0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.22 % Computer : n004.star.cs.uiowa.edu 0.03/0.22 % Model : x86_64 x86_64 0.03/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.22 % Memory : 32218.625MB 0.03/0.22 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.22 % CPULimit : 300 0.03/0.22 % DateTime : Sat Jul 14 04:57:40 CDT 2018 0.03/0.23 % CPUTime : 0.06/0.43 ============================== Prover9 =============================== 0.06/0.43 Prover9 (32) version 2009-11A, November 2009. 0.06/0.43 Process 40236 was started by sandbox2 on n004.star.cs.uiowa.edu, 0.06/0.43 Sat Jul 14 04:57:40 2018 0.06/0.43 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_40204_n004.star.cs.uiowa.edu". 0.06/0.43 ============================== end of head =========================== 0.06/0.43 0.06/0.43 ============================== INPUT ================================= 0.06/0.43 0.06/0.43 % Reading from file /tmp/Prover9_40204_n004.star.cs.uiowa.edu 0.06/0.43 0.06/0.43 set(prolog_style_variables). 0.06/0.43 set(auto2). 0.06/0.43 % set(auto2) -> set(auto). 0.06/0.43 % set(auto) -> set(auto_inference). 0.06/0.43 % set(auto) -> set(auto_setup). 0.06/0.43 % set(auto_setup) -> set(predicate_elim). 0.06/0.43 % set(auto_setup) -> assign(eq_defs, unfold). 0.06/0.43 % set(auto) -> set(auto_limits). 0.06/0.43 % set(auto_limits) -> assign(max_weight, "100.000"). 0.06/0.43 % set(auto_limits) -> assign(sos_limit, 20000). 0.06/0.43 % set(auto) -> set(auto_denials). 0.06/0.43 % set(auto) -> set(auto_process). 0.06/0.43 % set(auto2) -> assign(new_constants, 1). 0.06/0.43 % set(auto2) -> assign(fold_denial_max, 3). 0.06/0.43 % set(auto2) -> assign(max_weight, "200.000"). 0.06/0.43 % set(auto2) -> assign(max_hours, 1). 0.06/0.43 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.06/0.43 % set(auto2) -> assign(max_seconds, 0). 0.06/0.43 % set(auto2) -> assign(max_minutes, 5). 0.06/0.43 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.06/0.43 % set(auto2) -> set(sort_initial_sos). 0.06/0.43 % set(auto2) -> assign(sos_limit, -1). 0.06/0.43 % set(auto2) -> assign(lrs_ticks, 3000). 0.06/0.43 % set(auto2) -> assign(max_megs, 400). 0.06/0.43 % set(auto2) -> assign(stats, some). 0.06/0.43 % set(auto2) -> clear(echo_input). 0.06/0.43 % set(auto2) -> set(quiet). 0.06/0.43 % set(auto2) -> clear(print_initial_clauses). 0.06/0.43 % set(auto2) -> clear(print_given). 0.06/0.43 assign(lrs_ticks,-1). 0.06/0.43 assign(sos_limit,10000). 0.06/0.43 assign(order,kbo). 0.06/0.43 set(lex_order_vars). 0.06/0.43 clear(print_given). 0.06/0.43 0.06/0.43 % formulas(sos). % not echoed (13 formulas) 0.06/0.43 0.06/0.43 ============================== end of input ========================== 0.06/0.43 0.06/0.43 % From the command line: assign(max_seconds, 300). 