0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n005.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 % WCLimit : 120 0.12/0.33 % DateTime : Tue Aug 9 05:17:49 EDT 2022 0.12/0.33 % CPUTime : 3.24/3.55 ============================== Prover9 =============================== 3.24/3.55 Prover9 (32) version 2009-11A, November 2009. 3.24/3.55 Process 15255 was started by sandbox on n005.cluster.edu, 3.24/3.55 Tue Aug 9 05:17:50 2022 3.24/3.55 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_15100_n005.cluster.edu". 3.24/3.55 ============================== end of head =========================== 3.24/3.55 3.24/3.55 ============================== INPUT ================================= 3.24/3.55 3.24/3.55 % Reading from file /tmp/Prover9_15100_n005.cluster.edu 3.24/3.55 3.24/3.55 set(prolog_style_variables). 3.24/3.55 set(auto2). 3.24/3.55 % set(auto2) -> set(auto). 3.24/3.55 % set(auto) -> set(auto_inference). 3.24/3.55 % set(auto) -> set(auto_setup). 3.24/3.55 % set(auto_setup) -> set(predicate_elim). 3.24/3.55 % set(auto_setup) -> assign(eq_defs, unfold). 3.24/3.55 % set(auto) -> set(auto_limits). 3.24/3.55 % set(auto_limits) -> assign(max_weight, "100.000"). 3.24/3.55 % set(auto_limits) -> assign(sos_limit, 20000). 3.24/3.55 % set(auto) -> set(auto_denials). 3.24/3.55 % set(auto) -> set(auto_process). 3.24/3.55 % set(auto2) -> assign(new_constants, 1). 3.24/3.55 % set(auto2) -> assign(fold_denial_max, 3). 3.24/3.55 % set(auto2) -> assign(max_weight, "200.000"). 3.24/3.55 % set(auto2) -> assign(max_hours, 1). 3.24/3.55 % assign(max_hours, 1) -> assign(max_seconds, 3600). 3.24/3.55 % set(auto2) -> assign(max_seconds, 0). 3.24/3.55 % set(auto2) -> assign(max_minutes, 5). 3.24/3.55 % assign(max_minutes, 5) -> assign(max_seconds, 300). 3.24/3.55 % set(auto2) -> set(sort_initial_sos). 3.24/3.55 % set(auto2) -> assign(sos_limit, -1). 3.24/3.55 % set(auto2) -> assign(lrs_ticks, 3000). 3.24/3.55 % set(auto2) -> assign(max_megs, 400). 3.24/3.55 % set(auto2) -> assign(stats, some). 3.24/3.55 % set(auto2) -> clear(echo_input). 3.24/3.55 % set(auto2) -> set(quiet). 3.24/3.55 % set(auto2) -> clear(print_initial_clauses). 3.24/3.55 % set(auto2) -> clear(print_given). 3.24/3.55 assign(lrs_ticks,-1). 3.24/3.55 assign(sos_limit,10000). 3.24/3.55 assign(order,kbo). 3.24/3.55 set(lex_order_vars). 3.24/3.55 clear(print_given). 3.24/3.55 3.24/3.55 % formulas(sos). % not echoed (9 formulas) 3.24/3.55 3.24/3.55 ============================== end of input ========================== 3.24/3.55 3.24/3.55 % From the command line: assign(max_seconds, 960). 3.24/3.55 3.24/3.55 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 3.24/3.55 3.24/3.55 % Formulas that are not ordinary clauses: 3.24/3.55 1 (all C all B all A mult(A,mult(mult(B,C),B)) = mult(mult(mult(A,B),C),B)) # label(f07) # label(axiom) # label(non_clause). [assumption]. 3.24/3.55 2 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 3.24/3.55 3 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 3.24/3.55 4 (all A A = mult(A,unit)) # label(f05) # label(axiom) # label(non_clause). [assumption]. 