0.08/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n013.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 05:53:17 EDT 2023 0.13/0.34 % CPUTime : 2.42/2.70 ============================== Prover9 =============================== 2.42/2.70 Prover9 (32) version 2009-11A, November 2009. 2.42/2.70 Process 17256 was started by sandbox on n013.cluster.edu, 2.42/2.70 Mon Jul 3 05:53:18 2023 2.42/2.70 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_17069_n013.cluster.edu". 2.42/2.70 ============================== end of head =========================== 2.42/2.70 2.42/2.70 ============================== INPUT ================================= 2.42/2.70 2.42/2.70 % Reading from file /tmp/Prover9_17069_n013.cluster.edu 2.42/2.70 2.42/2.70 set(prolog_style_variables). 2.42/2.70 set(auto2). 2.42/2.70 % set(auto2) -> set(auto). 2.42/2.70 % set(auto) -> set(auto_inference). 2.42/2.70 % set(auto) -> set(auto_setup). 2.42/2.70 % set(auto_setup) -> set(predicate_elim). 2.42/2.70 % set(auto_setup) -> assign(eq_defs, unfold). 2.42/2.70 % set(auto) -> set(auto_limits). 2.42/2.70 % set(auto_limits) -> assign(max_weight, "100.000"). 2.42/2.70 % set(auto_limits) -> assign(sos_limit, 20000). 2.42/2.70 % set(auto) -> set(auto_denials). 2.42/2.70 % set(auto) -> set(auto_process). 2.42/2.70 % set(auto2) -> assign(new_constants, 1). 2.42/2.70 % set(auto2) -> assign(fold_denial_max, 3). 2.42/2.70 % set(auto2) -> assign(max_weight, "200.000"). 2.42/2.70 % set(auto2) -> assign(max_hours, 1). 2.42/2.70 % assign(max_hours, 1) -> assign(max_seconds, 3600). 2.42/2.70 % set(auto2) -> assign(max_seconds, 0). 2.42/2.70 % set(auto2) -> assign(max_minutes, 5). 2.42/2.70 % assign(max_minutes, 5) -> assign(max_seconds, 300). 2.42/2.70 % set(auto2) -> set(sort_initial_sos). 2.42/2.70 % set(auto2) -> assign(sos_limit, -1). 2.42/2.70 % set(auto2) -> assign(lrs_ticks, 3000). 2.42/2.70 % set(auto2) -> assign(max_megs, 400). 2.42/2.70 % set(auto2) -> assign(stats, some). 2.42/2.70 % set(auto2) -> clear(echo_input). 2.42/2.70 % set(auto2) -> set(quiet). 2.42/2.70 % set(auto2) -> clear(print_initial_clauses). 2.42/2.70 % set(auto2) -> clear(print_given). 2.42/2.70 assign(lrs_ticks,-1). 2.42/2.70 assign(sos_limit,10000). 2.42/2.70 assign(order,kbo). 2.42/2.70 set(lex_order_vars). 2.42/2.70 clear(print_given). 2.42/2.70 2.42/2.70 % formulas(sos). % not echoed (6 formulas) 2.42/2.70 2.42/2.70 ============================== end of input ========================== 2.42/2.70 2.42/2.70 % From the command line: assign(max_seconds, 1440). 2.42/2.70 2.42/2.70 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 2.42/2.70 2.42/2.70 % Formulas that are not ordinary clauses: 2.42/2.70 1 (all C all B all A mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B)) # label(f05) # label(axiom) # label(non_clause). [assumption]. 2.42/2.70 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 2.42/2.70 3 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption]. 2.42/2.70 4 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 2.42/2.70 5 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 2.42/2.70 6 -(all X0 all X1 (mult(rd(X1,X1),X0) = X0 & X0 = mult(X0,rd(X1,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 2.42/2.70 2.42/2.70 ============================== end of process non-clausal formulas === 2.42/2.70 2.42/2.70 ============================== PROCESS INITIAL CLAUSES =============== 2.42/2.70 2.42/2.70 ============================== PREDICATE ELIMINATION ================= 2.42/2.70 2.42/2.70 ============================== end predicate elimination ============= 2.42/2.70 2.42/2.70 Auto_denials: 2.42/2.70 % copying label goals to answer in negative clause 2.42/2.70 2.42/2.70 Term ordering decisions: 2.42/2.70 Function symbol KB weights: c1=1. c2=1. mult=1. ld=1. rd=1. 2.42/2.70 2.42/2.70 ============================== end of process initial clauses ======== 2.42/2.70 2.42/2.70 ============================== CLAUSES FOR SEARCH ==================== 2.42/2.70 2.42/2.70 ============================== end of clauses for search ============= 2.42/2.70 2.42/2.70 ============================== SEARCH ================================ 2.42/2.70 2.42/2.70 % Starting search at 0.01 seconds. 