0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.32 % Computer : n017.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 : 960 0.12/0.32 % WCLimit : 120 0.12/0.32 % DateTime : Tue Aug 9 04:22:45 EDT 2022 0.12/0.32 % CPUTime : 3.33/3.63 ============================== Prover9 =============================== 3.33/3.63 Prover9 (32) version 2009-11A, November 2009. 3.33/3.63 Process 16616 was started by sandbox on n017.cluster.edu, 3.33/3.63 Tue Aug 9 04:22:45 2022 3.33/3.63 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_16234_n017.cluster.edu". 3.33/3.63 ============================== end of head =========================== 3.33/3.63 3.33/3.63 ============================== INPUT ================================= 3.33/3.63 3.33/3.63 % Reading from file /tmp/Prover9_16234_n017.cluster.edu 3.33/3.63 3.33/3.63 set(prolog_style_variables). 3.33/3.63 set(auto2). 3.33/3.63 % set(auto2) -> set(auto). 3.33/3.63 % set(auto) -> set(auto_inference). 3.33/3.63 % set(auto) -> set(auto_setup). 3.33/3.63 % set(auto_setup) -> set(predicate_elim). 3.33/3.63 % set(auto_setup) -> assign(eq_defs, unfold). 3.33/3.63 % set(auto) -> set(auto_limits). 3.33/3.63 % set(auto_limits) -> assign(max_weight, "100.000"). 3.33/3.63 % set(auto_limits) -> assign(sos_limit, 20000). 3.33/3.63 % set(auto) -> set(auto_denials). 3.33/3.63 % set(auto) -> set(auto_process). 3.33/3.63 % set(auto2) -> assign(new_constants, 1). 3.33/3.63 % set(auto2) -> assign(fold_denial_max, 3). 3.33/3.63 % set(auto2) -> assign(max_weight, "200.000"). 3.33/3.63 % set(auto2) -> assign(max_hours, 1). 3.33/3.63 % assign(max_hours, 1) -> assign(max_seconds, 3600). 3.33/3.63 % set(auto2) -> assign(max_seconds, 0). 3.33/3.63 % set(auto2) -> assign(max_minutes, 5). 3.33/3.63 % assign(max_minutes, 5) -> assign(max_seconds, 300). 3.33/3.63 % set(auto2) -> set(sort_initial_sos). 3.33/3.63 % set(auto2) -> assign(sos_limit, -1). 3.33/3.63 % set(auto2) -> assign(lrs_ticks, 3000). 3.33/3.63 % set(auto2) -> assign(max_megs, 400). 3.33/3.63 % set(auto2) -> assign(stats, some). 3.33/3.63 % set(auto2) -> clear(echo_input). 3.33/3.63 % set(auto2) -> set(quiet). 3.33/3.63 % set(auto2) -> clear(print_initial_clauses). 3.33/3.63 % set(auto2) -> clear(print_given). 3.33/3.63 assign(lrs_ticks,-1). 3.33/3.63 assign(sos_limit,10000). 3.33/3.63 assign(order,kbo). 3.33/3.63 set(lex_order_vars). 3.33/3.63 clear(print_given). 3.33/3.63 3.33/3.63 % formulas(sos). % not echoed (6 formulas) 3.33/3.63 3.33/3.63 ============================== end of input ========================== 3.33/3.63 3.33/3.63 % From the command line: assign(max_seconds, 960). 3.33/3.63 3.33/3.63 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 3.33/3.63 3.33/3.63 % Formulas that are not ordinary clauses: 3.33/3.63 1 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 3.33/3.63 2 (all C all B all A mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B)))) # label(f05) # label(axiom) # label(non_clause). [assumption]. 3.33/3.63 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 3.33/3.63 4 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 3.33/3.63 5 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 3.33/3.63 6 -(all X0 all X1 (X0 = mult(rd(X1,X1),X0) & X0 = mult(X0,rd(X1,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 3.33/3.63 3.33/3.63 ============================== end of process non-clausal formulas === 3.33/3.63 3.33/3.63 ============================== PROCESS INITIAL CLAUSES =============== 3.33/3.63 3.33/3.63 ============================== PREDICATE ELIMINATION ================= 3.33/3.63 3.33/3.63 ============================== end predicate elimination ============= 3.33/3.63 3.33/3.63 Auto_denials: 3.33/3.63 % copying label goals to answer in negative clause 3.33/3.63 3.33/3.63 Term ordering decisions: 3.33/3.63 Function symbol KB weights: c1=1. c2=1. mult=1. ld=1. rd=1. 