3.24/3.55 5 (all X0 all X1 all X2 (mult(X0,mult(X2,X1)) = mult(X0,mult(X1,X2)) & mult(mult(X0,X2),X1) = mult(mult(X0,X1),X2) | mult(mult(X0,X2),X1) = mult(X0,mult(X2,X1)) & mult(mult(X0,X1),X2) = mult(X0,mult(X1,X2)))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 3.24/3.55 6 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 3.24/3.55 7 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 3.24/3.55 8 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 3.24/3.55 3.24/3.55 ============================== end of process non-clausal formulas === 3.24/3.55 3.24/3.55 ============================== PROCESS INITIAL CLAUSES =============== 3.24/3.55 3.24/3.55 ============================== PREDICATE ELIMINATION ================= 3.24/3.55 3.24/3.55 ============================== end predicate elimination ============= 3.24/3.55 3.24/3.55 Auto_denials: (non-Horn, no changes). 3.24/3.55 3.24/3.55 Term ordering decisions: 3.24/3.55 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. 3.24/3.55 3.24/3.55 ============================== end of process initial clauses ======== 3.24/3.55 3.24/3.55 ============================== CLAUSES FOR SEARCH ==================== 3.24/3.55 3.24/3.55 ============================== end of clauses for search ============= 3.24/3.55 3.24/3.55 ============================== SEARCH ================================ 3.24/3.55 3.24/3.55 % Starting search at 0.01 seconds. 3.24/3.55 3.24/3.55 Low Water (keep): wt=121.000, iters=3415 3.24/3.55 3.24/3.55 Low Water (keep): wt=113.000, iters=3398 3.24/3.55 3.24/3.55 Low Water (keep): wt=112.000, iters=3385 3.24/3.55 3.24/3.55 Low Water (keep): wt=106.000, iters=3443 3.24/3.55 3.24/3.55 Low Water (keep): wt=97.000, iters=3371 3.24/3.55 3.24/3.55 Low Water (keep): wt=96.000, iters=3353 9.64/9.93 9.64/9.93 Low Water (keep): wt=90.000, iters=3393 9.64/9.93 9.64/9.93 Low Water (keep): wt=85.000, iters=3359 9.64/9.93 9.64/9.93 Low Water (keep): wt=83.000, iters=3413 9.64/9.93 9.64/9.93 Low Water (keep): wt=81.000, iters=3409 9.64/9.93 9.64/9.93 Low Water (keep): wt=80.000, iters=3350 9.64/9.93 9.64/9.93 Low Water (keep): wt=77.000, iters=3417 9.64/9.93 9.64/9.93 Low Water (keep): wt=76.000, iters=3363 9.64/9.93 9.64/9.93 Low Water (keep): wt=73.000, iters=3386 9.64/9.93 9.64/9.93 Low Water (keep): wt=72.000, iters=3346 9.64/9.93 9.64/9.93 Low Water (keep): wt=70.000, iters=3455 9.64/9.93 9.64/9.93 Low Water (keep): wt=69.000, iters=3428 9.64/9.93 9.64/9.93 Low Water (keep): wt=65.000, iters=3345 9.64/9.93 9.64/9.93 Low Water (keep): wt=62.000, iters=3358 9.64/9.93 9.64/9.93 Low Water (keep): wt=61.000, iters=3350 9.64/9.93 9.64/9.93 Low Water (keep): wt=58.000, iters=3347 9.64/9.93 9.64/9.93 Low Water (keep): wt=57.000, iters=3401 9.64/9.93 9.64/9.93 Low Water (keep): wt=54.000, iters=3337 9.64/9.93 9.64/9.93 Low Water (keep): wt=53.000, iters=3383 9.64/9.93 9.64/9.93 Low Water (keep): wt=50.000, iters=3382 9.64/9.93 9.64/9.93 Low Water (keep): wt=49.000, iters=3456 9.64/9.93 9.64/9.93 Low Water (keep): wt=48.000, iters=3380 9.64/9.93 9.64/9.93 Low Water (keep): wt=47.000, iters=3364 9.64/9.93 9.64/9.93 Low Water (keep): wt=46.000, iters=3396 9.64/9.93 9.64/9.93 Low Water (displace): id=4496, wt=165.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5758, wt=156.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4488, wt=153.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4278, wt=142.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5539, wt=141.