0.06/0.43 0.06/0.43 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.06/0.43 0.06/0.43 % Formulas that are not ordinary clauses: 0.06/0.43 1 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 2 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 3 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 4 (all X0 all X1 all X2 (mult(mult(mult(X0,X1),X2),X1) = mult(X0,mult(X1,mult(X2,X1))) -> mult(mult(mult(X1,X0),X1),X2) = mult(X1,mult(X0,mult(X1,X2))))) # label(f10) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 5 (all X3 all X4 all X5 (mult(mult(X3,mult(X4,X5)),X3) = mult(mult(X3,X4),mult(X5,X3)) -> mult(mult(mult(X3,X4),X3),X5) = mult(X3,mult(X4,mult(X3,X5))))) # label(f11) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 6 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 7 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 8 (all X6 all X7 all X8 (mult(mult(X6,X7),mult(X8,X6)) = mult(X6,mult(mult(X7,X8),X6)) -> mult(mult(mult(X6,X7),X6),X8) = mult(X6,mult(X7,mult(X6,X8))))) # label(f12) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 9 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 10 (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]. 0.06/0.43 11 (all B all A mult(A,mult(B,A)) = mult(mult(A,B),A)) # label(f08) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 12 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 0.06/0.43 ============================== end of process non-clausal formulas === 0.06/0.43 0.06/0.43 ============================== PROCESS INITIAL CLAUSES =============== 0.06/0.43 0.06/0.43 ============================== PREDICATE ELIMINATION ================= 0.06/0.43 0.06/0.43 ============================== end predicate elimination ============= 0.06/0.43 0.06/0.43 Auto_denials: 0.06/0.43 % copying label goals to answer in negative clause 7.60/7.86 7.60/7.86 Term ordering decisions: 7.60/7.86 7.60/7.86 % Assigning unary symbol f kb_weight 0 and highest precedence (9). 7.60/7.86 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. f=0. 7.60/7.86 7.60/7.86 ============================== end of process initial clauses ======== 7.60/7.86 7.60/7.86 ============================== CLAUSES FOR SEARCH ==================== 7.60/7.86 7.60/7.86 ============================== end of clauses for search ============= 7.60/7.86 7.60/7.86 ============================== SEARCH ================================ 7.60/7.86 7.60/7.86 % Starting search at 0.01 seconds. 7.60/7.86 7.60/7.86 Low Water (keep): wt=130.000, iters=3382 7.60/7.86 7.60/7.86 Low Water (keep): wt=120.000, iters=3360 7.60/7.86 7.60/7.86 Low Water (keep): wt=102.000, iters=3347 7.60/7.86 7.60/7.86 Low Water (keep): wt=94.000, iters=3426 7.60/7.86 7.60/7.86 Low Water (keep): wt=90.000, iters=3359 7.60/7.86 7.60/7.86 Low Water (keep): wt=88.000, iters=3335 7.60/7.86 7.60/7.86 Low Water (keep): wt=82.000, iters=3348 7.60/7.86 7.60/7.86 Low Water (keep): wt=78.000, iters=3362 7.60/7.86 7.60/7.86 Low Water (keep): wt=74.000, iters=3358 7.60/7.86 7.60/7.86 Low Water (keep): wt=70.000, iters=3383 7.60/7.86 7.60/7.86 Low Water (keep): wt=67.000, iters=3336 7.60/7.86 7.60/7.86 Low Water (keep): wt=66.000, iters=3339 7.60/7.86 7.60/7.86 Low Water (keep): wt=62.000, iters=3367 7.60/7.86 7.60/7.86 Low Water (keep): wt=60.000, iters=3370 7.60/7.86 7.60/7.86 Low Water (keep): wt=59.000, iters=3388 7.60/7.86 7.60/7.86 Low Water (keep): wt=58.000, iters=3351 7.60/7.86 7.60/7.86 Low Water (keep): wt=57.000, iters=3385 7.60/7.86 7.60/7.86 Low Water (keep): wt=56.000, iters=3368 7.60/7.86 7.60/7.86 Low Water (keep): wt=54.000, iters=3430 7.60/7.86 7.60/7.86 Low Water (keep): wt=53.000, iters=3360 7.60/7.86 7.60/7.86 Low Water (keep): wt=52.000, iters=3392 