3.33/3.63 3.33/3.63 ============================== end of process initial clauses ======== 3.33/3.63 3.33/3.63 ============================== CLAUSES FOR SEARCH ==================== 3.33/3.63 3.33/3.63 ============================== end of clauses for search ============= 3.33/3.63 3.33/3.63 ============================== SEARCH ================================ 3.33/3.63 3.33/3.63 % Starting search at 0.01 seconds. 3.33/3.63 3.33/3.63 Low Water (keep): wt=91.000, iters=3419 3.33/3.63 3.33/3.63 Low Water (keep): wt=75.000, iters=3335 3.33/3.63 3.33/3.63 Low Water (keep): wt=67.000, iters=3345 3.33/3.63 3.33/3.63 Low Water (keep): wt=63.000, iters=3345 3.33/3.63 3.33/3.63 Low Water (keep): wt=59.000, iters=3365 3.33/3.63 3.33/3.63 Low Water (keep): wt=55.000, iters=3400 3.33/3.63 3.33/3.63 Low Water (keep): wt=51.000, iters=3377 3.33/3.63 3.33/3.63 Low Water (keep): wt=47.000, iters=3338 3.33/3.63 3.33/3.63 Low Water (keep): wt=43.000, iters=3356 3.33/3.63 3.33/3.63 Low Water (keep): wt=39.000, iters=3351 3.33/3.63 3.33/3.63 Low Water (keep): wt=35.000, iters=3357 3.33/3.63 3.33/3.63 Low Water (keep): wt=31.000, iters=3351 3.33/3.63 3.33/3.63 Low Water (displace): id=6847, wt=191.000 25.92/26.27 25.92/26.27 Low Water (displace): id=2395, wt=183.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6845, wt=179.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6843, wt=171.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6841, wt=151.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6812, wt=147.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6825, wt=143.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6831, wt=139.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6805, wt=135.000 25.92/26.27 25.92/26.27 Low Water (displace): id=2396, wt=131.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6819, wt=127.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6773, wt=123.000 25.92/26.27 25.92/26.27 Low Water (displace): id=6833, wt=119.000 25.92/26.27 25.92/26.27 Low Water (displace): id=12817, wt=27.000 25.92/26.27 25.92/26.27 Low Water (displace): id=12819, wt=23.000 25.92/26.27 25.92/26.27 Low Water (displace): id=12958, wt=19.000 25.92/26.27 25.92/26.27 Low Water (keep): wt=27.000, iters=3349 25.92/26.27 25.92/26.27 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 8.06 sec). 25.92/26.27 25.92/26.27 ============================== PROOF ================================= 25.92/26.27 % SZS status Theorem 25.92/26.27 % SZS output start Refutation 25.92/26.27 25.92/26.27 % Proof 1 at 24.75 (+ 0.58) seconds: goals. 25.92/26.27 % Length of proof is 192. 25.92/26.27 % Level of proof is 33. 25.92/26.27 % Maximum clause weight is 35.000. 25.92/26.27 % Given clauses 852. 25.92/26.27 25.92/26.27 1 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 25.92/26.27 2 (all C all B all A mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B)))) # label(f05) # label(axiom) # label(non_clause). [assumption]. 25.92/26.27 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 25.92/26.27 4 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 25.92/26.27 5 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption]. 25.92/26.27 6 -(all X0 all X1 (X0 = mult(rd(X1,X1),X0) & X0 = mult(X0,rd(X1,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 25.92/26.27 7 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(1)]. 25.92/26.27 8 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)]. 25.92/26.27 9 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(4)]. 25.92/26.27 10 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(5)]. 