0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n005.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 : 960 0.13/0.34 % DateTime : Thu Jul 2 07:18:51 EDT 2020 0.13/0.34 % CPUTime : 0.44/1.00 ============================== Prover9 =============================== 0.44/1.00 Prover9 (32) version 2009-11A, November 2009. 0.44/1.00 Process 24033 was started by sandbox on n005.cluster.edu, 0.44/1.00 Thu Jul 2 07:18:51 2020 0.44/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_23880_n005.cluster.edu". 0.44/1.00 ============================== end of head =========================== 0.44/1.00 0.44/1.00 ============================== INPUT ================================= 0.44/1.00 0.44/1.00 % Reading from file /tmp/Prover9_23880_n005.cluster.edu 0.44/1.00 0.44/1.00 set(prolog_style_variables). 0.44/1.00 set(auto2). 0.44/1.00 % set(auto2) -> set(auto). 0.44/1.00 % set(auto) -> set(auto_inference). 0.44/1.00 % set(auto) -> set(auto_setup). 0.44/1.00 % set(auto_setup) -> set(predicate_elim). 0.44/1.00 % set(auto_setup) -> assign(eq_defs, unfold). 0.44/1.00 % set(auto) -> set(auto_limits). 0.44/1.00 % set(auto_limits) -> assign(max_weight, "100.000"). 0.44/1.00 % set(auto_limits) -> assign(sos_limit, 20000). 0.44/1.00 % set(auto) -> set(auto_denials). 0.44/1.00 % set(auto) -> set(auto_process). 0.44/1.00 % set(auto2) -> assign(new_constants, 1). 0.44/1.00 % set(auto2) -> assign(fold_denial_max, 3). 0.44/1.00 % set(auto2) -> assign(max_weight, "200.000"). 0.44/1.00 % set(auto2) -> assign(max_hours, 1). 0.44/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.44/1.00 % set(auto2) -> assign(max_seconds, 0). 0.44/1.00 % set(auto2) -> assign(max_minutes, 5). 0.44/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.44/1.00 % set(auto2) -> set(sort_initial_sos). 0.44/1.00 % set(auto2) -> assign(sos_limit, -1). 0.44/1.00 % set(auto2) -> assign(lrs_ticks, 3000). 0.44/1.00 % set(auto2) -> assign(max_megs, 400). 0.44/1.00 % set(auto2) -> assign(stats, some). 0.44/1.00 % set(auto2) -> clear(echo_input). 0.44/1.00 % set(auto2) -> set(quiet). 0.44/1.00 % set(auto2) -> clear(print_initial_clauses). 0.44/1.00 % set(auto2) -> clear(print_given). 0.44/1.00 assign(lrs_ticks,-1). 0.44/1.00 assign(sos_limit,10000). 0.44/1.00 assign(order,kbo). 0.44/1.00 set(lex_order_vars). 0.44/1.00 clear(print_given). 0.44/1.00 0.44/1.00 % formulas(sos). % not echoed (13 formulas) 0.44/1.00 0.44/1.00 ============================== end of input ========================== 0.44/1.00 0.44/1.00 % From the command line: assign(max_seconds, 960). 0.44/1.00 0.44/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.44/1.00 0.44/1.00 % Formulas that are not ordinary clauses: 0.44/1.00 1 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 2 (all A A = mult(f(A),f(A))) # label(f09) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 3 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 4 (all X6 all X7 all X8 (mult(X6,mult(mult(X7,X8),X6)) = mult(mult(X6,X7),mult(X8,X6)) -> mult(mult(mult(X6,X7),X6),X8) = mult(X6,mult(X7,mult(X6,X8))))) # label(f12) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 5 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 6 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 7 (all X0 all X1 