2.42/2.70 2.42/2.70 Low Water (keep): wt=95.000, iters=3370 2.42/2.70 2.42/2.70 Low Water (keep): wt=83.000, iters=3348 2.42/2.70 2.42/2.70 Low Water (keep): wt=79.000, iters=3351 2.42/2.70 2.42/2.70 Low Water (keep): wt=71.000, iters=3372 2.42/2.70 2.42/2.70 Low Water (keep): wt=67.000, iters=3346 2.42/2.70 2.42/2.70 Low Water (keep): wt=59.000, iters=3369 2.42/2.70 2.42/2.70 Low Water (keep): wt=55.000, iters=3401 2.42/2.70 2.42/2.70 Low Water (keep): wt=51.000, iters=3333 2.42/2.70 2.42/2.70 Low Water (keep): wt=47.000, iters=3396 2.42/2.70 2.42/2.70 Low Water (keep): wt=43.000, iters=3349 2.42/2.70 2.42/2.70 Low Water (keep): wt=39.000, iters=3353 2.42/2.70 2.42/2.70 Low Water (keep): wt=35.000, iters=3337 2.42/2.70 2.42/2.70 Low Water (keep): wt=31.000, iters=3335 18.64/18.96 18.64/18.96 Low Water (displace): id=2260, wt=183.000 18.64/18.96 18.64/18.96 Low Water (displace): id=5046, wt=151.000 18.64/18.96 18.64/18.96 Low Water (displace): id=6202, wt=147.000 18.64/18.96 18.64/18.96 Low Water (displace): id=2905, wt=143.000 18.64/18.96 18.64/18.96 Low Water (displace): id=5029, wt=139.000 18.64/18.96 18.64/18.96 Low Water (displace): id=5095, wt=135.000 18.64/18.96 18.64/18.96 Low Water (displace): id=5030, wt=131.000 18.64/18.96 18.64/18.96 Low Water (displace): id=5011, wt=127.000 18.64/18.96 18.64/18.96 Low Water (displace): id=2932, wt=123.000 18.64/18.96 18.64/18.96 Low Water (displace): id=6916, wt=119.000 18.64/18.96 18.64/18.96 Low Water (displace): id=12648, wt=23.000 18.64/18.96 18.64/18.96 Low Water (displace): id=13134, wt=19.000 18.64/18.96 18.64/18.96 Low Water (keep): wt=27.000, iters=3339 18.64/18.96 18.64/18.96 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 40 (0.00 of 7.43 sec). 18.64/18.96 18.64/18.96 ============================== PROOF ================================= 18.64/18.96 % SZS status Theorem 18.64/18.96 % SZS output start Refutation 18.64/18.96 18.64/18.96 % Proof 1 at 17.55 (+ 0.41) seconds: goals. 18.64/18.96 % Length of proof is 205. 18.64/18.96 % Level of proof is 37. 18.64/18.96 % Maximum clause weight is 59.000. 18.64/18.96 % Given clauses 735. 18.64/18.96 18.64/18.96 1 (all C all B all A mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B)) # label(f05) # label(axiom) # label(non_clause). [assumption]. 18.64/18.96 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 18.64/18.96 3 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption]. 18.64/18.96 4 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 18.64/18.96 5 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 18.64/18.96 6 -(all X0 all X1 (mult(rd(X1,X1),X0) = X0 & X0 = mult(X0,rd(X1,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 18.64/18.96 7 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)]. 18.64/18.96 8 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(3)]. 18.64/18.96 9 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(4)]. 18.64/18.96 10 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(5)]. 18.64/18.96 11 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))) # label(f05) # label(axiom). [clausify(1)]. 18.64/18.96 12 mult(rd(c2,c2),c1) != c1 | mult(c1,rd(c2,c2)) != c1 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(6)]. 18.64/18.96 13 ld(rd(A,B),A) = B. [para(9(a,1),7(a,1,2))]. 18.64/18.96 14 rd(A,ld(B,A)) = B. [para(8(a,1),10(a,1,1))]. 18.64/18.96 15 ld(mult(mult(A,B),C),mult(A,mult(B,mult(C,B)))) = B. [para(11(a,1),7(a,1,2))]. 18.64/18.96 16 mult(A,mult(ld(A,B),mult(C,ld(A,B)))) = mult(mult(B,C),ld(A,B)). [para(8(a,1),11(a,1,1,1)),flip(a)]. 18.64/18.96 17 mult(A,mult(B,mult(ld(mult(A,B),C),B))) = mult(C,B). [para(8(a,1),11(a,1,1)),flip(a)]. 18.64/18.96 18 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(9(a,1),11(a,1,1,1)),flip(a)]. 18.64/18.96 19 rd(mult(A,mult(B,mult(C,B))),B) = mult(mult(A,B),C). [para(11(a,1),10(a,1,1))]. 18.64/18.96 20 mult(mult(mult(A,mult(B,mult(C,B))),D),B) = mult(mult(mult(A,B),C),mult(B,mult(D,B))). [para(11(a,1),11(a,1,1,1))]. 18.64/18.96 21 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [para(11(a,1),11(a,1,1))]. 