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5742, wt=140.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5757, wt=136.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4495, wt=133.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5304, wt=132.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4388, wt=129.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5305, wt=128.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4267, wt=126.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4478, wt=125.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5753, wt=124.000 9.64/9.93 9.64/9.93 Low Water (keep): wt=45.000, iters=3384 9.64/9.93 9.64/9.93 Low Water (displace): id=4445, wt=121.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5741, wt=120.000 9.64/9.93 9.64/9.93 Low Water (displace): id=3948, wt=118.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5538, wt=117.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5756, wt=116.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5789, wt=115.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5069, wt=113.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5711, wt=112.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5783, wt=111.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4274, wt=110.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5522, wt=109.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5751, wt=108.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5788, wt=107.000 9.64/9.93 9.64/9.93 Low Water (displace): id=2924, wt=106.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6172, wt=105.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5755, wt=104.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5782, wt=103.000 9.64/9.93 9.64/9.93 Low Water (displace): id=3947, wt=102.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5211, wt=101.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5745, wt=100.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5787, wt=99.000 9.64/9.93 9.64/9.93 Low Water (displace): id=3611, wt=98.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6166, wt=97.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5695, wt=96.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5781, wt=95.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4291, wt=94.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6623, wt=93.000 9.64/9.93 9.64/9.93 Low Water (keep): wt=44.000, iters=3385 9.64/9.93 9.64/9.93 Low Water (displace): id=6647, wt=92.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5766, wt=91.000 9.64/9.93 9.64/9.93 Low Water (displace): id=3301, wt=90.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6629, wt=89.000 9.64/9.93 9.64/9.93 Low Water (keep): wt=42.000, iters=3365 9.64/9.93 9.64/9.93 Low Water (displace): id=6652, wt=88.000 9.64/9.93 9.64/9.93 Low Water (displace): id=5786, wt=87.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4269, wt=86.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6587, wt=85.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6965, wt=84.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6950, wt=83.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6526, wt=82.