25.92/26.27 11 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))) # label(f05) # label(axiom). [clausify(2)]. 25.92/26.27 12 mult(rd(c2,c2),c1) != c1 | mult(c1,rd(c2,c2)) != c1 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(6)]. 25.92/26.27 13 ld(rd(A,B),A) = B. [para(8(a,1),7(a,1,2))]. 25.92/26.27 14 rd(A,ld(B,A)) = B. [para(9(a,1),10(a,1,1))]. 25.92/26.27 15 ld(mult(mult(A,B),C),mult(A,mult(B,mult(C,B)))) = B. [para(11(a,1),7(a,1,2))]. 25.92/26.27 16 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(8(a,1),11(a,1,1,1)),flip(a)]. 25.92/26.27 17 mult(A,mult(ld(A,B),mult(C,ld(A,B)))) = mult(mult(B,C),ld(A,B)). [para(9(a,1),11(a,1,1,1)),flip(a)]. 25.92/26.27 18 mult(A,mult(B,mult(ld(mult(A,B),C),B))) = mult(C,B). [para(9(a,1),11(a,1,1)),flip(a)]. 25.92/26.27 19 rd(mult(A,mult(B,mult(C,B))),B) = mult(mult(A,B),C). [para(11(a,1),10(a,1,1))]. 25.92/26.27 20 mult(mult(mult(A,mult(B,mult(C,B))),D),B) = mult(mult(mult(A,B),C),mult(B,mult(D,B))). [para(11(a,1),11(a,1,1,1))]. 25.92/26.27 21 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [para(11(a,1),11(a,1,1))]. 25.92/26.27 22 mult(A,mult(mult(B,mult(C,B)),mult(D,mult(B,mult(C,B))))) = mult(A,mult(B,mult(mult(C,mult(mult(B,mult(D,B)),C)),B))). [para(11(a,1),11(a,2)),rewrite([20(5),11(6),11(7)]),flip(a)]. 25.92/26.27 23 ld(mult(mult(A,B),rd(C,B)),mult(A,mult(B,C))) = B. [para(8(a,1),15(a,1,2,2,2))]. 25.92/26.27 25 ld(mult(mult(A,ld(B,C)),B),mult(A,mult(ld(B,C),C))) = ld(B,C). [para(9(a,1),15(a,1,2,2,2))]. 25.92/26.27 29 ld(rd(A,B),mult(mult(A,C),B)) = mult(B,mult(C,B)). [para(16(a,1),7(a,1,2))]. 25.92/26.27 30 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)). [para(8(a,1),16(a,1,2,2)),flip(a)]. 25.92/26.27 32 rd(mult(mult(A,B),C),mult(C,mult(B,C))) = rd(A,C). [para(16(a,1),10(a,1,1))]. 25.92/26.27 37 mult(A,mult(ld(mult(B,A),C),A)) = ld(B,mult(C,A)). [para(18(a,1),7(a,1,2)),flip(a)]. 25.92/26.27 39 ld(A,mult(mult(B,C),ld(A,B))) = mult(ld(A,B),mult(C,ld(A,B))). [para(17(a,1),7(a,1,2))]. 25.92/26.27 40 mult(mult(A,B),ld(B,A)) = mult(B,mult(ld(B,A),A)). [para(9(a,1),17(a,1,2,2)),flip(a)]. 25.92/26.27 45 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(8(a,1),19(a,1,1,2,2))]. 25.92/26.27 46 mult(mult(rd(A,mult(B,mult(C,B))),B),C) = rd(A,B). [para(8(a,1),19(a,1,1)),flip(a)]. 25.92/26.27 47 ld(mult(A,rd(B,C)),mult(rd(A,C),mult(C,B))) = C. [para(8(a,1),23(a,1,1,1))]. 25.92/26.27 62 ld(rd(A,B),mult(C,B)) = mult(B,mult(ld(A,C),B)). [para(9(a,1),29(a,1,2,1))]. 25.92/26.27 78 ld(mult(mult(mult(A,rd(B,mult(C,D))),C),rd(D,C)),mult(rd(A,mult(C,D)),mult(mult(C,D),B))) = C. [para(30(a,1),23(a,1,2))]. 25.92/26.27 96 rd(mult(A,B),mult(B,mult(C,B))) = rd(rd(A,C),B). [para(8(a,1),32(a,1,1,1))]. 25.92/26.27 103 ld(A,ld(B,mult(C,A))) = mult(ld(mult(B,A),C),A). [para(37(a,1),7(a,1,2))]. 25.92/26.27 147 mult(mult(rd(A,mult(B,C)),B),rd(C,B)) = rd(A,B). [para(8(a,1),45(a,1,1)),flip(a)]. 25.92/26.27 148 mult(mult(A,B),rd(ld(B,C),B)) = rd(mult(A,C),B). [para(9(a,1),45(a,1,1,2)),flip(a)]. 25.92/26.27 167 ld(mult(mult(mult(A,B),mult(C,mult(B,C))),D),mult(mult(A,mult(B,mult(C,B))),mult(C,mult(D,C)))) = C. [para(21(a,1),15(a,1,1,1))]. 25.92/26.27 168 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(mult(C,mult(mult(B,mult(C,B)),C)),B)))) = mult(B,mult(C,B)). [para(21(a,1),15(a,1,1)),rewrite([22(11)])]. 25.92/26.27 189 mult(rd(A,mult(B,mult(C,B))),B) = rd(rd(A,B),C). [para(46(a,1),10(a,1,1)),flip(a)]. 25.92/26.27 220 mult(A,mult(ld(B,rd(C,A)),A)) = ld(rd(B,A),C). [para(8(a,1),62(a,1,2)),flip(a)]. 25.92/26.27 229 ld(mult(mult(A,B),rd(C,B)),mult(D,B)) = mult(B,mult(ld(mult(A,mult(B,C)),D),B)). [para(45(a,1),62(a,1,1))]. 25.92/26.27 277 rd(rd(rd(A,B),C),B) = rd(A,mult(B,mult(C,B))). [para(8(a,1),96(a,1,1)),flip(a)]. 25.92/26.27 294 mult(ld(mult(A,B),A),B) = ld(B,B). [para(7(a,1),103(a,1,2)),flip(a)]. 