all X2 (mult(X0,mult(X1,mult(X2,X1))) = mult(mult(mult(X0,X1),X2),X1) -> mult(mult(mult(X1,X0),X1),X2) = mult(X1,mult(X0,mult(X1,X2))))) # label(f10) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 8 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 9 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 10 (all X3 all X4 all X5 (mult(mult(X3,mult(X4,X5)),X3) = mult(mult(X3,X4),mult(X5,X3)) -> mult(X3,mult(X4,mult(X3,X5))) = mult(mult(mult(X3,X4),X3),X5))) # label(f11) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 11 (all C all B all A mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C))) # label(f07) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 12 (all A A = mult(unit,A)) # label(f06) # label(axiom) # label(non_clause). [assumption]. 0.44/1.00 0.44/1.00 ============================== end of process non-clausal formulas === 0.44/1.00 0.44/1.00 ============================== PROCESS INITIAL CLAUSES =============== 0.44/1.00 0.44/1.00 ============================== PREDICATE ELIMINATION ================= 0.44/1.00 0.44/1.00 ============================== end predicate elimination ============= 0.44/1.00 0.44/1.00 Auto_denials: 0.44/1.00 % copying label goals to answer in negative clause 6.84/7.19 6.84/7.19 Term ordering decisions: 6.84/7.19 6.84/7.19 % Assigning unary symbol f kb_weight 0 and highest precedence (9). 6.84/7.19 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. f=0. 6.84/7.19 6.84/7.19 ============================== end of process initial clauses ======== 6.84/7.19 6.84/7.19 ============================== CLAUSES FOR SEARCH ==================== 6.84/7.19 6.84/7.19 ============================== end of clauses for search ============= 6.84/7.19 6.84/7.19 ============================== SEARCH ================================ 6.84/7.19 6.84/7.19 % Starting search at 0.01 seconds. 6.84/7.19 6.84/7.19 Low Water (keep): wt=158.000, iters=3341 6.84/7.19 6.84/7.19 Low Water (keep): wt=126.000, iters=3357 6.84/7.19 6.84/7.19 Low Water (keep): wt=110.000, iters=3408 6.84/7.19 6.84/7.19 Low Water (keep): wt=106.000, iters=3370 6.84/7.19 6.84/7.19 Low Water (keep): wt=94.000, iters=3349 6.84/7.19 6.84/7.19 Low Water (keep): wt=90.000, iters=3358 6.84/7.19 6.84/7.19 Low Water (keep): wt=88.000, iters=3466 6.84/7.19 6.84/7.19 Low Water (keep): wt=78.000, iters=3351 6.84/7.19 6.84/7.19 Low Water (keep): wt=74.000, iters=3350 6.84/7.19 6.84/7.19 Low Water (keep): wt=70.000, iters=3392 6.84/7.19 6.84/7.19 Low Water (keep): wt=68.000, iters=3386 6.84/7.19 6.84/7.19 Low Water (keep): wt=67.000, iters=3418 6.84/7.19 6.84/7.19 Low Water (keep): wt=66.000, iters=3372 6.84/7.19 6.84/7.19 Low Water (keep): wt=62.000, iters=3347 6.84/7.19 6.84/7.19 Low Water (keep): wt=61.000, iters=3408 6.84/7.19 6.84/7.19 Low Water (keep): wt=59.000, iters=3377 6.84/7.19 6.84/7.19 Low Water (keep): wt=58.000, iters=3346 6.84/7.19 6.84/7.19 Low Water (keep): wt=56.000, iters=3357 6.84/7.19 6.84/7.19 Low Water (keep): wt=54.000, iters=3340 6.84/7.19 6.84/7.19 Low Water (keep): wt=53.000, iters=3417 6.84/7.19 6.84/7.19 Low Water (keep): wt=52.000, iters=3416 6.84/7.19 6.84/7.19 Low Water (keep): wt=50.000, iters=3371 6.84/7.19 6.84/7.19 Low Water (keep): wt=49.000, iters=3345 6.84/7.19 6.84/7.19 