0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.09/0.31 % Computer : n003.cluster.edu 0.09/0.31 % Model : x86_64 x86_64 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.31 % Memory : 8042.1875MB 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.31 % CPULimit : 960 0.09/0.31 % DateTime : Thu Jul 2 07:48:11 EDT 2020 0.09/0.31 % CPUTime : 0.69/1.01 ============================== Prover9 =============================== 0.69/1.01 Prover9 (32) version 2009-11A, November 2009. 0.69/1.01 Process 24895 was started by sandbox2 on n003.cluster.edu, 0.69/1.01 Thu Jul 2 07:48:12 2020 0.69/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_24735_n003.cluster.edu". 0.69/1.01 ============================== end of head =========================== 0.69/1.01 0.69/1.01 ============================== INPUT ================================= 0.69/1.01 0.69/1.01 % Reading from file /tmp/Prover9_24735_n003.cluster.edu 0.69/1.01 0.69/1.01 set(prolog_style_variables). 0.69/1.01 set(auto2). 0.69/1.01 % set(auto2) -> set(auto). 0.69/1.01 % set(auto) -> set(auto_inference). 0.69/1.01 % set(auto) -> set(auto_setup). 0.69/1.01 % set(auto_setup) -> set(predicate_elim). 0.69/1.01 % set(auto_setup) -> assign(eq_defs, unfold). 0.69/1.01 % set(auto) -> set(auto_limits). 0.69/1.01 % set(auto_limits) -> assign(max_weight, "100.000"). 0.69/1.01 % set(auto_limits) -> assign(sos_limit, 20000). 0.69/1.01 % set(auto) -> set(auto_denials). 0.69/1.01 % set(auto) -> set(auto_process). 0.69/1.01 % set(auto2) -> assign(new_constants, 1). 0.69/1.01 % set(auto2) -> assign(fold_denial_max, 3). 0.69/1.01 % set(auto2) -> assign(max_weight, "200.000"). 0.69/1.01 % set(auto2) -> assign(max_hours, 1). 0.69/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.69/1.01 % set(auto2) -> assign(max_seconds, 0). 0.69/1.01 % set(auto2) -> assign(max_minutes, 5). 0.69/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.69/1.01 % set(auto2) -> set(sort_initial_sos). 0.69/1.01 % set(auto2) -> assign(sos_limit, -1). 0.69/1.01 % set(auto2) -> assign(lrs_ticks, 3000). 0.69/1.01 % set(auto2) -> assign(max_megs, 400). 0.69/1.01 % set(auto2) -> assign(stats, some). 0.69/1.01 % set(auto2) -> clear(echo_input). 0.69/1.01 % set(auto2) -> set(quiet). 0.69/1.01 % set(auto2) -> clear(print_initial_clauses). 0.69/1.01 % set(auto2) -> clear(print_given). 0.69/1.01 assign(lrs_ticks,-1). 0.69/1.01 assign(sos_limit,10000). 0.69/1.01 assign(order,kbo). 0.69/1.01 set(lex_order_vars). 0.69/1.01 clear(print_given). 0.69/1.01 0.69/1.01 % formulas(sos). % not echoed (10 formulas) 0.69/1.01 0.69/1.01 ============================== end of input ========================== 0.69/1.01 0.69/1.01 % From the command line: assign(max_seconds, 960). 0.69/1.01 0.69/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.69/1.01 0.69/1.01 % Formulas that are not ordinary clauses: 0.69/1.01 1 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 0.69/1.01 2 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 0.69/1.01 3 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 0.69/1.01 4 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 0.69/1.01 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 0.69/1.01 6 (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]. 0.69/1.01 7 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 0.69/1.01 8 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 0.69/1.01 9 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 0.69/1.01 10 -((all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5)))) | (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 X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 0.69/1.01 0.69/1.01 ============================== end of process non-clausal formulas === 0.69/1.01 0.69/1.01 ============================== PROCESS INITIAL CLAUSES =============== 0.69/1.01 0.69/1.01 ============================== PREDICATE ELIMINATION ================= 0.69/1.01 0.69/1.01 ============================== end predicate elimination ============= 0.69/1.01 0.69/1.01 Auto_denials: 0.69/1.01 % copying label goals to answer in negative clause 0.69/1.01 % copying label goals to answer in negative clause 0.69/1.01 % copying label goals to answer in negative clause 0.69/1.01 % copying label goals to answer in negative clause 0.69/1.01 % assign(max_proofs, 4). % (Horn set with more than one neg. clause) 9.69/10.00 9.69/10.00 Term ordering decisions: 9.69/10.00 9.69/10.00 % Assigning unary symbol f kb_weight 0 and highest precedence (18). 9.69/10.00 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. 9.69/10.00 9.69/10.00 ============================== end of process initial clauses ======== 9.69/10.00 9.69/10.00 ============================== CLAUSES FOR SEARCH ==================== 9.69/10.00 9.69/10.00 ============================== end of clauses for search ============= 9.69/10.00 9.69/10.00 ============================== SEARCH ================================ 9.69/10.00 9.69/10.00 % Starting search at 0.01 seconds. 9.69/10.00 9.69/10.00 Low Water (keep): wt=107.000, iters=3375 9.69/10.00 9.69/10.00 Low Water (keep): wt=103.000, iters=3355 9.69/10.00 9.69/10.00 Low Water (keep): wt=99.000, iters=3341 9.69/10.00 9.69/10.00 Low Water (keep): wt=91.000, iters=3538 9.69/10.00 9.69/10.00 Low Water (keep): wt=71.000, iters=3341 9.69/10.00 9.69/10.00 Low Water (keep): wt=67.000, iters=3456 9.69/10.00 9.69/10.00 Low Water (keep): wt=63.000, iters=3361 9.69/10.00 9.69/10.00 Low Water (keep): wt=59.000, iters=3362 9.69/10.00 9.69/10.00 Low Water (keep): wt=55.000, iters=3353 9.69/10.00 9.69/10.00 Low Water (keep): wt=51.000, iters=3365 9.69/10.00 9.69/10.00 Low Water (keep): wt=49.000, iters=3355 9.69/10.00 9.69/10.00 Low Water (keep): wt=47.000, iters=3361 9.69/10.00 9.69/10.00 Low Water (keep): wt=45.000, iters=3334 9.69/10.00 9.69/10.00 Low Water (keep): wt=43.000, iters=3345 9.69/10.00 9.69/10.00 Low Water (keep): wt=41.000, iters=3348 9.69/10.00 9.69/10.00 Low Water (keep): wt=39.000, iters=3341 9.69/10.00 9.69/10.00 Low Water (keep): wt=37.000, iters=3346 9.69/10.00 9.69/10.00 Low Water (keep): wt=35.000, iters=3358 9.69/10.00 9.69/10.00 Low Water (keep): wt=33.000, iters=3348 9.69/10.00 9.69/10.00 Low Water (keep): wt=31.000, iters=3351 9.69/10.00 9.69/10.00 Low Water (keep): wt=29.000, iters=3351 9.69/10.00 9.69/10.00 Low Water (keep): wt=27.000, iters=3360 9.69/10.00 9.69/10.00 Low Water (keep): wt=25.000, iters=3343 9.69/10.00 9.69/10.00 Low Water (displace): id=8768, wt=191.000 9.69/10.00 9.69/10.00 Low Water (displace): id=8759, wt=187.000 9.69/10.00 9.69/10.00 Low Water (displace): id=16619, wt=21.000 9.69/10.00 9.69/10.00 Low Water (displace): id=16626, wt=20.000 9.69/10.00 9.69/10.00 Low Water (displace): id=16630, wt=19.000 9.69/10.00 9.69/10.00 Low Water (keep): wt=23.000, iters=3346 9.69/10.00 9.69/10.00 Low Water (displace): id=18119, wt=17.000 9.69/10.00 9.69/10.00 ============================== PROOF ================================= 9.69/10.00 % SZS status Theorem 9.69/10.00 % SZS output start Refutation 9.69/10.00 9.69/10.00 % Proof 1 at 8.80 (+ 0.17) seconds: goals. 