18.64/18.96 22 mult(A,mult(mult(B,mult(C,B)),mult(D,mult(B,mult(C,B))))) = mult(A,mult(B,mult(mult(C,mult(mult(B,mult(D,B)),C)),B))). [para(11(a,1),11(a,2)),rewrite([20(5),11(6),11(7)]),flip(a)]. 18.64/18.96 23 ld(mult(mult(A,ld(B,C)),B),mult(A,mult(ld(B,C),C))) = ld(B,C). [para(8(a,1),15(a,1,2,2,2))]. 18.64/18.96 26 ld(mult(mult(A,mult(B,mult(C,B))),D),mult(mult(mult(A,B),C),mult(B,mult(D,B)))) = B. [para(11(a,1),15(a,1,1,1))]. 18.64/18.96 29 mult(A,mult(ld(mult(B,A),C),A)) = ld(B,mult(C,A)). [para(17(a,1),7(a,1,2)),flip(a)]. 18.64/18.96 33 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)). [para(9(a,1),18(a,1,2,2)),flip(a)]. 18.64/18.96 34 rd(mult(mult(A,B),C),mult(C,mult(B,C))) = rd(A,C). [para(18(a,1),10(a,1,1))]. 18.64/18.96 39 ld(A,mult(mult(B,C),ld(A,B))) = mult(ld(A,B),mult(C,ld(A,B))). [para(16(a,1),7(a,1,2))]. 18.64/18.96 40 mult(mult(A,B),ld(B,A)) = mult(B,mult(ld(B,A),A)). [para(8(a,1),16(a,1,2,2)),flip(a)]. 18.64/18.96 46 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(9(a,1),19(a,1,1,2,2))]. 18.64/18.96 47 mult(mult(rd(A,mult(B,mult(C,B))),B),C) = rd(A,B). [para(9(a,1),19(a,1,1)),flip(a)]. 18.64/18.96 62 ld(A,ld(B,mult(C,A))) = mult(ld(mult(B,A),C),A). [para(29(a,1),7(a,1,2))]. 18.64/18.96 64 ld(rd(A,B),mult(C,B)) = mult(B,mult(ld(A,C),B)). [para(9(a,1),29(a,1,2,1,1)),flip(a)]. 18.64/18.96 72 mult(mult(A,ld(mult(B,C),D)),C) = mult(rd(A,C),ld(B,mult(D,C))). [para(29(a,1),18(a,1,2)),flip(a)]. 18.64/18.96 79 mult(rd(rd(A,rd(B,C)),C),mult(C,B)) = mult(A,C). [para(9(a,1),33(a,1,1)),flip(a)]. 18.64/18.96 117 rd(mult(A,B),mult(B,mult(C,B))) = rd(rd(A,C),B). [para(9(a,1),34(a,1,1,1))]. 18.64/18.96 149 mult(mult(A,B),rd(ld(B,C),B)) = rd(mult(A,C),B). [para(8(a,1),46(a,1,1,2)),flip(a)]. 18.64/18.96 151 mult(mult(rd(A,mult(B,C)),B),rd(C,B)) = rd(A,B). [para(9(a,1),46(a,1,1)),flip(a)]. 18.64/18.96 166 mult(rd(A,mult(B,mult(C,B))),B) = rd(rd(A,B),C). [para(47(a,1),10(a,1,1)),flip(a)]. 18.64/18.96 183 ld(mult(mult(mult(A,B),mult(C,mult(B,C))),D),mult(mult(A,mult(B,mult(C,B))),mult(C,mult(D,C)))) = C. [para(21(a,1),15(a,1,1,1))]. 18.64/18.96 184 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(mult(C,mult(mult(B,mult(C,B)),C)),B)))) = mult(B,mult(C,B)). [para(21(a,1),15(a,1,1)),rewrite([22(11)])]. 18.64/18.96 218 mult(ld(mult(A,B),A),B) = ld(B,B). [para(7(a,1),62(a,1,2)),flip(a)]. 18.64/18.96 220 mult(ld(mult(A,B),rd(C,B)),B) = ld(B,ld(A,C)). [para(9(a,1),62(a,1,2,2)),flip(a)]. 18.64/18.96 222 mult(ld(mult(rd(mult(A,B),C),B),A),B) = ld(B,C). [para(13(a,1),62(a,1,2)),flip(a)]. 18.64/18.96 233 ld(ld(mult(A,B),A),ld(B,B)) = B. [para(218(a,1),7(a,1,2))]. 18.64/18.96 234 ld(ld(A,B),ld(A,B)) = mult(ld(B,A),ld(A,B)). [para(8(a,1),218(a,1,1,1)),flip(a)]. 18.64/18.96 235 mult(ld(A,rd(A,B)),B) = ld(B,B). [para(9(a,1),218(a,1,1,1))]. 18.64/18.96 236 rd(ld(A,A),A) = ld(mult(B,A),B). [para(218(a,1),10(a,1,1))]. 18.64/18.96 237 mult(ld(mult(A,B),A),mult(B,mult(C,B))) = mult(mult(ld(B,B),C),B). [para(218(a,1),11(a,1,1,1)),flip(a)]. 18.64/18.96 246 ld(ld(mult(A,B),A),mult(C,B)) = mult(B,mult(ld(ld(B,B),C),B)). [para(218(a,1),29(a,1,2,1,1)),flip(a)]. 18.64/18.96 259 mult(ld(mult(A,B),ld(mult(C,B),C)),B) = ld(B,ld(A,ld(B,B))). [para(218(a,1),62(a,1,2,2)),flip(a)]. 18.64/18.96 269 mult(mult(A,mult(B,A)),mult(C,mult(A,mult(B,A)))) = mult(A,mult(mult(B,mult(mult(A,mult(C,A)),B)),A)). [para(22(a,1),7(a,1,2)),rewrite([7(8)]),flip(a)]. 18.64/18.96 296 mult(mult(A,mult(mult(B,mult(C,mult(D,C))),mult(C,mult(mult(D,mult(mult(C,mult(B,C)),D)),C)))),mult(C,mult(D,C))) = mult(mult(A,mult(B,mult(C,mult(D,C)))),mult(C,mult(mult(D,mult(mult(C,mult(mult(B,mult(C,mult(D,C))),C)),D)),C))). [para(22(a,1),21(a,1,1,2)),rewrite([269(27)])]. 18.64/18.96 309 rd(ld(A,A),A) = ld(B,rd(B,A)). [para(235(a,1),10(a,1,1))]. 18.64/18.96 313 mult(mult(A,ld(B,rd(B,C))),C) = A. [para(235(a,1),18(a,1,2,2)),rewrite([8(3),9(2)]),flip(a)]. 18.64/18.96 317 ld(ld(A,rd(A,B)),mult(C,B)) = mult(B,mult(ld(ld(B,B),C),B)). [para(235(a,1),29(a,1,2,1,1)),flip(a)]. 18.64/18.96 322 mult(mult(A,ld(B,rd(B,C))),rd(C,ld(B,rd(B,C)))) = rd(mult(A,ld(C,C)),ld(B,rd(B,C))). [para(235(a,1),46(a,1,1,2)),flip(a)]. 18.64/18.96 328 mult(ld(mult(A,B),ld(C,rd(C,B))),B) = ld(B,ld(A,ld(B,B))). [para(235(a,1),62(a,1,2,2)),flip(a)]. 