0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.32 % Computer : n027.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 1440 0.12/0.32 % WCLimit : 180 0.12/0.32 % DateTime : Mon Jul 3 04:11:01 EDT 2023 0.12/0.33 % CPUTime : 0.72/1.20 ============================== Prover9 =============================== 0.72/1.20 Prover9 (32) version 2009-11A, November 2009. 0.72/1.20 Process 22277 was started by sandbox2 on n027.cluster.edu, 0.72/1.20 Mon Jul 3 04:11:02 2023 0.72/1.20 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_22124_n027.cluster.edu". 0.72/1.20 ============================== end of head =========================== 0.72/1.20 0.72/1.20 ============================== INPUT ================================= 0.72/1.20 0.72/1.20 % Reading from file /tmp/Prover9_22124_n027.cluster.edu 0.72/1.20 0.72/1.20 set(prolog_style_variables). 0.72/1.20 set(auto2). 0.72/1.20 % set(auto2) -> set(auto). 0.72/1.20 % set(auto) -> set(auto_inference). 0.72/1.20 % set(auto) -> set(auto_setup). 0.72/1.20 % set(auto_setup) -> set(predicate_elim). 0.72/1.20 % set(auto_setup) -> assign(eq_defs, unfold). 0.72/1.20 % set(auto) -> set(auto_limits). 0.72/1.20 % set(auto_limits) -> assign(max_weight, "100.000"). 0.72/1.20 % set(auto_limits) -> assign(sos_limit, 20000). 0.72/1.20 % set(auto) -> set(auto_denials). 0.72/1.20 % set(auto) -> set(auto_process). 0.72/1.20 % set(auto2) -> assign(new_constants, 1). 0.72/1.20 % set(auto2) -> assign(fold_denial_max, 3). 0.72/1.20 % set(auto2) -> assign(max_weight, "200.000"). 0.72/1.20 % set(auto2) -> assign(max_hours, 1). 0.72/1.20 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.72/1.20 % set(auto2) -> assign(max_seconds, 0). 0.72/1.20 % set(auto2) -> assign(max_minutes, 5). 0.72/1.20 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.72/1.20 % set(auto2) -> set(sort_initial_sos). 0.72/1.20 % set(auto2) -> assign(sos_limit, -1). 0.72/1.20 % set(auto2) -> assign(lrs_ticks, 3000). 0.72/1.20 % set(auto2) -> assign(max_megs, 400). 0.72/1.20 % set(auto2) -> assign(stats, some). 0.72/1.20 % set(auto2) -> clear(echo_input). 0.72/1.20 % set(auto2) -> set(quiet). 0.72/1.20 % set(auto2) -> clear(print_initial_clauses). 0.72/1.20 % set(auto2) -> clear(print_given). 0.72/1.20 assign(lrs_ticks,-1). 0.72/1.20 assign(sos_limit,10000). 0.72/1.20 assign(order,kbo). 0.72/1.20 set(lex_order_vars). 0.72/1.20 clear(print_given). 0.72/1.20 0.72/1.20 % formulas(sos). % not echoed (10 formulas) 0.72/1.20 0.72/1.20 ============================== end of input ========================== 0.72/1.20 0.72/1.20 % From the command line: assign(max_seconds, 1440). 0.72/1.20 0.72/1.20 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.72/1.20 0.72/1.20 % Formulas that are not ordinary clauses: 0.72/1.20 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption]. 0.72/1.20 2 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption]. 0.72/1.20 3 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 0.72/1.20 4 (all B all A B = ld(A,mult(A,B))) # label(f02) # label(axiom) # label(non_clause). [assumption]. 0.72/1.20 5 (all A A = mult(A,unit)) # label(f05) # label(axiom) # label(non_clause). [assumption]. 0.72/1.20 6 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 0.72/1.20 7 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 0.72/1.20 8 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 0.72/1.20 9 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 0.72/1.20 10 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 0.72/1.20 0.72/1.20 ============================== end of process non-clausal formulas === 0.72/1.20 0.72/1.20 ============================== PROCESS INITIAL CLAUSES =============== 0.72/1.20 0.72/1.20 ============================== PREDICATE ELIMINATION ================= 0.72/1.20 0.72/1.20 ============================== end predicate elimination ============= 0.72/1.20 0.72/1.20 Auto_denials: 0.72/1.20 % copying label goals to answer in negative clause 0.72/1.20 % copying label goals to answer in negative clause 0.72/1.20 % copying label goals to answer in negative clause 0.72/1.20 % copying label goals to answer in negative clause 0.72/1.20 % assign(max_proofs, 4). % (Horn set with more than one neg. clause) 4.36/4.85 4.36/4.85 Term ordering decisions: 4.36/4.85 4.36/4.85 % Assigning unary symbol f kb_weight 0 and highest precedence (18). 4.36/4.85 Function symbol KB weights: unit=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. mult=1. ld=1. rd=1. f=0. 4.36/4.85 4.36/4.85 ============================== end of process initial clauses ======== 4.36/4.85 4.36/4.85 ============================== CLAUSES FOR SEARCH ==================== 4.36/4.85 4.36/4.85 ============================== end of clauses for search ============= 4.36/4.85 4.36/4.85 ============================== SEARCH ================================ 4.36/4.85 4.36/4.85 % Starting search at 0.01 seconds. 4.36/4.85 4.36/4.85 Low Water (keep): wt=83.000, iters=3357 4.36/4.85 4.36/4.85 Low Water (keep): wt=75.000, iters=3335 4.36/4.85 4.36/4.85 Low Water (keep): wt=73.000, iters=3409 4.36/4.85 4.36/4.85 Low Water (keep): wt=67.000, iters=3374 4.36/4.85 4.36/4.85 Low Water (keep): wt=63.000, iters=3408 4.36/4.85 4.36/4.85 Low Water (keep): wt=61.000, iters=3345 4.36/4.85 4.36/4.85 Low Water (keep): wt=59.000, iters=3403 4.36/4.85 4.36/4.85 Low Water (keep): wt=55.000, iters=3336 4.36/4.85 4.36/4.85 Low Water (keep): wt=53.000, iters=3406 4.36/4.85 4.36/4.85 Low Water (keep): wt=51.000, iters=3397 4.36/4.85 4.36/4.85 Low Water (keep): wt=49.000, iters=3338 4.36/4.85 4.36/4.85 Low Water (keep): wt=47.000, iters=3345 4.36/4.85 4.36/4.85 Low Water (keep): wt=45.000, iters=3334 4.36/4.85 4.36/4.85 Low Water (keep): wt=43.000, iters=3343 4.36/4.85 4.36/4.85 Low Water (keep): wt=41.000, iters=3351 4.36/4.85 4.36/4.85 Low Water (keep): wt=39.000, iters=3380 4.36/4.85 4.36/4.85 Low Water (keep): wt=37.000, iters=3350 4.36/4.85 4.36/4.85 Low Water (keep): wt=35.000, iters=3365 4.36/4.85 4.36/4.85 Low Water (keep): wt=33.000, iters=3343 4.36/4.85 4.36/4.85 Low Water (keep): wt=31.000, iters=3358 4.36/4.85 4.36/4.85 Low Water (keep): wt=29.000, iters=3334 4.36/4.85 4.36/4.85 Low Water (keep): wt=27.000, iters=3348 4.36/4.85 4.36/4.85 Low Water (keep): wt=25.000, iters=3333 4.36/4.85 4.36/4.85 Low Water (displace): id=9285, wt=191.000 4.36/4.85 4.36/4.85 Low Water (displace): id=9276, wt=187.000 4.36/4.85 4.36/4.85 Low Water (displace): id=16290, wt=20.000 4.36/4.85 4.36/4.85 Low Water (displace): id=16291, wt=19.000 4.36/4.85 4.36/4.85 Low Water (displace): id=16616, wt=17.000 4.36/4.85 4.36/4.85 Low Water (keep): wt=24.000, iters=3336 4.36/4.85 4.36/4.85 Low Water (keep): wt=23.000, iters=3338 4.36/4.85 4.36/4.85 ============================== PROOF ================================= 4.36/4.85 % SZS status Theorem 4.36/4.85 % SZS output start Refutation 4.36/4.85 4.36/4.85 % Proof 1 at 3.62 (+ 0.05) seconds: goals. 4.36/4.85 % Length of proof is 111. 4.36/4.85 % Level of proof is 23. 4.36/4.85 % Maximum clause weight is 29.000. 4.36/4.85 % Given clauses 394. 4.36/4.85 4.36/4.85 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption]. 4.36/4.85 2 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption]. 4.36/4.85 3 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 4.36/4.85 4 (all B all A B = ld(A,mult(A,B))) # label(f02) # label(axiom) # label(non_clause). [assumption]. 4.36/4.85 5 (all A A = mult(A,unit)) # label(f05) # label(axiom) # label(non_clause). [assumption]. 4.36/4.85 6 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 4.36/4.85 7 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 4.36/4.85 8 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 4.36/4.85 9 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 4.36/4.85 10 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 4.36/4.85 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)]. 4.36/4.85 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(9)]. 4.36/4.85 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)]. 4.36/4.85 14 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(3)]. 4.36/4.85 15 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(4)]. 4.36/4.85 16 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(7)]. 4.36/4.85 17 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(8)]. 4.36/4.85 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(6)]. 4.36/4.85 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(2)]. 4.36/4.85 20 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(19),rewrite([18(2),18(7)])]. 4.36/4.85 26 mult(mult(mult(c10,c12),c11),c12) != mult(c10,mult(c12,mult(c11,c12))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)]. 4.36/4.85 31 ld(A,A) = unit. [para(11(a,1),15(a,1,2))]. 4.36/4.85 32 ld(rd(A,B),A) = B. [para(16(a,1),15(a,1,2))]. 4.36/4.85 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)]. 4.36/4.85 36 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),14(a,1,1))]. 4.36/4.85 37 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),15(a,1,2))]. 4.36/4.85 38 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(16(a,1),18(a,1,1)),flip(a)]. 4.36/4.85 39 mult(f(A),A) = mult(A,f(A)). [para(17(a,1),18(a,1,1)),rewrite([17(6)]),flip(a)]. 4.36/4.85 41 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),11(a,1)),rewrite([11(4),12(3),12(4)])]. 4.36/4.85 42 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(12(a,1),20(a,1,1)),rewrite([12(5)])]. 4.36/4.85 45 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),14(a,1,1))]. 4.36/4.85 47 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(16(a,1),20(a,1,1,2,2)),rewrite([38(9)])]. 4.36/4.85 48 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(16(a,1),20(a,1,1)),flip(a)]. 4.36/4.85 52 mult(mult(A,B),mult(A,mult(B,A))) = mult(A,mult(B,mult(A,mult(B,A)))). [para(20(a,1),18(a,1)),rewrite([42(7)])]. 4.36/4.85 58 rd(mult(A,f(A)),A) = f(A). [para(39(a,1),14(a,1,1))]. 