9.69/10.00 % Length of proof is 100. 9.69/10.00 % Level of proof is 20. 9.69/10.00 % Maximum clause weight is 43.000. 9.69/10.00 % Given clauses 424. 9.69/10.00 9.69/10.00 1 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 9.69/10.00 2 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 9.69/10.00 3 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 9.69/10.00 4 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 9.69/10.00 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 9.69/10.00 6 (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]. 9.69/10.00 7 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 9.69/10.00 8 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 9.69/10.00 9 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 9.69/10.00 10 -((all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5)))) | (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 X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 9.69/10.00 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)]. 9.69/10.00 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(8)]. 9.69/10.00 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)]. 9.69/10.00 14 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(3)]. 9.69/10.00 15 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(4)]. 9.69/10.00 16 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(7)]. 9.69/10.00 17 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(9)]. 9.69/10.00 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(2)]. 9.69/10.00 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(6)]. 9.69/10.00 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)])]. 9.69/10.00 21 mult(mult(mult(c1,c3),c2),c3) != mult(c1,mult(c3,mult(c2,c3))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)]. 9.69/10.00 29 ld(A,A) = unit. [para(11(a,1),16(a,1,2))]. 9.69/10.00 30 ld(f(A),A) = f(A). [para(14(a,1),16(a,1,2))]. 9.69/10.00 31 ld(rd(A,B),A) = B. [para(15(a,1),16(a,1,2))]. 9.69/10.00 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)]. 9.69/10.00 36 mult(f(A),A) = mult(A,f(A)). [para(14(a,1),18(a,1,1)),rewrite([14(6)]),flip(a)]. 9.69/10.00 37 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(15(a,1),18(a,1,1)),flip(a)]. 9.69/10.00 38 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),16(a,1,2))]. 9.69/10.00 39 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),17(a,1,1))]. 9.69/10.00 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)])]. 9.69/10.00 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)])]. 9.69/10.00 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)])]. 9.69/10.00 45 mult(mult(A,mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(14(a,1),20(a,1,1,2,2)),rewrite([36(2),14(11),36(9)])]. 9.69/10.00 46 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(15(a,1),20(a,1,1,2,2)),rewrite([37(9)])]. 9.69/10.00 47 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(15(a,1),20(a,1,1)),flip(a)]. 9.69/10.00 50 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),17(a,1,1))]. 9.69/10.00 59 rd(mult(A,f(A)),A) = f(A). [para(36(a,1),17(a,1,1))]. 9.69/10.00 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(36(a,1),18(a,1,1)),rewrite([41(4),14(3)]),flip(a)]. 9.69/10.00 64 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),16(a,1,2))]. 9.69/10.00 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)]. 9.69/10.00 76 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(36(a,1),38(a,1,1)),rewrite([60(6)])]. 9.69/10.00 81 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(15(a,1),39(a,1,1,2))]. 9.69/10.00 84 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),39(a,2)),rewrite([41(3),66(4)])]. 9.69/10.00 85 mult(A,rd(f(A),A)) = f(A). [back_rewrite(59),rewrite([81(3)])]. 9.69/10.00 86 rd(f(A),A) = ld(A,f(A)). [para(85(a,1),16(a,1,2)),flip(a)]. 9.69/10.00 101 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(15(a,1),41(a,1,1)),flip(a)]. 9.69/10.00 145 mult(ld(A,unit),A) = unit. [para(12(a,1),64(a,1,2)),rewrite([29(1)]),flip(a)]. 9.69/10.00 147 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(15(a,1),64(a,1,2)),flip(a)]. 9.69/10.00 154 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),64(a,1,2)),rewrite([76(4)]),flip(a)]. 9.69/10.00 155 ld(ld(A,unit),unit) = A. [para(145(a,1),16(a,1,2))]. 9.69/10.00 156 rd(unit,A) = ld(A,unit). [para(145(a,1),17(a,1,1))]. 9.69/10.00 158 mult(ld(A,unit),mult(A,A)) = A. [para(145(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)]. 9.69/10.00 171 mult(mult(A,f(A)),mult(A,f(A))) = mult(A,mult(A,A)). [para(36(a,1),42(a,1,1,2)),rewrite([45(5),60(9)])]. 9.69/10.00 191 mult(ld(f(A),unit),A) = f(A). [para(14(a,1),158(a,1,2))]. 9.69/10.00 192 ld(ld(A,unit),A) = mult(A,A). [para(158(a,1),16(a,1,2))]. 9.69/10.00 203 ld(f(A),unit) = ld(A,f(A)). [para(191(a,1),17(a,1,1)),rewrite([86(2)]),flip(a)]. 9.69/10.00 204 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(191(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)]. 9.69/10.00 205 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(191(a,1),20(a,1,1,2,2)),rewrite([204(16),11(10)])]. 9.69/10.00 207 mult(mult(A,ld(f(B),unit)),mult(B,f(B))) = mult(A,B). [para(191(a,1),20(a,2,2,2)),rewrite([204(8),11(2)]),flip(a)]. 9.69/10.00 212 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(191(a,1),42(a,1,1,2)),rewrite([204(14),11(8)])]. 9.69/10.00 214 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(31(a,1),192(a,1,1)),rewrite([156(2),156(5),156(7)]),flip(a)]. 9.69/10.00 215 mult(mult(A,A),ld(A,unit)) = A. [para(192(a,1),64(a,2,1)),rewrite([13(5),155(4)]),flip(a)]. 9.69/10.00 240 mult(A,ld(f(A),unit)) = f(A). [para(203(a,2),13(a,1,2))]. 9.69/10.00 294 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(240(a,1),41(a,1,1)),rewrite([13(5),214(8)]),flip(a)]. 9.69/10.00 302 mult(mult(rd(A,mult(B,f(B))),f(B)),mult(B,f(B))) = mult(A,f(B)). [para(15(a,1),45(a,1,1)),flip(a)]. 63.41/63.85 314 mult(mult(A,mult(B,f(B))),B) = mult(mult(A,B),mult(B,f(B))). [para(45(a,1),41(a,1,1)),rewrite([45(7),41(4),14(3),14(10)]),flip(a)]. 63.41/63.85 393 mult(mult(A,mult(mult(B,C),mult(ld(C,D),D))),rd(ld(C,D),mult(B,mult(D,C)))) = mult(mult(A,mult(B,mult(D,C))),mult(ld(C,D),rd(ld(C,D),mult(B,mult(D,C))))). [para(44(a,1),46(a,1,1,2))]. 63.41/63.85 436 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(14(a,1),84(a,1,1,2))]. 63.41/63.85 437 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(15(a,1),84(a,1,1)),flip(a)]. 63.41/63.85 447 rd(mult(mult(A,B),mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(45(a,1),84(a,2)),rewrite([14(6),314(4)])]. 63.41/63.85 479 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = mult(A,ld(B,unit)). [para(158(a,1),47(a,1,1,1,2,2)),rewrite([18(2),215(11),145(8),11(7)])]. 63.41/63.85 498 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(101(a,1),16(a,1,2))]. 63.41/63.85 608 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(212(a,1),17(a,1,1))]. 63.41/63.85 611 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(212(a,1),41(a,1,1)),rewrite([240(4),214(10)]),flip(a)]. 63.41/63.85 739 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(294(a,1),16(a,1,2)),flip(a)]. 