TSTP Solution File: GRP655+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP655+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:20:20 EDT 2022
% Result : Theorem 18.27s 18.55s
% Output : Refutation 18.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP655+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 06:14:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.46/2.74 ============================== Prover9 ===============================
% 2.46/2.74 Prover9 (32) version 2009-11A, November 2009.
% 2.46/2.74 Process 16488 was started by sandbox on n025.cluster.edu,
% 2.46/2.74 Tue Jun 14 06:14:10 2022
% 2.46/2.74 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16198_n025.cluster.edu".
% 2.46/2.74 ============================== end of head ===========================
% 2.46/2.74
% 2.46/2.74 ============================== INPUT =================================
% 2.46/2.74
% 2.46/2.74 % Reading from file /tmp/Prover9_16198_n025.cluster.edu
% 2.46/2.74
% 2.46/2.74 set(prolog_style_variables).
% 2.46/2.74 set(auto2).
% 2.46/2.74 % set(auto2) -> set(auto).
% 2.46/2.74 % set(auto) -> set(auto_inference).
% 2.46/2.74 % set(auto) -> set(auto_setup).
% 2.46/2.74 % set(auto_setup) -> set(predicate_elim).
% 2.46/2.74 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.46/2.74 % set(auto) -> set(auto_limits).
% 2.46/2.74 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.46/2.74 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.46/2.74 % set(auto) -> set(auto_denials).
% 2.46/2.74 % set(auto) -> set(auto_process).
% 2.46/2.74 % set(auto2) -> assign(new_constants, 1).
% 2.46/2.74 % set(auto2) -> assign(fold_denial_max, 3).
% 2.46/2.74 % set(auto2) -> assign(max_weight, "200.000").
% 2.46/2.74 % set(auto2) -> assign(max_hours, 1).
% 2.46/2.74 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.46/2.74 % set(auto2) -> assign(max_seconds, 0).
% 2.46/2.74 % set(auto2) -> assign(max_minutes, 5).
% 2.46/2.74 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.46/2.74 % set(auto2) -> set(sort_initial_sos).
% 2.46/2.74 % set(auto2) -> assign(sos_limit, -1).
% 2.46/2.74 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.46/2.74 % set(auto2) -> assign(max_megs, 400).
% 2.46/2.74 % set(auto2) -> assign(stats, some).
% 2.46/2.74 % set(auto2) -> clear(echo_input).
% 2.46/2.74 % set(auto2) -> set(quiet).
% 2.46/2.74 % set(auto2) -> clear(print_initial_clauses).
% 2.46/2.74 % set(auto2) -> clear(print_given).
% 2.46/2.74 assign(lrs_ticks,-1).
% 2.46/2.74 assign(sos_limit,10000).
% 2.46/2.74 assign(order,kbo).
% 2.46/2.74 set(lex_order_vars).
% 2.46/2.74 clear(print_given).
% 2.46/2.74
% 2.46/2.74 % formulas(sos). % not echoed (6 formulas)
% 2.46/2.74
% 2.46/2.74 ============================== end of input ==========================
% 2.46/2.74
% 2.46/2.74 % From the command line: assign(max_seconds, 300).
% 2.46/2.74
% 2.46/2.74 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.46/2.74
% 2.46/2.74 % Formulas that are not ordinary clauses:
% 2.46/2.74 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.74 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.74 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.74 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.74 5 (all C all B all A mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.74 6 -(all X0 all X1 (mult(X0,rd(X1,X1)) = X0 & mult(rd(X1,X1),X0) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.46/2.74
% 2.46/2.74 ============================== end of process non-clausal formulas ===
% 2.46/2.74
% 2.46/2.74 ============================== PROCESS INITIAL CLAUSES ===============
% 2.46/2.74
% 2.46/2.74 ============================== PREDICATE ELIMINATION =================
% 2.46/2.74
% 2.46/2.74 ============================== end predicate elimination =============
% 2.46/2.74
% 2.46/2.74 Auto_denials:
% 2.46/2.74 % copying label goals to answer in negative clause
% 2.46/2.74
% 2.46/2.74 Term ordering decisions:
% 2.46/2.74 Function symbol KB weights: c1=1. c2=1. mult=1. ld=1. rd=1.
% 2.46/2.74
% 2.46/2.74 ============================== end of process initial clauses ========
% 2.46/2.74
% 2.46/2.74 ============================== CLAUSES FOR SEARCH ====================
% 2.46/2.74
% 2.46/2.74 ============================== end of clauses for search =============
% 2.46/2.74
% 2.46/2.74 ============================== SEARCH ================================
% 2.46/2.74
% 2.46/2.74 % Starting search at 0.01 seconds.
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=95.000, iters=3360
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=83.000, iters=3339
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=79.000, iters=3347
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=71.000, iters=3385
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=67.000, iters=3345
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=59.000, iters=3377
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=55.000, iters=3404
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=51.000, iters=3348
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=47.000, iters=3343
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=43.000, iters=3343
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=39.000, iters=3334
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=35.000, iters=3347
% 2.46/2.74
% 2.46/2.74 Low Water (keep): wt=31.000, iters=3395
% 18.27/18.55
% 18.27/18.55 Low Water (displace): id=4353, wt=183.000
% 18.27/18.55
% 18.27/18.55 Low Water (displace): id=4371, wt=151.000
% 18.27/18.55
% 18.27/18.55 Low Water (displace): id=6136, wt=147.000
% 18.27/18.55
% 18.27/18.55 Low Water (displace): id=12616, wt=23.000
% 18.27/18.55
% 18.27/18.55 Low Water (displace): id=13175, wt=19.000
% 18.27/18.55
% 18.27/18.55 Low Water (keep): wt=27.000, iters=3371
% 18.27/18.55
% 18.27/18.55 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 42 (0.00 of 6.99 sec).