4.36/4.85 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(39(a,1),18(a,1,1)),rewrite([41(4),17(3)]),flip(a)]. 4.36/4.85 64 rd(mult(A,B),mult(ld(B,A),B)) = B. [para(35(a,1),14(a,1,1))]. 4.36/4.85 65 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),15(a,1,2))]. 4.36/4.85 66 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(35(a,1),18(a,1,1)),rewrite([41(2),41(5)]),flip(a)]. 4.36/4.85 71 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(16(a,1),36(a,1,1,2))]. 4.36/4.85 74 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),36(a,2)),rewrite([41(3),66(4)])]. 4.36/4.85 75 mult(A,rd(f(A),A)) = f(A). [back_rewrite(58),rewrite([71(3)])]. 4.36/4.85 77 rd(f(A),A) = ld(A,f(A)). [para(75(a,1),15(a,1,2)),flip(a)]. 4.36/4.85 78 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),f(B))). [para(75(a,1),20(a,2,2,2)),rewrite([77(2),35(4),39(2),77(5),77(9)])]. 4.36/4.85 79 mult(ld(A,f(A)),A) = f(A). [para(77(a,1),16(a,1,1))]. 4.36/4.85 81 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(79(a,1),18(a,1,1)),rewrite([13(9)]),flip(a)]. 4.36/4.85 84 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(f(B),ld(B,f(B)))). [back_rewrite(78),rewrite([81(11)])]. 4.36/4.85 91 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(39(a,1),37(a,1,1)),rewrite([60(6)])]. 4.36/4.85 96 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(16(a,1),41(a,1,1)),flip(a)]. 4.36/4.85 118 rd(A,mult(ld(A,unit),A)) = A. [para(12(a,1),64(a,1,1))]. 4.36/4.85 134 mult(ld(A,unit),A) = unit. [para(118(a,1),32(a,1,1)),rewrite([31(1)]),flip(a)]. 4.36/4.85 136 rd(unit,A) = ld(A,unit). [para(134(a,1),14(a,1,1))]. 4.36/4.85 139 mult(ld(A,unit),mult(A,A)) = A. [para(134(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)]. 4.36/4.85 162 rd(A,mult(A,A)) = ld(A,unit). [para(139(a,1),14(a,1,1))]. 4.36/4.85 163 ld(ld(A,unit),A) = mult(A,A). [para(139(a,1),15(a,1,2))]. 4.36/4.85 164 mult(ld(f(A),unit),A) = f(A). [para(17(a,1),139(a,1,2))]. 4.36/4.85 172 ld(f(A),unit) = ld(A,f(A)). [para(17(a,1),162(a,1,2)),rewrite([77(2)]),flip(a)]. 4.36/4.85 174 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(32(a,1),163(a,1,1)),rewrite([136(2),136(5),136(7)]),flip(a)]. 4.36/4.85 176 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(164(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)]. 4.36/4.85 187 mult(mult(A,B),rd(B,A)) = mult(A,mult(B,rd(B,A))). [para(16(a,1),42(a,1,1,2)),rewrite([38(7)])]. 4.36/4.85 214 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(164(a,1),42(a,1,1,2)),rewrite([176(14),11(8)])]. 4.36/4.85 218 mult(f(A),ld(A,f(A))) = unit. [para(172(a,1),13(a,1,2))]. 4.36/4.85 219 mult(A,ld(f(A),unit)) = f(A). [para(172(a,2),13(a,1,2))]. 4.36/4.85 224 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(A,B). [back_rewrite(84),rewrite([218(11),11(9)])]. 4.36/4.85 228 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(219(a,1),41(a,1,1)),rewrite([13(5),174(8)]),flip(a)]. 4.36/4.85 257 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(16(a,1),65(a,1,2)),flip(a)]. 4.36/4.85 263 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),65(a,1,2)),rewrite([91(4)]),flip(a)]. 4.36/4.85 342 rd(mult(A,mult(B,mult(C,B))),B) = mult(rd(A,C),mult(C,mult(B,C))). [para(16(a,1),45(a,1,1,1))]. 4.36/4.85 367 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(134(a,1),45(a,1,1,1)),rewrite([12(4),71(3),14(2)]),flip(a)]. 4.36/4.85 389 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(16(a,1),74(a,1,1)),flip(a)]. 4.36/4.85 481 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(96(a,1),15(a,1,2))]. 4.36/4.85 482 mult(rd(A,f(B)),B) = mult(A,f(B)). [para(17(a,1),96(a,1,2))]. 4.36/4.85 513 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(214(a,1),14(a,1,1))]. 4.36/4.85 517 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(214(a,1),41(a,1,1)),rewrite([219(4),174(10)]),flip(a)]. 4.36/4.85 617 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(228(a,1),15(a,1,2)),flip(a)]. 4.36/4.85 622 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(517),rewrite([617(7)])]. 4.36/4.85 680 rd(ld(A,B),A) = ld(A,rd(B,A)). [para(257(a,1),14(a,1,1))]. 4.36/4.85 690 mult(ld(A,unit),f(A)) = ld(A,f(A)). [para(172(a,1),257(a,2)),rewrite([136(4),617(5)])]. 4.36/4.85 783 ld(rd(A,mult(B,B)),rd(A,B)) = B. [para(389(a,1),15(a,1,2))]. 4.36/4.85 784 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(17(a,1),389(a,1,1,2))]. 4.36/4.85 994 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(219(a,1),481(a,1,2)),rewrite([513(4),174(11),617(9)])]. 4.36/4.85 1010 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(263),rewrite([994(4)])]. 4.36/4.85 1028 mult(rd(A,f(B)),rd(B,rd(A,f(B)))) = rd(mult(A,f(B)),rd(A,f(B))). [para(482(a,1),71(a,1,1)),flip(a)]. 4.36/4.85 1350 mult(A,ld(B,unit)) = rd(A,B). [para(622(a,1),48(a,1,2,2)),rewrite([1010(7),41(4),17(3),690(9),224(8),389(3)]),flip(a)]. 4.36/4.85 2027 ld(rd(A,B),rd(A,f(B))) = f(B). [para(17(a,1),783(a,1,1,2))]. 4.36/4.85 2054 mult(mult(A,rd(B,C)),mult(f(C),rd(f(C),rd(B,C)))) = mult(mult(A,rd(B,f(C))),rd(f(C),rd(B,C))). [para(784(a,1),47(a,1,1,2)),flip(a)]. 4.36/4.85 2517 ld(rd(A,B),rd(rd(A,f(B)),rd(A,B))) = rd(f(B),rd(A,B)). [para(2027(a,1),680(a,1,1)),flip(a)]. 4.36/4.85 3190 mult(ld(A,unit),B) = ld(A,B). [para(257(a,1),367(a,1,2,2)),rewrite([13(4),257(6)])]. 4.36/4.85 3746 rd(ld(A,B),B) = ld(A,unit). [para(3190(a,1),14(a,1,1))]. 4.36/4.85 4059 rd(A,mult(B,A)) = ld(B,unit). [para(15(a,1),3746(a,1,1))]. 4.36/4.85 4060 ld(rd(A,B),unit) = rd(B,A). [para(32(a,1),3746(a,1,1)),flip(a)]. 4.36/4.85 4074 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2027(a,1),3746(a,1,1)),rewrite([4060(7)])]. 4.36/4.85 4160 rd(A,mult(B,f(A))) = rd(f(A),B). [para(482(a,1),4059(a,1,2)),rewrite([4060(7)])]. 4.36/4.85 4325 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4060(a,1),1350(a,1,2)),flip(a)]. 4.36/4.85 4330 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4060(a,1),3190(a,1,1)),flip(a)]. 4.36/4.85 4334 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4074),rewrite([4325(4)])]. 4.36/4.85 4337 mult(rd(A,B),mult(rd(B,f(A)),rd(A,B))) = mult(f(A),rd(A,B)). [back_rewrite(2517),rewrite([4325(5),4330(6),4325(9)])]. 4.36/4.85 4338 mult(mult(A,rd(B,C)),mult(f(C),mult(f(C),rd(C,B)))) = mult(mult(A,rd(B,f(C))),mult(f(C),rd(C,B))). [back_rewrite(2054),rewrite([4325(6),4325(14)])]. 4.36/4.85 4345 mult(rd(A,f(B)),mult(B,rd(f(B),A))) = mult(A,rd(B,A)). [back_rewrite(1028),rewrite([4325(5),4325(11),187(11),4334(10)])]. 4.36/4.85 4385 mult(rd(A,B),rd(B,f(A))) = f(A). [back_rewrite(2027),rewrite([4330(4)])]. 4.36/4.85 5985 mult(f(A),rd(A,B)) = mult(A,rd(f(A),B)). [para(784(a,1),4160(a,1,2)),rewrite([4325(3),4325(6)]),flip(a)]. 4.36/4.85 5995 mult(mult(A,rd(B,C)),mult(f(C),mult(C,rd(f(C),B)))) = mult(mult(A,rd(B,f(C))),mult(C,rd(f(C),B))). [back_rewrite(4338),rewrite([5985(6),5985(14)])]. 4.36/4.85 5996 mult(rd(A,B),mult(rd(B,f(A)),rd(A,B))) = mult(A,rd(f(A),B)). [back_rewrite(4337),rewrite([5985(9)])]. 4.36/4.85 6328 mult(rd(A,f(B)),rd(B,A)) = mult(A,rd(f(B),A)). [para(4334(a,1),65(a,1,2)),rewrite([4330(4),4330(8),16(8)])]. 4.36/4.85 6377 mult(rd(A,B),mult(B,rd(f(A),B))) = mult(A,rd(f(A),B)). [back_rewrite(5996),rewrite([6328(5)])]. 4.36/4.85 6671 mult(mult(A,rd(B,f(C))),mult(C,rd(f(C),B))) = mult(mult(A,B),rd(C,B)). [para(4385(a,1),20(a,1,1,2,2)),rewrite([16(4),6328(11),6377(11)]),flip(a)]. 4.36/4.85 6693 mult(f(A),mult(A,rd(f(A),B))) = mult(A,rd(A,B)). [para(4385(a,1),52(a,1,1)),rewrite([6328(6),6377(6),6328(13),6377(13),4345(12),38(9)])]. 4.36/4.85 6722 mult(mult(A,rd(B,C)),mult(C,rd(C,B))) = mult(mult(A,B),rd(C,B)). [back_rewrite(5995),rewrite([6693(7),6671(12)])]. 23.50/24.01 17767 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(16(a,1),342(a,1,1,2,2)),rewrite([4325(5),38(9),6722(8)])]. 23.50/24.01 17768 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [para(342(a,2),20(a,1,1)),rewrite([17767(4),14(3),16(5)])]. 23.50/24.01 17769 $F # answer(goals). [resolve(17768,a,26,a)]. 23.50/24.01 23.50/24.01 % SZS output end Refutation 23.50/24.01 ============================== end of proof ========================== 23.50/24.01 % Redundant proof: 17867 $F # answer(goals). [back_rewrite(26),rewrite([17768(7)]),xx(a)]. 23.50/24.01 23.50/24.01 % Disable descendants (x means already disabled): 23.50/24.01 26x 23.50/24.01 23.50/24.01 Low Water (keep): wt=22.000, iters=3363 23.50/24.01 23.50/24.01 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 42 (0.00 of 5.10 sec). 23.50/24.01 23.50/24.01 Low Water (keep): wt=21.000, iters=3336 23.50/24.01 23.50/24.01 Low Water (displace): id=22036, wt=15.000 23.50/24.01 23.50/24.01 ============================== PROOF ================================= 23.50/24.01 % SZS status Theorem 23.50/24.01 % SZS output start Refutation 23.50/24.01 23.50/24.01 % Proof 2 at 22.42 (+ 0.41) seconds: goals. 23.50/24.01 % Length of proof is 171. 23.50/24.01 % Level of proof is 27. 23.50/24.01 % Maximum clause weight is 29.000. 23.50/24.01 % Given clauses 983. 23.50/24.01 23.50/24.01 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 2 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 3 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 4 (all B all A B = ld(A,mult(A,B))) # label(f02) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 5 (all A A = mult(A,unit)) # label(f05) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 6 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 7 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 8 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 9 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 10 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 23.50/24.01 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)]. 23.50/24.01 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(9)]. 23.50/24.01 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)]. 23.50/24.01 14 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(3)]. 