63.41/63.85 743 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(611),rewrite([739(7)])]. 63.41/63.85 773 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(145(a,1),50(a,1,1,1)),rewrite([12(4),81(3),17(2)]),flip(a)]. 63.41/63.85 877 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(15(a,1),436(a,1,1)),flip(a)]. 63.41/63.85 884 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(145(a,1),436(a,1,1)),rewrite([156(3)]),flip(a)]. 63.41/63.85 1025 mult(mult(rd(A,mult(B,mult(B,B))),f(B)),mult(B,f(B))) = mult(rd(A,mult(B,f(B))),f(B)). [para(437(a,1),45(a,1,1)),rewrite([171(10)]),flip(a)]. 63.41/63.85 1107 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(240(a,1),498(a,1,2)),rewrite([608(4),214(11),739(9)])]. 63.41/63.85 1134 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(154),rewrite([1107(4)])]. 63.41/63.85 1609 mult(A,ld(B,unit)) = rd(A,B). [para(743(a,1),47(a,1,2,2)),rewrite([1134(7),41(4),14(3),884(9),205(9),437(3)]),flip(a)]. 63.41/63.85 1661 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = rd(A,B). [back_rewrite(479),rewrite([1609(8)])]. 63.41/63.85 1663 mult(rd(A,f(B)),mult(B,f(B))) = mult(A,B). [back_rewrite(207),rewrite([1609(4)])]. 63.41/63.85 1664 rd(mult(A,mult(B,f(B))),f(B)) = mult(A,B). [back_rewrite(205),rewrite([1609(7)])]. 63.41/63.85 1683 mult(mult(A,f(B)),mult(B,f(B))) = mult(A,mult(B,B)). [back_rewrite(447),rewrite([1664(6),41(2)]),flip(a)]. 63.41/63.85 1701 mult(rd(A,mult(B,f(B))),f(B)) = rd(A,B). [back_rewrite(1025),rewrite([1683(8),1661(5)]),flip(a)]. 63.41/63.85 1743 mult(rd(A,B),mult(B,f(B))) = mult(A,f(B)). [back_rewrite(302),rewrite([1701(5)])]. 63.41/63.85 2220 ld(rd(A,B),rd(A,f(B))) = f(B). [para(877(a,1),16(a,1,2))]. 63.41/63.85 3412 mult(ld(A,unit),B) = ld(A,B). [para(147(a,1),773(a,1,2,2)),rewrite([13(4),147(6)])]. 63.41/63.85 4028 rd(ld(A,B),B) = ld(A,unit). [para(3412(a,1),17(a,1,1))]. 63.41/63.85 4341 rd(A,mult(B,A)) = ld(B,unit). [para(16(a,1),4028(a,1,1))]. 63.41/63.85 4342 ld(rd(A,B),unit) = rd(B,A). [para(31(a,1),4028(a,1,1)),flip(a)]. 63.41/63.85 4356 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2220(a,1),4028(a,1,1)),rewrite([4342(7)])]. 63.41/63.85 4681 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4342(a,1),1609(a,1,2)),flip(a)]. 63.41/63.85 4689 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4356),rewrite([4681(4)])]. 63.41/63.85 18694 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(1743(a,1),393(a,1,2,2)),rewrite([877(3),30(4),36(4),1663(5),30(4),4341(6),1609(5),1743(7),30(8),30(9),1743(12),4341(11),1609(10),46(9),4689(8)])]. 63.41/63.85 18722 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [back_rewrite(50),rewrite([18694(5),17(4)])]. 63.41/63.85 18723 $F # answer(goals). [resolve(18722,a,21,a)]. 63.41/63.85 63.41/63.85 % SZS output end Refutation 63.41/63.85 ============================== end of proof ========================== 63.41/63.85 % Redundant proof: 18731 $F # answer(goals). [back_rewrite(21),rewrite([18722(7)]),xx(a)]. 63.41/63.85 63.41/63.85 % Disable descendants (x means already disabled): 63.41/63.85 21x 63.41/63.85 63.41/63.85 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 42 (0.00 of 11.27 sec). 63.41/63.85 63.41/63.85 Low Water (keep): wt=22.000, iters=3362 63.41/63.85 63.41/63.85 Low Water (displace): id=20956, wt=15.000 63.41/63.85 63.41/63.85 Low Water (keep): wt=21.000, iters=3338 63.41/63.85 63.41/63.85 ============================== PROOF ================================= 63.41/63.85 % SZS status Theorem 63.41/63.85 % SZS output start Refutation 63.41/63.85 63.41/63.85 % Proof 2 at 61.65 (+ 1.11) seconds: goals. 63.41/63.85 % Length of proof is 108. 63.41/63.85 % Level of proof is 23. 63.41/63.85 % Maximum clause weight is 43.000. 63.41/63.85 % Given clauses 1051. 63.41/63.85 63.41/63.85 1 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 63.41/63.85 2 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 63.41/63.85 3 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 63.41/63.85 4 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 63.41/63.85 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 63.41/63.85 6 (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]. 63.41/63.85 7 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 63.41/63.85 8 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 63.41/63.85 9 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 63.41/63.85 10 -((all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5)))) | (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 X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 63.41/63.85 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)]. 63.41/63.85 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(8)]. 63.41/63.85 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)]. 63.41/63.85 14 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(3)]. 63.41/63.85 15 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(4)]. 63.41/63.85 16 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(7)]. 63.41/63.85 17 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(9)]. 63.41/63.85 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(2)]. 63.41/63.85 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(6)]. 63.41/63.85 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)])]. 63.41/63.85 24 mult(mult(c9,c7),mult(c8,c9)) != mult(c9,mult(mult(c7,c8),c9)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)]. 63.41/63.85 29 ld(A,A) = unit. [para(11(a,1),16(a,1,2))]. 63.41/63.85 30 ld(f(A),A) = f(A). [para(14(a,1),16(a,1,2))]. 63.41/63.85 31 ld(rd(A,B),A) = B. [para(15(a,1),16(a,1,2))]. 63.41/63.85 33 rd(A,ld(B,A)) = B. [para(13(a,1),17(a,1,1))]. 63.41/63.85 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)]. 63.41/63.85 36 mult(f(A),A) = mult(A,f(A)). [para(14(a,1),18(a,1,1)),rewrite([14(6)]),flip(a)]. 63.41/63.85 37 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(15(a,1),18(a,1,1)),flip(a)]. 63.41/63.85 38 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),16(a,1,2))]. 63.41/63.85 39 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),17(a,1,1))]. 63.41/63.85 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)])]. 63.41/63.85 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)])]. 63.41/63.85 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)])]. 63.41/63.85 45 mult(mult(A,mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(14(a,1),20(a,1,1,2,2)),rewrite([36(2),14(11),36(9)])]. 63.41/63.85 46 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(15(a,1),20(a,1,1,2,2)),rewrite([37(9)])]. 63.41/63.85 47 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(15(a,1),20(a,1,1)),flip(a)]. 63.41/63.85 50 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),17(a,1,1))]. 63.41/63.85 59 rd(mult(A,f(A)),A) = f(A). [para(36(a,1),17(a,1,1))]. 63.41/63.85 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(36(a,1),18(a,1,1)),rewrite([41(4),14(3)]),flip(a)]. 63.41/63.85 64 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),16(a,1,2))]. 63.41/63.85 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)]. 