% 18.27/18.55
% 18.27/18.55 ============================== PROOF =================================
% 18.27/18.55 % SZS status Theorem
% 18.27/18.55 % SZS output start Refutation
% 18.27/18.55
% 18.27/18.55 % Proof 1 at 17.06 (+ 0.46) seconds: goals.
% 18.27/18.55 % Length of proof is 205.
% 18.27/18.55 % Level of proof is 37.
% 18.27/18.55 % Maximum clause weight is 59.000.
% 18.27/18.55 % Given clauses 736.
% 18.27/18.55
% 18.27/18.55 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 18.27/18.55 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 18.27/18.55 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 18.27/18.55 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 18.27/18.55 5 (all C all B all A mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 18.27/18.55 6 -(all X0 all X1 (mult(X0,rd(X1,X1)) = X0 & mult(rd(X1,X1),X0) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 18.27/18.55 7 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 18.27/18.55 8 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 18.27/18.55 9 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 18.27/18.55 10 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 18.27/18.55 11 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))) # label(f05) # label(axiom). [clausify(5)].
% 18.27/18.55 12 mult(c1,rd(c2,c2)) != c1 | mult(rd(c2,c2),c1) != c1 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(6)].
% 18.27/18.55 13 ld(rd(A,B),A) = B. [para(9(a,1),8(a,1,2))].
% 18.27/18.55 14 rd(A,ld(B,A)) = B. [para(7(a,1),10(a,1,1))].
% 18.27/18.55 15 mult(A,mult(ld(A,B),mult(C,ld(A,B)))) = mult(mult(B,C),ld(A,B)). [para(7(a,1),11(a,1,1,1)),flip(a)].
% 18.27/18.55 16 mult(A,mult(B,mult(ld(mult(A,B),C),B))) = mult(C,B). [para(7(a,1),11(a,1,1)),flip(a)].
% 18.27/18.55 17 ld(mult(mult(A,B),C),mult(A,mult(B,mult(C,B)))) = B. [para(11(a,1),8(a,1,2))].
% 18.27/18.55 18 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(9(a,1),11(a,1,1,1)),flip(a)].
% 18.27/18.55 19 rd(mult(A,mult(B,mult(C,B))),B) = mult(mult(A,B),C). [para(11(a,1),10(a,1,1))].
% 18.27/18.55 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))].
% 18.27/18.55 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))].
% 18.27/18.55 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)].
% 18.27/18.55 23 mult(A,mult(ld(mult(B,A),C),A)) = ld(B,mult(C,A)). [para(16(a,1),8(a,1,2)),flip(a)].
% 18.27/18.55 25 ld(mult(mult(A,ld(B,C)),B),mult(A,mult(ld(B,C),C))) = ld(B,C). [para(7(a,1),17(a,1,2,2,2))].
% 18.27/18.55 28 ld(mult(mult(A,mult(B,mult(C,B))),D),mult(mult(mult(A,B),C),mult(B,mult(D,B)))) = B. [para(11(a,1),17(a,1,1,1))].
% 18.27/18.55 33 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)). [para(9(a,1),18(a,1,2,2)),flip(a)].
% 18.27/18.55 34 rd(mult(mult(A,B),C),mult(C,mult(B,C))) = rd(A,C). [para(18(a,1),10(a,1,1))].
% 18.27/18.55 39 mult(mult(A,B),ld(B,A)) = mult(B,mult(ld(B,A),A)). [para(7(a,1),15(a,1,2,2)),flip(a)].
% 18.27/18.55 40 ld(A,mult(mult(B,C),ld(A,B))) = mult(ld(A,B),mult(C,ld(A,B))). [para(15(a,1),8(a,1,2))].
% 18.27/18.55 46 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(9(a,1),19(a,1,1,2,2))].
% 18.27/18.55 47 mult(mult(rd(A,mult(B,mult(C,B))),B),C) = rd(A,B). [para(9(a,1),19(a,1,1)),flip(a)].
% 18.27/18.55 49 ld(A,ld(B,mult(C,A))) = mult(ld(mult(B,A),C),A). [para(23(a,1),8(a,1,2))].
% 18.27/18.55 50 ld(rd(A,B),mult(C,B)) = mult(B,mult(ld(A,C),B)). [para(9(a,1),23(a,1,2,1,1)),flip(a)].
% 18.27/18.55 58 mult(mult(A,ld(mult(B,C),D)),C) = mult(rd(A,C),ld(B,mult(D,C))). [para(23(a,1),18(a,1,2)),flip(a)].
% 18.27/18.55 79 mult(rd(rd(A,rd(B,C)),C),mult(C,B)) = mult(A,C). [para(9(a,1),33(a,1,1)),flip(a)].