Low Water (keep): wt=47.000, iters=3373 6.84/7.19 6.84/7.19 Low Water (keep): wt=46.000, iters=3347 6.84/7.19 6.84/7.19 Low Water (keep): wt=45.000, iters=3338 6.84/7.19 6.84/7.19 Low Water (keep): wt=43.000, iters=3391 6.84/7.19 6.84/7.19 Low Water (keep): wt=39.000, iters=3337 6.84/7.19 6.84/7.19 Low Water (keep): wt=35.000, iters=3342 6.84/7.19 6.84/7.19 Low Water (keep): wt=33.000, iters=3392 6.84/7.19 6.84/7.19 Low Water (keep): wt=31.000, iters=3344 6.84/7.19 6.84/7.19 Low Water (displace): id=9181, wt=198.000 6.84/7.19 6.84/7.19 Low Water (displace): id=7243, wt=194.000 6.84/7.19 6.84/7.19 Low Water (displace): id=15435, wt=27.000 6.84/7.19 6.84/7.19 Low Water (keep): wt=29.000, iters=3341 6.84/7.19 6.84/7.19 Low Water (displace): id=15472, wt=25.000 6.84/7.19 6.84/7.19 Low Water (displace): id=15473, wt=23.000 6.84/7.19 6.84/7.19 Low Water (displace): id=15478, wt=21.000 6.84/7.19 6.84/7.19 Low Water (displace): id=15729, wt=19.000 6.84/7.19 6.84/7.19 Low Water (keep): wt=27.000, iters=3341 6.84/7.19 6.84/7.19 Low Water (displace): id=15966, wt=17.000 6.84/7.19 6.84/7.19 Low Water (keep): wt=25.000, iters=3336 6.84/7.19 6.84/7.19 Low Water (displace): id=18187, wt=15.000 6.84/7.19 6.84/7.19 ============================== PROOF ================================= 6.84/7.19 % SZS status Theorem 6.84/7.19 % SZS output start Refutation 6.84/7.19 6.84/7.19 % Proof 1 at 6.12 (+ 0.08) seconds: goals. 6.84/7.19 % Length of proof is 102. 6.84/7.19 % Level of proof is 21. 6.84/7.19 % Maximum clause weight is 38.000. 6.84/7.19 % Given clauses 439. 6.84/7.19 6.84/7.19 1 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 2 (all A A = mult(f(A),f(A))) # label(f09) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 3 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 4 (all X6 all X7 all X8 (mult(X6,mult(mult(X7,X8),X6)) = mult(mult(X6,X7),mult(X8,X6)) -> mult(mult(mult(X6,X7),X6),X8) = mult(X6,mult(X7,mult(X6,X8))))) # label(f12) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 5 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 6 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 7 (all X0 all X1 all X2 (mult(X0,mult(X1,mult(X2,X1))) = mult(mult(mult(X0,X1),X2),X1) -> mult(mult(mult(X1,X0),X1),X2) = mult(X1,mult(X0,mult(X1,X2))))) # label(f10) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 8 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 9 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 11 (all C all B all A mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C))) # label(f07) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 12 (all A A = mult(unit,A)) # label(f06) # label(axiom) # label(non_clause). [assumption]. 6.84/7.19 13 mult(A,unit) = A # label(f05) # label(axiom). [clausify(8)]. 6.84/7.19 14 mult(unit,A) = A # label(f06) # label(axiom). [clausify(12)]. 6.84/7.19 15 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)]. 6.84/7.19 16 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(2)]. 6.84/7.19 17 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)]. 6.84/7.19 18 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(6)]. 6.84/7.19 19 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(9)]. 6.84/7.19 20 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(5)]. 