18.64/18.96 342 ld(mult(A,mult(ld(A,B),B)),mult(B,A)) = ld(B,A). [para(40(a,1),236(a,2,1)),rewrite([234(3),10(5)]),flip(a)]. 18.64/18.96 343 mult(mult(A,B),ld(mult(C,B),C)) = A. [para(236(a,1),46(a,2,2)),rewrite([8(2),10(2)]),flip(a)]. 18.64/18.96 344 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = rd(ld(C,C),C). [para(21(a,1),236(a,2,1)),flip(a)]. 18.64/18.96 347 ld(ld(A,A),ld(mult(B,A),B)) = rd(ld(A,A),A). [para(218(a,1),236(a,2,1)),flip(a)]. 18.64/18.96 349 ld(mult(A,B),A) = ld(mult(C,B),C). [para(236(a,1),236(a,1))]. 18.64/18.96 351 mult(A,rd(ld(B,B),B)) = rd(A,B). [para(309(a,2),8(a,1,2))]. 18.64/18.96 362 ld(mult(A,B),A) = ld(C,rd(C,B)). [para(309(a,1),236(a,1)),flip(a)]. 18.64/18.96 363 ld(A,rd(A,B)) = ld(C,rd(C,B)). [para(309(a,1),309(a,1))]. 18.64/18.96 396 rd(A,ld(B,rd(B,C))) = mult(A,C). [para(9(a,1),313(a,1,1)),flip(a)]. 18.64/18.96 397 mult(A,ld(B,rd(B,C))) = rd(A,C). [para(313(a,1),10(a,1,1)),flip(a)]. 18.64/18.96 400 mult(mult(A,ld(B,C)),ld(C,B)) = A. [para(14(a,1),313(a,1,1,2,2))]. 18.64/18.96 405 mult(mult(A,ld(B,B)),B) = mult(rd(A,B),mult(B,B)). [back_rewrite(322),rewrite([397(3),396(4),396(8)]),flip(a)]. 18.64/18.96 419 mult(A,ld(mult(B,C),B)) = rd(A,C). [para(9(a,1),343(a,1,1))]. 18.64/18.96 421 mult(A,mult(ld(mult(B,C),B),rd(C,C))) = rd(A,C). [para(343(a,1),11(a,1)),rewrite([419(3),419(6)]),flip(a)]. 18.64/18.96 433 mult(A,mult(ld(mult(B,C),B),rd(D,C))) = rd(mult(rd(A,C),D),C). [para(343(a,1),20(a,1)),rewrite([419(5),419(8),419(12),421(12)])]. 18.64/18.96 437 mult(A,mult(B,mult(ld(mult(C,D),C),B))) = mult(rd(mult(A,B),D),B). [para(343(a,1),21(a,2,1)),rewrite([419(6),433(6),10(2)]),flip(a)]. 18.64/18.96 444 ld(mult(A,ld(B,C)),A) = ld(C,B). [para(8(a,1),349(a,1,1)),flip(a)]. 18.64/18.96 445 ld(mult(mult(A,B),C),rd(A,C)) = ld(mult(D,mult(C,mult(B,C))),D). [para(18(a,1),349(a,1,1))]. 18.64/18.96 482 mult(mult(A,B),rd(rd(ld(C,C),C),B)) = rd(mult(A,rd(B,C)),B). [para(351(a,1),46(a,1,1,2)),flip(a)]. 18.64/18.96 498 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(14(a,1),396(a,1,2,2))]. 18.64/18.96 548 mult(mult(A,mult(B,ld(C,D))),ld(D,C)) = mult(mult(A,ld(C,D)),mult(ld(D,C),B)). [para(400(a,1),18(a,1,2,2)),rewrite([498(2)]),flip(a)]. 18.64/18.96 551 ld(mult(A,ld(B,C)),mult(D,ld(C,B))) = mult(ld(C,B),mult(ld(A,D),ld(C,B))). [para(400(a,1),29(a,1,2,1,1)),flip(a)]. 18.64/18.96 567 rd(A,mult(ld(B,C),mult(D,ld(B,C)))) = mult(A,ld(mult(mult(C,D),ld(B,C)),B)). [para(16(a,1),419(a,1,2,1)),flip(a)]. 18.64/18.96 632 mult(mult(A,mult(ld(B,C),D)),ld(C,B)) = mult(mult(A,ld(B,C)),mult(D,ld(C,B))). [para(498(a,1),46(a,1)),rewrite([498(9)])]. 18.64/18.96 634 mult(ld(A,B),mult(ld(C,A),ld(A,B))) = ld(mult(C,ld(B,A)),B). [para(8(a,1),64(a,1,2)),rewrite([498(2)]),flip(a)]. 18.64/18.96 635 mult(A,mult(ld(B,rd(C,A)),A)) = ld(rd(B,A),C). [para(9(a,1),64(a,1,2)),flip(a)]. 18.64/18.96 663 rd(rd(A,rd(B,C)),C) = rd(mult(A,C),mult(C,B)). [para(79(a,1),10(a,1,1)),flip(a)]. 18.64/18.96 674 rd(rd(rd(A,B),C),B) = rd(A,mult(B,mult(C,B))). [para(9(a,1),117(a,1,1)),flip(a)]. 18.64/18.96 701 mult(rd(mult(A,ld(B,C)),D),ld(B,C)) = mult(A,ld(mult(mult(B,D),ld(C,B)),C)). [para(400(a,1),117(a,1,1)),rewrite([567(5),498(10)]),flip(a)]. 18.64/18.96 783 ld(mult(A,B),rd(mult(A,C),B)) = rd(ld(B,C),B). [para(149(a,1),7(a,1,2))]. 18.64/18.96 821 rd(A,rd(ld(B,C),B)) = mult(rd(mult(A,B),C),B). [para(149(a,1),419(a,1,2,1)),rewrite([64(4),437(5)]),flip(a)]. 18.64/18.96 854 mult(mult(mult(rd(A,mult(mult(B,mult(C,B)),D)),B),C),mult(B,rd(rd(D,B),C))) = rd(rd(A,B),C). [para(151(a,1),20(a,1,1)),rewrite([166(4),166(12)]),flip(a)]. 18.64/18.96 869 ld(rd(A,mult(B,mult(C,B))),rd(rd(A,B),C)) = B. [para(151(a,1),26(a,1,1)),rewrite([166(13),854(13)])]. 18.64/18.96 1036 rd(ld(A,ld(B,C)),A) = ld(mult(B,A),rd(C,A)). [para(220(a,1),10(a,1,1))]. 18.64/18.96 1102 ld(mult(rd(mult(A,B),C),B),A) = rd(ld(B,C),B). [para(222(a,1),10(a,1,1)),flip(a)]. 18.64/18.96 1113 rd(mult(A,mult(B,A)),A) = ld(rd(ld(A,A),A),B). [para(222(a,1),351(a,1)),rewrite([351(6),351(8),674(6),13(7)]),flip(a)]. 18.64/18.96 1115 mult(ld(ld(A,B),C),ld(B,A)) = mult(ld(B,A),mult(C,ld(B,A))). [para(222(a,1),400(a,1,1)),rewrite([701(9),444(10),39(8)])]. 