% 18.27/18.55 117 rd(mult(A,B),mult(B,mult(C,B))) = rd(rd(A,C),B). [para(9(a,1),34(a,1,1,1))].
% 18.27/18.55 149 mult(mult(A,B),rd(ld(B,C),B)) = rd(mult(A,C),B). [para(7(a,1),46(a,1,1,2)),flip(a)].
% 18.27/18.55 151 mult(mult(rd(A,mult(B,C)),B),rd(C,B)) = rd(A,B). [para(9(a,1),46(a,1,1)),flip(a)].
% 18.27/18.55 166 mult(rd(A,mult(B,mult(C,B))),B) = rd(rd(A,B),C). [para(47(a,1),10(a,1,1)),flip(a)].
% 18.27/18.55 183 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),17(a,1,1,1))].
% 18.27/18.55 184 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),17(a,1,1)),rewrite([22(11)])].
% 18.27/18.55 203 mult(ld(mult(A,B),A),B) = ld(B,B). [para(8(a,1),49(a,1,2)),flip(a)].
% 18.27/18.55 204 mult(ld(mult(A,B),rd(C,B)),B) = ld(B,ld(A,C)). [para(9(a,1),49(a,1,2,2)),flip(a)].
% 18.27/18.55 206 mult(ld(mult(rd(mult(A,B),C),B),A),B) = ld(B,C). [para(13(a,1),49(a,1,2)),flip(a)].
% 18.27/18.55 216 ld(ld(A,B),ld(A,B)) = mult(ld(B,A),ld(A,B)). [para(7(a,1),203(a,1,1,1)),flip(a)].
% 18.27/18.55 217 ld(ld(mult(A,B),A),ld(B,B)) = B. [para(203(a,1),8(a,1,2))].
% 18.27/18.55 218 mult(ld(A,rd(A,B)),B) = ld(B,B). [para(9(a,1),203(a,1,1,1))].
% 18.27/18.55 219 rd(ld(A,A),A) = ld(mult(B,A),B). [para(203(a,1),10(a,1,1))].
% 18.27/18.55 220 mult(ld(mult(A,B),A),mult(B,mult(C,B))) = mult(mult(ld(B,B),C),B). [para(203(a,1),11(a,1,1,1)),flip(a)].
% 18.27/18.55 226 mult(A,mult(ld(ld(A,A),B),A)) = ld(ld(mult(C,A),C),mult(B,A)). [para(203(a,1),23(a,1,2,1,1))].
% 18.27/18.55 241 mult(ld(mult(A,B),ld(mult(C,B),C)),B) = ld(B,ld(A,ld(B,B))). [para(203(a,1),49(a,1,2,2)),flip(a)].
% 18.27/18.55 251 rd(ld(A,A),A) = ld(B,rd(B,A)). [para(218(a,1),10(a,1,1))].
% 18.27/18.55 255 mult(mult(A,ld(B,rd(B,C))),C) = A. [para(218(a,1),18(a,1,2,2)),rewrite([7(3),9(2)]),flip(a)].
% 18.27/18.55 256 mult(A,mult(ld(ld(A,A),B),A)) = ld(ld(C,rd(C,A)),mult(B,A)). [para(218(a,1),23(a,1,2,1,1))].
% 18.27/18.55 264 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(218(a,1),46(a,1,1,2)),flip(a)].
% 18.27/18.55 269 mult(ld(mult(A,B),ld(C,rd(C,B))),B) = ld(B,ld(A,ld(B,B))). [para(218(a,1),49(a,1,2,2)),flip(a)].
% 18.27/18.55 274 mult(mult(A,mult(B,A)),mult(C,mult(A,mult(B,A)))) = mult(A,mult(mult(B,mult(mult(A,mult(C,A)),B)),A)). [para(22(a,1),8(a,1,2)),rewrite([8(8)]),flip(a)].
% 18.27/18.55 299 mult(mult(A,mult(mult(B,mult(C,mult(D,C))),mult(C,mult(mult(D,mult(mult(C,mult(B,C)),D)),C)))),mult(C,mult(D,C))) = mult(mult(A,mult(B,mult(C,mult(D,C)))),mult(C,mult(mult(D,mult(mult(C,mult(mult(B,mult(C,mult(D,C))),C)),D)),C))). [para(22(a,1),21(a,1,1,2)),rewrite([274(27)])].
% 18.27/18.55 325 ld(mult(A,mult(ld(A,B),B)),mult(B,A)) = ld(B,A). [para(39(a,1),219(a,2,1)),rewrite([216(3),10(5)]),flip(a)].
% 18.27/18.55 326 mult(mult(A,B),ld(mult(C,B),C)) = A. [para(219(a,1),46(a,2,2)),rewrite([7(2),10(2)]),flip(a)].
% 18.27/18.55 327 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),219(a,2,1)),flip(a)].
% 18.27/18.55 329 ld(ld(A,A),ld(mult(B,A),B)) = rd(ld(A,A),A). [para(203(a,1),219(a,2,1)),flip(a)].
% 18.27/18.55 331 ld(mult(A,B),A) = ld(mult(C,B),C). [para(219(a,1),219(a,1))].
% 18.27/18.55 333 mult(A,rd(ld(B,B),B)) = rd(A,B). [para(251(a,2),7(a,1,2))].