25.92/26.27 295 mult(ld(mult(A,B),rd(C,B)),B) = ld(B,ld(A,C)). [para(8(a,1),103(a,1,2,2)),flip(a)]. 25.92/26.27 298 mult(ld(mult(rd(mult(A,B),C),B),A),B) = ld(B,C). [para(13(a,1),103(a,1,2)),flip(a)]. 25.92/26.27 310 ld(ld(mult(A,B),A),ld(B,B)) = B. [para(294(a,1),7(a,1,2))]. 25.92/26.27 311 mult(ld(A,rd(A,B)),B) = ld(B,B). [para(8(a,1),294(a,1,1,1))]. 25.92/26.27 312 ld(ld(A,B),ld(A,B)) = mult(ld(B,A),ld(A,B)). [para(9(a,1),294(a,1,1,1)),flip(a)]. 25.92/26.27 313 rd(ld(A,A),A) = ld(mult(B,A),B). [para(294(a,1),10(a,1,1))]. 25.92/26.27 327 ld(ld(mult(A,B),A),mult(C,B)) = mult(B,mult(ld(ld(B,B),C),B)). [para(294(a,1),37(a,1,2,1,1)),flip(a)]. 25.92/26.27 338 mult(ld(mult(A,B),ld(mult(C,B),C)),B) = ld(B,ld(A,ld(B,B))). [para(294(a,1),103(a,1,2,2)),flip(a)]. 25.92/26.27 367 rd(ld(A,A),A) = ld(B,rd(B,A)). [para(311(a,1),10(a,1,1))]. 25.92/26.27 371 mult(mult(A,ld(B,rd(B,C))),C) = A. [para(311(a,1),16(a,1,2,2)),rewrite([9(3),8(2)]),flip(a)]. 25.92/26.27 378 ld(ld(A,rd(A,B)),mult(C,B)) = mult(B,mult(ld(ld(B,B),C),B)). [para(311(a,1),37(a,1,2,1,1)),flip(a)]. 25.92/26.27 380 mult(mult(A,ld(B,rd(B,C))),rd(C,ld(B,rd(B,C)))) = rd(mult(A,ld(C,C)),ld(B,rd(B,C))). [para(311(a,1),45(a,1,1,2)),flip(a)]. 25.92/26.27 390 mult(ld(mult(A,B),ld(C,rd(C,B))),B) = ld(B,ld(A,ld(B,B))). [para(311(a,1),103(a,1,2,2)),flip(a)]. 25.92/26.27 406 ld(mult(A,mult(ld(A,B),B)),mult(B,A)) = ld(B,A). [para(40(a,1),313(a,2,1)),rewrite([312(3),10(5)]),flip(a)]. 25.92/26.27 407 mult(mult(A,B),ld(mult(C,B),C)) = A. [para(313(a,1),45(a,2,2)),rewrite([9(2),10(2)]),flip(a)]. 25.92/26.27 408 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = rd(ld(C,C),C). [para(21(a,1),313(a,2,1)),flip(a)]. 25.92/26.27 417 ld(mult(A,B),A) = ld(mult(C,B),C). [para(313(a,1),313(a,1))]. 25.92/26.27 420 mult(A,rd(ld(B,B),B)) = rd(A,B). [para(367(a,2),9(a,1,2))]. 25.92/26.27 436 ld(mult(A,B),A) = ld(C,rd(C,B)). [para(367(a,1),313(a,1)),flip(a)]. 25.92/26.27 437 ld(A,rd(A,B)) = ld(C,rd(C,B)). [para(367(a,1),367(a,1))]. 25.92/26.27 476 rd(A,ld(B,rd(B,C))) = mult(A,C). [para(8(a,1),371(a,1,1)),flip(a)]. 25.92/26.27 477 mult(A,ld(B,rd(B,C))) = rd(A,C). [para(371(a,1),10(a,1,1)),flip(a)]. 25.92/26.27 480 mult(mult(A,ld(B,C)),ld(C,B)) = A. [para(14(a,1),371(a,1,1,2,2))]. 25.92/26.27 486 mult(mult(A,ld(B,B)),B) = mult(rd(A,B),mult(B,B)). [back_rewrite(380),rewrite([477(3),476(4),476(8)]),flip(a)]. 25.92/26.27 500 mult(A,ld(mult(B,C),B)) = rd(A,C). [para(8(a,1),407(a,1,1))]. 25.92/26.27 512 mult(ld(mult(A,B),A),rd(ld(C,D),B)) = ld(mult(C,B),rd(D,B)). [para(407(a,1),37(a,1,2,1,1)),rewrite([500(6),500(9)])]. 25.92/26.27 528 ld(mult(A,ld(B,C)),A) = ld(C,B). [para(9(a,1),417(a,1,1)),flip(a)]. 25.92/26.27 529 ld(mult(mult(A,B),C),rd(A,C)) = ld(mult(D,mult(C,mult(B,C))),D). [para(16(a,1),417(a,1,1))]. 25.92/26.27 582 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(14(a,1),476(a,1,2,2))]. 25.92/26.27 656 mult(mult(A,mult(B,ld(C,D))),ld(D,C)) = mult(mult(A,ld(C,D)),mult(ld(D,C),B)). [para(480(a,1),16(a,1,2,2)),rewrite([582(2)]),flip(a)]. 25.92/26.27 661 ld(mult(A,ld(B,C)),mult(D,ld(C,B))) = mult(ld(C,B),mult(ld(A,D),ld(C,B))). [para(480(a,1),37(a,1,2,1,1)),flip(a)]. 25.92/26.27 671 rd(A,mult(ld(B,C),mult(D,ld(B,C)))) = mult(rd(mult(A,ld(C,B)),D),ld(C,B)). [para(480(a,1),96(a,1,1)),rewrite([582(10)])]. 25.92/26.27 687 mult(rd(mult(A,ld(B,C)),D),ld(B,C)) = mult(A,ld(mult(mult(B,D),ld(C,B)),C)). [para(17(a,1),500(a,1,2,1)),rewrite([671(10)]),flip(a)]. 25.92/26.27 793 rd(rd(A,B),rd(C,B)) = mult(rd(A,mult(B,C)),B). [para(147(a,1),10(a,1,1))]. 25.92/26.27 824 ld(mult(A,rd(B,C)),A) = mult(C,mult(ld(D,rd(D,mult(C,B))),C)). [para(147(a,1),417(a,1,1)),rewrite([62(5)]),flip(a)]. 25.92/26.27 834 ld(mult(A,B),rd(mult(A,C),B)) = rd(ld(B,C),B). [para(148(a,1),7(a,1,2))]. 