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6762, wt=81.000 9.64/9.93 9.64/9.93 Low Water (displace): id=6945, wt=80.000 9.64/9.93 9.64/9.93 Low Water (displace): id=7141, wt=79.000 9.64/9.93 9.64/9.93 Low Water (displace): id=4295, wt=78.000 9.64/9.93 9.64/9.93 Low Water (keep): wt=41.000, iters=3344 9.64/9.93 9.64/9.93 Low Water (displace): id=12645, wt=38.000 9.64/9.93 9.64/9.93 Low Water (displace): id=12740, wt=31.000 9.64/9.93 9.64/9.93 Low Water (keep): wt=40.000, iters=3347 9.64/9.93 9.64/9.93 Low Water (displace): id=12919, wt=30.000 9.64/9.93 9.64/9.93 Low Water (keep): wt=39.000, iters=3359 9.64/9.93 9.64/9.93 Low Water (keep): wt=38.000, iters=3361 9.64/9.93 9.64/9.93 Low Water (displace): id=13289, wt=25.000 9.64/9.93 9.64/9.93 Low Water (displace): id=13297, wt=23.000 9.64/9.93 9.64/9.93 Low Water (keep): wt=37.000, iters=3365 9.64/9.93 9.64/9.93 Low Water (keep): wt=36.000, iters=3391 9.64/9.93 9.64/9.93 Low Water (keep): wt=35.000, iters=3343 9.64/9.93 9.64/9.93 Low Water (keep): wt=34.000, iters=3335 9.64/9.93 9.64/9.93 Low Water (displace): id=18005, wt=21.000 9.64/9.93 9.64/9.93 Low Water (displace): id=18043, wt=19.000 66.82/67.14 66.82/67.14 Low Water (keep): wt=33.000, iters=3367 66.82/67.14 66.82/67.14 Low Water (displace): id=18111, wt=17.000 66.82/67.14 66.82/67.14 Low Water (displace): id=18160, wt=15.000 66.82/67.14 66.82/67.14 Low Water (keep): wt=32.000, iters=3344 66.82/67.14 66.82/67.14 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 100 (0.00 of 9.58 sec). 66.82/67.14 66.82/67.14 Low Water (keep): wt=31.000, iters=3348 66.82/67.14 66.82/67.14 Low Water (keep): wt=30.000, iters=3333 66.82/67.14 66.82/67.14 Low Water (keep): wt=29.000, iters=3342 66.82/67.14 66.82/67.14 Low Water (keep): wt=27.000, iters=3333 66.82/67.14 66.82/67.14 Low Water (keep): wt=26.000, iters=3412 66.82/67.14 66.82/67.14 Low Water (keep): wt=25.000, iters=3341 66.82/67.14 66.82/67.14 Low Water (keep): wt=24.000, iters=3333 66.82/67.14 66.82/67.14 Low Water (keep): wt=23.000, iters=3348 66.82/67.14 66.82/67.14 Low Water (keep): wt=22.000, iters=3348 66.82/67.14 66.82/67.14 Low Water (keep): wt=21.000, iters=3335 66.82/67.14 66.82/67.14 ============================== PROOF ================================= 66.82/67.14 % SZS status Theorem 66.82/67.14 % SZS output start Refutation 66.82/67.14 66.82/67.14 % Proof 1 at 64.57 (+ 1.57) seconds. 66.82/67.14 % Length of proof is 126. 66.82/67.14 % Level of proof is 26. 66.82/67.14 % Maximum clause weight is 26.000. 66.82/67.14 % Given clauses 2723. 66.82/67.14 66.82/67.14 1 (all C all B all A mult(A,mult(mult(B,C),B)) = mult(mult(mult(A,B),C),B)) # label(f07) # label(axiom) # label(non_clause). [assumption]. 66.82/67.14 2 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 66.82/67.14 3 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 66.82/67.14 4 (all A A = mult(A,unit)) # label(f05) # label(axiom) # label(non_clause). [assumption]. 66.82/67.14 5 (all X0 all X1 all X2 (mult(X0,mult(X2,X1)) = mult(X0,mult(X1,X2)) & mult(mult(X0,X2),X1) = mult(mult(X0,X1),X2) | mult(mult(X0,X2),X1) = mult(X0,mult(X2,X1)) & mult(mult(X0,X1),X2) = mult(X0,mult(X1,X2)))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 66.82/67.14 6 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 66.82/67.14 7 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 66.82/67.14 8 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 66.82/67.14 9 mult(A,unit) = A # label(f05) # label(axiom). [clausify(4)]. 