% 18.27/18.55 343 ld(mult(A,B),A) = ld(C,rd(C,B)). [para(251(a,1),219(a,1)),flip(a)].
% 18.27/18.55 344 ld(A,rd(A,B)) = ld(C,rd(C,B)). [para(251(a,1),251(a,1))].
% 18.27/18.55 354 rd(A,ld(B,rd(B,C))) = mult(A,C). [para(9(a,1),255(a,1,1)),flip(a)].
% 18.27/18.55 355 mult(A,ld(B,rd(B,C))) = rd(A,C). [para(255(a,1),10(a,1,1)),flip(a)].
% 18.27/18.55 358 mult(mult(A,ld(B,C)),ld(C,B)) = A. [para(14(a,1),255(a,1,1,2,2))].
% 18.27/18.55 362 mult(mult(A,ld(B,B)),B) = mult(rd(A,B),mult(B,B)). [back_rewrite(264),rewrite([355(3),354(4),354(8)]),flip(a)].
% 18.27/18.55 397 mult(A,ld(mult(B,C),B)) = rd(A,C). [para(9(a,1),326(a,1,1))].
% 18.27/18.55 399 mult(A,mult(ld(mult(B,C),B),rd(C,C))) = rd(A,C). [para(326(a,1),11(a,1)),rewrite([397(3),397(6)]),flip(a)].
% 18.27/18.55 411 mult(A,mult(ld(mult(B,C),B),rd(D,C))) = rd(mult(rd(A,C),D),C). [para(326(a,1),20(a,1)),rewrite([397(5),397(8),397(12),399(12)])].
% 18.27/18.55 415 mult(A,mult(B,mult(ld(mult(C,D),C),B))) = mult(rd(mult(A,B),D),B). [para(326(a,1),21(a,2,1)),rewrite([397(6),411(6),10(2)]),flip(a)].
% 18.27/18.55 421 ld(mult(A,ld(B,C)),A) = ld(C,B). [para(7(a,1),331(a,1,1)),flip(a)].
% 18.27/18.55 422 ld(mult(mult(A,B),C),rd(A,C)) = ld(mult(D,mult(C,mult(B,C))),D). [para(18(a,1),331(a,1,1))].
% 18.27/18.55 430 mult(mult(A,B),rd(rd(ld(C,C),C),B)) = rd(mult(A,rd(B,C)),B). [para(333(a,1),46(a,1,1,2)),flip(a)].
% 18.27/18.55 474 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(14(a,1),354(a,1,2,2))].
% 18.27/18.55 523 mult(mult(A,mult(B,ld(C,D))),ld(D,C)) = mult(mult(A,ld(C,D)),mult(ld(D,C),B)). [para(358(a,1),18(a,1,2,2)),rewrite([474(2)]),flip(a)].
% 18.27/18.55 524 ld(mult(A,ld(B,C)),mult(D,ld(C,B))) = mult(ld(C,B),mult(ld(A,D),ld(C,B))). [para(358(a,1),23(a,1,2,1,1)),flip(a)].
% 18.27/18.55 541 rd(A,mult(ld(B,C),mult(D,ld(B,C)))) = mult(A,ld(mult(mult(C,D),ld(B,C)),B)). [para(15(a,1),397(a,1,2,1)),flip(a)].
% 18.27/18.55 563 mult(mult(A,mult(ld(B,C),D)),ld(C,B)) = mult(mult(A,ld(B,C)),mult(D,ld(C,B))). [para(474(a,1),46(a,1)),rewrite([474(9)])].
% 18.27/18.55 607 mult(ld(A,B),mult(ld(C,A),ld(A,B))) = ld(mult(C,ld(B,A)),B). [para(7(a,1),50(a,1,2)),rewrite([474(2)]),flip(a)].
% 18.27/18.55 608 mult(A,mult(ld(B,rd(C,A)),A)) = ld(rd(B,A),C). [para(9(a,1),50(a,1,2)),flip(a)].
% 18.27/18.55 659 rd(rd(A,rd(B,C)),C) = rd(mult(A,C),mult(C,B)). [para(79(a,1),10(a,1,1)),flip(a)].
% 18.27/18.55 670 rd(rd(rd(A,B),C),B) = rd(A,mult(B,mult(C,B))). [para(9(a,1),117(a,1,1)),flip(a)].
% 18.27/18.55 696 mult(rd(mult(A,ld(B,C)),D),ld(B,C)) = mult(A,ld(mult(mult(B,D),ld(C,B)),C)). [para(358(a,1),117(a,1,1)),rewrite([541(5),474(10)]),flip(a)].
% 18.27/18.55 780 ld(mult(A,B),rd(mult(A,C),B)) = rd(ld(B,C),B). [para(149(a,1),8(a,1,2))].
% 18.27/18.55 816 rd(A,rd(ld(B,C),B)) = mult(rd(mult(A,B),C),B). [para(149(a,1),397(a,1,2,1)),rewrite([50(4),415(5)]),flip(a)].
% 18.27/18.55 850 mult(mult(mult(rd(A,mult(mult(B,mult(C,B)),D)),B),C),mult(B,rd(rd(D,B),C))) = rd(rd(A,B),C). [para(151(a,1),20(a,1,1)),rewrite([166(4),166(12)]),flip(a)].