23.50/24.01 15 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(4)]. 23.50/24.01 16 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(7)]. 23.50/24.01 17 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(8)]. 23.50/24.01 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(6)]. 23.50/24.01 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(2)]. 23.50/24.01 20 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(19),rewrite([18(2),18(7)])]. 23.50/24.01 25 mult(mult(c9,c7),mult(c8,c9)) != mult(c9,mult(mult(c7,c8),c9)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)]. 23.50/24.01 27 ld(unit,A) = A. [para(13(a,1),12(a,1)),flip(a)]. 23.50/24.01 30 rd(A,ld(B,A)) = B. [para(13(a,1),14(a,1,1))]. 23.50/24.01 31 ld(A,A) = unit. [para(11(a,1),15(a,1,2))]. 23.50/24.01 32 ld(rd(A,B),A) = B. [para(16(a,1),15(a,1,2))]. 23.50/24.01 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)]. 23.50/24.01 36 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),14(a,1,1))]. 23.50/24.01 37 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),15(a,1,2))]. 23.50/24.01 38 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(16(a,1),18(a,1,1)),flip(a)]. 23.50/24.01 39 mult(f(A),A) = mult(A,f(A)). [para(17(a,1),18(a,1,1)),rewrite([17(6)]),flip(a)]. 23.50/24.01 40 mult(mult(A,mult(B,A)),mult(A,B)) = mult(mult(A,B),mult(A,mult(A,B))). [para(18(a,1),18(a,1,1))]. 23.50/24.01 41 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),11(a,1)),rewrite([11(4),12(3),12(4)])]. 23.50/24.01 42 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(12(a,1),20(a,1,1)),rewrite([12(5)])]. 23.50/24.01 43 mult(mult(A,mult(ld(B,C),C)),B) = mult(mult(A,ld(B,C)),mult(C,B)). [para(13(a,1),20(a,1,1,2,2)),rewrite([35(9)])]. 23.50/24.01 45 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),14(a,1,1))]. 23.50/24.01 47 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(16(a,1),20(a,1,1,2,2)),rewrite([38(9)])]. 23.50/24.01 48 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(16(a,1),20(a,1,1)),flip(a)]. 23.50/24.01 52 mult(mult(A,B),mult(A,mult(B,A))) = mult(A,mult(B,mult(A,mult(B,A)))). [para(20(a,1),18(a,1)),rewrite([42(7)])]. 23.50/24.01 53 mult(mult(A,mult(B,mult(B,mult(C,B)))),mult(B,C)) = mult(mult(A,B),mult(mult(B,C),mult(B,mult(B,C)))). [para(18(a,1),20(a,1,1,2,2))]. 23.50/24.01 58 rd(mult(A,f(A)),A) = f(A). [para(39(a,1),14(a,1,1))]. 23.50/24.01 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(39(a,1),18(a,1,1)),rewrite([41(4),17(3)]),flip(a)]. 23.50/24.01 64 rd(mult(A,B),mult(ld(B,A),B)) = B. [para(35(a,1),14(a,1,1))]. 23.50/24.01 65 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),15(a,1,2))]. 23.50/24.01 66 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(35(a,1),18(a,1,1)),rewrite([41(2),41(5)]),flip(a)]. 23.50/24.01 71 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(16(a,1),36(a,1,1,2))]. 23.50/24.01 74 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),36(a,2)),rewrite([41(3),66(4)])]. 23.50/24.01 75 mult(A,rd(f(A),A)) = f(A). [back_rewrite(58),rewrite([71(3)])]. 23.50/24.01 77 rd(f(A),A) = ld(A,f(A)). [para(75(a,1),15(a,1,2)),flip(a)]. 23.50/24.01 78 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),f(B))). [para(75(a,1),20(a,2,2,2)),rewrite([77(2),35(4),39(2),77(5),77(9)])]. 23.50/24.01 79 mult(ld(A,f(A)),A) = f(A). [para(77(a,1),16(a,1,1))]. 23.50/24.01 81 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(79(a,1),18(a,1,1)),rewrite([13(9)]),flip(a)]. 23.50/24.01 84 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(f(B),ld(B,f(B)))). [back_rewrite(78),rewrite([81(11)])]. 23.50/24.01 87 ld(mult(A,mult(B,A)),mult(mult(A,B),mult(A,mult(A,B)))) = mult(A,B). [para(18(a,1),37(a,1,1))]. 23.50/24.01 91 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(39(a,1),37(a,1,1)),rewrite([60(6)])]. 23.50/24.01 93 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(35(a,1),37(a,1,1)),rewrite([41(4),66(5)])]. 23.50/24.01 96 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(16(a,1),41(a,1,1)),flip(a)]. 23.50/24.01 118 rd(A,mult(ld(A,unit),A)) = A. [para(12(a,1),64(a,1,1))]. 23.50/24.01 134 mult(ld(A,unit),A) = unit. [para(118(a,1),32(a,1,1)),rewrite([31(1)]),flip(a)]. 23.50/24.01 136 rd(unit,A) = ld(A,unit). [para(134(a,1),14(a,1,1))]. 23.50/24.01 139 mult(ld(A,unit),mult(A,A)) = A. [para(134(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)]. 23.50/24.01 162 rd(A,mult(A,A)) = ld(A,unit). [para(139(a,1),14(a,1,1))]. 23.50/24.01 163 ld(ld(A,unit),A) = mult(A,A). [para(139(a,1),15(a,1,2))]. 23.50/24.01 164 mult(ld(f(A),unit),A) = f(A). [para(17(a,1),139(a,1,2))]. 23.50/24.01 172 ld(f(A),unit) = ld(A,f(A)). [para(17(a,1),162(a,1,2)),rewrite([77(2)]),flip(a)]. 23.50/24.01 174 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(32(a,1),163(a,1,1)),rewrite([136(2),136(5),136(7)]),flip(a)]. 23.50/24.01 176 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(164(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)]. 23.50/24.01 187 mult(mult(A,B),rd(B,A)) = mult(A,mult(B,rd(B,A))). [para(16(a,1),42(a,1,1,2)),rewrite([38(7)])]. 23.50/24.01 214 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(164(a,1),42(a,1,1,2)),rewrite([176(14),11(8)])]. 23.50/24.01 218 mult(f(A),ld(A,f(A))) = unit. [para(172(a,1),13(a,1,2))]. 23.50/24.01 219 mult(A,ld(f(A),unit)) = f(A). [para(172(a,2),13(a,1,2))]. 23.50/24.01 224 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(A,B). [back_rewrite(84),rewrite([218(11),11(9)])]. 23.50/24.01 226 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(81),rewrite([218(8)])]. 23.50/24.01 228 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(219(a,1),41(a,1,1)),rewrite([13(5),174(8)]),flip(a)]. 23.50/24.01 257 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(16(a,1),65(a,1,2)),flip(a)]. 23.50/24.01 263 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),65(a,1,2)),rewrite([91(4)]),flip(a)]. 23.50/24.01 342 rd(mult(A,mult(B,mult(C,B))),B) = mult(rd(A,C),mult(C,mult(B,C))). [para(16(a,1),45(a,1,1,1))]. 23.50/24.01 367 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(134(a,1),45(a,1,1,1)),rewrite([12(4),71(3),14(2)]),flip(a)]. 23.50/24.01 389 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(16(a,1),74(a,1,1)),flip(a)]. 23.50/24.01 414 ld(mult(A,f(B)),mult(A,B)) = f(B). [para(17(a,1),93(a,1,2,2))]. 23.50/24.01 481 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(96(a,1),15(a,1,2))]. 23.50/24.01 482 mult(rd(A,f(B)),B) = mult(A,f(B)). [para(17(a,1),96(a,1,2))]. 23.50/24.01 513 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(214(a,1),14(a,1,1))]. 23.50/24.01 517 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(214(a,1),41(a,1,1)),rewrite([219(4),174(10)]),flip(a)]. 23.50/24.01 617 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(228(a,1),15(a,1,2)),flip(a)]. 23.50/24.01 622 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(517),rewrite([617(7)])]. 23.50/24.01 638 mult(rd(A,mult(B,f(B))),B) = mult(A,ld(B,f(B))). [para(79(a,1),48(a,1,1,1,2,2)),rewrite([13(9),226(8),11(6)])]. 23.50/24.01 652 mult(A,ld(f(B),unit)) = mult(A,ld(B,f(B))). [para(164(a,1),48(a,1,1,1,2,2)),rewrite([638(4),219(10),134(8),11(5)]),flip(a)]. 23.50/24.01 680 rd(ld(A,B),A) = ld(A,rd(B,A)). [para(257(a,1),14(a,1,1))]. 23.50/24.01 690 mult(ld(A,unit),f(A)) = ld(A,f(A)). [para(172(a,1),257(a,2)),rewrite([136(4),617(5)])]. 23.50/24.01 783 ld(rd(A,mult(B,B)),rd(A,B)) = B. [para(389(a,1),15(a,1,2))]. 23.50/24.01 784 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(17(a,1),389(a,1,1,2))]. 23.50/24.01 994 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(219(a,1),481(a,1,2)),rewrite([513(4),174(11),617(9)])]. 23.50/24.01 1010 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(263),rewrite([994(4)])]. 23.50/24.01 1028 mult(rd(A,f(B)),rd(B,rd(A,f(B)))) = rd(mult(A,f(B)),rd(A,f(B))). [para(482(a,1),71(a,1,1)),flip(a)]. 23.50/24.01 1350 mult(A,ld(B,unit)) = rd(A,B). [para(622(a,1),48(a,1,2,2)),rewrite([1010(7),41(4),17(3),690(9),224(8),389(3)]),flip(a)]. 23.50/24.01 1380 mult(A,ld(B,f(B))) = rd(A,f(B)). [back_rewrite(652),rewrite([1350(4)]),flip(a)]. 23.50/24.01 1496 ld(A,rd(A,B)) = ld(B,unit). [para(1350(a,1),15(a,1,2))]. 23.50/24.01 1575 ld(mult(A,B),A) = ld(B,unit). [para(14(a,1),1496(a,1,2))]. 23.50/24.01 1576 ld(ld(A,B),unit) = ld(B,A). [para(30(a,1),1496(a,1,2)),flip(a)]. 23.50/24.01 1578 ld(mult(ld(A,B),A),unit) = ld(mult(B,A),A). [para(64(a,1),1496(a,1,2)),flip(a)]. 23.50/24.01 1689 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(mult(A,B),unit). [para(40(a,1),1575(a,1,1))]. 23.50/24.01 1711 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(1576(a,1),1350(a,1,2)),flip(a)]. 23.50/24.01 2027 ld(rd(A,B),rd(A,f(B))) = f(B). [para(17(a,1),783(a,1,1,2))]. 23.50/24.01 2054 mult(mult(A,rd(B,C)),mult(f(C),rd(f(C),rd(B,C)))) = mult(mult(A,rd(B,f(C))),rd(f(C),rd(B,C))). [para(784(a,1),47(a,1,1,2)),flip(a)]. 23.50/24.01 2387 mult(mult(A,ld(B,ld(C,f(C)))),mult(ld(C,f(C)),B)) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [para(1380(a,1),43(a,1,1,2)),flip(a)]. 23.50/24.01 2412 mult(mult(A,ld(B,C)),ld(C,B)) = A. [para(1711(a,1),14(a,1))]. 23.50/24.01 2517 ld(rd(A,B),rd(rd(A,f(B)),rd(A,B))) = rd(f(B),rd(A,B)). [para(2027(a,1),680(a,1,1)),flip(a)]. 23.50/24.01 3168 mult(ld(A,unit),mult(A,B)) = B. [para(16(a,1),367(a,1,2,2)),rewrite([16(6)])]. 23.50/24.01 3174 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),367(a,1,2))]. 23.50/24.01 3177 mult(mult(A,B),mult(ld(B,A),B)) = mult(A,mult(A,B)). [para(367(a,1),40(a,1,2)),rewrite([1350(7),71(5),14(4),3168(4),3168(7),3168(10),3174(7)]),flip(a)]. 23.50/24.01 3190 mult(ld(A,unit),B) = ld(A,B). [para(257(a,1),367(a,1,2,2)),rewrite([13(4),257(6)])]. 23.50/24.01 3200 mult(mult(A,ld(B,C)),mult(C,B)) = mult(rd(A,B),mult(C,mult(C,B))). [para(367(a,1),53(a,1,2)),rewrite([1350(9),71(7),14(6),3190(6),15(4),3190(3),1350(7),3190(10),15(8),3190(13),15(11),3190(10),65(8),3177(9)])]. 