18.64/18.96 1116 mult(mult(ld(A,B),ld(A,B)),mult(ld(B,A),C)) = ld(ld(B,A),C). [para(400(a,1),222(a,1,1,1,1,1)),rewrite([551(6),13(3),548(6)])]. 18.64/18.96 1121 mult(ld(A,B),mult(mult(ld(B,A),ld(A,B)),ld(A,B))) = ld(ld(B,A),ld(A,B)). [para(234(a,1),40(a,1,2)),rewrite([1116(7),234(7)]),flip(a)]. 18.64/18.96 1151 ld(ld(mult(A,B),A),mult(mult(ld(B,B),C),B)) = mult(B,mult(C,B)). [para(233(a,1),39(a,1,2,2)),rewrite([233(10),233(10)])]. 18.64/18.96 1153 mult(ld(mult(A,B),A),rd(C,B)) = rd(ld(B,C),B). [para(236(a,2),39(a,1,2,2)),rewrite([351(5),783(4),419(7)]),flip(a)]. 18.64/18.96 1154 mult(rd(ld(A,A),A),rd(B,A)) = rd(ld(A,B),A). [para(236(a,2),39(a,2,1)),rewrite([419(5),783(4),419(7)]),flip(a)]. 18.64/18.96 1158 mult(ld(A,B),mult(rd(ld(C,C),C),ld(A,B))) = ld(A,mult(rd(B,C),ld(A,B))). [para(351(a,1),39(a,1,2,1)),flip(a)]. 18.64/18.96 1162 mult(ld(A,B),mult(ld(mult(C,D),C),ld(A,B))) = ld(A,mult(rd(B,D),ld(A,B))). [para(419(a,1),39(a,1,2,1)),flip(a)]. 18.64/18.96 1188 ld(mult(A,mult(ld(A,A),A)),mult(A,mult(A,A))) = A. [para(218(a,1),342(a,1,1,2)),rewrite([40(3),7(8)])]. 18.64/18.96 1227 ld(ld(A,A),rd(mult(ld(mult(B,A),B),C),A)) = rd(ld(A,C),A). [para(347(a,1),39(a,1,2,2)),rewrite([351(7),347(10),347(12),351(11),1154(10)])]. 18.64/18.96 1233 mult(rd(A,A),mult(A,A)) = mult(A,A). [para(8(a,1),405(a,1,1)),flip(a)]. 18.64/18.96 1234 mult(A,rd(B,B)) = mult(A,ld(B,B)). [para(405(a,1),10(a,1,1)),rewrite([46(4),9(2)])]. 18.64/18.96 1282 ld(ld(A,B),ld(B,A)) = mult(ld(B,A),ld(B,A)). [para(405(a,1),39(a,1,2)),rewrite([498(2),8(2),7(5),234(7),1121(10)]),flip(a)]. 18.64/18.96 1284 mult(rd(c2,c2),c1) != c1 | mult(c1,ld(c2,c2)) != c1 # answer(goals). [back_rewrite(12),rewrite([1234(12)])]. 18.64/18.96 1342 mult(A,mult(ld(A,A),A)) = mult(A,A). [para(1233(a,1),7(a,1,2)),rewrite([64(3)])]. 18.64/18.96 1343 rd(mult(A,A),mult(A,A)) = rd(A,A). [para(1233(a,1),10(a,1,1))]. 18.64/18.96 1383 ld(mult(A,A),mult(A,mult(A,A))) = A. [back_rewrite(1188),rewrite([1342(3)])]. 18.64/18.96 1391 rd(A,A) = ld(A,A). [para(1234(a,1),7(a,1,2)),rewrite([7(3)]),flip(a)]. 18.64/18.96 1418 ld(mult(A,A),mult(A,A)) = ld(A,A). [back_rewrite(1343),rewrite([1391(3),1391(4)])]. 18.64/18.96 1419 mult(ld(c2,c2),c1) != c1 | mult(c1,ld(c2,c2)) != c1 # answer(goals). [back_rewrite(1284),rewrite([1391(3)])]. 18.64/18.96 1432 mult(ld(A,A),A) = A. [para(1391(a,1),9(a,1,1))]. 18.64/18.96 1433 ld(ld(A,A),A) = A. [para(1391(a,1),13(a,1,1))]. 18.64/18.96 1434 mult(ld(A,A),mult(A,mult(B,A))) = mult(mult(A,B),A). [para(1391(a,1),18(a,1,1))]. 18.64/18.96 1436 mult(ld(A,ld(A,A)),A) = ld(A,A). [para(1391(a,1),235(a,1,1,2))]. 18.64/18.96 1438 rd(ld(A,A),A) = ld(A,ld(A,A)). [para(1391(a,1),309(a,2,2))]. 18.64/18.96 1439 ld(mult(A,B),A) = ld(B,ld(B,B)). [para(1391(a,1),362(a,2,2))]. 18.64/18.96 1440 ld(A,rd(A,B)) = ld(B,ld(B,B)). [para(1391(a,1),363(a,1,2)),flip(a)]. 18.64/18.96 1441 mult(A,ld(B,ld(B,B))) = rd(A,B). [para(1391(a,1),397(a,1,2,2))]. 18.64/18.96 1444 mult(mult(ld(mult(A,B),mult(A,B)),A),rd(B,A)) = rd(mult(A,B),A). [para(1391(a,1),151(a,1,1,1))]. 18.64/18.96 1446 ld(rd(A,B),rd(A,B)) = mult(rd(A,mult(B,A)),B). [para(1391(a,1),166(a,2)),rewrite([9(2)]),flip(a)]. 18.64/18.96 1490 mult(ld(A,B),mult(ld(C,ld(C,C)),ld(A,B))) = ld(A,mult(rd(B,C),ld(A,B))). [back_rewrite(1158),rewrite([1438(3)])]. 18.64/18.96 1494 rd(mult(A,mult(B,A)),A) = ld(ld(A,ld(A,A)),B). [back_rewrite(1113),rewrite([1438(5)])]. 18.64/18.96 1518 mult(mult(A,B),rd(ld(C,ld(C,C)),B)) = rd(mult(A,rd(B,C)),B). [back_rewrite(482),rewrite([1438(3)])]. 18.64/18.96 1532 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = ld(C,ld(C,C)). [back_rewrite(344),rewrite([1438(10)])]. 18.64/18.96 1554 mult(rd(A,B),mult(B,B)) = mult(mult(A,B),ld(B,B)). [para(1432(a,1),33(a,2,2)),rewrite([498(2),8(2),498(5),405(6)]),flip(a)]. 18.64/18.96 1563 ld(ld(A,B),mult(ld(B,A),ld(A,B))) = ld(B,A). [para(1432(a,1),444(a,1,1)),rewrite([234(4)])]. 18.64/18.96 1569 rd(rd(ld(A,A),B),A) = rd(A,mult(A,mult(B,A))). [para(1432(a,1),117(a,1,1)),flip(a)]. 18.64/18.96 1612 mult(mult(A,ld(B,B)),B) = mult(mult(A,B),ld(B,B)). [back_rewrite(405),rewrite([1554(6)])]. 