% 18.27/18.55 865 ld(rd(A,mult(B,mult(C,B))),rd(rd(A,B),C)) = B. [para(151(a,1),28(a,1,1)),rewrite([166(13),850(13)])].
% 18.27/18.55 995 rd(ld(A,ld(B,C)),A) = ld(mult(B,A),rd(C,A)). [para(204(a,1),10(a,1,1))].
% 18.27/18.55 1060 ld(mult(rd(mult(A,B),C),B),A) = rd(ld(B,C),B). [para(206(a,1),10(a,1,1)),flip(a)].
% 18.27/18.55 1070 rd(mult(A,mult(B,A)),A) = ld(rd(ld(A,A),A),B). [para(206(a,1),333(a,1)),rewrite([333(6),333(8),670(6),13(7)]),flip(a)].
% 18.27/18.55 1072 mult(ld(ld(A,B),C),ld(B,A)) = mult(ld(B,A),mult(C,ld(B,A))). [para(206(a,1),358(a,1,1)),rewrite([696(9),421(10),40(8)])].
% 18.27/18.55 1073 mult(mult(ld(A,B),ld(A,B)),mult(ld(B,A),C)) = ld(ld(B,A),C). [para(358(a,1),206(a,1,1,1,1,1)),rewrite([524(6),13(3),523(6)])].
% 18.27/18.55 1079 mult(ld(A,B),mult(mult(ld(B,A),ld(A,B)),ld(A,B))) = ld(ld(B,A),ld(A,B)). [para(216(a,1),39(a,1,2)),rewrite([1073(7),216(7)]),flip(a)].
% 18.27/18.55 1105 ld(mult(A,mult(ld(A,A),A)),mult(A,mult(A,A))) = A. [para(203(a,1),325(a,1,1,2)),rewrite([39(3),8(8)])].
% 18.27/18.55 1147 ld(ld(mult(A,B),A),mult(mult(ld(B,B),C),B)) = mult(B,mult(C,B)). [para(217(a,1),40(a,1,2,2)),rewrite([217(10),217(10)])].
% 18.27/18.55 1149 mult(ld(mult(A,B),A),rd(C,B)) = rd(ld(B,C),B). [para(219(a,2),40(a,1,2,2)),rewrite([333(5),780(4),397(7)]),flip(a)].
% 18.27/18.55 1150 mult(rd(ld(A,A),A),rd(B,A)) = rd(ld(A,B),A). [para(219(a,2),40(a,2,1)),rewrite([397(5),780(4),397(7)]),flip(a)].
% 18.27/18.55 1154 mult(ld(A,B),mult(rd(ld(C,C),C),ld(A,B))) = ld(A,mult(rd(B,C),ld(A,B))). [para(333(a,1),40(a,1,2,1)),flip(a)].
% 18.27/18.55 1158 mult(ld(A,B),mult(ld(mult(C,D),C),ld(A,B))) = ld(A,mult(rd(B,D),ld(A,B))). [para(397(a,1),40(a,1,2,1)),flip(a)].
% 18.27/18.55 1180 ld(ld(A,A),rd(mult(ld(mult(B,A),B),C),A)) = rd(ld(A,C),A). [para(329(a,1),40(a,1,2,2)),rewrite([333(7),329(10),329(12),333(11),1150(10)])].
% 18.27/18.55 1185 mult(rd(A,A),mult(A,A)) = mult(A,A). [para(7(a,1),362(a,1,1)),flip(a)].
% 18.27/18.55 1187 mult(A,rd(B,B)) = mult(A,ld(B,B)). [para(362(a,1),10(a,1,1)),rewrite([46(4),9(2)])].
% 18.27/18.55 1235 ld(ld(A,B),ld(B,A)) = mult(ld(B,A),ld(B,A)). [para(362(a,1),40(a,1,2)),rewrite([474(2),7(2),8(5),216(7),1079(10)]),flip(a)].
% 18.27/18.55 1236 mult(c1,ld(c2,c2)) != c1 | mult(rd(c2,c2),c1) != c1 # answer(goals). [back_rewrite(12),rewrite([1187(5)])].
% 18.27/18.55 1240 mult(A,mult(ld(A,A),A)) = mult(A,A). [para(1185(a,1),8(a,1,2)),rewrite([50(3)])].
% 18.27/18.55 1241 rd(mult(A,A),mult(A,A)) = rd(A,A). [para(1185(a,1),10(a,1,1))].
% 18.27/18.55 1281 ld(mult(A,A),mult(A,mult(A,A))) = A. [back_rewrite(1105),rewrite([1240(3)])].
% 18.27/18.55 1341 rd(A,A) = ld(A,A). [para(1187(a,1),8(a,1,2)),rewrite([8(3)]),flip(a)].
% 18.27/18.55 1367 ld(mult(A,A),mult(A,A)) = ld(A,A). [back_rewrite(1241),rewrite([1341(3),1341(4)])].
% 18.27/18.55 1368 mult(c1,ld(c2,c2)) != c1 | mult(ld(c2,c2),c1) != c1 # answer(goals). [back_rewrite(1236),rewrite([1341(10)])].
% 18.27/18.55 1381 mult(ld(A,A),A) = A. [para(1341(a,1),9(a,1,1))].