23.50/24.01 3446 mult(rd(A,B),mult(ld(C,f(C)),mult(ld(C,f(C)),B))) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [back_rewrite(2387),rewrite([3200(8)])]. 23.50/24.01 3746 rd(ld(A,B),B) = ld(A,unit). [para(3190(a,1),14(a,1,1))]. 23.50/24.01 3751 ld(rd(A,B),mult(A,ld(B,A))) = A. [para(3190(a,1),37(a,1,2,2)),rewrite([1350(3)])]. 23.50/24.01 3752 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(3190(a,1),41(a,1,1)),rewrite([3190(6)]),flip(a)]. 23.50/24.01 3756 mult(ld(A,f(A)),B) = ld(f(A),B). [para(172(a,1),3190(a,1,1))]. 23.50/24.01 3770 ld(ld(A,f(B)),ld(A,B)) = f(B). [para(3190(a,1),414(a,1,1)),rewrite([3190(5)])]. 23.50/24.01 3779 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [para(3190(a,1),1350(a,1)),flip(a)]. 23.50/24.01 3783 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1576(a,1),3190(a,1,1)),flip(a)]. 23.50/24.01 3812 mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B) = mult(rd(A,B),ld(f(C),ld(f(C),B))). [back_rewrite(3446),rewrite([3756(6),3756(6)]),flip(a)]. 23.50/24.01 3860 mult(ld(f(A),B),ld(B,A)) = f(A). [back_rewrite(3770),rewrite([3783(4)])]. 23.50/24.01 4059 rd(A,mult(B,A)) = ld(B,unit). [para(15(a,1),3746(a,1,1))]. 23.50/24.01 4060 ld(rd(A,B),unit) = rd(B,A). [para(32(a,1),3746(a,1,1)),flip(a)]. 23.50/24.01 4071 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(1575(a,1),3746(a,1,1)),rewrite([3779(3)]),flip(a)]. 23.50/24.01 4074 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2027(a,1),3746(a,1,1)),rewrite([4060(7)])]. 23.50/24.01 4097 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(B,ld(A,unit)). [back_rewrite(1689),rewrite([4071(10)])]. 23.50/24.01 4098 ld(mult(A,B),B) = ld(B,ld(A,B)). [back_rewrite(1578),rewrite([4071(4),3783(3),11(3)]),flip(a)]. 23.50/24.01 4160 rd(A,mult(B,f(A))) = rd(f(A),B). [para(482(a,1),4059(a,1,2)),rewrite([4060(7)])]. 23.50/24.01 4325 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4060(a,1),1350(a,1,2)),flip(a)]. 23.50/24.01 4329 mult(mult(A,rd(B,C)),rd(C,B)) = A. [para(4060(a,1),2412(a,1,1,2)),rewrite([27(5)])]. 23.50/24.01 4330 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4060(a,1),3190(a,1,1)),flip(a)]. 23.50/24.01 4334 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4074),rewrite([4325(4)])]. 23.50/24.01 4337 mult(rd(A,B),mult(rd(B,f(A)),rd(A,B))) = mult(f(A),rd(A,B)). [back_rewrite(2517),rewrite([4325(5),4330(6),4325(9)])]. 23.50/24.01 4338 mult(mult(A,rd(B,C)),mult(f(C),mult(f(C),rd(C,B)))) = mult(mult(A,rd(B,f(C))),mult(f(C),rd(C,B))). [back_rewrite(2054),rewrite([4325(6),4325(14)])]. 23.50/24.01 4345 mult(rd(A,f(B)),mult(B,rd(f(B),A))) = mult(A,rd(B,A)). [back_rewrite(1028),rewrite([4325(5),4325(11),187(11),4334(10)])]. 23.50/24.01 4370 mult(rd(A,B),mult(B,ld(A,B))) = B. [back_rewrite(3751),rewrite([4330(4)])]. 23.50/24.01 4385 mult(rd(A,B),rd(B,f(A))) = f(A). [back_rewrite(2027),rewrite([4330(4)])]. 23.50/24.01 4708 rd(ld(A,ld(B,f(B))),f(B)) = ld(A,ld(B,unit)). [para(1380(a,1),3752(a,1,2)),rewrite([3746(4),1380(9)]),flip(a)]. 23.50/24.01 5037 mult(rd(A,B),ld(f(C),ld(f(C),B))) = mult(mult(A,ld(B,ld(C,unit))),B). [back_rewrite(3812),rewrite([4708(5)]),flip(a)]. 23.50/24.01 5216 rd(A,mult(ld(B,C),D)) = mult(A,ld(D,ld(C,B))). [para(3783(a,1),1711(a,1,2))]. 23.50/24.01 5220 mult(ld(A,ld(B,unit)),C) = ld(mult(B,A),C). [para(87(a,1),3783(a,1,1)),rewrite([4097(9)]),flip(a)]. 23.50/24.01 5569 ld(f(A),ld(f(A),B)) = ld(A,B). [para(3860(a,1),1575(a,1,1)),rewrite([3783(7),11(7)])]. 23.50/24.01 5588 mult(mult(A,ld(B,ld(C,unit))),B) = mult(rd(A,B),ld(C,B)). [back_rewrite(5037),rewrite([5569(5)]),flip(a)]. 23.50/24.01 5783 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(4071(a,1),1350(a,1,2))]. 23.50/24.01 5794 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [back_rewrite(5588),rewrite([5783(4)])]. 23.50/24.01 5985 mult(f(A),rd(A,B)) = mult(A,rd(f(A),B)). [para(784(a,1),4160(a,1,2)),rewrite([4325(3),4325(6)]),flip(a)]. 23.50/24.01 5995 mult(mult(A,rd(B,C)),mult(f(C),mult(C,rd(f(C),B)))) = mult(mult(A,rd(B,f(C))),mult(C,rd(f(C),B))). [back_rewrite(4338),rewrite([5985(6),5985(14)])]. 23.50/24.01 5996 mult(rd(A,B),mult(rd(B,f(A)),rd(A,B))) = mult(A,rd(f(A),B)). [back_rewrite(4337),rewrite([5985(9)])]. 23.50/24.01 5999 mult(mult(rd(A,B),C),rd(B,A)) = mult(rd(A,B),mult(C,rd(B,A))). [para(4325(a,1),71(a,1)),rewrite([4325(7)])]. 23.50/24.01 6042 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(4329(a,1),35(a,2)),rewrite([4330(5),5999(7),4329(6)])]. 23.50/24.01 6328 mult(rd(A,f(B)),rd(B,A)) = mult(A,rd(f(B),A)). [para(4334(a,1),65(a,1,2)),rewrite([4330(4),4330(8),16(8)])]. 23.50/24.01 6377 mult(rd(A,B),mult(B,rd(f(A),B))) = mult(A,rd(f(A),B)). [back_rewrite(5996),rewrite([6328(5)])]. 23.50/24.01 6671 mult(mult(A,rd(B,f(C))),mult(C,rd(f(C),B))) = mult(mult(A,B),rd(C,B)). [para(4385(a,1),20(a,1,1,2,2)),rewrite([16(4),6328(11),6377(11)]),flip(a)]. 23.50/24.01 6693 mult(f(A),mult(A,rd(f(A),B))) = mult(A,rd(A,B)). [para(4385(a,1),52(a,1,1)),rewrite([6328(6),6377(6),6328(13),6377(13),4345(12),38(9)])]. 23.50/24.01 6722 mult(mult(A,rd(B,C)),mult(C,rd(C,B))) = mult(mult(A,B),rd(C,B)). [back_rewrite(5995),rewrite([6693(7),6671(12)])]. 23.50/24.01 13060 mult(ld(A,ld(B,ld(C,unit))),D) = ld(mult(mult(C,B),A),D). [para(4071(a,1),5220(a,1,1,2))]. 23.50/24.01 17767 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(16(a,1),342(a,1,1,2,2)),rewrite([4325(5),38(9),6722(8)])]. 23.50/24.01 17768 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [para(342(a,2),20(a,1,1)),rewrite([17767(4),14(3),16(5)])]. 23.50/24.01 17771 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(342(a,2),35(a,2)),rewrite([35(10),17767(8),14(7)])]. 23.50/24.01 17791 rd(mult(A,mult(B,A)),mult(mult(C,B),A)) = rd(A,C). [para(342(a,2),4059(a,1,2)),rewrite([17767(6),14(5),4330(8),11(8)])]. 23.50/24.01 17802 mult(mult(mult(A,B),C),mult(B,ld(mult(A,mult(B,mult(C,B))),B))) = B. [para(342(a,1),4370(a,1,1)),rewrite([17771(4)])]. 23.50/24.01 17806 mult(rd(A,B),mult(mult(B,C),A)) = mult(A,mult(C,A)). [para(342(a,2),6042(a,1,2)),rewrite([17767(5),14(4)])]. 23.50/24.01 19568 ld(mult(mult(A,B),C),B) = ld(mult(B,C),ld(A,B)). [para(3779(a,1),5794(a,1,1)),rewrite([4071(3),13060(5),3779(6),5220(8)])]. 23.50/24.01 23471 ld(mult(A,mult(B,mult(C,B))),B) = ld(B,ld(mult(B,C),ld(A,B))). [para(17768(a,1),4098(a,1,1)),rewrite([19568(7)])]. 23.50/24.01 23496 mult(mult(mult(A,B),C),ld(mult(B,C),ld(A,B))) = B. [back_rewrite(17802),rewrite([23471(6),13(7)])]. 23.50/24.01 23673 mult(mult(A,mult(B,A)),ld(A,ld(B,C))) = mult(A,C). [para(3190(a,1),17791(a,1,2,1)),rewrite([5216(5),1711(8),27(7)])]. 23.50/24.01 23706 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(mult(B,C),mult(A,B))). [para(14(a,1),17806(a,1,1)),flip(a)]. 23.50/24.01 25006 mult(A,mult(ld(A,B),mult(A,C))) = mult(mult(B,A),C). [para(23496(a,1),14(a,1,1)),rewrite([1711(4),3783(3)])]. 23.50/24.01 25184 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(23673(a,1),17768(a,1,1)),rewrite([23706(9),13(6),25006(7)])]. 23.50/24.01 25185 $F # answer(goals). [resolve(25184,a,25,a)]. 23.50/24.01 23.50/24.01 % SZS output end Refutation 23.50/24.01 ============================== end of proof ========================== 23.50/24.01 23.50/24.01 ============================== PROOF ================================= 23.50/24.01 % SZS status Theorem 23.50/24.01 % SZS output start Refutation 23.50/24.01 23.50/24.01 % Proof 3 at 22.42 (+ 0.41) seconds: goals. 23.50/24.01 % Length of proof is 172. 23.50/24.01 % Level of proof is 27. 23.50/24.01 % Maximum clause weight is 29.000. 23.50/24.01 % Given clauses 983. 23.50/24.01 23.50/24.01 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 2 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 3 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 4 (all B all A B = ld(A,mult(A,B))) # label(f02) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 5 (all A A = mult(A,unit)) # label(f05) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 6 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 7 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 8 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 9 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 10 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 23.50/24.01 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)]. 23.50/24.01 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(9)]. 23.50/24.01 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)]. 23.50/24.01 14 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(3)]. 23.50/24.01 15 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(4)]. 23.50/24.01 16 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(7)]. 23.50/24.01 17 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(8)]. 23.50/24.01 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(6)]. 23.50/24.01 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(2)]. 23.50/24.01 20 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(19),rewrite([18(2),18(7)])]. 23.50/24.01 23 mult(mult(c6,mult(c4,c5)),c6) != mult(mult(c6,c4),mult(c5,c6)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)]. 23.50/24.01 24 mult(mult(c6,c4),mult(c5,c6)) != mult(c6,mult(mult(c4,c5),c6)) # answer(goals). [copy(23),rewrite([18(7)]),flip(a)]. 23.50/24.01 27 ld(unit,A) = A. [para(13(a,1),12(a,1)),flip(a)]. 23.50/24.01 30 rd(A,ld(B,A)) = B. [para(13(a,1),14(a,1,1))]. 23.50/24.01 31 ld(A,A) = unit. [para(11(a,1),15(a,1,2))]. 23.50/24.01 32 ld(rd(A,B),A) = B. [para(16(a,1),15(a,1,2))]. 23.50/24.01 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)]. 23.50/24.01 36 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),14(a,1,1))]. 23.50/24.01 37 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),15(a,1,2))]. 23.50/24.01 38 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(16(a,1),18(a,1,1)),flip(a)]. 23.50/24.01 39 mult(f(A),A) = mult(A,f(A)). [para(17(a,1),18(a,1,1)),rewrite([17(6)]),flip(a)]. 23.50/24.01 40 mult(mult(A,mult(B,A)),mult(A,B)) = mult(mult(A,B),mult(A,mult(A,B))). [para(18(a,1),18(a,1,1))]. 