6.84/7.19 21 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(11)]. 6.84/7.19 22 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(21),rewrite([20(2),20(7)])]. 6.84/7.19 23 mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c) # label(goals) # label(negated_conjecture) # answer(goals). [assumption]. 6.84/7.19 24 mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))) # answer(goals). [copy(23),rewrite([20(12)]),flip(a)]. 6.84/7.19 25 mult(mult(A,B),mult(C,A)) != mult(A,mult(mult(B,C),A)) | mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))) # label(f12) # label(axiom). [clausify(4)]. 6.84/7.19 26 mult(mult(A,B),mult(C,A)) != mult(A,mult(mult(B,C),A)) | mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [copy(25),rewrite([20(9)])]. 6.84/7.19 27 mult(mult(mult(A,B),C),B) != mult(A,mult(B,mult(C,B))) | mult(mult(mult(B,A),B),C) = mult(B,mult(A,mult(B,C))) # label(f10) # label(axiom). [clausify(7)]. 6.84/7.19 28 mult(mult(mult(A,B),C),B) != mult(A,mult(B,mult(C,B))) | mult(mult(B,mult(A,B)),C) = mult(B,mult(A,mult(B,C))). [copy(27),rewrite([20(9)])]. 6.84/7.19 32 ld(A,A) = unit. [para(13(a,1),18(a,1,2))]. 6.84/7.19 34 ld(rd(A,B),A) = B. [para(17(a,1),18(a,1,2))]. 6.84/7.19 36 rd(A,ld(B,A)) = B. [para(15(a,1),19(a,1,1))]. 6.84/7.19 38 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(15(a,1),20(a,1,1)),flip(a)]. 6.84/7.19 39 mult(f(A),A) = mult(A,f(A)). [para(16(a,1),20(a,1,1)),rewrite([16(6)]),flip(a)]. 6.84/7.19 40 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(17(a,1),20(a,1,1)),flip(a)]. 6.84/7.19 42 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(20(a,1),19(a,1,1))]. 6.84/7.19 44 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(22(a,1),13(a,1)),rewrite([13(4),14(3),14(4)])]. 6.84/7.19 45 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(14(a,1),22(a,1,1)),rewrite([14(5)])]. 6.84/7.19 47 mult(mult(A,mult(B,C)),ld(C,B)) = mult(mult(A,C),mult(ld(C,B),B)). [para(15(a,1),22(a,2,2,2)),rewrite([38(3)])]. 6.84/7.19 50 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(17(a,1),22(a,1,1)),flip(a)]. 6.84/7.19 61 mult(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)) # answer(goals). [ur(26,b,24,a)]. 6.84/7.19 62 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(13(a,1),26(a,1,1)),rewrite([14(4),14(7),14(10)]),xx(a)]. 6.84/7.19 67 mult(f(A),mult(f(A),mult(B,f(A)))) != mult(A,mult(B,f(A))) | mult(f(A),mult(f(A),mult(f(A),B))) = mult(mult(A,f(A)),B). [para(16(a,1),26(a,1,1)),rewrite([20(8),16(14),39(12)]),flip(a),flip(b)]. 6.84/7.19 85 mult(rd(A,B),mult(B,mult(C,B))) != mult(mult(A,C),B) | mult(B,mult(rd(A,B),mult(B,C))) = mult(mult(B,A),C). [para(17(a,1),28(a,1,1,1)),rewrite([17(9)]),flip(a),flip(b)]. 6.84/7.19 97 rd(mult(A,f(A)),A) = f(A). [para(39(a,1),19(a,1,1))]. 6.84/7.19 108 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(38(a,1),18(a,1,2))]. 6.84/7.19 110 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(38(a,1),20(a,1,1)),rewrite([44(2),44(5)]),flip(a)]. 6.84/7.19 133 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(17(a,1),42(a,1,1,2))]. 6.84/7.19 136 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(38(a,1),42(a,2)),rewrite([44(3),110(4)])]. 6.84/7.19 137 mult(A,rd(f(A),A)) = f(A). [back_rewrite(97),rewrite([133(3)])]. 