% 18.27/18.55 1382 ld(ld(A,A),A) = A. [para(1341(a,1),13(a,1,1))].
% 18.27/18.55 1383 mult(ld(A,A),mult(A,mult(B,A))) = mult(mult(A,B),A). [para(1341(a,1),18(a,1,1))].
% 18.27/18.55 1384 mult(ld(A,ld(A,A)),A) = ld(A,A). [para(1341(a,1),218(a,1,1,2))].
% 18.27/18.55 1386 rd(ld(A,A),A) = ld(A,ld(A,A)). [para(1341(a,1),251(a,2,2))].
% 18.27/18.55 1387 ld(mult(A,B),A) = ld(B,ld(B,B)). [para(1341(a,1),343(a,2,2))].
% 18.27/18.55 1388 ld(A,rd(A,B)) = ld(B,ld(B,B)). [para(1341(a,1),344(a,1,2)),flip(a)].
% 18.27/18.55 1389 mult(A,ld(B,ld(B,B))) = rd(A,B). [para(1341(a,1),355(a,1,2,2))].
% 18.27/18.55 1393 mult(mult(ld(mult(A,B),mult(A,B)),A),rd(B,A)) = rd(mult(A,B),A). [para(1341(a,1),151(a,1,1,1))].
% 18.27/18.55 1395 ld(rd(A,B),rd(A,B)) = mult(rd(A,mult(B,A)),B). [para(1341(a,1),166(a,2)),rewrite([9(2)]),flip(a)].
% 18.27/18.55 1426 mult(ld(A,B),mult(ld(C,ld(C,C)),ld(A,B))) = ld(A,mult(rd(B,C),ld(A,B))). [back_rewrite(1154),rewrite([1386(3)])].
% 18.27/18.55 1441 rd(mult(A,mult(B,A)),A) = ld(ld(A,ld(A,A)),B). [back_rewrite(1070),rewrite([1386(5)])].
% 18.27/18.55 1463 mult(mult(A,B),rd(ld(C,ld(C,C)),B)) = rd(mult(A,rd(B,C)),B). [back_rewrite(430),rewrite([1386(3)])].
% 18.27/18.55 1477 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = ld(C,ld(C,C)). [back_rewrite(327),rewrite([1386(10)])].
% 18.27/18.55 1496 mult(rd(A,B),mult(B,B)) = mult(mult(A,B),ld(B,B)). [para(1381(a,1),33(a,2,2)),rewrite([474(2),7(2),474(5),362(6)]),flip(a)].
% 18.27/18.55 1505 ld(ld(A,B),mult(ld(B,A),ld(A,B))) = ld(B,A). [para(1381(a,1),421(a,1,1)),rewrite([216(4)])].
% 18.27/18.55 1511 rd(rd(ld(A,A),B),A) = rd(A,mult(A,mult(B,A))). [para(1381(a,1),117(a,1,1)),flip(a)].
% 18.27/18.55 1554 mult(mult(A,ld(B,B)),B) = mult(mult(A,B),ld(B,B)). [back_rewrite(362),rewrite([1496(6)])].
% 18.27/18.55 1618 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(1281(a,1),7(a,1,2))].
% 18.27/18.55 1637 mult(ld(A,A),ld(A,A)) = ld(A,A). [para(355(a,1),1367(a,1,1)),rewrite([355(8),1395(7),355(5),1341(3),474(4),1554(5),218(3),216(8),13(5),355(6),1341(4)])].
% 18.27/18.55 1649 mult(ld(A,ld(A,A)),mult(A,mult(B,A))) = mult(mult(ld(A,A),B),A). [para(1384(a,1),11(a,1,1,1)),flip(a)].
% 18.27/18.55 1743 mult(ld(A,ld(A,A)),ld(A,A)) = ld(A,ld(A,A)). [para(1387(a,2),25(a,1,1,1,2)),rewrite([397(3),9(2),8(6)])].
% 18.27/18.55 1758 mult(ld(A,rd(A,B)),ld(B,B)) = ld(B,ld(B,B)). [para(1388(a,2),25(a,1,2,2,1)),rewrite([1389(3),9(2),8(6)])].
% 18.27/18.55 1856 ld(ld(A,ld(A,A)),A) = mult(A,A). [para(1618(a,1),10(a,1,1)),rewrite([1441(3)])].
% 18.27/18.55 1932 mult(ld(A,A),mult(ld(A,A),mult(B,ld(A,A)))) = mult(mult(ld(A,A),B),ld(A,A)). [para(1637(a,1),11(a,1,1,1)),flip(a)].
% 18.27/18.55 1933 ld(ld(A,A),mult(B,ld(A,A))) = mult(mult(ld(A,A),B),ld(A,A)). [para(1637(a,1),23(a,1,2,1,1)),rewrite([1072(5),1932(6)]),flip(a)].
% 18.27/18.55 1937 mult(ld(A,A),mult(ld(B,ld(A,A)),ld(A,A))) = ld(mult(B,ld(A,A)),ld(A,A)). [para(1637(a,1),50(a,1,2)),rewrite([474(2)]),flip(a)].