66.82/67.14 10 mult(unit,A) = A # label(f06) # label(axiom). [clausify(8)]. 66.82/67.14 11 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(2)]. 66.82/67.14 12 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(3)]. 66.82/67.14 13 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(6)]. 66.82/67.14 14 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(7)]. 66.82/67.14 15 mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) # label(f07) # label(axiom). [clausify(1)]. 66.82/67.14 16 mult(A,mult(B,C)) = mult(A,mult(C,B)) | mult(mult(A,B),C) = mult(A,mult(B,C)) # label(f08) # label(axiom). [clausify(5)]. 66.82/67.14 17 mult(A,mult(B,C)) = mult(A,mult(C,B)) | mult(mult(A,C),B) = mult(A,mult(C,B)) # label(f08) # label(axiom). [clausify(5)]. 66.82/67.14 18 mult(mult(A,B),C) = mult(mult(A,C),B) | mult(mult(A,B),C) = mult(A,mult(B,C)) # label(f08) # label(axiom). [clausify(5)]. 66.82/67.14 20 mult(a,mult(b,c)) != mult(mult(a,b),c) # label(goals) # label(negated_conjecture). [assumption]. 66.82/67.14 21 mult(mult(a,b),c) != mult(a,mult(b,c)). [copy(20),flip(a)]. 66.82/67.14 23 rd(A,A) = unit. [para(10(a,1),11(a,1,1))]. 66.82/67.14 24 ld(unit,A) = A. [para(12(a,1),10(a,1)),flip(a)]. 66.82/67.14 27 ld(rd(A,B),A) = B. [para(13(a,1),14(a,1,2))]. 66.82/67.14 28 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(9(a,1),15(a,1,1)),rewrite([9(4)])]. 66.82/67.14 29 rd(mult(A,mult(mult(B,C),B)),B) = mult(mult(A,B),C). [para(15(a,1),11(a,1,1))]. 66.82/67.14 31 mult(A,mult(mult(B,ld(mult(A,B),C)),B)) = mult(C,B). [para(12(a,1),15(a,1,1)),flip(a)]. 66.82/67.14 32 mult(rd(A,B),mult(mult(B,C),B)) = mult(mult(A,C),B). [para(13(a,1),15(a,1,1,1)),flip(a)]. 66.82/67.14 39 mult(A,mult(ld(A,B),C)) = mult(A,mult(C,ld(A,B))) | mult(A,mult(ld(A,B),C)) = mult(B,C). [para(12(a,1),16(b,1,1)),flip(b)]. 66.82/67.14 70 mult(mult(A,B),ld(A,C)) = mult(C,B) | mult(A,mult(ld(A,C),B)) = mult(C,B). [para(12(a,1),18(a,1,1)),rewrite([12(7)]),flip(a),flip(b)]. 66.82/67.14 106 mult(a,mult(c,b)) = mult(a,mult(b,c)). [resolve(21,a,17,b)]. 66.82/67.14 107 mult(mult(a,c),b) != mult(a,mult(b,c)). [para(18(a,1),21(a,1)),unit_del(a,21)]. 66.82/67.14 111 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(28(a,1),14(a,1,2))]. 66.82/67.14 126 mult(c,b) = mult(b,c). [para(106(a,1),14(a,1,2)),rewrite([14(7)]),flip(a)]. 66.82/67.14 127 rd(mult(b,c),b) = c. [para(126(a,1),11(a,1,1))]. 66.82/67.14 134 rd(mult(A,mult(B,C)),C) = mult(mult(A,C),ld(C,B)). [para(12(a,1),29(a,1,1,2,1))]. 66.82/67.14 248 mult(mult(A,ld(mult(B,A),C)),A) = ld(B,mult(C,A)). [para(31(a,1),14(a,1,2)),flip(a)]. 66.82/67.14 276 mult(mult(A,ld(B,C)),B) = mult(rd(A,B),mult(C,B)). [para(12(a,1),32(a,1,2,1)),flip(a)]. 66.82/67.14 296 mult(rd(A,c),mult(b,mult(c,c))) = mult(mult(A,b),c). [para(126(a,1),32(a,1,2,1)),rewrite([28(7)])]. 66.82/67.14 554 mult(mult(A,B),ld(B,unit)) = A. [para(10(a,1),134(a,1,1,2)),rewrite([11(2)]),flip(a)]. 66.82/67.14 591 rd(A,ld(B,unit)) = mult(A,B). [para(554(a,1),11(a,1,1))]. 66.82/67.14 593 mult(A,ld(B,unit)) = rd(A,B). [para(13(a,1),554(a,1,1))]. 66.82/67.14 594 ld(mult(A,B),A) = ld(B,unit). [para(554(a,1),14(a,1,2))]. 66.82/67.14 602 mult(mult(A,B),rd(ld(B,unit),B)) = rd(A,B). [para(554(a,1),28(a,1,1)),rewrite([593(3),593(7)]),flip(a)]. 