25.92/26.27 835 rd(mult(rd(A,B),C),B) = mult(A,rd(ld(B,C),B)). [para(8(a,1),148(a,1,1)),flip(a)]. 25.92/26.27 979 ld(rd(rd(A,B),C),rd(A,mult(B,mult(C,B)))) = rd(ld(B,B),B). [para(189(a,1),313(a,2,1)),flip(a)]. 25.92/26.27 1148 mult(ld(mult(A,B),A),rd(C,B)) = rd(ld(B,C),B). [para(313(a,2),39(a,1,2,2)),rewrite([420(5),834(4),500(7)]),flip(a)]. 25.92/26.27 1149 mult(rd(ld(A,A),A),rd(B,A)) = rd(ld(A,B),A). [para(313(a,2),39(a,2,1)),rewrite([500(5),834(4),500(7)]),flip(a)]. 25.92/26.27 1151 mult(ld(A,rd(A,B)),rd(C,B)) = rd(ld(B,C),B). [para(367(a,2),39(a,1,2,2)),rewrite([420(5),835(3),7(4),477(7)]),flip(a)]. 25.92/26.27 1169 rd(ld(A,ld(B,C)),A) = ld(mult(B,A),rd(C,A)). [back_rewrite(512),rewrite([1148(5)])]. 25.92/26.27 1227 ld(A,ld(mult(B,C),B)) = ld(A,ld(mult(D,C),D)). [para(417(a,1),295(a,2,2)),rewrite([295(5)])]. 25.92/26.27 1265 rd(mult(A,mult(B,A)),A) = ld(rd(ld(A,A),A),B). [para(298(a,1),420(a,1)),rewrite([420(6),420(8),277(6),13(7)]),flip(a)]. 25.92/26.27 1266 mult(ld(ld(A,B),C),ld(B,A)) = mult(ld(B,A),mult(C,ld(B,A))). [para(298(a,1),480(a,1,1)),rewrite([687(9),528(10),39(8)])]. 25.92/26.27 1267 mult(mult(ld(A,B),ld(A,B)),mult(ld(B,A),C)) = ld(ld(B,A),C). [para(480(a,1),298(a,1,1,1,1,1)),rewrite([661(6),13(3),656(6)])]. 25.92/26.27 1268 ld(ld(ld(A,B),C),mult(ld(B,A),mult(C,ld(B,A)))) = ld(B,A). [para(298(a,1),528(a,1,1)),rewrite([687(7),528(8),39(6)])]. 25.92/26.27 1272 mult(ld(A,B),mult(mult(ld(B,A),ld(A,B)),ld(A,B))) = ld(ld(B,A),ld(A,B)). [para(312(a,1),40(a,1,2)),rewrite([1267(7),312(7)]),flip(a)]. 25.92/26.27 1355 ld(mult(A,mult(ld(A,A),A)),mult(A,mult(A,A))) = A. [para(294(a,1),406(a,1,1,2)),rewrite([40(3),7(8)])]. 25.92/26.27 1564 mult(rd(A,A),mult(A,A)) = mult(A,A). [para(9(a,1),486(a,1,1)),flip(a)]. 25.92/26.27 1565 mult(A,rd(B,B)) = mult(A,ld(B,B)). [para(486(a,1),10(a,1,1)),rewrite([45(4),8(2)])]. 25.92/26.27 1612 ld(ld(A,B),ld(B,A)) = mult(ld(B,A),ld(B,A)). [para(486(a,1),39(a,1,2)),rewrite([582(2),9(2),7(5),312(7),1272(10)]),flip(a)]. 25.92/26.27 1624 mult(rd(c2,c2),c1) != c1 | mult(c1,ld(c2,c2)) != c1 # answer(goals). [back_rewrite(12),rewrite([1565(12)])]. 25.92/26.27 1628 mult(A,mult(ld(A,A),A)) = mult(A,A). [para(1564(a,1),7(a,1,2)),rewrite([62(3)])]. 25.92/26.27 1629 rd(mult(A,A),mult(A,A)) = rd(A,A). [para(1564(a,1),10(a,1,1))]. 25.92/26.27 1640 mult(mult(A,ld(B,B)),rd(mult(B,B),rd(B,B))) = rd(mult(A,mult(B,B)),rd(B,B)). [para(1564(a,1),45(a,1,1,2)),rewrite([1565(6)]),flip(a)]. 25.92/26.27 1655 ld(mult(A,A),rd(A,A)) = ld(B,rd(B,mult(A,A))). [para(1564(a,1),436(a,1,1))]. 25.92/26.27 1671 ld(mult(A,A),mult(A,mult(A,A))) = A. [back_rewrite(1355),rewrite([1628(3)])]. 25.92/26.27 1679 rd(A,A) = ld(A,A). [para(1565(a,1),7(a,1,2)),rewrite([7(3)]),flip(a)]. 25.92/26.27 1692 ld(mult(A,A),ld(A,A)) = ld(B,rd(B,mult(A,A))). [back_rewrite(1655),rewrite([1679(2)])]. 25.92/26.27 1703 mult(mult(A,ld(B,B)),mult(B,B)) = mult(mult(A,mult(B,B)),ld(B,B)). [back_rewrite(1640),rewrite([1679(4),582(5),40(5),1628(5),1679(7),582(8)])]. 25.92/26.27 1708 ld(mult(A,A),mult(A,A)) = ld(A,A). [back_rewrite(1629),rewrite([1679(3),1679(4)])]. 25.92/26.27 1709 mult(ld(c2,c2),c1) != c1 | mult(c1,ld(c2,c2)) != c1 # answer(goals). [back_rewrite(1624),rewrite([1679(3)])]. 25.92/26.27 1792 mult(ld(A,A),A) = A. [para(1679(a,1),8(a,1,1))]. 25.92/26.27 1797 mult(ld(A,ld(A,A)),A) = ld(A,A). [para(1679(a,1),311(a,1,1,2))]. 25.92/26.27 1799 rd(ld(A,A),A) = ld(A,ld(A,A)). [para(1679(a,1),367(a,2,2))]. 25.92/26.27 1800 ld(mult(A,B),A) = ld(B,ld(B,B)). [para(1679(a,1),436(a,2,2))]. 25.92/26.27 1801 ld(A,rd(A,B)) = ld(B,ld(B,B)). [para(1679(a,1),437(a,1,2)),flip(a)]. 25.92/26.27 1802 mult(A,ld(B,ld(B,B))) = rd(A,B). [para(1679(a,1),477(a,1,2,2))]. 25.92/26.27 1807 ld(rd(A,B),rd(A,B)) = mult(rd(A,mult(B,A)),B). [para(1679(a,1),189(a,2)),rewrite([8(2)]),flip(a)]. 