% 18.27/18.55 1939 ld(ld(A,A),ld(ld(A,A),B)) = mult(ld(A,A),B). [para(1637(a,1),204(a,1,1,1)),rewrite([474(3),1933(4),358(6)]),flip(a)].
% 18.27/18.55 1941 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(1637(a,1),40(a,1,2,1)),flip(a)].
% 18.27/18.55 1950 rd(ld(mult(A,B),A),B) = ld(B,ld(mult(A,B),A)). [para(397(a,1),1856(a,2)),rewrite([216(7),8(4),397(5),1341(3),217(4)]),flip(a)].
% 18.27/18.55 2444 mult(rd(ld(mult(A,B),mult(A,B)),B),ld(A,mult(mult(A,B),B))) = mult(ld(mult(A,B),mult(A,B)),B). [para(1637(a,1),58(a,1,1)),flip(a)].
% 18.27/18.55 2517 mult(rd(A,mult(B,ld(C,A))),ld(C,A)) = rd(C,mult(ld(A,C),B)). [para(7(a,1),659(a,2,1)),rewrite([474(2),474(5)])].
% 18.27/18.55 2897 ld(rd(A,mult(A,mult(B,A))),rd(ld(A,A),B)) = A. [para(1341(a,1),865(a,1,2,1))].
% 18.27/18.55 3569 ld(mult(rd(A,B),A),ld(A,A)) = rd(ld(A,B),A). [para(1381(a,1),1060(a,1,1,1,1))].
% 18.27/18.55 3721 mult(ld(A,ld(mult(B,A),B)),mult(A,C)) = ld(A,C). [para(1149(a,1),33(a,1,1)),rewrite([9(3),1950(4)]),flip(a)].
% 18.27/18.55 4428 ld(mult(A,ld(B,C)),mult(A,ld(B,C))) = mult(rd(A,mult(ld(C,B),A)),ld(C,B)). [para(474(a,1),1395(a,1,1)),rewrite([474(4)])].
% 18.27/18.55 4439 mult(A,mult(mult(rd(B,mult(A,B)),A),A)) = ld(rd(rd(B,A),A),B). [para(1395(a,1),608(a,1,2,1))].
% 18.27/18.55 5289 mult(mult(ld(A,B),B),ld(B,A)) = ld(ld(B,A),A). [para(7(a,1),1441(a,1,1,2)),rewrite([474(4),216(8),1505(9)])].
% 18.27/18.55 5302 ld(ld(A,B),mult(C,ld(A,B))) = mult(mult(ld(B,A),C),ld(A,B)). [para(358(a,1),1441(a,1,1,2)),rewrite([474(4),216(8),1505(9)]),flip(a)].
% 18.27/18.55 5341 mult(ld(A,A),mult(ld(A,A),B)) = ld(ld(A,A),B). [para(1235(a,1),1441(a,2,1,2)),rewrite([474(6),523(6),1637(3),1637(8),216(7),1637(7)])].
% 18.27/18.55 6914 ld(rd(ld(A,A),B),rd(A,mult(A,mult(B,A)))) = ld(A,ld(A,A)). [para(1511(a,1),1388(a,1,2))].
% 18.27/18.55 7272 mult(mult(rd(A,mult(ld(B,B),A)),ld(B,B)),mult(mult(A,ld(B,B)),mult(B,mult(A,ld(B,B))))) = mult(mult(mult(A,B),ld(B,B)),mult(A,ld(B,B))). [para(1554(a,1),1383(a,2,1)),rewrite([4428(5)])].
% 18.27/18.55 7655 ld(mult(rd(ld(A,ld(A,A)),B),ld(A,A)),ld(A,ld(A,A))) = mult(ld(A,A),mult(B,ld(A,A))). [para(1743(a,1),1060(a,1,1,1,1)),rewrite([474(12),1072(12)])].
% 18.27/18.55 7806 mult(rd(ld(A,rd(A,B)),mult(C,ld(B,B))),ld(B,B)) = rd(ld(B,ld(B,B)),mult(ld(B,B),C)). [para(1758(a,1),659(a,2,1)),rewrite([474(4),474(7)])].
% 18.27/18.55 8156 rd(A,mult(mult(ld(B,B),C),ld(B,B))) = mult(A,ld(mult(C,ld(B,B)),ld(B,B))). [para(1939(a,1),816(a,1,2,1)),rewrite([474(4),474(10),11(12),1937(11)])].
% 18.27/18.55 10500 ld(mult(mult(rd(A,B),A),C),rd(ld(A,A),C)) = rd(ld(C,rd(ld(A,B),A)),C). [para(3569(a,1),995(a,1,1,2)),flip(a)].
% 18.27/18.55 10545 mult(ld(A,ld(mult(B,A),B)),C) = ld(A,ld(A,C)). [para(7(a,1),3721(a,1,2))].
% 18.27/18.55 11605 ld(ld(ld(A,A),B),ld(A,A)) = ld(C,rd(C,mult(ld(A,A),B))). [para(5341(a,1),343(a,1,1))].
% 18.27/18.55 13081 ld(ld(A,B),ld(ld(A,B),C)) = mult(mult(ld(B,A),ld(B,A)),C). [para(7(a,1),10545(a,1,1,2,1)),rewrite([1235(3)]),flip(a)].