6.84/7.19 138 rd(f(A),A) = ld(A,f(A)). [para(137(a,1),18(a,1,2)),flip(a)]. 6.84/7.19 139 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),f(B))). [para(137(a,1),22(a,2,2,2)),rewrite([138(2),38(4),39(2),138(5),138(9)])]. 6.84/7.19 154 mult(ld(A,f(A)),A) = f(A). [para(138(a,1),17(a,1,1))]. 6.84/7.19 156 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(138(a,1),40(a,1,1)),rewrite([138(4),15(5),138(7)])]. 6.84/7.19 157 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(f(B),ld(B,f(B)))). [back_rewrite(139),rewrite([156(11)])]. 6.84/7.19 216 mult(A,mult(A,ld(mult(A,A),B))) = B. [para(62(a,1),15(a,1))]. 6.84/7.19 217 mult(f(A),mult(f(A),B)) = mult(A,B). [para(16(a,1),62(a,1,1)),flip(a)]. 6.84/7.19 219 rd(mult(A,mult(A,B)),B) = mult(A,A). [para(62(a,1),19(a,1,1))]. 6.84/7.19 239 mult(mult(A,f(A)),B) = mult(f(A),mult(A,B)). [back_rewrite(67),rewrite([217(6),217(12)]),flip(b),xx(a)]. 6.84/7.19 260 mult(ld(A,unit),A) = unit. [para(14(a,1),108(a,1,2)),rewrite([32(1)]),flip(a)]. 6.84/7.19 272 rd(unit,A) = ld(A,unit). [para(260(a,1),19(a,1,1))]. 6.84/7.19 280 mult(ld(A,unit),mult(A,A)) = A. [para(260(a,1),44(a,1,1)),rewrite([14(2)]),flip(a)]. 6.84/7.19 285 mult(mult(A,rd(A,B)),B) = mult(rd(A,B),mult(B,A)). [para(17(a,1),45(a,2,2,2)),rewrite([40(4)])]. 6.84/7.19 348 mult(ld(f(A),unit),A) = f(A). [para(16(a,1),280(a,1,2))]. 6.84/7.19 349 ld(ld(A,unit),A) = mult(A,A). [para(280(a,1),18(a,1,2))]. 6.84/7.19 362 ld(f(A),unit) = ld(A,f(A)). [para(348(a,1),19(a,1,1)),rewrite([138(2)]),flip(a)]. 6.84/7.19 363 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(348(a,1),20(a,1,1)),rewrite([15(5)]),flip(a)]. 6.84/7.19 377 mult(ld(f(A),unit),mult(A,f(A))) = A. [para(348(a,1),45(a,2,2,2)),rewrite([363(8),14(2)]),flip(a)]. 6.84/7.19 411 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(34(a,1),349(a,1,1)),rewrite([272(2),272(5),272(7)]),flip(a)]. 6.84/7.19 413 mult(f(A),ld(A,f(A))) = unit. [para(362(a,1),15(a,1,2))]. 6.84/7.19 415 ld(ld(A,f(A)),unit) = f(A). [para(362(a,1),36(a,1,2)),rewrite([272(4)])]. 6.84/7.19 421 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(A,B). [back_rewrite(157),rewrite([413(11),13(9)])]. 6.84/7.19 422 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(156),rewrite([413(8)])]. 6.84/7.19 490 mult(ld(A,f(A)),ld(A,f(A))) = ld(f(A),ld(A,f(A))). [para(415(a,1),349(a,1,1)),flip(a)]. 6.84/7.19 496 mult(ld(f(A),ld(A,f(A))),f(A)) = ld(A,f(A)). [para(422(a,1),62(a,2,2)),rewrite([490(5),13(10)])]. 6.84/7.19 652 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(17(a,1),136(a,1,1)),flip(a)]. 6.84/7.19 751 mult(A,ld(mult(A,A),B)) = ld(A,B). [para(216(a,1),18(a,1,2)),flip(a)]. 6.84/7.19 755 mult(A,ld(f(A),B)) = mult(f(A),B). [para(15(a,1),217(a,1,2)),flip(a)]. 6.84/7.19 772 mult(f(A),mult(A,B)) = mult(A,mult(f(A),B)). [para(217(a,1),62(a,2,2)),rewrite([16(3)]),flip(a)]. 6.84/7.19 805 mult(mult(A,f(A)),B) = mult(A,mult(f(A),B)). [back_rewrite(239),rewrite([772(6)])]. 6.84/7.19 813 rd(mult(A,B),ld(A,B)) = mult(A,A). [para(15(a,1),219(a,1,1,2))]. 6.84/7.19 819 ld(f(A),ld(A,f(A))) = ld(A,unit). [para(154(a,1),219(a,1,1,2)),rewrite([422(4),272(2),490(7)]),flip(a)]. 6.84/7.19 825 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(348(a,1),219(a,1,1,2)),rewrite([260(5),272(2),411(9)]),flip(a)]. 