7.60/7.86 7.60/7.86 Low Water (keep): wt=51.000, iters=3440 7.60/7.86 7.60/7.86 Low Water (keep): wt=47.000, iters=3356 7.60/7.86 7.60/7.86 Low Water (keep): wt=46.000, iters=3337 7.60/7.86 7.60/7.86 Low Water (keep): wt=44.000, iters=3370 7.60/7.86 7.60/7.86 Low Water (keep): wt=43.000, iters=3356 7.60/7.86 7.60/7.86 Low Water (keep): wt=42.000, iters=3365 7.60/7.86 7.60/7.86 Low Water (keep): wt=41.000, iters=3334 7.60/7.86 7.60/7.86 Low Water (keep): wt=39.000, iters=3390 7.60/7.86 7.60/7.86 Low Water (keep): wt=38.000, iters=3354 7.60/7.86 7.60/7.86 Low Water (keep): wt=35.000, iters=3398 7.60/7.86 7.60/7.86 Low Water (keep): wt=33.000, iters=3366 7.60/7.86 7.60/7.86 Low Water (keep): wt=31.000, iters=3335 7.60/7.86 7.60/7.86 Low Water (keep): wt=29.000, iters=3349 7.60/7.86 7.60/7.86 Low Water (displace): id=9128, wt=198.000 7.60/7.86 7.60/7.86 Low Water (displace): id=8292, wt=194.000 7.60/7.86 7.60/7.86 Low Water (displace): id=4580, wt=190.000 7.60/7.86 7.60/7.86 Low Water (displace): id=2118, wt=187.000 7.60/7.86 7.60/7.86 Low Water (displace): id=3120, wt=186.000 7.60/7.86 7.60/7.86 Low Water (displace): id=9123, wt=182.000 7.60/7.86 7.60/7.86 Low Water (displace): id=8539, wt=174.000 7.60/7.86 7.60/7.86 Low Water (displace): id=2279, wt=171.000 7.60/7.86 7.60/7.86 Low Water (displace): id=15524, wt=23.000 7.60/7.86 7.60/7.86 Low Water (displace): id=15543, wt=21.000 7.60/7.86 7.60/7.86 Low Water (displace): id=15617, wt=20.000 7.60/7.86 7.60/7.86 Low Water (displace): id=15714, wt=19.000 7.60/7.86 7.60/7.86 Low Water (keep): wt=27.000, iters=3337 7.60/7.86 7.60/7.86 Low Water (displace): id=15966, wt=18.000 7.60/7.86 7.60/7.86 Low Water (displace): id=16233, wt=17.000 7.60/7.86 7.60/7.86 Low Water (displace): id=17165, wt=15.000 7.60/7.86 7.60/7.86 Low Water (keep): wt=25.000, iters=3333 7.60/7.86 7.60/7.86 ============================== PROOF ================================= 7.60/7.86 % SZS status Theorem 7.60/7.86 % SZS output start Refutation 7.60/7.86 7.60/7.86 % Proof 1 at 7.36 (+ 0.07) seconds: goals. 7.60/7.86 % Length of proof is 101. 7.60/7.86 % Level of proof is 22. 7.60/7.86 % Maximum clause weight is 38.000. 7.60/7.86 % Given clauses 447. 7.60/7.86 7.60/7.86 1 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 2 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 3 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 4 (all X0 all X1 all X2 (mult(mult(mult(X0,X1),X2),X1) = mult(X0,mult(X1,mult(X2,X1))) -> mult(mult(mult(X1,X0),X1),X2) = mult(X1,mult(X0,mult(X1,X2))))) # label(f10) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 5 (all X3 all X4 all X5 (mult(mult(X3,mult(X4,X5)),X3) = mult(mult(X3,X4),mult(X5,X3)) -> mult(mult(mult(X3,X4),X3),X5) = mult(X3,mult(X4,mult(X3,X5))))) # label(f11) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 6 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 7 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 9 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 10 (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]. 7.60/7.86 11 (all B all A mult(A,mult(B,A)) = mult(mult(A,B),A)) # label(f08) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 12 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 7.60/7.86 13 mult(unit,A) = A # label(f06) # label(axiom). [clausify(1)]. 