63.41/63.85 76 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(36(a,1),38(a,1,1)),rewrite([60(6)])]. 63.41/63.85 81 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(15(a,1),39(a,1,1,2))]. 63.41/63.85 84 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),39(a,2)),rewrite([41(3),66(4)])]. 63.41/63.85 85 mult(A,rd(f(A),A)) = f(A). [back_rewrite(59),rewrite([81(3)])]. 63.41/63.85 86 rd(f(A),A) = ld(A,f(A)). [para(85(a,1),16(a,1,2)),flip(a)]. 63.41/63.85 101 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(15(a,1),41(a,1,1)),flip(a)]. 63.41/63.85 145 mult(ld(A,unit),A) = unit. [para(12(a,1),64(a,1,2)),rewrite([29(1)]),flip(a)]. 63.41/63.85 147 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(15(a,1),64(a,1,2)),flip(a)]. 63.41/63.85 154 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),64(a,1,2)),rewrite([76(4)]),flip(a)]. 63.41/63.85 155 ld(ld(A,unit),unit) = A. [para(145(a,1),16(a,1,2))]. 63.41/63.85 156 rd(unit,A) = ld(A,unit). [para(145(a,1),17(a,1,1))]. 63.41/63.85 158 mult(ld(A,unit),mult(A,A)) = A. [para(145(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)]. 63.41/63.85 171 mult(mult(A,f(A)),mult(A,f(A))) = mult(A,mult(A,A)). [para(36(a,1),42(a,1,1,2)),rewrite([45(5),60(9)])]. 63.41/63.85 191 mult(ld(f(A),unit),A) = f(A). [para(14(a,1),158(a,1,2))]. 63.41/63.85 192 ld(ld(A,unit),A) = mult(A,A). [para(158(a,1),16(a,1,2))]. 63.41/63.85 203 ld(f(A),unit) = ld(A,f(A)). [para(191(a,1),17(a,1,1)),rewrite([86(2)]),flip(a)]. 63.41/63.85 204 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(191(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)]. 63.41/63.85 205 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(191(a,1),20(a,1,1,2,2)),rewrite([204(16),11(10)])]. 63.41/63.85 207 mult(mult(A,ld(f(B),unit)),mult(B,f(B))) = mult(A,B). [para(191(a,1),20(a,2,2,2)),rewrite([204(8),11(2)]),flip(a)]. 63.41/63.85 212 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(191(a,1),42(a,1,1,2)),rewrite([204(14),11(8)])]. 63.41/63.85 214 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(31(a,1),192(a,1,1)),rewrite([156(2),156(5),156(7)]),flip(a)]. 63.41/63.85 215 mult(mult(A,A),ld(A,unit)) = A. [para(192(a,1),64(a,2,1)),rewrite([13(5),155(4)]),flip(a)]. 63.41/63.85 240 mult(A,ld(f(A),unit)) = f(A). [para(203(a,2),13(a,1,2))]. 63.41/63.85 294 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(240(a,1),41(a,1,1)),rewrite([13(5),214(8)]),flip(a)]. 63.41/63.85 302 mult(mult(rd(A,mult(B,f(B))),f(B)),mult(B,f(B))) = mult(A,f(B)). [para(15(a,1),45(a,1,1)),flip(a)]. 63.41/63.85 314 mult(mult(A,mult(B,f(B))),B) = mult(mult(A,B),mult(B,f(B))). [para(45(a,1),41(a,1,1)),rewrite([45(7),41(4),14(3),14(10)]),flip(a)]. 63.41/63.85 393 mult(mult(A,mult(mult(B,C),mult(ld(C,D),D))),rd(ld(C,D),mult(B,mult(D,C)))) = mult(mult(A,mult(B,mult(D,C))),mult(ld(C,D),rd(ld(C,D),mult(B,mult(D,C))))). [para(44(a,1),46(a,1,1,2))]. 63.41/63.85 436 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(14(a,1),84(a,1,1,2))]. 63.41/63.85 437 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(15(a,1),84(a,1,1)),flip(a)]. 63.41/63.85 447 rd(mult(mult(A,B),mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(45(a,1),84(a,2)),rewrite([14(6),314(4)])]. 63.41/63.85 479 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = mult(A,ld(B,unit)). [para(158(a,1),47(a,1,1,1,2,2)),rewrite([18(2),215(11),145(8),11(7)])]. 63.41/63.85 498 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(101(a,1),16(a,1,2))]. 63.41/63.85 608 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(212(a,1),17(a,1,1))]. 63.41/63.85 611 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(212(a,1),41(a,1,1)),rewrite([240(4),214(10)]),flip(a)]. 63.41/63.85 739 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(294(a,1),16(a,1,2)),flip(a)]. 63.41/63.85 743 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(611),rewrite([739(7)])]. 63.41/63.85 773 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(145(a,1),50(a,1,1,1)),rewrite([12(4),81(3),17(2)]),flip(a)]. 63.41/63.85 877 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(15(a,1),436(a,1,1)),flip(a)]. 63.41/63.85 884 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(145(a,1),436(a,1,1)),rewrite([156(3)]),flip(a)]. 63.41/63.85 1025 mult(mult(rd(A,mult(B,mult(B,B))),f(B)),mult(B,f(B))) = mult(rd(A,mult(B,f(B))),f(B)). [para(437(a,1),45(a,1,1)),rewrite([171(10)]),flip(a)]. 63.41/63.85 1107 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(240(a,1),498(a,1,2)),rewrite([608(4),214(11),739(9)])]. 63.41/63.85 1134 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(154),rewrite([1107(4)])]. 63.41/63.85 1609 mult(A,ld(B,unit)) = rd(A,B). [para(743(a,1),47(a,1,2,2)),rewrite([1134(7),41(4),14(3),884(9),205(9),437(3)]),flip(a)]. 63.49/63.86 1661 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = rd(A,B). [back_rewrite(479),rewrite([1609(8)])]. 63.49/63.86 1663 mult(rd(A,f(B)),mult(B,f(B))) = mult(A,B). [back_rewrite(207),rewrite([1609(4)])]. 63.49/63.86 1664 rd(mult(A,mult(B,f(B))),f(B)) = mult(A,B). [back_rewrite(205),rewrite([1609(7)])]. 63.49/63.86 1683 mult(mult(A,f(B)),mult(B,f(B))) = mult(A,mult(B,B)). [back_rewrite(447),rewrite([1664(6),41(2)]),flip(a)]. 63.49/63.86 1701 mult(rd(A,mult(B,f(B))),f(B)) = rd(A,B). [back_rewrite(1025),rewrite([1683(8),1661(5)]),flip(a)]. 63.49/63.86 1743 mult(rd(A,B),mult(B,f(B))) = mult(A,f(B)). [back_rewrite(302),rewrite([1701(5)])]. 63.49/63.86 1766 ld(A,rd(A,B)) = ld(B,unit). [para(1609(a,1),16(a,1,2))]. 63.49/63.86 1851 ld(ld(A,B),unit) = ld(B,A). [para(33(a,1),1766(a,1,2)),flip(a)]. 63.49/63.86 2220 ld(rd(A,B),rd(A,f(B))) = f(B). [para(877(a,1),16(a,1,2))]. 63.49/63.86 3412 mult(ld(A,unit),B) = ld(A,B). [para(147(a,1),773(a,1,2,2)),rewrite([13(4),147(6)])]. 63.49/63.86 4028 rd(ld(A,B),B) = ld(A,unit). [para(3412(a,1),17(a,1,1))]. 63.49/63.86 4048 rd(mult(ld(A,B),mult(C,mult(B,C))),C) = ld(A,mult(B,mult(C,B))). [para(3412(a,1),50(a,1,1,1)),rewrite([3412(10)])]. 63.49/63.86 4069 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1851(a,1),3412(a,1,1)),flip(a)]. 63.49/63.86 4341 rd(A,mult(B,A)) = ld(B,unit). [para(16(a,1),4028(a,1,1))]. 63.49/63.86 4342 ld(rd(A,B),unit) = rd(B,A). [para(31(a,1),4028(a,1,1)),flip(a)]. 63.49/63.86 4356 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2220(a,1),4028(a,1,1)),rewrite([4342(7)])]. 63.49/63.86 4681 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4342(a,1),1609(a,1,2)),flip(a)]. 63.49/63.86 4689 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4356),rewrite([4681(4)])]. 63.49/63.86 18694 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(1743(a,1),393(a,1,2,2)),rewrite([877(3),30(4),36(4),1663(5),30(4),4341(6),1609(5),1743(7),30(8),30(9),1743(12),4341(11),1609(10),46(9),4689(8)])]. 63.49/63.86 18712 ld(A,mult(B,mult(C,B))) = mult(mult(ld(A,B),C),B). [back_rewrite(4048),rewrite([18694(5),17(4)]),flip(a)]. 63.49/63.86 24048 mult(A,mult(mult(ld(A,B),C),B)) = mult(B,mult(C,B)). [para(18712(a,1),13(a,1,2))]. 63.49/63.86 25433 mult(A,mult(mult(ld(A,B),C),A)) = mult(B,mult(C,A)). [para(13(a,1),24048(a,1,2,1)),rewrite([4069(4)]),flip(a)]. 