6.84/7.19 848 mult(ld(A,unit),f(A)) = ld(A,f(A)). [back_rewrite(496),rewrite([819(4)])]. 6.84/7.19 1062 mult(ld(A,unit),mult(A,f(A))) = f(A). [para(377(a,1),62(a,2,2)),rewrite([411(7),825(5),348(9)])]. 6.84/7.19 1631 mult(f(A),ld(A,B)) = ld(f(A),B). [para(16(a,1),751(a,1,2,1))]. 6.84/7.19 2494 mult(A,ld(B,unit)) = rd(A,B). [para(1062(a,1),50(a,1,1,1,2,2)),rewrite([44(4),16(3),805(12),1631(11),755(11),13(10),848(9),421(8),652(3)]),flip(a)]. 6.84/7.19 2793 ld(A,rd(A,B)) = ld(B,unit). [para(2494(a,1),18(a,1,2))]. 6.84/7.19 2804 rd(A,ld(B,unit)) = mult(A,B). [para(34(a,1),2494(a,1,2)),rewrite([272(3)]),flip(a)]. 6.84/7.19 2816 mult(mult(A,rd(B,C)),ld(ld(C,unit),B)) = mult(rd(A,C),mult(ld(ld(C,unit),B),B)). [para(2494(a,1),47(a,1,1,2)),rewrite([2494(9)])]. 6.84/7.19 2824 mult(f(A),rd(f(A),B)) = rd(A,B). [para(2494(a,1),217(a,1,2)),rewrite([2494(7)])]. 6.84/7.19 2825 mult(rd(A,B),mult(B,A)) = mult(A,A). [para(2494(a,1),219(a,1,1,2)),rewrite([2804(5),285(3)])]. 6.84/7.19 2920 ld(ld(A,B),unit) = ld(B,A). [para(36(a,1),2793(a,1,2)),flip(a)]. 6.84/7.19 2929 ld(mult(A,B),mult(A,A)) = ld(B,A). [para(813(a,1),2793(a,1,2)),rewrite([2920(6)])]. 6.84/7.19 3908 mult(mult(A,rd(f(B),C)),mult(C,f(B))) = mult(mult(A,rd(B,C)),C). [para(2824(a,1),47(a,1,1,2)),rewrite([34(6),34(10)]),flip(a)]. 6.84/7.19 3958 ld(rd(A,B),mult(A,A)) = mult(B,A). [para(2825(a,1),18(a,1,2))]. 6.84/7.19 4518 ld(ld(A,unit),B) = mult(A,B). [para(2494(a,1),2929(a,1,1)),rewrite([3958(3)]),flip(a)]. 6.84/7.19 4551 mult(mult(A,rd(B,C)),mult(C,B)) = mult(rd(A,C),mult(C,mult(B,B))). [back_rewrite(2816),rewrite([4518(5),4518(8),44(7)])]. 6.84/7.19 4573 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)). [back_rewrite(3908),rewrite([4551(6),16(4)]),flip(a)]. 6.84/7.19 8639 mult(rd(A,B),mult(B,mult(C,mult(B,B)))) != mult(mult(A,mult(C,B)),B) | mult(B,mult(rd(A,B),mult(B,mult(C,B)))) = mult(mult(B,A),mult(C,B)). [para(44(a,1),85(a,1,2,2))]. 6.84/7.19 20564 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(19(a,1),4573(a,1,1,2)),flip(a)]. 6.84/7.19 20576 mult(rd(A,B),mult(B,mult(C,mult(B,B)))) = mult(mult(A,mult(C,B)),B). [para(136(a,1),4573(a,1,1,2)),flip(a)]. 6.84/7.19 20724 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [back_rewrite(8639),rewrite([20576(5),20564(11)]),flip(b),xx(a)]. 6.84/7.19 20725 $F # answer(goals). [resolve(20724,a,61,a)]. 6.84/7.19 6.84/7.19 % SZS output end Refutation 6.84/7.19 ============================== end of proof ========================== 6.84/7.19 6.84/7.19 ============================== STATISTICS ============================ 6.84/7.19 6.84/7.19 Given=439. Generated=111071. Kept=20707. proofs=1. 6.84/7.19 Usable=353. Sos=9942. Demods=7950. Limbo=160, Disabled=10264. Hints=0. 6.84/7.19 Megabytes=26.39. 6.84/7.19 User_CPU=6.12, System_CPU=0.08, Wall_clock=6. 6.84/7.19 6.84/7.19 ============================== end of statistics ===================== 6.84/7.19 6.84/7.19 ============================== end of search ========================= 6.84/7.19 6.84/7.19 THEOREM PROVED 6.84/7.19 % SZS status Theorem 6.84/7.19 6.84/7.19 Exiting with 1 proof. 6.84/7.19 6.84/7.19 Process 24033 exit (max_proofs) Thu Jul 2 07:18:57 2020 6.84/7.19 Prover9 interrupted 6.84/7.19 EOF