25.92/26.27 1937 rd(mult(A,mult(B,A)),A) = ld(ld(A,ld(A,A)),B). [back_rewrite(1265),rewrite([1799(5)])]. 25.92/26.27 1942 mult(ld(A,ld(A,A)),rd(B,A)) = rd(ld(A,B),A). [back_rewrite(1149),rewrite([1799(2)])]. 25.92/26.27 1951 ld(rd(rd(A,B),C),rd(A,mult(B,mult(C,B)))) = ld(B,ld(B,B)). [back_rewrite(979),rewrite([1799(8)])]. 25.92/26.27 1980 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = ld(C,ld(C,C)). [back_rewrite(408),rewrite([1799(10)])]. 25.92/26.27 2006 mult(rd(A,B),mult(B,B)) = mult(mult(A,B),ld(B,B)). [para(1792(a,1),30(a,2,2)),rewrite([582(2),9(2),582(5),486(6)]),flip(a)]. 25.92/26.27 2010 mult(mult(A,mult(B,B)),ld(B,B)) = mult(mult(A,B),B). [para(1792(a,1),21(a,1,1,2,2)),rewrite([9(8),1792(7)])]. 25.92/26.27 2071 mult(mult(A,ld(B,B)),B) = mult(mult(A,B),ld(B,B)). [back_rewrite(486),rewrite([2006(6)])]. 25.92/26.27 2072 mult(mult(A,ld(B,B)),mult(B,B)) = mult(mult(A,B),B). [back_rewrite(1703),rewrite([2010(8)])]. 25.92/26.27 2085 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(1671(a,1),9(a,1,2))]. 25.92/26.27 2086 mult(mult(mult(A,mult(A,A)),B),A) = mult(mult(A,A),mult(A,mult(B,A))). [para(1671(a,1),17(a,1,2,1)),rewrite([1671(5),1671(11)]),flip(a)]. 25.92/26.27 2177 mult(ld(A,A),ld(A,A)) = ld(A,A). [para(477(a,1),1708(a,1,1)),rewrite([477(8),1807(7),477(5),1679(3),582(4),2071(5),311(3),312(8),13(5),477(6),1679(4)])]. 25.92/26.27 2191 mult(ld(A,ld(A,A)),mult(A,mult(B,A))) = mult(mult(ld(A,A),B),A). [para(1797(a,1),11(a,1,1,1)),flip(a)]. 25.92/26.27 2308 ld(mult(rd(A,B),C),mult(A,rd(ld(B,C),B))) = ld(C,rd(C,B)). [para(1801(a,1),25(a,1,1,1,2)),rewrite([1802(3),1151(6)])]. 25.92/26.27 2409 ld(ld(A,ld(A,A)),A) = mult(A,A). [para(2085(a,1),10(a,1,1)),rewrite([1937(3)])]. 25.92/26.27 2510 mult(ld(A,A),mult(ld(A,A),mult(B,ld(A,A)))) = mult(mult(ld(A,A),B),ld(A,A)). [para(2177(a,1),11(a,1,1,1)),flip(a)]. 25.92/26.27 2512 ld(ld(A,A),mult(B,ld(A,A))) = mult(mult(ld(A,A),B),ld(A,A)). [para(2177(a,1),37(a,1,2,1,1)),rewrite([1266(5),2510(6)]),flip(a)]. 25.92/26.27 2518 mult(ld(A,ld(B,B)),mult(ld(B,B),ld(A,ld(B,B)))) = ld(A,mult(ld(B,B),ld(A,ld(B,B)))). [para(2177(a,1),39(a,1,2,1)),flip(a)]. 25.92/26.27 2519 ld(ld(A,A),ld(ld(A,A),B)) = mult(ld(A,A),B). [para(2177(a,1),295(a,1,1,1)),rewrite([582(3),2512(4),480(6)]),flip(a)]. 25.92/26.27 2523 mult(ld(A,ld(A,A)),mult(A,A)) = A. [para(2409(a,1),9(a,1,2))]. 25.92/26.27 2530 rd(ld(mult(A,B),A),B) = ld(B,ld(mult(A,B),A)). [para(500(a,1),2409(a,2)),rewrite([312(7),7(4),500(5),1679(3),310(4)]),flip(a)]. 25.92/26.27 2537 ld(mult(A,A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [para(2409(a,1),406(a,1,1,2,1)),rewrite([2085(4),2191(5),1792(2),9(4)])]. 25.92/26.27 2554 ld(A,rd(A,mult(B,B))) = ld(B,ld(B,ld(B,B))). [back_rewrite(1692),rewrite([2537(3)]),flip(a)]. 25.92/26.27 2584 mult(ld(mult(A,B),A),mult(B,B)) = B. [para(1800(a,2),2523(a,1,1))]. 25.92/26.27 2715 ld(A,rd(A,mult(B,B))) = ld(B,ld(mult(C,B),C)). [para(2584(a,1),436(a,1,1)),flip(a)]. 25.92/26.27 3144 mult(ld(ld(mult(A,B),A),C),B) = mult(B,mult(C,B)). [para(500(a,1),834(a,1,1)),rewrite([582(5),7(4),62(4),7(2),582(8),7(7)]),flip(a)]. 25.92/26.27 3672 mult(ld(A,ld(mult(B,A),B)),mult(A,C)) = ld(A,C). [para(1148(a,1),30(a,1,1)),rewrite([8(3),2530(4)]),flip(a)]. 25.92/26.27 3709 rd(A,mult(rd(B,C),rd(ld(C,B),C))) = mult(A,rd(ld(rd(B,C),C),rd(B,C))). [para(1148(a,1),277(a,2,2,2)),rewrite([582(5),7(4),835(5)]),flip(a)]. 25.92/26.27 3963 ld(mult(ld(mult(A,B),A),C),ld(mult(D,B),D)) = ld(mult(E,C),E). [para(1227(a,1),417(a,1))]. 25.92/26.27 3967 mult(A,ld(mult(ld(mult(B,C),B),D),ld(mult(E,C),E))) = rd(A,D). [para(1227(a,1),500(a,1,2))]. 25.92/26.27 3989 ld(mult(ld(mult(A,B),A),C),ld(mult(D,B),D)) = ld(C,ld(C,C)). [para(1227(a,1),1800(a,1))]. 