5.30 4.82/5.30 Low Water (keep): wt=35.000, iters=3344 4.82/5.30 4.82/5.30 Low Water (keep): wt=33.000, iters=3358 4.82/5.30 4.82/5.30 Low Water (keep): wt=32.000, iters=3465 4.82/5.30 4.82/5.30 Low Water (keep): wt=31.000, iters=3412 4.82/5.30 4.82/5.30 Low Water (keep): wt=29.000, iters=3355 4.82/5.30 4.82/5.30 Low Water (keep): wt=28.000, iters=3343 4.82/5.30 4.82/5.30 Low Water (keep): wt=27.000, iters=3344 4.82/5.30 4.82/5.30 Low Water (keep): wt=25.000, iters=3366 4.82/5.30 4.82/5.30 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 52 (0.00 of 1.45 sec). 4.82/5.30 4.82/5.30 Low Water (keep): wt=24.000, iters=3383 4.82/5.30 4.82/5.30 Low Water (keep): wt=23.000, iters=3363 4.82/5.30 4.82/5.30 Low Water (keep): wt=22.000, iters=3338 4.82/5.30 4.82/5.30 Low Water (keep): wt=21.000, iters=3361 4.82/5.30 4.82/5.30 Low Water (keep): wt=20.000, iters=3350 4.82/5.30 4.82/5.30 Low Water (keep): wt=19.000, iters=3356 4.82/5.30 4.82/5.30 Low Water (displace): id=5586, wt=46.000 4.82/5.30 4.82/5.30 Low Water (displace): id=5562, wt=44.000 4.82/5.30 4.82/5.30 Low Water (displace): id=6242, wt=43.000 4.82/5.30 4.82/5.30 Low Water (displace): id=5808, wt=42.000 4.82/5.30 4.82/5.30 Low Water (displace): id=6254, wt=41.000 4.82/5.30 4.82/5.30 Low Water (displace): id=6238, wt=40.000 4.82/5.30 4.82/5.30 Low Water (displace): id=6180, wt=39.000 4.82/5.30 4.82/5.30 Low Water (displace): id=6218, wt=38.000 4.82/5.30 4.82/5.30 Low Water (displace): id=6155, wt=37.000 4.82/5.30 4.82/5.30 Low Water (displace): id=11623, wt=18.000 4.82/5.30 4.82/5.30 Low Water (displace): id=11976, wt=17.000 4.82/5.30 4.82/5.30 Low Water (displace): id=11982, wt=16.000 4.82/5.30 4.82/5.30 Low Water (displace): id=12091, wt=15.000 4.82/5.30 4.82/5.30 Low Water (displace): id=12608, wt=14.000 4.82/5.30 4.82/5.30 Low Water (displace): id=12613, wt=13.000 4.82/5.30 4.82/5.30 Low Water (keep): wt=18.000, iters=3420 4.82/5.30 4.82/5.30 Low Water (displace): id=14533, wt=12.000 4.82/5.30 4.82/5.30 Low Water (keep): wt=17.000, iters=3340 4.82/5.30 4.82/5.30 ============================== PROOF ================================= 4.82/5.30 % SZS status Theorem 4.82/5.30 % SZS output start Refutation 4.82/5.30 4.82/5.30 % Proof 1 at 4.01 (+ 0.10) seconds: a. 4.82/5.30 % Length of proof is 113. 4.82/5.30 % Level of proof is 23. 4.82/5.30 % Maximum clause weight is 20.000. 4.82/5.30 % Given clauses 1370. 4.82/5.30 4.82/5.30 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]. 4.82/5.30 2 (all A all B (addition(A,B) = B <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 4.82/5.30 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]. 4.82/5.30 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 4.82/5.30 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]. 4.82/5.30 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]. 4.82/5.30 9 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 4.82/5.30 10 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 4.82/5.30 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]. 4.82/5.30 12 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 4.82/5.30 13 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption]. 4.82/5.30 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]. 4.82/5.30 16 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption]. 4.82/5.30 18 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(5)]. 4.82/5.30 20 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(9)]. 