63.49/63.86 26445 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(16(a,1),25433(a,1,2,1,1)),flip(a)]. 63.49/63.86 26446 $F # answer(goals). [resolve(26445,a,24,a)]. 63.49/63.86 63.49/63.86 % SZS output end Refutation 63.49/63.86 ============================== end of proof ========================== 63.49/63.86 63.49/63.86 ============================== PROOF ================================= 63.49/63.86 % SZS status Theorem 63.49/63.86 % SZS output start Refutation 63.49/63.86 63.49/63.86 % Proof 3 at 61.65 (+ 1.11) seconds: goals. 63.49/63.86 % Length of proof is 109. 63.49/63.86 % Level of proof is 23. 63.49/63.86 % Maximum clause weight is 43.000. 63.49/63.86 % Given clauses 1051. 63.49/63.86 63.49/63.86 1 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 63.49/63.86 2 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 63.49/63.86 3 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 63.49/63.86 4 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 63.49/63.86 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 63.49/63.86 6 (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]. 63.49/63.86 7 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 63.49/63.86 8 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 63.49/63.86 9 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 63.49/63.86 10 -((all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5)))) | (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 X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 63.49/63.86 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)]. 63.49/63.86 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(8)]. 63.49/63.86 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)]. 63.49/63.86 14 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(3)]. 63.49/63.86 15 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(4)]. 63.49/63.86 16 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(7)]. 63.49/63.86 17 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(9)]. 63.49/63.86 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(2)]. 63.49/63.86 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(6)]. 63.49/63.86 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)])]. 63.49/63.86 22 mult(mult(c6,mult(c4,c5)),c6) != mult(mult(c6,c4),mult(c5,c6)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)]. 63.49/63.86 23 mult(mult(c6,c4),mult(c5,c6)) != mult(c6,mult(mult(c4,c5),c6)) # answer(goals). [copy(22),rewrite([18(7)]),flip(a)]. 63.49/63.86 29 ld(A,A) = unit. [para(11(a,1),16(a,1,2))]. 63.49/63.86 30 ld(f(A),A) = f(A). [para(14(a,1),16(a,1,2))]. 63.49/63.86 31 ld(rd(A,B),A) = B. [para(15(a,1),16(a,1,2))]. 63.49/63.86 33 rd(A,ld(B,A)) = B. [para(13(a,1),17(a,1,1))]. 63.49/63.86 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)]. 63.49/63.86 36 mult(f(A),A) = mult(A,f(A)). [para(14(a,1),18(a,1,1)),rewrite([14(6)]),flip(a)]. 63.49/63.86 37 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(15(a,1),18(a,1,1)),flip(a)]. 63.49/63.86 38 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),16(a,1,2))]. 63.49/63.86 39 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),17(a,1,1))]. 63.49/63.86 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)])]. 63.49/63.86 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)])]. 63.49/63.86 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)])]. 63.49/63.86 45 mult(mult(A,mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(14(a,1),20(a,1,1,2,2)),rewrite([36(2),14(11),36(9)])]. 63.49/63.86 46 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(15(a,1),20(a,1,1,2,2)),rewrite([37(9)])]. 63.49/63.86 47 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(15(a,1),20(a,1,1)),flip(a)]. 63.49/63.86 50 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),17(a,1,1))]. 63.49/63.86 59 rd(mult(A,f(A)),A) = f(A). [para(36(a,1),17(a,1,1))]. 63.49/63.86 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(36(a,1),18(a,1,1)),rewrite([41(4),14(3)]),flip(a)]. 63.49/63.86 64 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),16(a,1,2))]. 63.49/63.86 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)]. 63.49/63.86 76 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(36(a,1),38(a,1,1)),rewrite([60(6)])]. 63.49/63.86 81 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(15(a,1),39(a,1,1,2))]. 63.49/63.86 84 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),39(a,2)),rewrite([41(3),66(4)])]. 63.49/63.86 85 mult(A,rd(f(A),A)) = f(A). [back_rewrite(59),rewrite([81(3)])]. 63.49/63.86 86 rd(f(A),A) = ld(A,f(A)). [para(85(a,1),16(a,1,2)),flip(a)]. 63.49/63.86 101 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(15(a,1),41(a,1,1)),flip(a)]. 63.49/63.86 145 mult(ld(A,unit),A) = unit. [para(12(a,1),64(a,1,2)),rewrite([29(1)]),flip(a)]. 63.49/63.86 147 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(15(a,1),64(a,1,2)),flip(a)]. 63.49/63.86 154 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),64(a,1,2)),rewrite([76(4)]),flip(a)]. 63.49/63.86 155 ld(ld(A,unit),unit) = A. [para(145(a,1),16(a,1,2))]. 63.49/63.86 156 rd(unit,A) = ld(A,unit). [para(145(a,1),17(a,1,1))]. 63.49/63.86 158 mult(ld(A,unit),mult(A,A)) = A. [para(145(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)]. 63.49/63.86 171 mult(mult(A,f(A)),mult(A,f(A))) = mult(A,mult(A,A)). [para(36(a,1),42(a,1,1,2)),rewrite([45(5),60(9)])]. 63.49/63.86 191 mult(ld(f(A),unit),A) = f(A). [para(14(a,1),158(a,1,2))]. 63.49/63.86 192 ld(ld(A,unit),A) = mult(A,A). [para(158(a,1),16(a,1,2))]. 63.49/63.86 203 ld(f(A),unit) = ld(A,f(A)). [para(191(a,1),17(a,1,1)),rewrite([86(2)]),flip(a)]. 63.49/63.86 204 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(191(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)]. 63.49/63.86 205 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(191(a,1),20(a,1,1,2,2)),rewrite([204(16),11(10)])]. 63.49/63.86 207 mult(mult(A,ld(f(B),unit)),mult(B,f(B))) = mult(A,B). [para(191(a,1),20(a,2,2,2)),rewrite([204(8),11(2)]),flip(a)]. 63.49/63.86 212 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(191(a,1),42(a,1,1,2)),rewrite([204(14),11(8)])]. 63.49/63.86 214 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(31(a,1),192(a,1,1)),rewrite([156(2),156(5),156(7)]),flip(a)]. 63.49/63.86 215 mult(mult(A,A),ld(A,unit)) = A. [para(192(a,1),64(a,2,1)),rewrite([13(5),155(4)]),flip(a)]. 63.49/63.86 240 mult(A,ld(f(A),unit)) = f(A). [para(203(a,2),13(a,1,2))]. 63.49/63.86 294 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(240(a,1),41(a,1,1)),rewrite([13(5),214(8)]),flip(a)]. 63.49/63.86 302 mult(mult(rd(A,mult(B,f(B))),f(B)),mult(B,f(B))) = mult(A,f(B)). [para(15(a,1),45(a,1,1)),flip(a)]. 63.49/63.86 314 mult(mult(A,mult(B,f(B))),B) = mult(mult(A,B),mult(B,f(B))). [para(45(a,1),41(a,1,1)),rewrite([45(7),41(4),14(3),14(10)]),flip(a)]. 63.49/63.86 393 mult(mult(A,mult(mult(B,C),mult(ld(C,D),D))),rd(ld(C,D),mult(B,mult(D,C)))) = mult(mult(A,mult(B,mult(D,C))),mult(ld(C,D),rd(ld(C,D),mult(B,mult(D,C))))). [para(44(a,1),46(a,1,1,2))]. 63.49/63.86 436 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(14(a,1),84(a,1,1,2))]. 