7.60/7.86 14 mult(A,unit) = A # label(f05) # label(axiom). [clausify(7)]. 7.60/7.86 15 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(2)]. 7.60/7.86 16 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(3)]. 7.60/7.86 17 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(6)]. 7.60/7.86 18 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(9)]. 7.60/7.86 19 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(12)]. 7.60/7.86 20 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(11)]. 7.60/7.86 21 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(10)]. 7.60/7.86 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)])]. 7.60/7.86 23 mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c) # label(goals) # label(negated_conjecture) # answer(goals). [assumption]. 7.60/7.86 24 mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))) # answer(goals). [copy(23),rewrite([20(12)]),flip(a)]. 7.60/7.86 25 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(4)]. 7.60/7.86 26 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(25),rewrite([20(9)])]. 7.60/7.86 27 mult(mult(A,mult(B,C)),A) != mult(mult(A,B),mult(C,A)) | mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))) # label(f11) # label(axiom). [clausify(5)]. 7.60/7.86 28 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(27),rewrite([20(3),20(9)]),flip(a)]. 7.60/7.86 31 rd(A,A) = unit. [para(13(a,1),17(a,1,1))]. 7.60/7.86 35 ld(rd(A,B),A) = B. [para(15(a,1),18(a,1,2))]. 7.60/7.86 37 rd(A,ld(B,A)) = B. [para(19(a,1),17(a,1,1))]. 7.60/7.86 38 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(15(a,1),20(a,1,1)),flip(a)]. 7.60/7.86 39 mult(f(A),A) = mult(A,f(A)). [para(16(a,1),20(a,1,1)),rewrite([16(6)]),flip(a)]. 7.60/7.86 40 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(20(a,1),17(a,1,1))]. 7.60/7.86 42 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(19(a,1),20(a,1,1)),flip(a)]. 7.60/7.86 44 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(13(a,1),22(a,1,1,2,2)),rewrite([14(4),14(6),13(5)]),flip(a)]. 7.60/7.86 45 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(13(a,1),22(a,1,1)),rewrite([13(5)])]. 7.60/7.86 47 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(15(a,1),22(a,1,1)),flip(a)]. 7.60/7.86 48 mult(mult(A,mult(B,rd(B,C))),C) = mult(mult(A,rd(B,C)),mult(C,B)). [para(15(a,1),22(a,2,2,2)),rewrite([38(4)])]. 7.60/7.86 53 mult(mult(A,mult(B,C)),ld(C,B)) = mult(mult(A,C),mult(ld(C,B),B)). [para(19(a,1),22(a,2,2,2)),rewrite([42(3)])]. 7.60/7.86 62 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(13(a,1),26(a,1,1,1)),rewrite([20(2),13(6),13(7),13(10)]),xx(a)]. 7.60/7.86 63 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(15(a,1),26(a,1,1,1)),rewrite([15(9)]),flip(a),flip(b)]. 7.60/7.86 78 mult(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)) # answer(goals). [ur(28,b,24,a)]. 7.60/7.86 82 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),28(a,1,1)),rewrite([20(8),16(14),39(12)]),flip(a),flip(b)]. 7.60/7.86 96 rd(mult(A,f(A)),A) = f(A). [para(39(a,1),17(a,1,1))]. 7.60/7.86 121 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(15(a,1),40(a,1,1,2))]. 