4.82/5.30 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(10)]. 4.82/5.30 23 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(12)]. 4.82/5.30 24 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(13)]. 4.82/5.30 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(16)]. 4.82/5.30 26 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(3)]. 4.82/5.30 27 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(26),rewrite([23(2)]),flip(a)]. 4.82/5.30 28 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(15)]. 4.82/5.30 29 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(1)]. 4.82/5.30 30 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(29),flip(a)]. 4.82/5.30 31 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(8)]. 4.82/5.30 32 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(31),flip(a)]. 4.82/5.30 33 -leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)) # label(a) # label(negated_conjecture) # answer(a). [assumption]. 4.82/5.30 34 addition(A,B) != B | leq(A,B) # label(order) # label(axiom). [clausify(2)]. 4.82/5.30 35 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom). [clausify(2)]. 4.82/5.30 36 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(7)]. 4.82/5.30 37 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(36),rewrite([23(2)])]. 4.82/5.30 38 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(11)]. 4.82/5.30 39 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(38),rewrite([23(2)])]. 4.82/5.30 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)])]. 4.82/5.30 44 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(18(a,1),30(a,1,1)),rewrite([23(4)]),flip(a)]. 4.82/5.30 46 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(21(a,1),32(a,1,1)),rewrite([23(4)]),flip(a)]. 4.82/5.30 49 leq(A,A). [hyper(34,a,20,a)]. 4.82/5.30 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)])]. 4.82/5.30 54 addition(A,addition(B,C)) != addition(A,B) | leq(C,addition(A,B)). [para(27(a,2),34(a,1))]. 4.82/5.30 57 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(35,b,25,a),rewrite([23(6)])]. 4.82/5.30 58 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(35,b,24,a),rewrite([23(6)])]. 4.82/5.30 61 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A). [para(20(a,1),37(a,1)),rewrite([28(5)])]. 4.82/5.30 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))]. 4.82/5.30 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)])]. 4.82/5.30 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)])]. 4.82/5.30 69 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B). [para(20(a,1),39(a,1))]. 4.82/5.30 80 leq(A,addition(A,B)). [hyper(34,a,42,a)]. 4.82/5.30 81 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(30(a,1),80(a,2))]. 4.82/5.30 138 addition(addition(A,multiplication(B,A)),multiplication(addition(B,one),C)) = multiplication(addition(B,one),addition(A,C)). [para(46(a,1),30(a,1,1))]. 4.82/5.30 147 -leq(multiplication(addition(A,one),B),B) | leq(multiplication(star(A),B),B). [para(46(a,2),39(a,1))]. 4.82/5.30 200 leq(A,addition(B,A)). [para(20(a,1),53(a,1,2)),xx(a)]. 4.82/5.30 206 leq(A,addition(B,addition(A,C))). [para(42(a,1),53(a,1,2)),xx(a)]. 4.82/5.30 209 addition(A,multiplication(addition(B,one),C)) != addition(A,multiplication(B,C)) | leq(C,addition(A,multiplication(B,C))). [para(46(a,2),53(a,1,2))]. 4.82/5.30 213 leq(addition(A,B),addition(A,addition(B,C))). [para(27(a,1),200(a,2)),rewrite([23(2),27(3,R),23(2)])]. 