23.50/24.01 41 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),11(a,1)),rewrite([11(4),12(3),12(4)])]. 23.50/24.01 42 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(12(a,1),20(a,1,1)),rewrite([12(5)])]. 23.50/24.01 43 mult(mult(A,mult(ld(B,C),C)),B) = mult(mult(A,ld(B,C)),mult(C,B)). [para(13(a,1),20(a,1,1,2,2)),rewrite([35(9)])]. 23.50/24.01 45 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),14(a,1,1))]. 23.50/24.01 47 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(16(a,1),20(a,1,1,2,2)),rewrite([38(9)])]. 23.50/24.01 48 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(16(a,1),20(a,1,1)),flip(a)]. 23.50/24.01 52 mult(mult(A,B),mult(A,mult(B,A))) = mult(A,mult(B,mult(A,mult(B,A)))). [para(20(a,1),18(a,1)),rewrite([42(7)])]. 23.50/24.01 53 mult(mult(A,mult(B,mult(B,mult(C,B)))),mult(B,C)) = mult(mult(A,B),mult(mult(B,C),mult(B,mult(B,C)))). [para(18(a,1),20(a,1,1,2,2))]. 23.50/24.01 58 rd(mult(A,f(A)),A) = f(A). [para(39(a,1),14(a,1,1))]. 23.50/24.01 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(39(a,1),18(a,1,1)),rewrite([41(4),17(3)]),flip(a)]. 23.50/24.01 64 rd(mult(A,B),mult(ld(B,A),B)) = B. [para(35(a,1),14(a,1,1))]. 23.50/24.01 65 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),15(a,1,2))]. 23.50/24.01 66 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(35(a,1),18(a,1,1)),rewrite([41(2),41(5)]),flip(a)]. 23.50/24.01 71 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(16(a,1),36(a,1,1,2))]. 23.50/24.01 74 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),36(a,2)),rewrite([41(3),66(4)])]. 23.50/24.01 75 mult(A,rd(f(A),A)) = f(A). [back_rewrite(58),rewrite([71(3)])]. 23.50/24.01 77 rd(f(A),A) = ld(A,f(A)). [para(75(a,1),15(a,1,2)),flip(a)]. 23.50/24.01 78 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),f(B))). [para(75(a,1),20(a,2,2,2)),rewrite([77(2),35(4),39(2),77(5),77(9)])]. 23.50/24.01 79 mult(ld(A,f(A)),A) = f(A). [para(77(a,1),16(a,1,1))]. 23.50/24.01 81 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(79(a,1),18(a,1,1)),rewrite([13(9)]),flip(a)]. 23.50/24.01 84 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(f(B),ld(B,f(B)))). [back_rewrite(78),rewrite([81(11)])]. 23.50/24.01 87 ld(mult(A,mult(B,A)),mult(mult(A,B),mult(A,mult(A,B)))) = mult(A,B). [para(18(a,1),37(a,1,1))]. 23.50/24.01 91 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(39(a,1),37(a,1,1)),rewrite([60(6)])]. 23.50/24.01 93 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(35(a,1),37(a,1,1)),rewrite([41(4),66(5)])]. 23.50/24.01 96 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(16(a,1),41(a,1,1)),flip(a)]. 23.50/24.01 118 rd(A,mult(ld(A,unit),A)) = A. [para(12(a,1),64(a,1,1))]. 23.50/24.01 134 mult(ld(A,unit),A) = unit. [para(118(a,1),32(a,1,1)),rewrite([31(1)]),flip(a)]. 23.50/24.01 136 rd(unit,A) = ld(A,unit). [para(134(a,1),14(a,1,1))]. 23.50/24.01 139 mult(ld(A,unit),mult(A,A)) = A. [para(134(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)]. 23.50/24.01 162 rd(A,mult(A,A)) = ld(A,unit). [para(139(a,1),14(a,1,1))]. 23.50/24.01 163 ld(ld(A,unit),A) = mult(A,A). [para(139(a,1),15(a,1,2))]. 23.50/24.01 164 mult(ld(f(A),unit),A) = f(A). [para(17(a,1),139(a,1,2))]. 23.50/24.01 172 ld(f(A),unit) = ld(A,f(A)). [para(17(a,1),162(a,1,2)),rewrite([77(2)]),flip(a)]. 23.50/24.01 174 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(32(a,1),163(a,1,1)),rewrite([136(2),136(5),136(7)]),flip(a)]. 23.50/24.01 176 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(164(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)]. 23.50/24.01 187 mult(mult(A,B),rd(B,A)) = mult(A,mult(B,rd(B,A))). [para(16(a,1),42(a,1,1,2)),rewrite([38(7)])]. 23.50/24.01 214 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(164(a,1),42(a,1,1,2)),rewrite([176(14),11(8)])]. 23.50/24.01 218 mult(f(A),ld(A,f(A))) = unit. [para(172(a,1),13(a,1,2))]. 23.50/24.01 219 mult(A,ld(f(A),unit)) = f(A). [para(172(a,2),13(a,1,2))]. 23.50/24.01 224 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(A,B). [back_rewrite(84),rewrite([218(11),11(9)])]. 23.50/24.01 226 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(81),rewrite([218(8)])]. 23.50/24.01 228 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(219(a,1),41(a,1,1)),rewrite([13(5),174(8)]),flip(a)]. 23.50/24.01 257 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(16(a,1),65(a,1,2)),flip(a)]. 23.50/24.01 263 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),65(a,1,2)),rewrite([91(4)]),flip(a)]. 23.50/24.01 342 rd(mult(A,mult(B,mult(C,B))),B) = mult(rd(A,C),mult(C,mult(B,C))). [para(16(a,1),45(a,1,1,1))]. 23.50/24.01 367 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(134(a,1),45(a,1,1,1)),rewrite([12(4),71(3),14(2)]),flip(a)]. 23.50/24.01 389 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(16(a,1),74(a,1,1)),flip(a)]. 23.50/24.01 414 ld(mult(A,f(B)),mult(A,B)) = f(B). [para(17(a,1),93(a,1,2,2))]. 23.50/24.01 481 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(96(a,1),15(a,1,2))]. 23.50/24.01 482 mult(rd(A,f(B)),B) = mult(A,f(B)). [para(17(a,1),96(a,1,2))]. 23.50/24.01 513 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(214(a,1),14(a,1,1))]. 23.50/24.01 517 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(214(a,1),41(a,1,1)),rewrite([219(4),174(10)]),flip(a)]. 23.50/24.01 617 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(228(a,1),15(a,1,2)),flip(a)]. 23.50/24.01 622 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(517),rewrite([617(7)])]. 23.50/24.01 638 mult(rd(A,mult(B,f(B))),B) = mult(A,ld(B,f(B))). [para(79(a,1),48(a,1,1,1,2,2)),rewrite([13(9),226(8),11(6)])]. 23.50/24.01 652 mult(A,ld(f(B),unit)) = mult(A,ld(B,f(B))). [para(164(a,1),48(a,1,1,1,2,2)),rewrite([638(4),219(10),134(8),11(5)]),flip(a)]. 23.50/24.01 680 rd(ld(A,B),A) = ld(A,rd(B,A)). [para(257(a,1),14(a,1,1))]. 23.50/24.01 690 mult(ld(A,unit),f(A)) = ld(A,f(A)). [para(172(a,1),257(a,2)),rewrite([136(4),617(5)])]. 23.50/24.01 783 ld(rd(A,mult(B,B)),rd(A,B)) = B. [para(389(a,1),15(a,1,2))]. 23.50/24.01 784 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(17(a,1),389(a,1,1,2))]. 23.50/24.01 994 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(219(a,1),481(a,1,2)),rewrite([513(4),174(11),617(9)])]. 23.50/24.01 1010 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(263),rewrite([994(4)])]. 23.50/24.01 1028 mult(rd(A,f(B)),rd(B,rd(A,f(B)))) = rd(mult(A,f(B)),rd(A,f(B))). [para(482(a,1),71(a,1,1)),flip(a)]. 23.50/24.01 1350 mult(A,ld(B,unit)) = rd(A,B). [para(622(a,1),48(a,1,2,2)),rewrite([1010(7),41(4),17(3),690(9),224(8),389(3)]),flip(a)]. 23.50/24.01 1380 mult(A,ld(B,f(B))) = rd(A,f(B)). [back_rewrite(652),rewrite([1350(4)]),flip(a)]. 23.50/24.01 1496 ld(A,rd(A,B)) = ld(B,unit). [para(1350(a,1),15(a,1,2))]. 23.50/24.01 1575 ld(mult(A,B),A) = ld(B,unit). [para(14(a,1),1496(a,1,2))]. 23.50/24.01 1576 ld(ld(A,B),unit) = ld(B,A). [para(30(a,1),1496(a,1,2)),flip(a)]. 23.50/24.01 1578 ld(mult(ld(A,B),A),unit) = ld(mult(B,A),A). [para(64(a,1),1496(a,1,2)),flip(a)]. 23.50/24.01 1689 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(mult(A,B),unit). [para(40(a,1),1575(a,1,1))]. 23.50/24.01 1711 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(1576(a,1),1350(a,1,2)),flip(a)]. 23.50/24.01 2027 ld(rd(A,B),rd(A,f(B))) = f(B). [para(17(a,1),783(a,1,1,2))]. 23.50/24.01 2054 mult(mult(A,rd(B,C)),mult(f(C),rd(f(C),rd(B,C)))) = mult(mult(A,rd(B,f(C))),rd(f(C),rd(B,C))). [para(784(a,1),47(a,1,1,2)),flip(a)]. 23.50/24.01 2387 mult(mult(A,ld(B,ld(C,f(C)))),mult(ld(C,f(C)),B)) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [para(1380(a,1),43(a,1,1,2)),flip(a)]. 23.50/24.01 2412 mult(mult(A,ld(B,C)),ld(C,B)) = A. [para(1711(a,1),14(a,1))]. 23.50/24.01 2517 ld(rd(A,B),rd(rd(A,f(B)),rd(A,B))) = rd(f(B),rd(A,B)). [para(2027(a,1),680(a,1,1)),flip(a)]. 23.50/24.01 3168 mult(ld(A,unit),mult(A,B)) = B. [para(16(a,1),367(a,1,2,2)),rewrite([16(6)])]. 23.50/24.01 3174 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),367(a,1,2))]. 23.50/24.01 3177 mult(mult(A,B),mult(ld(B,A),B)) = mult(A,mult(A,B)). [para(367(a,1),40(a,1,2)),rewrite([1350(7),71(5),14(4),3168(4),3168(7),3168(10),3174(7)]),flip(a)]. 23.50/24.01 3190 mult(ld(A,unit),B) = ld(A,B). [para(257(a,1),367(a,1,2,2)),rewrite([13(4),257(6)])]. 23.50/24.01 3200 mult(mult(A,ld(B,C)),mult(C,B)) = mult(rd(A,B),mult(C,mult(C,B))). [para(367(a,1),53(a,1,2)),rewrite([1350(9),71(7),14(6),3190(6),15(4),3190(3),1350(7),3190(10),15(8),3190(13),15(11),3190(10),65(8),3177(9)])]. 23.50/24.01 3446 mult(rd(A,B),mult(ld(C,f(C)),mult(ld(C,f(C)),B))) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [back_rewrite(2387),rewrite([3200(8)])]. 23.50/24.01 3746 rd(ld(A,B),B) = ld(A,unit). [para(3190(a,1),14(a,1,1))]. 23.50/24.01 3751 ld(rd(A,B),mult(A,ld(B,A))) = A. [para(3190(a,1),37(a,1,2,2)),rewrite([1350(3)])]. 23.50/24.01 3752 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(3190(a,1),41(a,1,1)),rewrite([3190(6)]),flip(a)]. 23.50/24.01 3756 mult(ld(A,f(A)),B) = ld(f(A),B). [para(172(a,1),3190(a,1,1))]. 23.50/24.01 3770 ld(ld(A,f(B)),ld(A,B)) = f(B). [para(3190(a,1),414(a,1,1)),rewrite([3190(5)])]. 23.50/24.01 3779 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [para(3190(a,1),1350(a,1)),flip(a)]. 23.50/24.01 3783 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1576(a,1),3190(a,1,1)),flip(a)]. 23.50/24.01 3812 mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B) = mult(rd(A,B),ld(f(C),ld(f(C),B))). [back_rewrite(3446),rewrite([3756(6),3756(6)]),flip(a)]. 23.50/24.01 3860 mult(ld(f(A),B),ld(B,A)) = f(A). [back_rewrite(3770),rewrite([3783(4)])]. 23.50/24.01 4059 rd(A,mult(B,A)) = ld(B,unit). [para(15(a,1),3746(a,1,1))]. 23.50/24.01 4060 ld(rd(A,B),unit) = rd(B,A). [para(32(a,1),3746(a,1,1)),flip(a)]. 23.50/24.01 4071 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(1575(a,1),3746(a,1,1)),rewrite([3779(3)]),flip(a)]. 