63.49/63.86 437 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(15(a,1),84(a,1,1)),flip(a)]. 63.49/63.86 447 rd(mult(mult(A,B),mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(45(a,1),84(a,2)),rewrite([14(6),314(4)])]. 63.49/63.86 479 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = mult(A,ld(B,unit)). [para(158(a,1),47(a,1,1,1,2,2)),rewrite([18(2),215(11),145(8),11(7)])]. 63.49/63.86 498 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(101(a,1),16(a,1,2))]. 63.49/63.86 608 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(212(a,1),17(a,1,1))]. 63.49/63.86 611 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(212(a,1),41(a,1,1)),rewrite([240(4),214(10)]),flip(a)]. 63.49/63.86 739 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(294(a,1),16(a,1,2)),flip(a)]. 63.49/63.86 743 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(611),rewrite([739(7)])]. 63.49/63.86 773 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(145(a,1),50(a,1,1,1)),rewrite([12(4),81(3),17(2)]),flip(a)]. 63.49/63.86 877 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(15(a,1),436(a,1,1)),flip(a)]. 63.49/63.86 884 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(145(a,1),436(a,1,1)),rewrite([156(3)]),flip(a)]. 63.49/63.86 1025 mult(mult(rd(A,mult(B,mult(B,B))),f(B)),mult(B,f(B))) = mult(rd(A,mult(B,f(B))),f(B)). [para(437(a,1),45(a,1,1)),rewrite([171(10)]),flip(a)]. 63.49/63.86 1107 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(240(a,1),498(a,1,2)),rewrite([608(4),214(11),739(9)])]. 63.49/63.86 1134 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(154),rewrite([1107(4)])]. 63.49/63.86 1609 mult(A,ld(B,unit)) = rd(A,B). [para(743(a,1),47(a,1,2,2)),rewrite([1134(7),41(4),14(3),884(9),205(9),437(3)]),flip(a)]. 63.49/63.86 1661 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = rd(A,B). [back_rewrite(479),rewrite([1609(8)])]. 63.49/63.86 1663 mult(rd(A,f(B)),mult(B,f(B))) = mult(A,B). [back_rewrite(207),rewrite([1609(4)])]. 63.49/63.86 1664 rd(mult(A,mult(B,f(B))),f(B)) = mult(A,B). [back_rewrite(205),rewrite([1609(7)])]. 63.49/63.86 1683 mult(mult(A,f(B)),mult(B,f(B))) = mult(A,mult(B,B)). [back_rewrite(447),rewrite([1664(6),41(2)]),flip(a)]. 63.49/63.86 1701 mult(rd(A,mult(B,f(B))),f(B)) = rd(A,B). [back_rewrite(1025),rewrite([1683(8),1661(5)]),flip(a)]. 63.49/63.86 1743 mult(rd(A,B),mult(B,f(B))) = mult(A,f(B)). [back_rewrite(302),rewrite([1701(5)])]. 63.49/63.86 1766 ld(A,rd(A,B)) = ld(B,unit). [para(1609(a,1),16(a,1,2))]. 63.49/63.86 1851 ld(ld(A,B),unit) = ld(B,A). [para(33(a,1),1766(a,1,2)),flip(a)]. 63.49/63.86 2220 ld(rd(A,B),rd(A,f(B))) = f(B). [para(877(a,1),16(a,1,2))]. 63.49/63.86 3412 mult(ld(A,unit),B) = ld(A,B). [para(147(a,1),773(a,1,2,2)),rewrite([13(4),147(6)])]. 63.49/63.86 4028 rd(ld(A,B),B) = ld(A,unit). [para(3412(a,1),17(a,1,1))]. 63.49/63.86 4048 rd(mult(ld(A,B),mult(C,mult(B,C))),C) = ld(A,mult(B,mult(C,B))). [para(3412(a,1),50(a,1,1,1)),rewrite([3412(10)])]. 63.49/63.86 4069 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1851(a,1),3412(a,1,1)),flip(a)]. 63.49/63.86 4341 rd(A,mult(B,A)) = ld(B,unit). [para(16(a,1),4028(a,1,1))]. 63.49/63.86 4342 ld(rd(A,B),unit) = rd(B,A). [para(31(a,1),4028(a,1,1)),flip(a)]. 63.49/63.86 4356 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2220(a,1),4028(a,1,1)),rewrite([4342(7)])]. 63.49/63.86 4681 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4342(a,1),1609(a,1,2)),flip(a)]. 63.49/63.86 4689 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4356),rewrite([4681(4)])]. 63.87/64.25 18694 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(1743(a,1),393(a,1,2,2)),rewrite([877(3),30(4),36(4),1663(5),30(4),4341(6),1609(5),1743(7),30(8),30(9),1743(12),4341(11),1609(10),46(9),4689(8)])]. 63.87/64.25 18712 ld(A,mult(B,mult(C,B))) = mult(mult(ld(A,B),C),B). [back_rewrite(4048),rewrite([18694(5),17(4)]),flip(a)]. 63.87/64.25 24048 mult(A,mult(mult(ld(A,B),C),B)) = mult(B,mult(C,B)). [para(18712(a,1),13(a,1,2))]. 63.87/64.25 25433 mult(A,mult(mult(ld(A,B),C),A)) = mult(B,mult(C,A)). [para(13(a,1),24048(a,1,2,1)),rewrite([4069(4)]),flip(a)]. 63.87/64.25 26445 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(16(a,1),25433(a,1,2,1,1)),flip(a)]. 63.87/64.25 26447 $F # answer(goals). [resolve(26445,a,23,a)]. 63.87/64.25 63.87/64.25 % SZS output end Refutation 63.87/64.25 ============================== end of proof ========================== 63.87/64.25 % Redundant proof: 26479 $F # answer(goals). [back_rewrite(24),rewrite([26445(7)]),xx(a)]. 63.87/64.25 % Redundant proof: 26480 $F # answer(goals). [back_rewrite(23),rewrite([26445(7)]),xx(a)]. 63.87/64.25 63.87/64.25 % Disable descendants (x means already disabled): 63.87/64.25 22x 23x 24x 63.87/64.25 63.87/64.25 ============================== PROOF ================================= 63.87/64.25 % SZS status Theorem 63.87/64.25 % SZS output start Refutation 63.87/64.25 63.87/64.25 % Proof 4 at 62.04 (+ 1.12) seconds: goals. 63.87/64.25 % Length of proof is 150. 63.87/64.25 % Level of proof is 25. 63.87/64.25 % Maximum clause weight is 43.000. 63.87/64.25 % Given clauses 1060. 63.87/64.25 63.87/64.25 1 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 63.87/64.25 2 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 63.87/64.25 3 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption]. 63.87/64.25 4 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 63.87/64.25 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 63.87/64.25 6 (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]. 63.87/64.25 7 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 63.87/64.25 8 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 63.87/64.25 9 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 63.87/64.25 10 -((all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5)))) | (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 X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 63.87/64.25 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)]. 63.87/64.25 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(8)]. 63.87/64.25 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)]. 63.87/64.25 14 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(3)]. 63.87/64.25 15 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(4)]. 63.87/64.25 16 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(7)]. 63.87/64.25 17 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(9)]. 63.87/64.25 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(2)]. 63.87/64.25 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(6)]. 63.87/64.25 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)])]. 63.87/64.25 25 mult(mult(mult(c12,c10),c12),c11) != mult(c12,mult(c10,mult(c12,c11))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)]. 63.87/64.25 26 mult(mult(c12,mult(c10,c12)),c11) != mult(c12,mult(c10,mult(c12,c11))) # answer(goals). [copy(25),rewrite([18(5)])]. 63.87/64.25 29 ld(A,A) = unit. [para(11(a,1),16(a,1,2))]. 63.87/64.25 30 ld(f(A),A) = f(A). [para(14(a,1),16(a,1,2))]. 63.87/64.25 31 ld(rd(A,B),A) = B. [para(15(a,1),16(a,1,2))]. 