66.82/67.14 604 ld(A,rd(A,B)) = ld(B,unit). [para(554(a,1),111(a,1,1)),rewrite([593(6),602(5)])]. 66.82/67.14 716 mult(ld(A,unit),A) = unit. [para(591(a,1),23(a,1))]. 66.82/67.14 720 rd(unit,A) = ld(A,unit). [para(716(a,1),11(a,1,1))]. 66.82/67.14 722 mult(ld(A,unit),mult(mult(A,B),A)) = mult(B,A). [para(716(a,1),15(a,1,1,1)),rewrite([10(2)]),flip(a)]. 66.82/67.14 807 mult(rd(mult(A,B),C),B) = mult(A,mult(rd(B,C),B)). [para(593(a,1),15(a,1,1)),rewrite([593(6)])]. 66.82/67.14 826 ld(ld(A,B),unit) = ld(B,A). [para(12(a,1),594(a,1,1)),flip(a)]. 66.82/67.14 863 mult(A,mult(ld(A,B),C)) = mult(B,C) | mult(ld(A,B),C) = mult(C,ld(A,B)). [para(39(a,1),14(a,1,2)),rewrite([14(9)]),flip(b)]. 66.82/67.14 947 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(826(a,1),591(a,1,2))]. 66.82/67.14 1537 rd(mult(A,B),mult(mult(B,A),B)) = ld(B,unit). [para(722(a,1),11(a,1,1))]. 66.82/67.14 1538 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(12(a,1),722(a,1,2,1))]. 66.82/67.14 1539 ld(ld(A,unit),mult(B,A)) = mult(mult(A,B),A). [para(722(a,1),14(a,1,2))]. 66.82/67.14 2033 rd(mult(ld(A,B),A),mult(B,A)) = ld(A,unit). [para(12(a,1),1537(a,1,2,1))]. 66.82/67.14 2303 rd(ld(ld(A,unit),B),A) = mult(A,rd(B,A)). [para(27(a,1),1538(a,1,1)),rewrite([720(2),593(3),720(4),720(7),593(8)]),flip(a)]. 66.82/67.14 2306 mult(ld(b,unit),mult(b,c)) = mult(ld(b,c),b). [para(126(a,1),1538(a,1,2))]. 66.82/67.14 2400 rd(mult(ld(A,unit),B),A) = ld(A,rd(B,A)). [para(27(a,1),1539(a,1,1)),rewrite([720(2),593(3),720(4),720(7),593(8)]),flip(a)]. 66.82/67.14 3206 mult(b,mult(ld(b,c),b)) = mult(b,c). [para(2306(a,1),39(a,1,2)),rewrite([593(15),127(13),2306(19),10(23)]),merge(b)]. 66.82/67.14 3445 mult(ld(b,c),b) = c. [para(3206(a,1),14(a,1,2)),rewrite([14(5)]),flip(a)]. 66.82/67.14 3472 rd(c,b) = ld(b,c). [para(3445(a,1),11(a,1,1))]. 66.82/67.14 8676 rd(mult(A,B),A) = B | mult(A,mult(ld(A,unit),B)) = B. [para(10(a,1),70(a,2)),rewrite([593(4),10(9)])]. 66.82/67.14 8915 mult(rd(A,mult(B,A)),A) = ld(B,A). [para(10(a,1),248(a,2,2)),rewrite([593(4)])]. 66.82/67.14 8916 rd(ld(A,mult(B,C)),C) = mult(C,ld(mult(A,C),B)). [para(248(a,1),11(a,1,1))]. 66.82/67.14 8918 ld(rd(A,B),mult(C,B)) = mult(mult(B,ld(A,C)),B). [para(13(a,1),248(a,1,1,2,1)),flip(a)]. 66.82/67.14 8970 ld(A,rd(ld(rd(B,A),C),A)) = ld(B,rd(C,A)). [para(248(a,1),593(a,1)),rewrite([593(3),593(7),2400(8)]),flip(a)]. 66.82/67.14 9247 rd(ld(A,B),B) = rd(B,mult(A,B)). [para(8915(a,1),11(a,1,1))]. 66.82/67.14 9249 ld(rd(A,B),B) = mult(rd(B,A),B). [para(13(a,1),8915(a,1,1,2)),flip(a)]. 66.82/67.14 9320 mult(mult(A,rd(A,mult(B,A))),A) = ld(ld(A,unit),ld(B,A)). [para(8915(a,1),1539(a,1,2)),flip(a)]. 66.82/67.14 9594 rd(A,mult(mult(A,B),A)) = rd(ld(B,unit),A). [para(594(a,1),9247(a,1,1)),flip(a)]. 66.82/67.14 11404 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [para(8915(a,1),276(a,2,2)),rewrite([604(3),593(4)])]. 66.82/67.14 17762 ld(rd(A,b),mult(b,c)) = mult(mult(b,ld(A,c)),b). [para(126(a,1),8918(a,1,2))]. 66.82/67.14 18148 rd(ld(rd(A,B),C),B) = mult(B,ld(A,rd(C,B))). [para(8970(a,1),12(a,1,2)),flip(a)]. 66.82/67.14 30584 rd(mult(A,B),A) = B | mult(ld(A,unit),B) = ld(A,B). [para(8676(b,1),14(a,1,2)),flip(b)]. 66.82/67.14 30722 rd(mult(A,B),A) = B | rd(B,mult(A,B)) = ld(A,unit). [para(30584(b,1),11(a,1,1)),rewrite([9247(5)])]. 