25.92/26.27 5093 mult(A,mult(mult(rd(B,mult(A,B)),A),A)) = ld(rd(rd(B,A),A),B). [para(1807(a,1),220(a,1,2,1))]. 25.92/26.27 6061 mult(ld(A,A),mult(ld(A,A),B)) = ld(ld(A,A),B). [para(1612(a,1),1937(a,2,1,2)),rewrite([582(6),656(6),2177(3),2177(8),312(7),2177(7)])]. 25.92/26.27 6436 mult(rd(ld(A,B),mult(A,B)),A) = ld(A,ld(A,A)). [para(1942(a,1),10(a,1,1)),rewrite([793(4)])]. 25.92/26.27 8275 ld(mult(A,rd(mult(B,B),mult(C,ld(B,B)))),mult(rd(A,mult(C,ld(B,B))),mult(mult(C,B),B))) = mult(C,ld(B,B)). [para(2072(a,1),47(a,1,2,2))]. 25.92/26.27 8344 ld(mult(mult(mult(A,rd(mult(B,B),mult(C,ld(B,B)))),C),rd(ld(B,B),C)),mult(rd(A,mult(C,ld(B,B))),mult(mult(C,B),B))) = C. [para(2072(a,1),78(a,1,2,2))]. 25.92/26.27 8854 ld(ld(A,A),ld(B,ld(B,B))) = mult(ld(A,A),rd(ld(A,A),B)). [para(1801(a,1),2519(a,1,2))]. 25.92/26.27 10229 mult(ld(A,ld(A,ld(A,A))),B) = mult(B,mult(rd(ld(mult(C,B),C),mult(A,A)),B)). [para(2554(a,1),3144(a,1,1))]. 25.92/26.27 10231 mult(ld(A,ld(mult(B,A),B)),C) = mult(C,mult(rd(ld(mult(D,C),D),mult(A,A)),C)). [para(2715(a,1),3144(a,1,1))]. 25.92/26.27 10418 mult(ld(A,ld(mult(B,A),B)),C) = ld(A,ld(A,C)). [para(9(a,1),3672(a,1,2))]. 25.92/26.27 10569 mult(A,mult(rd(ld(mult(B,A),B),mult(C,C)),A)) = ld(C,ld(C,A)). [back_rewrite(10231),rewrite([10418(4)]),flip(a)]. 25.92/26.27 10604 mult(ld(A,ld(A,ld(A,A))),B) = ld(A,ld(A,B)). [back_rewrite(10229),rewrite([10569(10)])]. 25.92/26.27 11777 ld(ld(ld(ld(A,A),B),ld(A,A)),ld(mult(ld(A,A),B),mult(ld(A,A),B))) = mult(ld(A,A),B). [para(6061(a,1),310(a,1,1,1))]. 25.92/26.27 11803 rd(ld(A,B),mult(A,B)) = ld(A,ld(A,ld(A,A))). [para(6436(a,1),10(a,1,1)),rewrite([1169(3),1679(2),2537(3)]),flip(a)]. 25.92/26.27 13261 ld(ld(A,B),ld(ld(A,B),C)) = mult(mult(ld(B,A),ld(B,A)),C). [para(9(a,1),10418(a,1,1,2,1)),rewrite([1612(3)]),flip(a)]. 25.92/26.27 14012 ld(ld(ld(A,ld(A,B)),ld(A,ld(A,ld(A,A)))),ld(B,B)) = B. [para(10604(a,1),310(a,1,1,1))]. 25.92/26.27 14018 ld(ld(A,ld(A,ld(B,C))),ld(A,ld(A,ld(A,A)))) = ld(C,B). [para(10604(a,1),528(a,1,1))]. 25.92/26.27 14572 ld(ld(A,B),ld(A,ld(A,ld(A,A)))) = ld(mult(C,mult(A,B)),C). [para(11803(a,1),436(a,2,2)),flip(a)]. 25.92/26.27 20932 mult(A,mult(ld(B,rd(B,mult(A,B))),A)) = ld(A,rd(A,rd(B,A))). [para(1148(a,1),1951(a,1,2,2,2)),rewrite([582(5),7(4),3709(8),2308(9),1807(7),62(8)]),flip(a)]. 25.92/26.27 21099 ld(mult(mult(A,A),mult(A,mult(B,A))),mult(mult(A,mult(A,A)),B)) = ld(A,ld(A,A)). [para(2086(a,1),1800(a,1,1))]. 25.92/26.27 21103 mult(A,mult(ld(B,rd(B,mult(A,C))),A)) = ld(A,rd(A,rd(C,A))). [para(2086(a,1),824(a,1,1)),rewrite([21099(15),1807(4),62(5),20932(5)]),flip(a)]. 25.92/26.27 21815 mult(A,mult(ld(mult(B,mult(A,C)),B),A)) = ld(A,rd(A,rd(C,A))). [para(436(a,1),229(a,2,2,1)),rewrite([229(5),21103(10)])]. 25.92/26.27 28081 mult(ld(A,A),rd(B,mult(ld(A,A),B))) = ld(B,B). [para(480(a,1),5093(a,1,2)),rewrite([582(7),582(9),480(9)])]. 25.92/26.27 28108 rd(A,mult(ld(B,B),A)) = ld(ld(B,B),ld(A,A)). [para(28081(a,1),7(a,1,2)),flip(a)]. 25.92/26.27 28109 mult(ld(A,ld(B,B)),ld(ld(B,B),A)) = mult(ld(B,B),rd(ld(ld(B,B),A),A)). [para(9(a,1),28081(a,1,2,2)),rewrite([312(10)]),flip(a)]. 25.92/26.27 28122 ld(ld(ld(A,A),ld(B,B)),ld(A,A)) = ld(B,B). [para(28081(a,1),327(a,1,2)),rewrite([28108(3),528(5),28108(8),28108(11),28108(14),312(15),28109(15),582(14),28108(20),21815(22),582(16),9(16),582(13),1266(13),1268(14)])]. 25.92/26.27 28124 mult(ld(A,A),mult(ld(ld(A,A),ld(B,B)),ld(B,B))) = ld(B,B). [para(28081(a,1),338(a,1,1,1)),rewrite([28108(4),528(6),13261(5),2177(3),28108(6),40(7),28108(10),28108(14),28108(17),312(18),28109(18),582(17),7(19),7(16)])]. 25.92/26.27 28126 mult(ld(ld(A,A),ld(B,B)),ld(B,B)) = ld(A,A). [para(28081(a,1),378(a,1,2)),rewrite([28108(3),582(4),7(5),28122(5),28108(4),28108(7),28108(10),312(11),28109(11),582(10),28124(11),28108(10),28109(11),582(10),28124(11)]),flip(a)]. 