63.87/64.25 33 rd(A,ld(B,A)) = B. [para(13(a,1),17(a,1,1))]. 63.87/64.25 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)]. 63.87/64.25 36 mult(f(A),A) = mult(A,f(A)). [para(14(a,1),18(a,1,1)),rewrite([14(6)]),flip(a)]. 63.87/64.25 37 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(15(a,1),18(a,1,1)),flip(a)]. 63.87/64.25 38 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),16(a,1,2))]. 63.87/64.25 39 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),17(a,1,1))]. 63.87/64.25 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))]. 63.87/64.25 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)])]. 63.87/64.25 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)])]. 63.87/64.25 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)])]. 63.87/64.25 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)])]. 63.87/64.25 45 mult(mult(A,mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(14(a,1),20(a,1,1,2,2)),rewrite([36(2),14(11),36(9)])]. 63.87/64.25 46 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(15(a,1),20(a,1,1,2,2)),rewrite([37(9)])]. 63.87/64.25 47 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(15(a,1),20(a,1,1)),flip(a)]. 63.87/64.25 50 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),17(a,1,1))]. 63.87/64.25 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))]. 63.87/64.25 59 rd(mult(A,f(A)),A) = f(A). [para(36(a,1),17(a,1,1))]. 63.87/64.25 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(36(a,1),18(a,1,1)),rewrite([41(4),14(3)]),flip(a)]. 63.87/64.25 64 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),16(a,1,2))]. 63.87/64.25 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)]. 63.87/64.25 76 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(36(a,1),38(a,1,1)),rewrite([60(6)])]. 63.87/64.25 78 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(35(a,1),38(a,1,1)),rewrite([41(4),66(5)])]. 63.87/64.25 81 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(15(a,1),39(a,1,1,2))]. 63.87/64.25 84 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),39(a,2)),rewrite([41(3),66(4)])]. 63.87/64.25 85 mult(A,rd(f(A),A)) = f(A). [back_rewrite(59),rewrite([81(3)])]. 63.87/64.25 86 rd(f(A),A) = ld(A,f(A)). [para(85(a,1),16(a,1,2)),flip(a)]. 63.87/64.25 94 mult(ld(A,f(A)),A) = f(A). [para(86(a,1),15(a,1,1))]. 63.87/64.25 96 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(86(a,1),37(a,1,1)),rewrite([86(4),13(5),86(7)])]. 63.87/64.25 101 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(15(a,1),41(a,1,1)),flip(a)]. 63.87/64.25 145 mult(ld(A,unit),A) = unit. [para(12(a,1),64(a,1,2)),rewrite([29(1)]),flip(a)]. 63.87/64.25 147 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(15(a,1),64(a,1,2)),flip(a)]. 63.87/64.25 154 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),64(a,1,2)),rewrite([76(4)]),flip(a)]. 63.87/64.25 155 ld(ld(A,unit),unit) = A. [para(145(a,1),16(a,1,2))]. 63.87/64.25 156 rd(unit,A) = ld(A,unit). [para(145(a,1),17(a,1,1))]. 63.87/64.25 158 mult(ld(A,unit),mult(A,A)) = A. [para(145(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)]. 63.87/64.25 171 mult(mult(A,f(A)),mult(A,f(A))) = mult(A,mult(A,A)). [para(36(a,1),42(a,1,1,2)),rewrite([45(5),60(9)])]. 63.87/64.25 191 mult(ld(f(A),unit),A) = f(A). [para(14(a,1),158(a,1,2))]. 63.87/64.25 192 ld(ld(A,unit),A) = mult(A,A). [para(158(a,1),16(a,1,2))]. 63.87/64.25 203 ld(f(A),unit) = ld(A,f(A)). [para(191(a,1),17(a,1,1)),rewrite([86(2)]),flip(a)]. 63.87/64.25 204 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(191(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)]. 63.87/64.25 205 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(191(a,1),20(a,1,1,2,2)),rewrite([204(16),11(10)])]. 63.87/64.25 207 mult(mult(A,ld(f(B),unit)),mult(B,f(B))) = mult(A,B). [para(191(a,1),20(a,2,2,2)),rewrite([204(8),11(2)]),flip(a)]. 63.87/64.25 212 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(191(a,1),42(a,1,1,2)),rewrite([204(14),11(8)])]. 63.87/64.25 214 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(31(a,1),192(a,1,1)),rewrite([156(2),156(5),156(7)]),flip(a)]. 63.87/64.25 215 mult(mult(A,A),ld(A,unit)) = A. [para(192(a,1),64(a,2,1)),rewrite([13(5),155(4)]),flip(a)]. 63.87/64.25 239 mult(f(A),ld(A,f(A))) = unit. [para(203(a,1),13(a,1,2))]. 63.87/64.25 240 mult(A,ld(f(A),unit)) = f(A). [para(203(a,2),13(a,1,2))]. 63.87/64.25 248 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(96),rewrite([239(8)])]. 63.87/64.25 294 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(240(a,1),41(a,1,1)),rewrite([13(5),214(8)]),flip(a)]. 63.87/64.25 302 mult(mult(rd(A,mult(B,f(B))),f(B)),mult(B,f(B))) = mult(A,f(B)). [para(15(a,1),45(a,1,1)),flip(a)]. 63.87/64.25 314 mult(mult(A,mult(B,f(B))),B) = mult(mult(A,B),mult(B,f(B))). [para(45(a,1),41(a,1,1)),rewrite([45(7),41(4),14(3),14(10)]),flip(a)]. 63.87/64.25 393 mult(mult(A,mult(mult(B,C),mult(ld(C,D),D))),rd(ld(C,D),mult(B,mult(D,C)))) = mult(mult(A,mult(B,mult(D,C))),mult(ld(C,D),rd(ld(C,D),mult(B,mult(D,C))))). [para(44(a,1),46(a,1,1,2))]. 63.87/64.25 399 ld(mult(A,f(B)),mult(A,B)) = f(B). [para(14(a,1),78(a,1,2,2))]. 63.87/64.25 436 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(14(a,1),84(a,1,1,2))]. 63.87/64.25 437 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(15(a,1),84(a,1,1)),flip(a)]. 63.87/64.25 447 rd(mult(mult(A,B),mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(45(a,1),84(a,2)),rewrite([14(6),314(4)])]. 63.87/64.25 465 mult(rd(A,mult(B,f(B))),B) = mult(A,ld(B,f(B))). [para(94(a,1),47(a,1,1,1,2,2)),rewrite([13(9),248(8),11(6)])]. 63.87/64.25 479 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = mult(A,ld(B,unit)). [para(158(a,1),47(a,1,1,1,2,2)),rewrite([18(2),215(11),145(8),11(7)])]. 63.87/64.25 480 mult(A,ld(f(B),unit)) = mult(A,ld(B,f(B))). [para(191(a,1),47(a,1,1,1,2,2)),rewrite([465(4),240(10),145(8),11(5)]),flip(a)]. 63.87/64.25 498 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(101(a,1),16(a,1,2))]. 63.87/64.25 608 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(212(a,1),17(a,1,1))]. 63.87/64.25 611 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(212(a,1),41(a,1,1)),rewrite([240(4),214(10)]),flip(a)]. 63.87/64.25 739 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(294(a,1),16(a,1,2)),flip(a)]. 63.87/64.25 743 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(611),rewrite([739(7)])]. 63.87/64.25 773 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(145(a,1),50(a,1,1,1)),rewrite([12(4),81(3),17(2)]),flip(a)]. 63.87/64.25 877 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(15(a,1),436(a,1,1)),flip(a)]. 63.87/64.25 884 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(145(a,1),436(a,1,1)),rewrite([156(3)]),flip(a)]. 63.87/64.25 1025 mult(mult(rd(A,mult(B,mult(B,B))),f(B)),mult(B,f(B))) = mult(rd(A,mult(B,f(B))),f(B)). [para(437(a,1),45(a,1,1)),rewrite([171(10)]),flip(a)]. 63.87/64.25 1107 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(240(a,1),498(a,1,2)),rewrite([608(4),214(11),739(9)])]. 63.87/64.25 1134 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(154),rewrite([1107(4)])]. 