18.64/18.96 1711 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(1383(a,1),8(a,1,2))]. 18.64/18.96 1730 mult(ld(A,A),ld(A,A)) = ld(A,A). [para(397(a,1),1418(a,1,1)),rewrite([397(8),1446(7),397(5),1391(3),498(4),1612(5),235(3),234(8),13(5),397(6),1391(4)])]. 18.64/18.96 1791 mult(ld(A,ld(A,A)),mult(A,mult(B,A))) = mult(mult(ld(A,A),B),A). [para(1436(a,1),11(a,1,1,1)),flip(a)]. 18.64/18.96 1832 mult(ld(A,ld(A,A)),ld(A,A)) = ld(A,ld(A,A)). [para(1439(a,2),23(a,1,1,1,2)),rewrite([419(3),9(2),7(6)])]. 18.64/18.96 1918 mult(ld(A,rd(A,B)),ld(B,B)) = ld(B,ld(B,B)). [para(1440(a,2),23(a,1,2,2,1)),rewrite([1441(3),9(2),7(6)])]. 18.64/18.96 1931 ld(ld(A,ld(A,A)),A) = mult(A,A). [para(1711(a,1),10(a,1,1)),rewrite([1494(3)])]. 18.64/18.96 2021 mult(ld(A,A),mult(ld(A,A),mult(B,ld(A,A)))) = mult(mult(ld(A,A),B),ld(A,A)). [para(1730(a,1),11(a,1,1,1)),flip(a)]. 18.64/18.96 2023 ld(ld(A,A),mult(B,ld(A,A))) = mult(mult(ld(A,A),B),ld(A,A)). [para(1730(a,1),29(a,1,2,1,1)),rewrite([1115(5),2021(6)]),flip(a)]. 18.64/18.96 2026 mult(ld(A,A),mult(ld(B,ld(A,A)),ld(A,A))) = ld(mult(B,ld(A,A)),ld(A,A)). [para(1730(a,1),64(a,1,2)),rewrite([498(2)]),flip(a)]. 18.64/18.96 2028 ld(ld(A,A),ld(ld(A,A),B)) = mult(ld(A,A),B). [para(1730(a,1),220(a,1,1,1)),rewrite([498(3),2023(4),400(6)]),flip(a)]. 18.64/18.96 2030 mult(ld(A,ld(B,B)),mult(ld(B,B),ld(A,ld(B,B)))) = ld(A,mult(ld(B,B),ld(A,ld(B,B)))). [para(1730(a,1),39(a,1,2,1)),flip(a)]. 18.64/18.96 2103 rd(ld(mult(A,B),A),B) = ld(B,ld(mult(A,B),A)). [para(419(a,1),1931(a,2)),rewrite([234(7),7(4),419(5),1391(3),233(4)]),flip(a)]. 18.64/18.96 2482 mult(rd(A,mult(B,ld(C,A))),ld(C,A)) = rd(C,mult(ld(A,C),B)). [para(8(a,1),663(a,2,1)),rewrite([498(2),498(5)])]. 18.64/18.96 2842 ld(rd(A,mult(A,mult(B,A))),rd(ld(A,A),B)) = A. [para(1391(a,1),869(a,1,2,1))]. 18.64/18.96 3499 ld(mult(rd(A,B),A),ld(A,A)) = rd(ld(A,B),A). [para(1432(a,1),1102(a,1,1,1,1))]. 18.64/18.96 3634 mult(ld(A,ld(mult(B,A),B)),mult(A,C)) = ld(A,C). [para(1153(a,1),33(a,1,1)),rewrite([9(3),2103(4)]),flip(a)]. 18.64/18.96 4365 mult(rd(ld(mult(A,B),mult(A,B)),B),ld(A,mult(mult(A,B),B))) = mult(ld(mult(A,B),mult(A,B)),B). [para(1730(a,1),72(a,1,1)),flip(a)]. 18.64/18.96 4427 ld(mult(A,ld(B,C)),mult(A,ld(B,C))) = mult(rd(A,mult(ld(C,B),A)),ld(C,B)). [para(498(a,1),1446(a,1,1)),rewrite([498(4)])]. 18.64/18.96 4437 mult(A,mult(mult(rd(B,mult(A,B)),A),A)) = ld(rd(rd(B,A),A),B). [para(1446(a,1),635(a,1,2,1))]. 18.64/18.96 5337 mult(mult(ld(A,B),B),ld(B,A)) = ld(ld(B,A),A). [para(8(a,1),1494(a,1,1,2)),rewrite([498(4),234(8),1563(9)])]. 18.64/18.96 5351 ld(ld(A,B),mult(C,ld(A,B))) = mult(mult(ld(B,A),C),ld(A,B)). [para(400(a,1),1494(a,1,1,2)),rewrite([498(4),234(8),1563(9)]),flip(a)]. 18.64/18.96 5390 mult(ld(A,A),mult(ld(A,A),B)) = ld(ld(A,A),B). [para(1282(a,1),1494(a,2,1,2)),rewrite([498(6),548(6),1730(3),1730(8),234(7),1730(7)])]. 18.64/18.96 6985 ld(rd(ld(A,A),B),rd(A,mult(A,mult(B,A)))) = ld(A,ld(A,A)). [para(1569(a,1),1440(a,1,2))]. 18.64/18.96 7328 mult(mult(rd(A,mult(ld(B,B),A)),ld(B,B)),mult(mult(A,ld(B,B)),mult(B,mult(A,ld(B,B))))) = mult(mult(mult(A,B),ld(B,B)),mult(A,ld(B,B))). [para(1612(a,1),1434(a,2,1)),rewrite([4427(5)])]. 18.64/18.96 7708 ld(mult(rd(ld(A,ld(A,A)),B),ld(A,A)),ld(A,ld(A,A))) = mult(ld(A,A),mult(B,ld(A,A))). [para(1832(a,1),1102(a,1,1,1,1)),rewrite([498(12),1115(12)])]. 18.64/18.96 7963 mult(rd(ld(A,rd(A,B)),mult(C,ld(B,B))),ld(B,B)) = rd(ld(B,ld(B,B)),mult(ld(B,B),C)). [para(1918(a,1),663(a,2,1)),rewrite([498(4),498(7)])]. 18.64/18.96 8330 rd(A,mult(mult(ld(B,B),C),ld(B,B))) = mult(A,ld(mult(C,ld(B,B)),ld(B,B))). [para(2028(a,1),821(a,1,2,1)),rewrite([498(4),498(10),11(12),2026(11)])]. 18.64/18.96 10544 ld(mult(mult(rd(A,B),A),C),rd(ld(A,A),C)) = rd(ld(C,rd(ld(A,B),A)),C). [para(3499(a,1),1036(a,1,1,2)),flip(a)]. 18.64/18.96 10590 mult(ld(A,ld(mult(B,A),B)),C) = ld(A,ld(A,C)). [para(8(a,1),3634(a,1,2))]. 18.64/18.96 11669 ld(ld(ld(A,A),B),ld(A,A)) = ld(C,rd(C,mult(ld(A,A),B))). [para(5390(a,1),362(a,1,1))]. 18.64/18.96 13199 ld(ld(A,B),ld(ld(A,B),C)) = mult(mult(ld(B,A),ld(B,A)),C). [para(8(a,1),10590(a,1,1,2,1)),rewrite([1282(3)]),flip(a)]. 