23.50/24.01 4074 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2027(a,1),3746(a,1,1)),rewrite([4060(7)])]. 23.50/24.01 4097 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(B,ld(A,unit)). [back_rewrite(1689),rewrite([4071(10)])]. 23.50/24.01 4098 ld(mult(A,B),B) = ld(B,ld(A,B)). [back_rewrite(1578),rewrite([4071(4),3783(3),11(3)]),flip(a)]. 23.50/24.01 4160 rd(A,mult(B,f(A))) = rd(f(A),B). [para(482(a,1),4059(a,1,2)),rewrite([4060(7)])]. 23.50/24.01 4325 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4060(a,1),1350(a,1,2)),flip(a)]. 23.50/24.01 4329 mult(mult(A,rd(B,C)),rd(C,B)) = A. [para(4060(a,1),2412(a,1,1,2)),rewrite([27(5)])]. 23.50/24.01 4330 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4060(a,1),3190(a,1,1)),flip(a)]. 23.50/24.01 4334 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4074),rewrite([4325(4)])]. 23.50/24.01 4337 mult(rd(A,B),mult(rd(B,f(A)),rd(A,B))) = mult(f(A),rd(A,B)). [back_rewrite(2517),rewrite([4325(5),4330(6),4325(9)])]. 23.50/24.01 4338 mult(mult(A,rd(B,C)),mult(f(C),mult(f(C),rd(C,B)))) = mult(mult(A,rd(B,f(C))),mult(f(C),rd(C,B))). [back_rewrite(2054),rewrite([4325(6),4325(14)])]. 23.50/24.01 4345 mult(rd(A,f(B)),mult(B,rd(f(B),A))) = mult(A,rd(B,A)). [back_rewrite(1028),rewrite([4325(5),4325(11),187(11),4334(10)])]. 23.50/24.01 4370 mult(rd(A,B),mult(B,ld(A,B))) = B. [back_rewrite(3751),rewrite([4330(4)])]. 23.50/24.01 4385 mult(rd(A,B),rd(B,f(A))) = f(A). [back_rewrite(2027),rewrite([4330(4)])]. 23.50/24.01 4708 rd(ld(A,ld(B,f(B))),f(B)) = ld(A,ld(B,unit)). [para(1380(a,1),3752(a,1,2)),rewrite([3746(4),1380(9)]),flip(a)]. 23.50/24.01 5037 mult(rd(A,B),ld(f(C),ld(f(C),B))) = mult(mult(A,ld(B,ld(C,unit))),B). [back_rewrite(3812),rewrite([4708(5)]),flip(a)]. 23.50/24.01 5216 rd(A,mult(ld(B,C),D)) = mult(A,ld(D,ld(C,B))). [para(3783(a,1),1711(a,1,2))]. 23.50/24.01 5220 mult(ld(A,ld(B,unit)),C) = ld(mult(B,A),C). [para(87(a,1),3783(a,1,1)),rewrite([4097(9)]),flip(a)]. 23.50/24.01 5569 ld(f(A),ld(f(A),B)) = ld(A,B). [para(3860(a,1),1575(a,1,1)),rewrite([3783(7),11(7)])]. 23.50/24.01 5588 mult(mult(A,ld(B,ld(C,unit))),B) = mult(rd(A,B),ld(C,B)). [back_rewrite(5037),rewrite([5569(5)]),flip(a)]. 23.50/24.01 5783 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(4071(a,1),1350(a,1,2))]. 23.50/24.01 5794 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [back_rewrite(5588),rewrite([5783(4)])]. 23.50/24.01 5985 mult(f(A),rd(A,B)) = mult(A,rd(f(A),B)). [para(784(a,1),4160(a,1,2)),rewrite([4325(3),4325(6)]),flip(a)]. 23.50/24.01 5995 mult(mult(A,rd(B,C)),mult(f(C),mult(C,rd(f(C),B)))) = mult(mult(A,rd(B,f(C))),mult(C,rd(f(C),B))). [back_rewrite(4338),rewrite([5985(6),5985(14)])]. 23.50/24.01 5996 mult(rd(A,B),mult(rd(B,f(A)),rd(A,B))) = mult(A,rd(f(A),B)). [back_rewrite(4337),rewrite([5985(9)])]. 23.50/24.01 5999 mult(mult(rd(A,B),C),rd(B,A)) = mult(rd(A,B),mult(C,rd(B,A))). [para(4325(a,1),71(a,1)),rewrite([4325(7)])]. 23.50/24.01 6042 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(4329(a,1),35(a,2)),rewrite([4330(5),5999(7),4329(6)])]. 23.50/24.01 6328 mult(rd(A,f(B)),rd(B,A)) = mult(A,rd(f(B),A)). [para(4334(a,1),65(a,1,2)),rewrite([4330(4),4330(8),16(8)])]. 23.50/24.01 6377 mult(rd(A,B),mult(B,rd(f(A),B))) = mult(A,rd(f(A),B)). [back_rewrite(5996),rewrite([6328(5)])]. 23.50/24.01 6671 mult(mult(A,rd(B,f(C))),mult(C,rd(f(C),B))) = mult(mult(A,B),rd(C,B)). [para(4385(a,1),20(a,1,1,2,2)),rewrite([16(4),6328(11),6377(11)]),flip(a)]. 23.50/24.01 6693 mult(f(A),mult(A,rd(f(A),B))) = mult(A,rd(A,B)). [para(4385(a,1),52(a,1,1)),rewrite([6328(6),6377(6),6328(13),6377(13),4345(12),38(9)])]. 23.50/24.01 6722 mult(mult(A,rd(B,C)),mult(C,rd(C,B))) = mult(mult(A,B),rd(C,B)). [back_rewrite(5995),rewrite([6693(7),6671(12)])]. 23.50/24.01 13060 mult(ld(A,ld(B,ld(C,unit))),D) = ld(mult(mult(C,B),A),D). [para(4071(a,1),5220(a,1,1,2))]. 23.50/24.01 17767 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(16(a,1),342(a,1,1,2,2)),rewrite([4325(5),38(9),6722(8)])]. 23.50/24.01 17768 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [para(342(a,2),20(a,1,1)),rewrite([17767(4),14(3),16(5)])]. 23.50/24.01 17771 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(342(a,2),35(a,2)),rewrite([35(10),17767(8),14(7)])]. 23.50/24.01 17791 rd(mult(A,mult(B,A)),mult(mult(C,B),A)) = rd(A,C). [para(342(a,2),4059(a,1,2)),rewrite([17767(6),14(5),4330(8),11(8)])]. 23.50/24.01 17802 mult(mult(mult(A,B),C),mult(B,ld(mult(A,mult(B,mult(C,B))),B))) = B. [para(342(a,1),4370(a,1,1)),rewrite([17771(4)])]. 23.50/24.01 17806 mult(rd(A,B),mult(mult(B,C),A)) = mult(A,mult(C,A)). [para(342(a,2),6042(a,1,2)),rewrite([17767(5),14(4)])]. 23.50/24.01 19568 ld(mult(mult(A,B),C),B) = ld(mult(B,C),ld(A,B)). [para(3779(a,1),5794(a,1,1)),rewrite([4071(3),13060(5),3779(6),5220(8)])]. 23.50/24.01 23471 ld(mult(A,mult(B,mult(C,B))),B) = ld(B,ld(mult(B,C),ld(A,B))). [para(17768(a,1),4098(a,1,1)),rewrite([19568(7)])]. 23.50/24.01 23496 mult(mult(mult(A,B),C),ld(mult(B,C),ld(A,B))) = B. [back_rewrite(17802),rewrite([23471(6),13(7)])]. 23.50/24.01 23673 mult(mult(A,mult(B,A)),ld(A,ld(B,C))) = mult(A,C). [para(3190(a,1),17791(a,1,2,1)),rewrite([5216(5),1711(8),27(7)])]. 23.50/24.01 23706 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(mult(B,C),mult(A,B))). [para(14(a,1),17806(a,1,1)),flip(a)]. 23.50/24.01 25006 mult(A,mult(ld(A,B),mult(A,C))) = mult(mult(B,A),C). [para(23496(a,1),14(a,1,1)),rewrite([1711(4),3783(3)])]. 23.50/24.01 25184 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(23673(a,1),17768(a,1,1)),rewrite([23706(9),13(6),25006(7)])]. 23.50/24.01 25186 $F # answer(goals). [resolve(25184,a,24,a)]. 23.50/24.01 23.50/24.01 % SZS output end Refutation 23.50/24.01 ============================== end of proof ========================== 23.50/24.01 23.50/24.01 ============================== PROOF ================================= 23.50/24.01 % SZS status Theorem 23.50/24.01 % SZS output start Refutation 23.50/24.01 23.50/24.01 % Proof 4 at 22.42 (+ 0.41) seconds: goals. 23.50/24.01 % Length of proof is 207. 23.50/24.01 % Level of proof is 28. 23.50/24.01 % Maximum clause weight is 29.000. 23.50/24.01 % Given clauses 983. 23.50/24.01 23.50/24.01 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 2 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 3 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 4 (all B all A B = ld(A,mult(A,B))) # label(f02) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 5 (all A A = mult(A,unit)) # label(f05) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 6 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 7 (all B all A A = mult(rd(A,B),B)) # label(f03) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 8 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 9 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 23.50/24.01 10 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 23.50/24.01 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)]. 23.50/24.01 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(9)]. 23.50/24.01 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)]. 23.50/24.01 14 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(3)]. 23.50/24.01 15 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(4)]. 23.50/24.01 16 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(7)]. 23.50/24.01 17 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(8)]. 23.50/24.01 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(6)]. 23.50/24.01 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(2)]. 23.50/24.01 20 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(19),rewrite([18(2),18(7)])]. 23.50/24.01 21 mult(mult(mult(c3,c1),c3),c2) != mult(c3,mult(c1,mult(c3,c2))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)]. 23.50/24.01 22 mult(mult(c3,mult(c1,c3)),c2) != mult(c3,mult(c1,mult(c3,c2))) # answer(goals). [copy(21),rewrite([18(5)])]. 23.50/24.01 27 ld(unit,A) = A. [para(13(a,1),12(a,1)),flip(a)]. 23.50/24.01 30 rd(A,ld(B,A)) = B. [para(13(a,1),14(a,1,1))]. 23.50/24.01 31 ld(A,A) = unit. [para(11(a,1),15(a,1,2))]. 23.50/24.01 32 ld(rd(A,B),A) = B. [para(16(a,1),15(a,1,2))]. 23.50/24.01 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)]. 23.50/24.01 36 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),14(a,1,1))]. 23.50/24.01 37 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),15(a,1,2))]. 23.50/24.01 38 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(16(a,1),18(a,1,1)),flip(a)]. 23.50/24.01 39 mult(f(A),A) = mult(A,f(A)). [para(17(a,1),18(a,1,1)),rewrite([17(6)]),flip(a)]. 23.50/24.01 40 mult(mult(A,mult(B,A)),mult(A,B)) = mult(mult(A,B),mult(A,mult(A,B))). [para(18(a,1),18(a,1,1))]. 23.50/24.01 41 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),11(a,1)),rewrite([11(4),12(3),12(4)])]. 23.50/24.01 42 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(12(a,1),20(a,1,1)),rewrite([12(5)])]. 23.50/24.01 43 mult(mult(A,mult(ld(B,C),C)),B) = mult(mult(A,ld(B,C)),mult(C,B)). [para(13(a,1),20(a,1,1,2,2)),rewrite([35(9)])]. 23.50/24.01 44 mult(mult(A,mult(B,C)),ld(C,B)) = mult(mult(A,C),mult(ld(C,B),B)). [para(13(a,1),20(a,2,2,2)),rewrite([35(3)])]. 23.50/24.01 45 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),14(a,1,1))]. 23.50/24.01 47 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(16(a,1),20(a,1,1,2,2)),rewrite([38(9)])]. 23.50/24.01 48 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(16(a,1),20(a,1,1)),flip(a)]. 23.50/24.01 52 mult(mult(A,B),mult(A,mult(B,A))) = mult(A,mult(B,mult(A,mult(B,A)))). [para(20(a,1),18(a,1)),rewrite([42(7)])]. 23.50/24.01 53 mult(mult(A,mult(B,mult(B,mult(C,B)))),mult(B,C)) = mult(mult(A,B),mult(mult(B,C),mult(B,mult(B,C)))). [para(18(a,1),20(a,1,1,2,2))]. 23.50/24.01 58 rd(mult(A,f(A)),A) = f(A). [para(39(a,1),14(a,1,1))]. 23.50/24.01 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(39(a,1),18(a,1,1)),rewrite([41(4),17(3)]),flip(a)]. 