4.82/5.30 214 leq(multiplication(A,B),addition(C,multiplication(A,addition(B,D)))). [para(30(a,1),206(a,2,2))]. 4.82/5.30 215 leq(multiplication(A,B),addition(C,multiplication(addition(A,D),B))). [para(32(a,1),206(a,2,2))]. 4.82/5.30 217 leq(A,addition(B,multiplication(addition(C,one),A))). [para(46(a,2),206(a,2,2))]. 4.82/5.30 251 addition(A,addition(B,multiplication(addition(C,one),A))) = addition(B,multiplication(addition(C,one),A)). [hyper(35,b,217,a)]. 4.82/5.30 252 leq(A,multiplication(addition(B,one),addition(A,C))). [para(30(a,1),217(a,2)),rewrite([23(3)])]. 4.82/5.30 288 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)])]. 4.82/5.30 291 leq(one,star(A)). [para(57(a,1),206(a,2))]. 4.82/5.30 293 addition(star(A),one) != star(A) | leq(multiplication(A,star(A)),addition(star(A),one)). [para(57(a,1),54(a,1)),flip(a)]. 4.82/5.30 294 leq(addition(star(A),one),star(A)). [para(57(a,1),213(a,2))]. 4.82/5.30 297 addition(one,star(A)) = star(A). [hyper(35,b,291,a)]. 4.82/5.30 298 addition(star(A),one) = star(A). [hyper(35,b,294,a),rewrite([23(5),42(5)])]. 4.82/5.30 299 leq(multiplication(A,star(A)),star(A)). [back_rewrite(293),rewrite([298(3),298(8)]),xx(a)]. 4.82/5.30 300 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)). [para(297(a,1),30(a,2,2)),rewrite([18(2)])]. 4.82/5.30 303 leq(A,multiplication(A,star(B))). [para(297(a,1),81(a,2,2)),rewrite([18(2)])]. 4.82/5.30 309 leq(one,multiplication(addition(A,one),star(B))). [para(297(a,1),252(a,2,2))]. 4.82/5.30 310 leq(multiplication(A,B),multiplication(A,multiplication(B,star(C)))). [para(28(a,1),303(a,2))]. 4.82/5.30 312 addition(star(A),multiplication(star(A),A)) = star(A). [para(58(a,1),27(a,1)),rewrite([298(6),23(5)]),flip(a)]. 4.82/5.30 317 leq(multiplication(star(A),A),star(A)). [para(58(a,1),54(a,1)),rewrite([298(4),298(8)]),xx(a)]. 4.82/5.30 323 leq(A,addition(B,multiplication(star(C),A))). [para(298(a,1),217(a,2,2,1))]. 4.82/5.30 329 addition(star(A),multiplication(A,star(A))) = star(A). [hyper(35,b,299,a),rewrite([23(4)])]. 4.82/5.30 356 addition(one,multiplication(addition(A,one),star(B))) = multiplication(addition(A,one),star(B)). [hyper(35,b,309,a)]. 4.82/5.30 358 multiplication(addition(A,one),star(addition(A,one))) = star(addition(A,one)). [back_rewrite(288),rewrite([356(8)])]. 4.82/5.30 400 -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)])]. 4.82/5.30 421 leq(multiplication(star(addition(A,B)),multiplication(A,star(B))),star(addition(A,B))). [hyper(65,a,317,a)]. 4.82/5.30 455 -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)])]. 4.82/5.30 489 multiplication(star(A),addition(A,one)) = star(A). [para(312(a,1),44(a,2))]. 4.82/5.30 494 leq(A,star(A)). [para(312(a,1),323(a,2))]. 4.82/5.30 500 addition(A,star(A)) = star(A). [hyper(35,b,494,a)]. 4.87/5.30 602 multiplication(star(star(A)),star(A)) = star(star(A)). [para(298(a,1),489(a,1,2))]. 4.87/5.30 657 multiplication(addition(A,one),star(A)) = star(A). [para(329(a,1),46(a,2))]. 4.87/5.30 696 leq(multiplication(A,addition(B,one)),multiplication(A,star(B))). [para(657(a,1),310(a,2,2))]. 4.87/5.30 810 multiplication(star(star(A)),multiplication(star(A),B)) = multiplication(star(star(A)),B). [para(602(a,1),28(a,1,1)),flip(a)]. 4.87/5.30 1374 leq(multiplication(star(star(A)),addition(A,one)),star(star(A))). [para(602(a,1),696(a,2))]. 4.87/5.30 1894 leq(multiplication(A,B),addition(C,multiplication(A,star(B)))). [para(500(a,1),214(a,2,2,2))]. 4.87/5.30 1934 leq(multiplication(A,A),star(A)). [para(329(a,1),1894(a,2))]. 