18.64/18.96 17683 ld(A,mult(mult(A,mult(B,A)),A)) = mult(mult(mult(ld(A,A),B),A),A). [para(237(a,1),5337(a,1,1)),rewrite([7(9),7(10)]),flip(a)]. 18.64/18.96 17898 ld(mult(mult(ld(A,A),B),ld(A,A)),ld(A,A)) = ld(A,mult(rd(A,B),ld(A,A))). [para(5390(a,1),445(a,2,1)),rewrite([498(5),551(6),1162(6),5351(8)]),flip(a)]. 18.64/18.96 18371 ld(mult(ld(A,A),ld(B,A)),B) = mult(ld(A,B),B). [para(1433(a,1),634(a,1,2,1)),rewrite([8(3)]),flip(a)]. 18.64/18.96 18429 rd(ld(A,mult(mult(ld(B,B),A),B)),A) = mult(B,rd(ld(B,B),A)). [para(2842(a,1),18371(a,2,1)),rewrite([1446(7),6985(13),1441(10),46(8),10(7),10544(9),17683(4),10(5)])]. 18.64/18.96 20181 rd(A,mult(ld(B,A),A)) = mult(ld(B,B),ld(A,B)). [para(8(a,1),2482(a,1,1,2)),rewrite([1391(1)]),flip(a)]. 18.64/18.96 20238 mult(rd(A,mult(ld(B,A),A)),ld(B,B)) = mult(ld(B,B),ld(mult(A,ld(B,B)),B)). [para(20181(a,2),1434(a,2,1)),rewrite([234(3),1730(3),634(6)]),flip(a)]. 18.64/18.96 20259 mult(ld(A,A),rd(B,mult(ld(A,B),B))) = ld(ld(A,A),ld(B,A)). [para(20181(a,2),5390(a,1,2))]. 18.64/18.96 24991 mult(ld(A,A),rd(B,mult(ld(A,A),B))) = ld(B,B). [para(400(a,1),4437(a,1,2)),rewrite([498(7),498(9),400(9)])]. 18.64/18.96 25022 rd(A,mult(ld(B,B),A)) = ld(ld(B,B),ld(A,A)). [para(24991(a,1),7(a,1,2)),flip(a)]. 18.64/18.96 25023 mult(ld(A,ld(B,B)),ld(ld(B,B),A)) = mult(ld(B,B),rd(ld(ld(B,B),A),A)). [para(8(a,1),24991(a,1,2,2)),rewrite([234(10)]),flip(a)]. 18.64/18.96 25035 ld(ld(ld(A,A),ld(B,B)),ld(A,A)) = ld(B,B). [para(24991(a,1),246(a,1,2)),rewrite([25022(3),444(5),25022(8),25022(11),25022(14),234(15),25023(15),498(14),25022(20),634(22),632(16),8(10),8(11),444(10)])]. 18.64/18.96 25036 mult(ld(A,A),mult(ld(ld(A,A),ld(B,B)),ld(B,B))) = ld(B,B). [para(24991(a,1),259(a,1,1,1)),rewrite([25022(4),444(6),13199(5),1730(3),25022(6),40(7),25022(10),25022(14),25022(17),234(18),25023(18),498(17),7(19),7(16)])]. 18.64/18.96 25038 mult(ld(ld(A,A),ld(B,B)),ld(B,B)) = ld(A,A). [para(24991(a,1),317(a,1,2)),rewrite([25022(3),498(4),7(5),25035(5),25022(4),25022(7),25022(10),234(11),25023(11),498(10),25036(11),25022(10),25023(11),498(10),25036(11)]),flip(a)]. 18.64/18.96 25039 ld(A,A) = ld(B,B). [para(24991(a,1),328(a,1,1,1)),rewrite([25022(4),498(5),7(6),13199(5),1730(3),25022(6),40(7),25038(6),1730(3),25022(4),25022(8),25022(11),234(12),25023(12),498(11),25038(11),1730(8),234(7),1730(7),25035(6)])]. 18.64/18.96 25040 ld(ld(A,A),mult(ld(B,B),ld(ld(A,A),ld(B,B)))) = ld(B,B). [para(24991(a,1),445(a,2,1,2,2)),rewrite([25022(5),25022(9),498(10),551(11),444(6),2030(9),25022(10),25038(12),444(10)])]. 18.64/18.96 25043 mult(ld(A,A),mult(ld(B,B),ld(A,A))) = ld(ld(A,A),ld(B,B)). [para(24991(a,1),183(a,1,2,2,2)),rewrite([25022(4),25022(7),25022(15),25022(21),25038(23),551(21),1532(18),234(11),25023(11),498(10),25038(10),1730(7),25035(6),25022(8)])]. 18.64/18.97 25044 ld(ld(A,A),ld(B,B)) = ld(B,B). [para(24991(a,1),184(a,1,1,2,2)),rewrite([25022(5),25038(7),400(4),25022(4),25022(8),1115(10),25043(10),8(9),25022(8),2030(10),25040(8),25043(5),7(5),25022(7),1115(9),25043(9),8(8)])]. 18.64/18.97 25045 ld(ld(A,A),mult(mult(ld(B,B),C),ld(B,B))) = mult(ld(B,B),mult(C,ld(B,B))). [para(24991(a,1),1151(a,1,1,1)),rewrite([25044(3),25022(4),25044(4),25022(5),25044(5),25044(4),25022(6),25044(6),25022(9),25044(9),25022(10),25044(10)])]. 18.64/18.97 25049 mult(mult(ld(A,A),mult(ld(B,B),C)),ld(A,A)) = mult(ld(A,A),mult(C,ld(A,A))). [para(24991(a,1),1227(a,1,2,1,1,1)),rewrite([25022(3),25044(3),25022(4),25044(4),25044(3),25044(4),25022(6),25044(6),498(5),5351(6),25022(9),25044(9),25022(11),25044(11),498(10),1115(10)])]. 18.64/18.97 25051 mult(mult(ld(A,A),ld(B,B)),ld(A,A)) = ld(A,A). [para(24991(a,1),1444(a,1,1,1,1)),rewrite([25022(5),25044(5),5351(5),11(7),25043(6),25044(4),1730(3),25022(4),25044(4),498(4),5390(5),25044(3),25022(5),25044(5),498(6)]),flip(a)]. 18.64/18.97 25052 mult(ld(A,A),ld(B,B)) = ld(A,A). [para(24991(a,1),1444(a,2,1)),rewrite([25022(4),25044(4),25022(7),25044(7),4427(7),25022(5),25044(4),25044(3),25051(5),25022(4),25044(4),498(4),25043(5),25044(3),498(4)]),flip(a)]. 18.64/18.97 25054 mult(mult(ld(A,A),rd(ld(B,B),C)),ld(B,B)) = ld(B,mult(rd(B,C),ld(B,B))). [para(24991(a,1),1518(a,1,1)),rewrite([25022(6),25044(6),498(5),1490(6),25022(8),25044(8),25022(11),25044(11),498(10)]),flip(a)]. 