7.60/7.86 125 mult(A,rd(f(A),A)) = f(A). [back_rewrite(96),rewrite([121(3)])]. 7.60/7.86 127 rd(f(A),A) = ld(A,f(A)). [para(125(a,1),18(a,1,2)),flip(a)]. 7.60/7.86 128 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),f(B))). [para(125(a,1),22(a,2,2,2)),rewrite([127(2),42(4),39(2),127(5),127(9)])]. 7.60/7.86 130 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(125(a,1),38(a,1,2)),rewrite([127(2),127(7)])]. 7.60/7.86 131 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(f(B),ld(B,f(B)))). [back_rewrite(128),rewrite([130(11)])]. 7.60/7.86 132 mult(ld(A,f(A)),A) = f(A). [para(127(a,1),15(a,1,1))]. 7.60/7.86 170 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(44(a,1),17(a,1,1))]. 7.60/7.86 220 mult(f(A),mult(f(A),B)) = mult(A,B). [para(16(a,1),62(a,1,1)),flip(a)]. 7.60/7.86 221 rd(mult(A,mult(A,B)),B) = mult(A,A). [para(62(a,1),17(a,1,1))]. 7.60/7.86 242 mult(mult(A,f(A)),B) = mult(f(A),mult(A,B)). [back_rewrite(82),rewrite([220(6),220(12)]),flip(b),xx(a)]. 7.60/7.86 263 mult(A,rd(unit,A)) = unit. [para(14(a,1),121(a,1,1)),rewrite([31(1)]),flip(a)]. 7.60/7.86 273 rd(unit,A) = ld(A,unit). [para(263(a,1),18(a,1,2)),flip(a)]. 7.60/7.86 281 mult(ld(A,unit),A) = unit. [para(37(a,1),263(a,1,2))]. 7.60/7.86 285 mult(mult(A,rd(A,B)),B) = mult(rd(A,B),mult(B,A)). [para(15(a,1),45(a,2,2,2)),rewrite([38(4)])]. 7.60/7.86 360 mult(ld(A,unit),mult(A,A)) = A. [para(281(a,1),44(a,1,1)),rewrite([13(2)]),flip(a)]. 7.60/7.86 362 mult(ld(f(A),unit),A) = f(A). [para(16(a,1),360(a,1,2))]. 7.60/7.86 364 ld(ld(A,unit),A) = mult(A,A). [para(360(a,1),18(a,1,2))]. 7.60/7.86 421 ld(f(A),unit) = ld(A,f(A)). [para(362(a,1),17(a,1,1)),rewrite([127(2)]),flip(a)]. 7.60/7.86 422 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(362(a,1),20(a,1,1)),rewrite([19(5)]),flip(a)]. 7.60/7.86 436 mult(ld(f(A),unit),mult(A,f(A))) = A. [para(362(a,1),45(a,2,2,2)),rewrite([422(8),13(2)]),flip(a)]. 7.60/7.86 440 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(35(a,1),364(a,1,1)),rewrite([273(2),273(5),273(7)]),flip(a)]. 7.60/7.86 441 mult(f(A),ld(A,f(A))) = unit. [para(421(a,1),19(a,1,2))]. 7.60/7.86 443 ld(ld(A,f(A)),unit) = f(A). [para(421(a,1),37(a,1,2)),rewrite([273(4)])]. 7.60/7.86 448 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(A,B). [back_rewrite(131),rewrite([441(11),14(9)])]. 7.60/7.86 449 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(130),rewrite([441(8)])]. 7.60/7.86 523 mult(ld(A,f(A)),ld(A,f(A))) = ld(f(A),ld(A,f(A))). [para(443(a,1),364(a,1,1)),flip(a)]. 7.60/7.86 567 mult(ld(f(A),ld(A,f(A))),f(A)) = ld(A,f(A)). [para(449(a,1),62(a,2,2)),rewrite([523(5),14(10)])]. 7.60/7.86 763 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(15(a,1),170(a,1,1)),flip(a)]. 7.60/7.86 779 ld(f(A),mult(A,B)) = mult(f(A),B). [para(220(a,1),18(a,1,2))]. 7.60/7.86 780 mult(A,ld(f(A),B)) = mult(f(A),B). [para(19(a,1),220(a,1,2)),flip(a)]. 7.60/7.86 795 mult(f(A),mult(A,B)) = mult(A,mult(f(A),B)). [para(220(a,1),62(a,2,2)),rewrite([16(3)]),flip(a)]. 7.60/7.86 834 mult(mult(A,f(A)),B) = mult(A,mult(f(A),B)). [back_rewrite(242),rewrite([795(6)])]. 7.60/7.86 836 rd(mult(A,B),ld(A,B)) = mult(A,A). [para(19(a,1),221(a,1,1,2))]. 7.60/7.86 840 ld(f(A),ld(A,f(A))) = ld(A,unit). [para(132(a,1),221(a,1,1,2)),rewrite([449(4),273(2),523(7)]),flip(a)]. 