66.82/67.14 31115 rd(A,mult(B,A)) = ld(B,unit) | mult(A,B) = mult(B,A). [para(30722(a,1),13(a,1,1))]. 66.82/67.14 32122 rd(A,mult(B,A)) = ld(B,unit) | mult(ld(B,A),B) = A. [para(12(a,1),31115(a,1,2)),rewrite([9247(2),12(9)])]. 66.82/67.14 32123 ld(rd(A,B),unit) = rd(B,A) | mult(B,rd(A,B)) = A. [para(13(a,1),31115(a,1,2)),rewrite([13(9)]),flip(a)]. 66.82/67.14 32991 rd(A,mult(B,A)) = ld(B,unit) | rd(A,mult(A,B)) = ld(B,unit). [para(32122(b,1),2033(a,1,1))]. 66.82/67.14 49814 rd(A,mult(B,A)) = ld(B,unit). [para(32122(b,1),32991(b,1,2)),rewrite([12(8),9247(7),9247(12)]),merge(b),merge(c)]. 66.82/67.14 49816 ld(rd(A,B),unit) = rd(B,A). [para(32123(b,1),32991(b,1,2)),rewrite([13(7)]),flip(b),flip(c),merge(b),merge(c)]. 66.82/67.14 49931 rd(ld(A,unit),B) = ld(mult(B,A),unit). [back_rewrite(9594),rewrite([49814(3)]),flip(a)]. 66.82/67.14 49936 ld(ld(A,unit),ld(B,A)) = mult(rd(A,B),A). [back_rewrite(9320),rewrite([49814(2),593(3)]),flip(a)]. 66.82/67.14 50265 ld(ld(A,unit),B) = mult(A,B). [para(49814(a,1),27(a,1,1))]. 66.82/67.14 50272 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(49814(a,1),604(a,1,2)),flip(a)]. 66.82/67.14 50283 mult(ld(A,unit),B) = ld(A,B). [para(49814(a,1),9249(a,2,1)),rewrite([11(2)]),flip(a)]. 66.82/67.14 50291 rd(A,mult(B,mult(rd(A,C),A))) = rd(C,mult(B,A)). [para(807(a,1),49814(a,1,2)),rewrite([49816(8)])]. 66.82/67.14 50439 mult(rd(A,B),A) = mult(A,ld(B,A)). [back_rewrite(49936),rewrite([50265(4)]),flip(a)]. 66.82/67.14 50711 rd(mult(A,B),A) = mult(A,rd(B,A)). [back_rewrite(2303),rewrite([50265(3)])]. 66.82/67.14 50712 mult(mult(A,B),A) = mult(A,mult(B,A)). [back_rewrite(1539),rewrite([50265(4)]),flip(a)]. 66.82/67.14 50762 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [back_rewrite(49931),rewrite([50272(6)])]. 66.82/67.14 51307 rd(A,mult(B,mult(A,ld(C,A)))) = rd(C,mult(B,A)). [back_rewrite(50291),rewrite([50439(2)])]. 66.82/67.14 52065 ld(rd(A,b),mult(b,c)) = mult(b,mult(ld(A,c),b)). [back_rewrite(17762),rewrite([50712(12)])]. 66.82/67.14 52423 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [back_rewrite(15),rewrite([50712(5)])]. 66.82/67.14 53284 mult(mult(A,rd(B,C)),rd(C,B)) = A. [para(49816(a,1),134(a,2,2)),rewrite([10(3),11(4)]),flip(a)]. 66.82/67.14 53285 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(49816(a,1),593(a,1,2)),flip(a)]. 66.82/67.14 53893 ld(ld(A,B),C) = mult(ld(B,A),C). [para(826(a,1),50265(a,1,1))]. 66.82/67.14 53906 mult(mult(A,B),ld(B,C)) = mult(B,mult(ld(B,A),C)). [para(50265(a,1),8916(a,1,1)),rewrite([134(3),50283(6),53893(5)])]. 66.82/67.14 53914 rd(mult(mult(A,B),C),A) = mult(A,mult(B,rd(C,A))). [para(50265(a,1),18148(a,2,2)),rewrite([50762(3),53893(4),53893(3),24(2)])]. 66.82/67.14 53947 ld(rd(A,B),C) = mult(rd(B,A),C). [para(49816(a,1),50265(a,1,1))]. 66.82/67.14 54633 mult(rd(b,A),mult(b,c)) = mult(b,mult(ld(A,c),b)). [back_rewrite(52065),rewrite([53947(6)])]. 66.82/67.14 57088 ld(mult(A,mult(B,A)),mult(A,B)) = ld(A,unit). [para(50712(a,1),594(a,1,1))]. 66.82/67.14 57698 mult(A,mult(rd(B,C),mult(ld(D,rd(C,B)),rd(B,C)))) = rd(A,mult(D,rd(C,B))). [para(11404(a,1),53284(a,1,1)),rewrite([53285(2),52423(7)])]. 66.82/67.14 57713 mult(ld(A,rd(B,C)),rd(C,B)) = ld(A,unit). [para(50283(a,1),53284(a,1,1))]. 