18.64/18.97 25060 mult(ld(A,A),B) = B. [para(24991(a,1),1791(a,2,1)),rewrite([25022(5),25044(5),1791(6),25052(3),1432(2)]),flip(a)]. 18.64/18.97 25072 mult(A,ld(B,B)) = A. [para(24991(a,1),2482(a,2,2)),rewrite([25060(2),1391(1),25060(3),498(2),8(2),8(2),498(2)]),flip(a)]. 18.64/18.97 25123 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(24991(a,1),296(a,1,1,2,1,2,2)),rewrite([25060(2),1391(1),25072(3),25072(2),25060(2),1391(1),25060(4),1391(3),25060(5),1391(4),25072(5),25060(4),25072(4),25060(3),25060(3),1391(2),25072(3),25060(2),25060(4),1391(3),25060(6),1391(5),25072(6),25072(5),25072(4),25060(4),1391(3),25060(6),1391(5),25072(6),25072(5),25072(4),25060(5),1391(4),25060(7),1391(6),25060(8),1391(7),25060(10),1391(9),25072(10),25072(9),25072(8),25060(8),1391(7),25072(8),25060(7),25072(7),25060(6),25060(6),1391(5),25072(6),25060(5)]),flip(a)]. 18.64/18.97 25132 mult(mult(A,B),A) = mult(A,mult(B,A)). [back_rewrite(7328),rewrite([25060(2),1391(1),25072(3),25072(3),25072(3),25060(4),25072(5),25072(5)]),flip(a)]. 18.64/18.97 25135 ld(A,A) = c_0. [new_symbol(25039)]. 18.64/18.97 25149 mult(c_0,mult(A,c_0)) = mult(c_0,A). [back_rewrite(4365),rewrite([25135(3),25123(4),7(5),1554(4),25135(3),25132(4),25135(7)])]. 18.64/18.97 25151 rd(c_0,A) = ld(A,c_0). [back_rewrite(1438),rewrite([25135(1),25135(3)])]. 18.64/18.97 25155 mult(c_0,mult(c_0,A)) = mult(c_0,A). [back_rewrite(25049),rewrite([25135(1),25135(2),25135(5),25132(6),25132(5),25149(5),25135(5),25135(6),25149(8)])]. 18.64/18.97 25156 ld(c_0,A) = mult(c_0,A). [back_rewrite(5390),rewrite([25135(1),25135(2),25155(4),25135(3)]),flip(a)]. 18.64/18.97 25158 ld(A,mult(rd(A,B),c_0)) = mult(c_0,ld(B,c_0)). [back_rewrite(25054),rewrite([25135(1),25135(2),25151(3),25135(5),25132(6),25149(6),25135(6)]),flip(a)]. 18.64/18.97 25164 mult(c_0,A) = A. [back_rewrite(25045),rewrite([25135(1),25135(2),25135(4),25132(5),25149(5),7(4),25135(1),25135(2),25149(4)]),flip(a)]. 18.64/18.97 25220 rd(A,mult(ld(B,A),A)) = ld(A,B). [back_rewrite(20259),rewrite([25135(1),25164(5),25135(4),25156(6),25164(6)])]. 18.64/18.97 25229 ld(mult(A,c_0),B) = mult(ld(A,B),c_0). [back_rewrite(20238),rewrite([25220(3),25135(2),25135(4),25135(5),25164(8)]),flip(a)]. 18.64/18.97 25285 mult(A,ld(B,c_0)) = rd(A,B). [back_rewrite(18429),rewrite([25135(1),25164(2),7(2),25135(2),25151(3)]),flip(a)]. 18.64/18.97 25295 mult(ld(A,c_0),c_0) = ld(A,c_0). [back_rewrite(17898),rewrite([25135(1),25164(2),25135(1),25135(3),25229(4),25135(6),25158(8),25285(8),25151(6)])]. 18.64/18.97 25336 ld(A,rd(A,B)) = ld(B,c_0). [back_rewrite(11669),rewrite([25135(1),25156(2),25164(2),25135(1),25135(3),25164(4)]),flip(a)]. 18.64/18.97 25454 rd(A,mult(B,c_0)) = rd(A,B). [back_rewrite(8330),rewrite([25135(1),25164(2),25135(1),25135(4),25135(6),25229(7),25295(7),25285(6)])]. 18.64/18.97 25462 mult(rd(ld(A,c_0),B),c_0) = rd(ld(A,c_0),B). [back_rewrite(7963),rewrite([25336(2),25135(3),25454(5),25135(4),25135(6),25135(8),25164(9)])]. 18.64/18.97 25472 mult(A,c_0) = A. [back_rewrite(7708),rewrite([25135(1),25135(4),25462(5),25135(4),13(6),25135(1),25135(2),25164(4)]),flip(a)]. 18.64/18.97 25530 $F # answer(goals). [back_rewrite(1419),rewrite([25135(3),25164(3),25135(7),25472(6)]),xx(a),xx(b)]. 18.64/18.97 18.64/18.97 % SZS output end Refutation 18.64/18.97 ============================== end of proof ========================== 18.64/18.97 18.64/18.97 ============================== STATISTICS ============================ 18.64/18.97 18.64/18.97 Given=735. Generated=717441. Kept=25523. proofs=1. 18.64/18.97 Usable=666. Sos=9238. Demods=8351. Limbo=470, Disabled=15155. Hints=0. 18.64/18.97 Megabytes=28.39. 18.64/18.97 User_CPU=17.56, System_CPU=0.41, Wall_clock=18. 18.64/18.97 18.64/18.97 ============================== end of statistics ===================== 18.64/18.97 18.64/18.97 ============================== end of search ========================= 18.64/18.97 18.64/18.97 THEOREM PROVED 18.64/18.97 % SZS status Theorem 18.64/18.97 18.64/18.97 Exiting with 1 proof. 18.64/18.97 18.64/18.97 Process 17256 exit (max_proofs) Mon Jul 3 05:53:36 2023 18.64/18.97 Prover9 interrupted 18.64/18.97 EOF