4.87/5.30 1950 addition(star(A),multiplication(A,A)) = star(A). [hyper(35,b,1934,a),rewrite([23(3)])]. 4.87/5.30 2327 leq(multiplication(A,star(addition(A,B))),star(addition(A,B))). [para(329(a,1),215(a,2))]. 4.87/5.30 3998 leq(multiplication(star(A),star(addition(A,one))),star(addition(A,one))). [hyper(147,a,299,a)]. 4.87/5.30 7327 leq(multiplication(star(star(A)),star(addition(A,one))),star(star(A))). [hyper(61,a,1374,a),rewrite([358(8)])]. 4.87/5.30 7918 multiplication(addition(A,one),star(addition(A,B))) = star(addition(A,B)). [hyper(35,b,2327,a),rewrite([23(6),46(6,R)])]. 4.87/5.30 8753 leq(A,multiplication(addition(B,one),addition(C,A))). [para(138(a,1),209(a,2)),rewrite([23(6),27(6,R),20(5),138(6),138(15)]),xx(a)]. 4.87/5.30 8763 leq(multiplication(A,A),multiplication(addition(B,one),star(A))). [para(1950(a,1),8753(a,2,2))]. 4.87/5.30 8775 leq(multiplication(A,A),multiplication(star(B),star(A))). [para(298(a,1),8763(a,2,1))]. 4.87/5.30 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)])]. 4.87/5.30 13728 -leq(star(A),star(A)) | leq(star(addition(A,one)),star(A)). [para(489(a,1),13709(a,1,2)),rewrite([297(3)])]. 4.87/5.30 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)])]. 4.87/5.30 14123 leq(multiplication(star(star(A)),star(addition(A,one))),star(addition(A,one))). [hyper(69,a,3998,a),rewrite([810(8)])]. 4.87/5.30 14506 leq(star(addition(A,one)),star(star(A))). [hyper(455,a,1374,a),rewrite([7918(6)])]. 4.87/5.30 14511 addition(star(star(A)),star(addition(A,one))) = star(star(A)). [hyper(35,b,14506,a),rewrite([23(6)])]. 4.87/5.30 14781 multiplication(star(star(A)),star(addition(A,one))) = star(star(A)). [hyper(35,b,7327,a),rewrite([23(9),300(9)])]. 4.87/5.30 14782 leq(star(star(A)),star(addition(A,one))). [back_rewrite(14123),rewrite([14781(6)])]. 4.87/5.30 14783 star(addition(A,one)) = star(star(A)). [hyper(35,b,14782,a),rewrite([14511(6)]),flip(a)]. 4.87/5.30 14822 -leq(star(A),star(A)) | leq(star(star(A)),star(A)). [back_rewrite(13728),rewrite([14783(6)])]. 4.87/5.30 15087 leq(star(star(A)),star(A)). [hyper(14822,a,49,a)]. 4.87/5.30 15088 star(star(A)) = star(A). [hyper(35,b,15087,a),rewrite([23(4),500(4)])]. 4.87/5.30 15267 leq(multiplication(star(A),star(multiplication(A,A))),star(A)). [back_rewrite(13864),rewrite([15088(2),15088(6)])]. 4.87/5.30 15774 multiplication(star(A),star(multiplication(A,A))) = star(A). [hyper(35,b,15267,a),rewrite([23(6),300(6)])]. 4.87/5.30 15803 leq(multiplication(A,multiplication(A,multiplication(A,A))),star(A)). [para(15774(a,1),8775(a,2)),rewrite([28(3)])]. 4.87/5.30 15804 $F # answer(a). [resolve(15803,a,33,a)]. 4.87/5.30 4.87/5.30 % SZS output end Refutation 4.87/5.30 ============================== end of proof ========================== 4.87/5.30 4.87/5.30 ============================== STATISTICS ============================ 4.87/5.30 4.87/5.30 Given=1370. Generated=100843. Kept=15782. proofs=1. 4.87/5.30 Usable=992. Sos=8093. Demods=410. Limbo=23, Disabled=6691. Hints=0. 4.87/5.30 Megabytes=11.68. 4.87/5.30 User_CPU=4.01, System_CPU=0.10, Wall_clock=4. 4.87/5.30 4.87/5.30 ============================== end of statistics ===================== 4.87/5.30 4.87/5.30 ============================== end of search ========================= 4.87/5.30 4.87/5.30 THEOREM PROVED 4.87/5.30 % SZS status Theorem 4.87/5.30 4.87/5.30 Exiting with 1 proof. 4.87/5.30 4.87/5.30 Process 26159 exit (max_proofs) Mon Jul 3 07:53:27 2023 4.87/5.30 Prover9 interrupted 4.87/5.30 EOF