66.82/67.14 57720 rd(A,mult(B,rd(C,D))) = mult(A,rd(rd(D,C),B)). [back_rewrite(57698),rewrite([57713(5),593(4)]),flip(a)]. 66.82/67.14 59846 mult(mult(A,mult(B,A)),ld(A,C)) = mult(mult(A,B),C) | rd(C,A) = ld(A,C). [para(57088(a,1),863(a,1,2,1)),rewrite([50283(5),57088(11),50283(10),57088(12),593(11)]),flip(b)]. 66.82/67.14 61304 rd(mult(A,B),mult(C,A)) = mult(A,rd(rd(B,A),C)). [para(594(a,1),51307(a,1,2,2,2)),rewrite([593(3),57720(3)]),flip(a)]. 66.82/67.14 62979 mult(mult(A,mult(B,A)),ld(A,C)) = mult(A,mult(B,C)). [para(14(a,1),53906(a,2,2,1)),rewrite([50712(2)])]. 66.82/67.14 63065 mult(mult(A,B),C) = mult(A,mult(B,C)) | rd(C,A) = ld(A,C). [back_rewrite(59846),rewrite([62979(4)]),flip(a)]. 66.82/67.14 66274 mult(mult(A,B),ld(A,C)) = mult(A,mult(rd(B,A),C)). [para(50283(a,1),61304(a,1,2)),rewrite([947(3),947(7),24(6)])]. 66.82/67.14 70756 rd(c,a) = ld(a,c). [resolve(63065,a,21,a)]. 66.82/67.14 70760 rd(b,a) = ld(a,b). [para(63065(a,1),107(a,1)),rewrite([126(11)]),xx(b)]. 66.82/67.14 70769 mult(ld(a,c),a) = c. [para(70756(a,1),13(a,1,1))]. 66.82/67.14 70963 mult(ld(a,b),a) = b. [para(70760(a,1),13(a,1,1))]. 66.82/67.14 70999 mult(ld(a,b),mult(b,c)) = mult(b,mult(ld(a,c),b)). [para(70760(a,1),54633(a,1,1))]. 66.82/67.14 71158 rd(a,c) = ld(c,a). [para(70769(a,1),49814(a,1,2)),rewrite([53893(8),9(8)])]. 66.82/67.14 71160 mult(c,a) = mult(a,c). [para(70769(a,1),50712(a,2,2)),rewrite([12(5)])]. 66.82/67.14 71253 mult(b,a) = mult(a,b). [para(70963(a,1),50712(a,2,2)),rewrite([12(5)])]. 66.82/67.14 71424 mult(ld(c,a),mult(b,mult(c,c))) = mult(mult(a,b),c). [para(71158(a,1),296(a,1,1))]. 66.82/67.14 71785 rd(mult(mult(a,b),A),b) = mult(b,mult(a,rd(A,b))). [para(71253(a,1),53914(a,1,1,1))]. 66.82/67.14 73327 mult(ld(a,b),mult(b,mult(ld(b,c),a))) = mult(b,c). [para(70999(a,1),50711(a,1,1)),rewrite([947(11),66274(11),11(8),70769(6),947(13),66274(13),3472(10)]),flip(a)]. 66.82/67.14 74020 mult(mult(a,c),b) = mult(mult(a,b),c). [para(18(a,1),71424(a,2)),rewrite([71424(20)]),flip(b),unit_del(a,21)]. 66.82/67.14 74038 mult(b,mult(a,ld(b,c))) = mult(a,c). [para(74020(a,1),11(a,1,1)),rewrite([71785(7),3472(5)])]. 66.82/67.14 74136 mult(b,mult(ld(b,c),a)) = mult(a,c). [para(74038(a,1),39(a,2)),rewrite([71160(21)]),merge(b)]. 66.82/67.14 74190 mult(ld(a,b),mult(a,c)) = mult(b,c). [back_rewrite(73327),rewrite([74136(10)])]. 66.82/67.14 74646 $F. [para(74190(a,1),53906(a,2,2)),rewrite([71253(3),14(8)]),unit_del(a,21)]. 66.82/67.14 66.82/67.14 % SZS output end Refutation 66.82/67.14 ============================== end of proof ========================== 66.82/67.14 66.82/67.14 ============================== STATISTICS ============================ 66.82/67.14 66.82/67.14 Given=2723. Generated=2555622. Kept=74636. proofs=1. 66.82/67.14 Usable=1068. Sos=9999. Demods=8892. Limbo=22, Disabled=63559. Hints=0. 66.82/67.14 Megabytes=59.24. 66.82/67.14 User_CPU=64.57, System_CPU=1.57, Wall_clock=66. 66.82/67.14 66.82/67.14 ============================== end of statistics ===================== 66.82/67.14 66.82/67.14 ============================== end of search ========================= 66.82/67.14 66.82/67.14 THEOREM PROVED 66.82/67.14 % SZS status Theorem 66.82/67.14 66.82/67.14 Exiting with 1 proof. 66.82/67.14 66.82/67.14 Process 15255 exit (max_proofs) Tue Aug 9 05:18:56 2022 66.82/67.14 Prover9 interrupted 66.82/67.14 EOF