23.50/24.01 64 rd(mult(A,B),mult(ld(B,A),B)) = B. [para(35(a,1),14(a,1,1))]. 23.50/24.01 65 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),15(a,1,2))]. 23.50/24.01 66 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(35(a,1),18(a,1,1)),rewrite([41(2),41(5)]),flip(a)]. 23.50/24.01 71 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(16(a,1),36(a,1,1,2))]. 23.50/24.01 74 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),36(a,2)),rewrite([41(3),66(4)])]. 23.50/24.01 75 mult(A,rd(f(A),A)) = f(A). [back_rewrite(58),rewrite([71(3)])]. 23.50/24.01 77 rd(f(A),A) = ld(A,f(A)). [para(75(a,1),15(a,1,2)),flip(a)]. 23.50/24.01 78 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),f(B))). [para(75(a,1),20(a,2,2,2)),rewrite([77(2),35(4),39(2),77(5),77(9)])]. 23.50/24.01 79 mult(ld(A,f(A)),A) = f(A). [para(77(a,1),16(a,1,1))]. 23.50/24.01 81 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(79(a,1),18(a,1,1)),rewrite([13(9)]),flip(a)]. 23.50/24.01 84 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(f(B),ld(B,f(B)))). [back_rewrite(78),rewrite([81(11)])]. 23.50/24.01 87 ld(mult(A,mult(B,A)),mult(mult(A,B),mult(A,mult(A,B)))) = mult(A,B). [para(18(a,1),37(a,1,1))]. 23.50/24.01 91 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(39(a,1),37(a,1,1)),rewrite([60(6)])]. 23.50/24.01 93 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(35(a,1),37(a,1,1)),rewrite([41(4),66(5)])]. 23.50/24.01 96 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(16(a,1),41(a,1,1)),flip(a)]. 23.50/24.01 118 rd(A,mult(ld(A,unit),A)) = A. [para(12(a,1),64(a,1,1))]. 23.50/24.01 134 mult(ld(A,unit),A) = unit. [para(118(a,1),32(a,1,1)),rewrite([31(1)]),flip(a)]. 23.50/24.01 136 rd(unit,A) = ld(A,unit). [para(134(a,1),14(a,1,1))]. 23.50/24.01 139 mult(ld(A,unit),mult(A,A)) = A. [para(134(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)]. 23.50/24.01 162 rd(A,mult(A,A)) = ld(A,unit). [para(139(a,1),14(a,1,1))]. 23.50/24.01 163 ld(ld(A,unit),A) = mult(A,A). [para(139(a,1),15(a,1,2))]. 23.50/24.01 164 mult(ld(f(A),unit),A) = f(A). [para(17(a,1),139(a,1,2))]. 23.50/24.01 172 ld(f(A),unit) = ld(A,f(A)). [para(17(a,1),162(a,1,2)),rewrite([77(2)]),flip(a)]. 23.50/24.01 174 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(32(a,1),163(a,1,1)),rewrite([136(2),136(5),136(7)]),flip(a)]. 23.50/24.01 176 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(164(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)]. 23.50/24.01 183 mult(mult(ld(A,B),B),A) = mult(ld(A,B),mult(B,A)). [para(13(a,1),42(a,1,1,2)),rewrite([35(7)])]. 23.50/24.01 187 mult(mult(A,B),rd(B,A)) = mult(A,mult(B,rd(B,A))). [para(16(a,1),42(a,1,1,2)),rewrite([38(7)])]. 23.50/24.01 214 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(164(a,1),42(a,1,1,2)),rewrite([176(14),11(8)])]. 23.50/24.01 218 mult(f(A),ld(A,f(A))) = unit. [para(172(a,1),13(a,1,2))]. 23.50/24.01 219 mult(A,ld(f(A),unit)) = f(A). [para(172(a,2),13(a,1,2))]. 23.50/24.01 224 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(A,B). [back_rewrite(84),rewrite([218(11),11(9)])]. 23.50/24.01 226 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(81),rewrite([218(8)])]. 23.50/24.01 228 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(219(a,1),41(a,1,1)),rewrite([13(5),174(8)]),flip(a)]. 23.50/24.01 231 mult(A,mult(ld(A,B),mult(B,A))) = mult(B,mult(B,A)). [para(13(a,1),43(a,2,1)),rewrite([18(4),183(3)])]. 23.50/24.01 257 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(16(a,1),65(a,1,2)),flip(a)]. 23.50/24.01 263 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),65(a,1,2)),rewrite([91(4)]),flip(a)]. 23.50/24.01 342 rd(mult(A,mult(B,mult(C,B))),B) = mult(rd(A,C),mult(C,mult(B,C))). [para(16(a,1),45(a,1,1,1))]. 23.50/24.01 367 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(134(a,1),45(a,1,1,1)),rewrite([12(4),71(3),14(2)]),flip(a)]. 23.50/24.01 389 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(16(a,1),74(a,1,1)),flip(a)]. 23.50/24.01 414 ld(mult(A,f(B)),mult(A,B)) = f(B). [para(17(a,1),93(a,1,2,2))]. 23.50/24.01 481 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(96(a,1),15(a,1,2))]. 23.50/24.01 482 mult(rd(A,f(B)),B) = mult(A,f(B)). [para(17(a,1),96(a,1,2))]. 23.50/24.01 513 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(214(a,1),14(a,1,1))]. 23.50/24.01 517 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(214(a,1),41(a,1,1)),rewrite([219(4),174(10)]),flip(a)]. 23.50/24.01 617 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(228(a,1),15(a,1,2)),flip(a)]. 23.50/24.01 622 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(517),rewrite([617(7)])]. 23.50/24.01 638 mult(rd(A,mult(B,f(B))),B) = mult(A,ld(B,f(B))). [para(79(a,1),48(a,1,1,1,2,2)),rewrite([13(9),226(8),11(6)])]. 23.50/24.01 652 mult(A,ld(f(B),unit)) = mult(A,ld(B,f(B))). [para(164(a,1),48(a,1,1,1,2,2)),rewrite([638(4),219(10),134(8),11(5)]),flip(a)]. 23.50/24.01 680 rd(ld(A,B),A) = ld(A,rd(B,A)). [para(257(a,1),14(a,1,1))]. 23.50/24.01 690 mult(ld(A,unit),f(A)) = ld(A,f(A)). [para(172(a,1),257(a,2)),rewrite([136(4),617(5)])]. 23.50/24.01 783 ld(rd(A,mult(B,B)),rd(A,B)) = B. [para(389(a,1),15(a,1,2))]. 23.50/24.01 784 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(17(a,1),389(a,1,1,2))]. 23.50/24.01 994 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(219(a,1),481(a,1,2)),rewrite([513(4),174(11),617(9)])]. 23.50/24.01 1010 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(263),rewrite([994(4)])]. 23.50/24.01 1028 mult(rd(A,f(B)),rd(B,rd(A,f(B)))) = rd(mult(A,f(B)),rd(A,f(B))). [para(482(a,1),71(a,1,1)),flip(a)]. 23.50/24.01 1350 mult(A,ld(B,unit)) = rd(A,B). [para(622(a,1),48(a,1,2,2)),rewrite([1010(7),41(4),17(3),690(9),224(8),389(3)]),flip(a)]. 23.50/24.01 1380 mult(A,ld(B,f(B))) = rd(A,f(B)). [back_rewrite(652),rewrite([1350(4)]),flip(a)]. 23.50/24.01 1496 ld(A,rd(A,B)) = ld(B,unit). [para(1350(a,1),15(a,1,2))]. 23.50/24.01 1498 mult(A,mult(ld(B,unit),A)) = mult(rd(A,B),A). [para(1350(a,1),18(a,1,1)),flip(a)]. 23.50/24.01 1516 mult(mult(A,rd(B,C)),ld(ld(C,unit),B)) = mult(rd(A,C),mult(ld(ld(C,unit),B),B)). [para(1350(a,1),44(a,1,1,2)),rewrite([1350(9)])]. 23.50/24.01 1575 ld(mult(A,B),A) = ld(B,unit). [para(14(a,1),1496(a,1,2))]. 23.50/24.01 1576 ld(ld(A,B),unit) = ld(B,A). [para(30(a,1),1496(a,1,2)),flip(a)]. 23.50/24.01 1578 ld(mult(ld(A,B),A),unit) = ld(mult(B,A),A). [para(64(a,1),1496(a,1,2)),flip(a)]. 23.50/24.01 1689 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(mult(A,B),unit). [para(40(a,1),1575(a,1,1))]. 23.50/24.01 1711 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(1576(a,1),1350(a,1,2)),flip(a)]. 23.50/24.01 2027 ld(rd(A,B),rd(A,f(B))) = f(B). [para(17(a,1),783(a,1,1,2))]. 23.50/24.01 2054 mult(mult(A,rd(B,C)),mult(f(C),rd(f(C),rd(B,C)))) = mult(mult(A,rd(B,f(C))),rd(f(C),rd(B,C))). [para(784(a,1),47(a,1,1,2)),flip(a)]. 23.50/24.01 2387 mult(mult(A,ld(B,ld(C,f(C)))),mult(ld(C,f(C)),B)) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [para(1380(a,1),43(a,1,1,2)),flip(a)]. 23.50/24.01 2412 mult(mult(A,ld(B,C)),ld(C,B)) = A. [para(1711(a,1),14(a,1))]. 23.50/24.01 2517 ld(rd(A,B),rd(rd(A,f(B)),rd(A,B))) = rd(f(B),rd(A,B)). [para(2027(a,1),680(a,1,1)),flip(a)]. 23.50/24.01 3168 mult(ld(A,unit),mult(A,B)) = B. [para(16(a,1),367(a,1,2,2)),rewrite([16(6)])]. 23.50/24.01 3174 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),367(a,1,2))]. 23.50/24.01 3177 mult(mult(A,B),mult(ld(B,A),B)) = mult(A,mult(A,B)). [para(367(a,1),40(a,1,2)),rewrite([1350(7),71(5),14(4),3168(4),3168(7),3168(10),3174(7)]),flip(a)]. 23.50/24.01 3190 mult(ld(A,unit),B) = ld(A,B). [para(257(a,1),367(a,1,2,2)),rewrite([13(4),257(6)])]. 23.50/24.01 3200 mult(mult(A,ld(B,C)),mult(C,B)) = mult(rd(A,B),mult(C,mult(C,B))). [para(367(a,1),53(a,1,2)),rewrite([1350(9),71(7),14(6),3190(6),15(4),3190(3),1350(7),3190(10),15(8),3190(13),15(11),3190(10),65(8),3177(9)])]. 23.50/24.01 3327 mult(rd(A,B),A) = mult(A,ld(B,A)). [back_rewrite(1498),rewrite([3190(3)]),flip(a)]. 23.50/24.01 3446 mult(rd(A,B),mult(ld(C,f(C)),mult(ld(C,f(C)),B))) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [back_rewrite(2387),rewrite([3200(8)])]. 23.50/24.01 3746 rd(ld(A,B),B) = ld(A,unit). [para(3190(a,1),14(a,1,1))]. 23.50/24.01 3751 ld(rd(A,B),mult(A,ld(B,A))) = A. [para(3190(a,1),37(a,1,2,2)),rewrite([1350(3)])]. 23.50/24.01 3752 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(3190(a,1),41(a,1,1)),rewrite([3190(6)]),flip(a)]. 23.50/24.01 3756 mult(ld(A,f(A)),B) = ld(f(A),B). [para(172(a,1),3190(a,1,1))]. 23.50/24.01 3761 mult(mult(mult(A,B),ld(C,rd(B,C))),C) = mult(A,mult(B,ld(C,B))). [para(3190(a,1),45(a,1,1,2)),rewrite([1350(4),1711(7),27(6),3190(8)])]. 23.50/24.01 3770 ld(ld(A,f(B)),ld(A,B)) = f(B). [para(3190(a,1),414(a,1,1)),rewrite([3190(5)])]. 23.50/24.01 3779 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [para(3190(a,1),1350(a,1)),flip(a)]. 23.50/24.01 3783 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1576(a,1),3190(a,1,1)),flip(a)]. 23.50/24.01 3805 mult(mult(A,rd(B,C)),mult(C,B)) = mult(rd(A,C),mult(C,mult(B,B))). [back_rewrite(1516),rewrite([3783(5),27(4),3783(8),27(7),41(7)])]. 23.50/24.01 3812 mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B) = mult(rd(A,B),ld(f(C),ld(f(C),B))). [back_rewrite(3446),rewrite([3756(6),3756(6)]),flip(a)]. 23.50/24.01 3860 mult(ld(f(A),B),ld(B,A)) = f(A). [back_rewrite(3770),rewrite([3783(4)])]. 23.50/24.01 4059 rd(A,mult(B,A)) = ld(B,unit). [para(15(a,1),3746(a,1,1))]. 23.50/24.01 4060 ld(rd(A,B),unit) = rd(B,A). [para(32(a,1),3746(a,1,1)),flip(a)]. 23.50/24.01 4061 rd(A,mult(A,mult(B,A))) = ld(mult(A,B),unit). [para(37(a,1),3746(a,1,1))]. 23.50/24.01 4070 mult(ld(A,f(B)),f(B)) = ld(A,B). [para(3746(a,1),482(a,1,1)),rewrite([3190(3)]),flip(a)]. 23.50/24.01 4071 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(1575(a,1),3746(a,1,1)),rewrite([3779(3)]),flip(a)]. 23.50/24.01 4074 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2027(a,1),3746(a,1,1)),rewrite([4060(7)])]. 