7.60/7.86 848 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(362(a,1),221(a,1,1,2)),rewrite([281(5),273(2),440(9)]),flip(a)]. 7.60/7.86 863 mult(ld(A,unit),f(A)) = ld(A,f(A)). [back_rewrite(567),rewrite([840(4)])]. 7.60/7.86 1047 mult(ld(A,unit),mult(A,f(A))) = f(A). [para(436(a,1),62(a,2,2)),rewrite([440(7),848(5),362(9)])]. 7.60/7.86 1831 mult(f(A),ld(A,B)) = ld(f(A),B). [para(19(a,1),779(a,1,2)),flip(a)]. 7.60/7.86 2401 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),63(a,1,2,2))]. 7.60/7.86 2635 mult(A,ld(B,unit)) = rd(A,B). [para(1047(a,1),47(a,1,1,1,2,2)),rewrite([44(4),16(3),834(12),1831(11),780(11),14(10),863(9),448(8),763(3)]),flip(a)]. 7.60/7.86 2936 ld(A,rd(A,B)) = ld(B,unit). [para(2635(a,1),18(a,1,2))]. 7.60/7.86 2946 rd(A,ld(B,unit)) = mult(A,B). [para(35(a,1),2635(a,1,2)),rewrite([273(3)]),flip(a)]. 7.60/7.86 2965 mult(f(A),rd(f(A),B)) = rd(A,B). [para(2635(a,1),220(a,1,2)),rewrite([2635(7)])]. 7.60/7.86 2966 mult(rd(A,B),mult(B,A)) = mult(A,A). [para(2635(a,1),221(a,1,1,2)),rewrite([2946(5),285(3)])]. 7.60/7.86 2970 mult(mult(A,rd(B,C)),ld(ld(C,unit),B)) = mult(rd(A,C),mult(ld(ld(C,unit),B),B)). [para(2635(a,1),53(a,1,1,2)),rewrite([2635(9)])]. 7.60/7.86 3064 ld(ld(A,B),unit) = ld(B,A). [para(37(a,1),2936(a,1,2)),flip(a)]. 7.60/7.86 3073 ld(mult(A,B),mult(A,A)) = ld(B,A). [para(836(a,1),2936(a,1,2)),rewrite([3064(6)])]. 7.60/7.86 4136 mult(mult(A,rd(f(B),C)),mult(C,f(B))) = mult(mult(A,rd(B,C)),C). [para(2965(a,1),48(a,1,1,2)),flip(a)]. 7.60/7.86 4185 ld(rd(A,B),mult(A,A)) = mult(B,A). [para(2966(a,1),18(a,1,2))]. 7.60/7.86 4711 ld(ld(A,unit),B) = mult(A,B). [para(2635(a,1),3073(a,1,1)),rewrite([4185(3)]),flip(a)]. 7.60/7.86 4742 mult(mult(A,rd(B,C)),mult(C,B)) = mult(rd(A,C),mult(C,mult(B,B))). [back_rewrite(2970),rewrite([4711(5),4711(8),44(7)])]. 7.60/7.86 4767 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)). [back_rewrite(4136),rewrite([4742(6),16(4)]),flip(a)]. 7.60/7.86 20596 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(17(a,1),4767(a,1,1,2)),flip(a)]. 7.60/7.86 20610 mult(rd(A,B),mult(B,mult(C,mult(B,B)))) = mult(mult(A,mult(C,B)),B). [para(170(a,1),4767(a,1,1,2)),flip(a)]. 7.60/7.86 20759 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [back_rewrite(2401),rewrite([20610(5),20596(11)]),flip(b),xx(a)]. 7.60/7.86 20760 $F # answer(goals). [resolve(20759,a,78,a)]. 7.60/7.86 7.60/7.86 % SZS output end Refutation 7.60/7.86 ============================== end of proof ========================== 7.60/7.86 7.60/7.86 ============================== STATISTICS ============================ 7.60/7.86 7.60/7.86 Given=447. Generated=115005. Kept=20742. proofs=1. 7.60/7.86 Usable=358. Sos=9933. Demods=7975. Limbo=163, Disabled=10300. Hints=0. 7.60/7.86 Megabytes=26.18. 7.60/7.86 User_CPU=7.36, System_CPU=0.07, Wall_clock=7. 7.60/7.86 7.60/7.86 ============================== end of statistics ===================== 7.60/7.86 7.60/7.86 ============================== end of search ========================= 7.60/7.86 7.60/7.86 THEOREM PROVED 7.60/7.86 % SZS status Theorem 7.60/7.86 7.60/7.86 Exiting with 1 proof. 7.60/7.86 7.60/7.86 Process 40236 exit (max_proofs) Sat Jul 14 04:57:47 2018 7.60/7.86 Prover9 interrupted 7.60/7.86 EOF