63.87/64.25 1609 mult(A,ld(B,unit)) = rd(A,B). [para(743(a,1),47(a,1,2,2)),rewrite([1134(7),41(4),14(3),884(9),205(9),437(3)]),flip(a)]. 63.87/64.25 1660 mult(A,ld(B,f(B))) = rd(A,f(B)). [back_rewrite(480),rewrite([1609(4)]),flip(a)]. 63.87/64.25 1661 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = rd(A,B). [back_rewrite(479),rewrite([1609(8)])]. 63.87/64.25 1663 mult(rd(A,f(B)),mult(B,f(B))) = mult(A,B). [back_rewrite(207),rewrite([1609(4)])]. 63.87/64.25 1664 rd(mult(A,mult(B,f(B))),f(B)) = mult(A,B). [back_rewrite(205),rewrite([1609(7)])]. 63.87/64.25 1683 mult(mult(A,f(B)),mult(B,f(B))) = mult(A,mult(B,B)). [back_rewrite(447),rewrite([1664(6),41(2)]),flip(a)]. 63.87/64.25 1701 mult(rd(A,mult(B,f(B))),f(B)) = rd(A,B). [back_rewrite(1025),rewrite([1683(8),1661(5)]),flip(a)]. 63.87/64.25 1743 mult(rd(A,B),mult(B,f(B))) = mult(A,f(B)). [back_rewrite(302),rewrite([1701(5)])]. 63.87/64.25 1766 ld(A,rd(A,B)) = ld(B,unit). [para(1609(a,1),16(a,1,2))]. 63.87/64.25 1850 ld(mult(A,B),A) = ld(B,unit). [para(17(a,1),1766(a,1,2))]. 63.87/64.25 1851 ld(ld(A,B),unit) = ld(B,A). [para(33(a,1),1766(a,1,2)),flip(a)]. 63.87/64.25 2053 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(1851(a,1),1609(a,1,2)),flip(a)]. 63.87/64.25 2220 ld(rd(A,B),rd(A,f(B))) = f(B). [para(877(a,1),16(a,1,2))]. 63.87/64.25 2630 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(1660(a,1),43(a,1,1,2)),flip(a)]. 63.87/64.25 3391 mult(ld(A,unit),mult(A,B)) = B. [para(15(a,1),773(a,1,2,2)),rewrite([15(6)])]. 63.87/64.25 3400 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),773(a,1,2))]. 63.87/64.25 3402 mult(mult(A,B),mult(ld(B,A),B)) = mult(A,mult(A,B)). [para(773(a,1),40(a,1,2)),rewrite([1609(7),81(5),17(4),3391(4),3391(7),3391(10),3400(7)]),flip(a)]. 63.87/64.25 3412 mult(ld(A,unit),B) = ld(A,B). [para(147(a,1),773(a,1,2,2)),rewrite([13(4),147(6)])]. 63.87/64.25 3426 mult(mult(A,ld(B,C)),mult(C,B)) = mult(rd(A,B),mult(C,mult(C,B))). [para(773(a,1),53(a,1,2)),rewrite([1609(9),81(7),17(6),3412(6),16(4),3412(3),1609(7),3412(10),16(8),3412(13),16(11),3412(10),64(8),3402(9)])]. 63.87/64.26 3675 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(2630),rewrite([3426(8)])]. 63.87/64.26 4028 rd(ld(A,B),B) = ld(A,unit). [para(3412(a,1),17(a,1,1))]. 63.87/64.26 4034 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(3412(a,1),41(a,1,1)),rewrite([3412(6)]),flip(a)]. 63.87/64.26 4038 mult(ld(A,f(A)),B) = ld(f(A),B). [para(203(a,1),3412(a,1,1))]. 63.87/64.26 4048 rd(mult(ld(A,B),mult(C,mult(B,C))),C) = ld(A,mult(B,mult(C,B))). [para(3412(a,1),50(a,1,1,1)),rewrite([3412(10)])]. 63.87/64.26 4050 ld(ld(A,f(B)),ld(A,B)) = f(B). [para(3412(a,1),399(a,1,1)),rewrite([3412(5)])]. 63.87/64.26 4064 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [para(3412(a,1),1609(a,1)),flip(a)]. 63.87/64.26 4069 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1851(a,1),3412(a,1,1)),flip(a)]. 63.87/64.26 4100 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(3675),rewrite([4038(6),4038(6)]),flip(a)]. 63.87/64.26 4158 mult(ld(f(A),B),ld(B,A)) = f(A). [back_rewrite(4050),rewrite([4069(4)])]. 63.87/64.26 4341 rd(A,mult(B,A)) = ld(B,unit). [para(16(a,1),4028(a,1,1))]. 63.87/64.26 4342 ld(rd(A,B),unit) = rd(B,A). [para(31(a,1),4028(a,1,1)),flip(a)]. 63.87/64.26 4353 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(1850(a,1),4028(a,1,1)),rewrite([4064(3)]),flip(a)]. 63.87/64.26 4356 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2220(a,1),4028(a,1,1)),rewrite([4342(7)])]. 63.87/64.26 4681 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4342(a,1),1609(a,1,2)),flip(a)]. 63.87/64.26 4685 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4342(a,1),3412(a,1,1)),flip(a)]. 63.87/64.26 4689 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4356),rewrite([4681(4)])]. 63.87/64.26 5035 rd(ld(A,ld(B,f(B))),f(B)) = ld(A,ld(B,unit)). [para(1660(a,1),4034(a,1,2)),rewrite([4028(4),1660(9)]),flip(a)]. 63.87/64.26 5391 mult(rd(A,B),ld(f(C),ld(f(C),B))) = mult(mult(A,ld(B,ld(C,unit))),B). [back_rewrite(4100),rewrite([5035(5)]),flip(a)]. 63.87/64.26 5859 ld(f(A),ld(f(A),B)) = ld(A,B). [para(4158(a,1),1850(a,1,1)),rewrite([4069(7),11(7)])]. 63.87/64.26 5877 mult(mult(A,ld(B,ld(C,unit))),B) = mult(rd(A,B),ld(C,B)). [back_rewrite(5391),rewrite([5859(5)]),flip(a)]. 63.87/64.26 6074 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(4353(a,1),1609(a,1,2))]. 63.87/64.26 6083 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [back_rewrite(5877),rewrite([6074(4)])]. 63.87/64.26 18694 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(1743(a,1),393(a,1,2,2)),rewrite([877(3),30(4),36(4),1663(5),30(4),4341(6),1609(5),1743(7),30(8),30(9),1743(12),4341(11),1609(10),46(9),4689(8)])]. 63.87/64.26 18712 ld(A,mult(B,mult(C,B))) = mult(mult(ld(A,B),C),B). [back_rewrite(4048),rewrite([18694(5),17(4)]),flip(a)]. 63.87/64.26 19946 mult(rd(mult(A,B),C),mult(rd(C,B),ld(A,B))) = B. [para(6083(a,1),16(a,1,2)),rewrite([4685(6)])]. 63.87/64.26 24048 mult(A,mult(mult(ld(A,B),C),B)) = mult(B,mult(C,B)). [para(18712(a,1),13(a,1,2))]. 63.87/64.26 24051 mult(A,mult(mult(mult(ld(A,B),C),B),A)) = mult(mult(B,mult(C,B)),A). [para(18712(a,1),35(a,1,2,1))]. 63.87/64.26 24457 mult(mult(mult(A,B),ld(B,C)),ld(C,ld(A,B))) = B. [para(4028(a,1),19946(a,1,2,1)),rewrite([2053(3),3412(7)])]. 63.87/64.26 25433 mult(A,mult(mult(ld(A,B),C),A)) = mult(B,mult(C,A)). [para(13(a,1),24048(a,1,2,1)),rewrite([4069(4)]),flip(a)]. 63.87/64.26 25434 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(mult(B,C),mult(A,B))). [para(16(a,1),24048(a,1,2,1,1)),flip(a)]. 63.87/64.26 25679 mult(mult(A,B),ld(B,C)) = mult(B,mult(ld(B,A),C)). [para(24457(a,1),17(a,1,1)),rewrite([2053(3),4069(2)]),flip(a)]. 63.87/64.26 26445 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(16(a,1),25433(a,1,2,1,1)),flip(a)]. 63.87/64.26 26478 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))). [back_rewrite(25434),rewrite([26445(7)])]. 63.87/64.26 26587 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [para(25679(a,1),18(a,1,1)),rewrite([26445(5),24051(5),26478(8),25433(7)])]. 63.87/64.26 26588 $F # answer(goals). [resolve(26587,a,26,a)]. 63.87/64.26 63.87/64.26 % SZS output end Refutation 63.87/64.26 ============================== end of proof ========================== 63.87/64.26 63.87/64.26 ============================== STATISTICS ============================ 63.87/64.26 63.87/64.26 Given=1060. Generated=922439. Kept=26568. proofs=4. 63.87/64.26 Usable=633. Sos=8765. Demods=8830. Limbo=1, Disabled=17181. Hints=0. 63.87/64.26 Megabytes=27.79. 63.87/64.26 User_CPU=62.04, System_CPU=1.12, Wall_clock=63. 63.87/64.26 63.87/64.26 ============================== end of statistics ===================== 63.87/64.26 63.87/64.26 ============================== end of search ========================= 63.87/64.26 63.87/64.26 THEOREM PROVED 63.87/64.26 % SZS status Theorem 63.87/64.26 63.87/64.26 Exiting with 4 proofs. 63.87/64.26 63.87/64.26 Process 24895 exit (max_proofs) Thu Jul 2 07:49:15 2020 63.87/64.26 Prover9 interrupted 63.87/64.26 EOF