23.50/24.01 4089 rd(A,mult(A,mult(B,A))) = ld(B,ld(A,unit)). [back_rewrite(4061),rewrite([4071(6)])]. 23.50/24.01 4097 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(B,ld(A,unit)). [back_rewrite(1689),rewrite([4071(10)])]. 23.50/24.01 4098 ld(mult(A,B),B) = ld(B,ld(A,B)). [back_rewrite(1578),rewrite([4071(4),3783(3),11(3)]),flip(a)]. 23.50/24.01 4153 ld(mult(A,B),ld(B,unit)) = ld(B,ld(A,ld(B,unit))). [para(40(a,1),4059(a,1,2)),rewrite([4089(6),4071(3),4071(8)]),flip(a)]. 23.50/24.01 4160 rd(A,mult(B,f(A))) = rd(f(A),B). [para(482(a,1),4059(a,1,2)),rewrite([4060(7)])]. 23.50/24.01 4325 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4060(a,1),1350(a,1,2)),flip(a)]. 23.50/24.01 4329 mult(mult(A,rd(B,C)),rd(C,B)) = A. [para(4060(a,1),2412(a,1,1,2)),rewrite([27(5)])]. 23.50/24.01 4330 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4060(a,1),3190(a,1,1)),flip(a)]. 23.50/24.01 4334 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4074),rewrite([4325(4)])]. 23.50/24.01 4337 mult(rd(A,B),mult(rd(B,f(A)),rd(A,B))) = mult(f(A),rd(A,B)). [back_rewrite(2517),rewrite([4325(5),4330(6),4325(9)])]. 23.50/24.01 4338 mult(mult(A,rd(B,C)),mult(f(C),mult(f(C),rd(C,B)))) = mult(mult(A,rd(B,f(C))),mult(f(C),rd(C,B))). [back_rewrite(2054),rewrite([4325(6),4325(14)])]. 23.50/24.01 4345 mult(rd(A,f(B)),mult(B,rd(f(B),A))) = mult(A,rd(B,A)). [back_rewrite(1028),rewrite([4325(5),4325(11),187(11),4334(10)])]. 23.50/24.01 4370 mult(rd(A,B),mult(B,ld(A,B))) = B. [back_rewrite(3751),rewrite([4330(4)])]. 23.50/24.01 4385 mult(rd(A,B),rd(B,f(A))) = f(A). [back_rewrite(2027),rewrite([4330(4)])]. 23.50/24.01 4695 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(3752(a,1),35(a,1,2,1)),rewrite([183(3),231(4)]),flip(a)]. 23.50/24.01 4708 rd(ld(A,ld(B,f(B))),f(B)) = ld(A,ld(B,unit)). [para(1380(a,1),3752(a,1,2)),rewrite([3746(4),1380(9)]),flip(a)]. 23.50/24.01 5037 mult(rd(A,B),ld(f(C),ld(f(C),B))) = mult(mult(A,ld(B,ld(C,unit))),B). [back_rewrite(3812),rewrite([4708(5)]),flip(a)]. 23.50/24.01 5216 rd(A,mult(ld(B,C),D)) = mult(A,ld(D,ld(C,B))). [para(3783(a,1),1711(a,1,2))]. 23.50/24.01 5220 mult(ld(A,ld(B,unit)),C) = ld(mult(B,A),C). [para(87(a,1),3783(a,1,1)),rewrite([4097(9)]),flip(a)]. 23.50/24.01 5569 ld(f(A),ld(f(A),B)) = ld(A,B). [para(3860(a,1),1575(a,1,1)),rewrite([3783(7),11(7)])]. 23.50/24.01 5588 mult(mult(A,ld(B,ld(C,unit))),B) = mult(rd(A,B),ld(C,B)). [back_rewrite(5037),rewrite([5569(5)]),flip(a)]. 23.50/24.01 5741 mult(rd(A,B),mult(f(C),mult(f(C),B))) = mult(mult(A,ld(B,C)),B). [para(4070(a,1),47(a,1,1,2)),rewrite([1711(6),13(6),1711(11),13(11),3200(9)]),flip(a)]. 23.50/24.01 5783 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(4071(a,1),1350(a,1,2))]. 23.50/24.01 5794 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [back_rewrite(5588),rewrite([5783(4)])]. 23.50/24.01 5985 mult(f(A),rd(A,B)) = mult(A,rd(f(A),B)). [para(784(a,1),4160(a,1,2)),rewrite([4325(3),4325(6)]),flip(a)]. 23.50/24.01 5995 mult(mult(A,rd(B,C)),mult(f(C),mult(C,rd(f(C),B)))) = mult(mult(A,rd(B,f(C))),mult(C,rd(f(C),B))). [back_rewrite(4338),rewrite([5985(6),5985(14)])]. 23.50/24.01 5996 mult(rd(A,B),mult(rd(B,f(A)),rd(A,B))) = mult(A,rd(f(A),B)). [back_rewrite(4337),rewrite([5985(9)])]. 23.50/24.01 5999 mult(mult(rd(A,B),C),rd(B,A)) = mult(rd(A,B),mult(C,rd(B,A))). [para(4325(a,1),71(a,1)),rewrite([4325(7)])]. 23.50/24.01 6018 rd(A,mult(B,rd(C,D))) = mult(A,rd(rd(D,C),B)). [para(4325(a,1),4325(a,1,2))]. 23.50/24.01 6042 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(4329(a,1),35(a,2)),rewrite([4330(5),5999(7),4329(6)])]. 23.50/24.01 6328 mult(rd(A,f(B)),rd(B,A)) = mult(A,rd(f(B),A)). [para(4334(a,1),65(a,1,2)),rewrite([4330(4),4330(8),16(8)])]. 23.50/24.01 6329 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)). [para(4334(a,1),44(a,1,1,2)),rewrite([4330(6),16(6),4330(10),16(10),3805(9),17(7)])]. 23.50/24.01 6377 mult(rd(A,B),mult(B,rd(f(A),B))) = mult(A,rd(f(A),B)). [back_rewrite(5996),rewrite([6328(5)])]. 23.50/24.01 6671 mult(mult(A,rd(B,f(C))),mult(C,rd(f(C),B))) = mult(mult(A,B),rd(C,B)). [para(4385(a,1),20(a,1,1,2,2)),rewrite([16(4),6328(11),6377(11)]),flip(a)]. 23.50/24.01 6693 mult(f(A),mult(A,rd(f(A),B))) = mult(A,rd(A,B)). [para(4385(a,1),52(a,1,1)),rewrite([6328(6),6377(6),6328(13),6377(13),4345(12),38(9)])]. 23.50/24.01 6722 mult(mult(A,rd(B,C)),mult(C,rd(C,B))) = mult(mult(A,B),rd(C,B)). [back_rewrite(5995),rewrite([6693(7),6671(12)])]. 23.50/24.01 6824 mult(f(A),mult(f(A),B)) = mult(A,B). [para(17(a,1),4695(a,1,1)),flip(a)]. 23.50/24.01 6924 mult(mult(A,ld(B,C)),B) = mult(rd(A,B),mult(C,B)). [back_rewrite(5741),rewrite([6824(5)]),flip(a)]. 23.50/24.01 7021 mult(rd(mult(A,B),C),B) = mult(A,mult(B,ld(C,B))). [back_rewrite(3761),rewrite([6924(5),16(4)])]. 23.50/24.01 13060 mult(ld(A,ld(B,ld(C,unit))),D) = ld(mult(mult(C,B),A),D). [para(4071(a,1),5220(a,1,1,2))]. 23.50/24.01 13743 mult(A,ld(B,ld(C,ld(D,unit)))) = rd(A,mult(mult(D,C),B)). [para(4071(a,1),5783(a,1,2,2))]. 23.50/24.01 17767 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(16(a,1),342(a,1,1,2,2)),rewrite([4325(5),38(9),6722(8)])]. 23.50/24.01 17768 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [para(342(a,2),20(a,1,1)),rewrite([17767(4),14(3),16(5)])]. 23.50/24.01 17771 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(342(a,2),35(a,2)),rewrite([35(10),17767(8),14(7)])]. 23.50/24.01 17779 mult(mult(A,B),ld(B,rd(C,B))) = rd(mult(A,C),B). [para(1350(a,1),342(a,2,2,2)),rewrite([3190(3),17767(4),3746(3),1350(4),1711(5),27(4),3190(7)]),flip(a)]. 23.50/24.01 17791 rd(mult(A,mult(B,A)),mult(mult(C,B),A)) = rd(A,C). [para(342(a,2),4059(a,1,2)),rewrite([17767(6),14(5),4330(8),11(8)])]. 23.50/24.01 17802 mult(mult(mult(A,B),C),mult(B,ld(mult(A,mult(B,mult(C,B))),B))) = B. [para(342(a,1),4370(a,1,1)),rewrite([17771(4)])]. 23.50/24.01 17806 mult(rd(A,B),mult(mult(B,C),A)) = mult(A,mult(C,A)). [para(342(a,2),6042(a,1,2)),rewrite([17767(5),14(4)])]. 23.50/24.01 19568 ld(mult(mult(A,B),C),B) = ld(mult(B,C),ld(A,B)). [para(3779(a,1),5794(a,1,1)),rewrite([4071(3),13060(5),3779(6),5220(8)])]. 23.50/24.01 19570 ld(A,rd(mult(B,A),C)) = mult(ld(A,B),rd(A,C)). [para(5794(a,1),4071(a,1,1)),rewrite([4071(5),4330(4),11(4),3783(3),4330(7),11(7)]),flip(a)]. 23.50/24.01 19614 rd(mult(A,B),mult(B,mult(C,B))) = rd(rd(A,C),B). [para(4153(a,1),5794(a,2,2)),rewrite([1350(4),14(2),1350(4),1711(5),27(4),13743(8),18(5)]),flip(a)]. 23.50/24.01 19764 rd(A,mult(B,mult(C,ld(D,E)))) = mult(A,rd(rd(ld(E,D),C),B)). [para(1711(a,1),6018(a,1,2,2))]. 23.50/24.01 20688 ld(mult(A,B),mult(A,C)) = mult(ld(B,rd(C,A)),A). [para(3190(a,1),6329(a,1,1)),rewrite([3779(6),5220(8)]),flip(a)]. 23.50/24.01 21176 ld(mult(A,B),rd(B,C)) = ld(B,rd(ld(A,B),C)). [para(6924(a,1),4071(a,1,1)),rewrite([4071(5),4330(4),11(4),4071(7),3783(7),1350(7)])]. 23.50/24.01 21212 mult(A,mult(ld(A,B),ld(C,ld(A,B)))) = mult(rd(B,C),ld(A,B)). [para(13(a,1),7021(a,1,1,1)),flip(a)]. 23.50/24.01 21225 ld(A,mult(B,ld(C,B))) = mult(rd(ld(A,B),C),B). [para(3190(a,1),7021(a,1,1,1)),rewrite([3190(8)]),flip(a)]. 23.50/24.01 23471 ld(mult(A,mult(B,mult(C,B))),B) = ld(B,ld(mult(B,C),ld(A,B))). [para(17768(a,1),4098(a,1,1)),rewrite([19568(7)])]. 23.50/24.01 23496 mult(mult(mult(A,B),C),ld(mult(B,C),ld(A,B))) = B. [back_rewrite(17802),rewrite([23471(6),13(7)])]. 23.50/24.01 23673 mult(mult(A,mult(B,A)),ld(A,ld(B,C))) = mult(A,C). [para(3190(a,1),17791(a,1,2,1)),rewrite([5216(5),1711(8),27(7)])]. 23.50/24.01 23706 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(mult(B,C),mult(A,B))). [para(14(a,1),17806(a,1,1)),flip(a)]. 23.50/24.01 24238 mult(rd(A,B),ld(C,A)) = mult(A,ld(mult(C,B),A)). [para(17779(a,1),19568(a,1,1)),rewrite([4330(3),3327(3),13(6),4330(6)]),flip(a)]. 23.50/24.01 24244 mult(A,mult(ld(A,B),ld(C,ld(A,B)))) = mult(B,ld(mult(A,C),B)). [back_rewrite(21212),rewrite([24238(8)])]. 23.50/24.01 24267 rd(ld(A,B),mult(A,C)) = ld(A,rd(rd(B,C),A)). [para(4089(a,1),19570(a,2,2)),rewrite([19614(4),5783(8)]),flip(a)]. 23.50/24.01 24398 mult(A,ld(B,mult(rd(B,C),D))) = mult(A,mult(ld(C,rd(D,B)),B)). [para(20688(a,1),1711(a,1,2)),rewrite([5216(4),4330(2),20688(7)])]. 23.50/24.01 24509 ld(mult(A,mult(B,A)),C) = ld(A,ld(B,ld(A,C))). [para(4089(a,1),21176(a,2,2)),rewrite([19764(6),1711(5),3327(5),24244(6),21225(5),1575(2),24267(4),136(2),3779(3),13060(5),18(2),3783(6),11(6)])]. 23.50/24.01 25006 mult(A,mult(ld(A,B),mult(A,C))) = mult(mult(B,A),C). [para(23496(a,1),14(a,1,1)),rewrite([1711(4),3783(3)])]. 23.50/24.01 25164 mult(mult(A,mult(B,A)),ld(A,C)) = mult(A,mult(B,C)). [para(15(a,1),23673(a,1,2,2))]. 23.50/24.01 25184 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(23673(a,1),17768(a,1,1)),rewrite([23706(9),13(6),25006(7)])]. 23.50/24.01 25187 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [para(17771(a,1),23673(a,1,1,2)),rewrite([25184(5),25184(3),4330(9),24509(10),25164(11),25164(8),24398(5),25184(5),13(3),16(2)]),flip(a)]. 23.50/24.01 25188 $F # answer(goals). [resolve(25187,a,22,a)]. 23.50/24.01 23.50/24.01 % SZS output end Refutation 23.50/24.01 ============================== end of proof ========================== 23.50/24.01 23.50/24.01 ============================== STATISTICS ============================ 23.50/24.01 23.50/24.01 Given=983. Generated=731166. Kept=25170. proofs=4. 23.50/24.01 Usable=656. Sos=9211. Demods=9346. Limbo=22, Disabled=15293. Hints=0. 23.50/24.01 Megabytes=26.72. 23.50/24.01 User_CPU=22.42, System_CPU=0.41, Wall_clock=23. 23.50/24.01 23.50/24.01 ============================== end of statistics ===================== 23.50/24.01 23.50/24.01 ============================== end of search ========================= 23.50/24.01 23.50/24.01 THEOREM PROVED 23.50/24.01 % SZS status Theorem 23.50/24.01 23.50/24.01 Exiting with 4 proofs. 23.50/24.01 23.50/24.01 Process 22277 exit (max_proofs) Mon Jul 3 04:11:25 2023 23.50/24.01 Prover9 interrupted 23.50/24.02 EOF