25.92/26.27 28127 ld(A,A) = ld(B,B). [para(28081(a,1),390(a,1,1,1)),rewrite([28108(4),582(5),7(6),13261(5),2177(3),28108(6),40(7),28126(6),2177(3),28108(4),28108(8),28108(11),312(12),28109(12),582(11),28126(11),2177(8),312(7),2177(7),28122(6)])]. 25.92/26.27 28128 ld(ld(A,A),mult(ld(B,B),ld(ld(A,A),ld(B,B)))) = ld(B,B). [para(28081(a,1),529(a,2,1,2,2)),rewrite([28108(5),28108(9),582(10),661(11),528(6),2518(9),28108(10),28126(12),528(10)])]. 25.92/26.27 28131 mult(ld(A,A),mult(ld(B,B),ld(A,A))) = ld(ld(A,A),ld(B,B)). [para(28081(a,1),167(a,1,2,2,2)),rewrite([28108(4),28108(7),28108(15),28108(21),28126(23),661(21),1980(18),312(11),28109(11),582(10),28126(10),2177(7),28122(6),28108(8)])]. 25.92/26.27 28132 ld(ld(A,A),ld(B,B)) = ld(B,B). [para(28081(a,1),168(a,1,1,2,2)),rewrite([28108(5),28126(7),480(4),28108(4),28108(8),1266(10),28131(10),9(9),28108(8),2518(10),28128(8),28131(5),7(5),28108(7),1266(9),28131(9),9(8)])]. 25.92/26.27 28194 ld(mult(ld(A,A),B),ld(C,C)) = ld(mult(D,B),D). [para(28081(a,1),3963(a,1,1,1,1)),rewrite([28132(3),28108(5),28132(5),528(5)])]. 25.92/26.27 28198 mult(A,ld(mult(ld(B,B),C),ld(D,D))) = rd(A,C). [para(28081(a,1),3967(a,1,2,1,1,1)),rewrite([28132(3),28108(5),28132(5),528(5)])]. 25.92/26.27 28203 ld(mult(ld(A,A),B),ld(C,C)) = ld(B,ld(B,B)). [para(28081(a,1),3989(a,1,1,1,1)),rewrite([28132(3),28108(5),28132(5),528(5)])]. 25.92/26.27 28221 ld(A,A) = c_0. [new_symbol(28127)]. 25.92/26.27 28271 ld(mult(c_0,A),c_0) = ld(A,c_0). [back_rewrite(28203),rewrite([28221(1),28221(3),28221(5)])]. 25.92/26.27 28273 mult(A,ld(B,c_0)) = rd(A,B). [back_rewrite(28198),rewrite([28221(1),28221(3),28271(4)])]. 25.92/26.27 28277 ld(mult(A,B),A) = ld(B,c_0). [back_rewrite(28194),rewrite([28221(1),28221(3),28271(4)]),flip(a)]. 25.92/26.27 28759 ld(ld(A,B),ld(A,ld(A,c_0))) = ld(mult(A,B),c_0). [back_rewrite(14572),rewrite([28221(2),28277(8)])]. 25.92/26.27 28781 ld(ld(A,B),c_0) = ld(B,A). [back_rewrite(14018),rewrite([28221(4),28759(7),9(3)])]. 25.92/26.27 28783 ld(c_0,A) = A. [back_rewrite(14012),rewrite([28221(3),28759(6),9(2),28221(3),28781(4)])]. 25.92/26.27 29012 mult(c_0,A) = A. [back_rewrite(11777),rewrite([28221(1),28783(2),28221(1),28221(3),28221(5),28221(7),28781(4),28783(2),28221(1)]),flip(a)]. 25.92/26.27 29547 rd(c_0,A) = ld(A,c_0). [back_rewrite(8854),rewrite([28221(1),28221(2),28783(4),28221(3),28221(4),29012(6)]),flip(a)]. 25.92/26.27 29669 ld(mult(A,rd(mult(B,B),mult(C,c_0))),mult(rd(A,mult(C,c_0)),mult(mult(C,B),B))) = C. [back_rewrite(8344),rewrite([28221(2),28221(7),29547(8),28273(9),10(7),28221(6)])]. 25.92/26.27 29693 mult(A,c_0) = A. [back_rewrite(8275),rewrite([28221(2),28221(6),29669(12),28221(1)]),flip(a)]. 25.92/26.27 30465 $F # answer(goals). [back_rewrite(1709),rewrite([28221(3),29012(3),28221(7),29693(6)]),xx(a),xx(b)]. 25.92/26.27 25.92/26.27 % SZS output end Refutation 25.92/26.27 ============================== end of proof ========================== 25.92/26.27 25.92/26.27 ============================== STATISTICS ============================ 25.92/26.27 25.92/26.27 Given=852. Generated=974747. Kept=30458. proofs=1. 25.92/26.27 Usable=572. Sos=5387. Demods=6953. Limbo=2244, Disabled=22261. Hints=0. 25.92/26.27 Megabytes=30.97. 25.92/26.27 User_CPU=24.75, System_CPU=0.58, Wall_clock=25. 25.92/26.27 25.92/26.27 ============================== end of statistics ===================== 25.92/26.27 25.92/26.27 ============================== end of search ========================= 25.92/26.27 25.92/26.27 THEOREM PROVED 25.92/26.27 % SZS status Theorem 25.92/26.27 25.92/26.27 Exiting with 1 proof. 25.92/26.27 25.92/26.27 Process 16616 exit (max_proofs) Tue Aug 9 04:23:10 2022 25.92/26.28 Prover9 interrupted 25.92/26.28 EOF