% 18.27/18.55 17509 ld(A,mult(mult(A,mult(B,A)),A)) = mult(mult(mult(ld(A,A),B),A),A). [para(220(a,1),5289(a,1,1)),rewrite([8(9),8(10)]),flip(a)].
% 18.27/18.55 17743 ld(mult(mult(ld(A,A),B),ld(A,A)),ld(A,A)) = ld(A,mult(rd(A,B),ld(A,A))). [para(5341(a,1),422(a,2,1)),rewrite([474(5),524(6),1158(6),5302(8)]),flip(a)].
% 18.27/18.55 18269 ld(mult(ld(A,A),ld(B,A)),B) = mult(ld(A,B),B). [para(1382(a,1),607(a,1,2,1)),rewrite([7(3)]),flip(a)].
% 18.27/18.55 18325 rd(ld(A,mult(mult(ld(B,B),A),B)),A) = mult(B,rd(ld(B,B),A)). [para(2897(a,1),18269(a,2,1)),rewrite([1395(7),6914(13),1389(10),46(8),10(7),10500(9),17509(4),10(5)])].
% 18.27/18.55 20327 rd(A,mult(ld(B,A),A)) = mult(ld(B,B),ld(A,B)). [para(7(a,1),2517(a,1,1,2)),rewrite([1341(1)]),flip(a)].
% 18.27/18.55 20388 mult(rd(A,mult(ld(B,A),A)),ld(B,B)) = mult(ld(B,B),ld(mult(A,ld(B,B)),B)). [para(20327(a,2),1383(a,2,1)),rewrite([216(3),1637(3),607(6)]),flip(a)].
% 18.27/18.55 20415 mult(ld(A,A),rd(B,mult(ld(A,B),B))) = ld(ld(A,A),ld(B,A)). [para(20327(a,2),5341(a,1,2))].
% 18.27/18.55 23946 mult(ld(A,A),rd(B,mult(ld(A,A),B))) = ld(B,B). [para(358(a,1),4439(a,1,2)),rewrite([474(7),474(9),358(9)])].
% 18.27/18.55 23978 mult(ld(A,ld(B,B)),ld(ld(B,B),A)) = mult(ld(B,B),rd(ld(ld(B,B),A),A)). [para(7(a,1),23946(a,1,2,2)),rewrite([216(10)]),flip(a)].
% 18.27/18.55 23979 rd(A,mult(ld(B,B),A)) = ld(ld(B,B),ld(A,A)). [para(23946(a,1),8(a,1,2)),flip(a)].
% 18.27/18.55 23992 ld(ld(ld(A,A),ld(B,B)),ld(A,A)) = ld(B,B). [para(23946(a,1),226(a,2,2)),rewrite([23979(3),23979(6),23979(9),216(10),23978(10),474(9),23979(15),607(17),563(11),7(5),7(6),421(5),23979(4),421(6)]),flip(a)].
% 18.27/18.55 23993 mult(ld(A,A),mult(ld(ld(A,A),ld(B,B)),ld(B,B))) = ld(B,B). [para(23946(a,1),241(a,1,1,1)),rewrite([23979(4),421(6),13081(5),1637(3),23979(6),39(7),23979(10),23979(14),23979(17),216(18),23978(18),474(17),8(19),8(16)])].
% 18.27/18.55 23995 mult(ld(ld(A,A),ld(B,B)),ld(B,B)) = ld(A,A). [para(23946(a,1),256(a,2,2)),rewrite([23979(3),23979(6),23979(9),216(10),23978(10),474(9),23993(10),23979(9),23978(10),474(9),23993(10),23979(8),474(9),8(10),23992(10)])].
% 18.27/18.55 23996 ld(A,A) = ld(B,B). [para(23946(a,1),269(a,1,1,1)),rewrite([23979(4),474(5),8(6),13081(5),1637(3),23979(6),39(7),23995(6),1637(3),23979(4),23979(8),23979(11),216(12),23978(12),474(11),23995(11),1637(8),216(7),1637(7),23992(6)])].
% 18.27/18.55 23997 ld(ld(A,A),mult(ld(B,B),ld(ld(A,A),ld(B,B)))) = ld(B,B). [para(23946(a,1),422(a,2,1,2,2)),rewrite([23979(5),23979(9),474(10),524(11),421(6),1941(9),23979(10),23995(12),421(10)])].
% 18.27/18.55 24000 mult(ld(A,A),mult(ld(B,B),ld(A,A))) = ld(ld(A,A),ld(B,B)). [para(23946(a,1),183(a,1,2,2,2)),rewrite([23979(4),23979(7),23979(15),23979(21),23995(23),524(21),1477(18),216(11),23978(11),474(10),23995(10),1637(7),23992(6),23979(8)])].
% 18.27/18.55 24001 ld(ld(A,A),ld(B,B)) = ld(B,B). [para(23946(a,1),184(a,1,1,2,2)),rewrite([23979(5),23995(7),358(4),23979(4),23979(8),1072(10),24000(10),7(9),23979(8),1941(10),23997(8),24000(5),8(5),23979(7),1072(9),24000(9),7(8)])].
% 18.27/18.55 24002 ld(ld(A,A),mult(mult(ld(B,B),C),ld(B,B))) = mult(ld(B,B),mult(C,ld(B,B))). [para(23946(a,1),1147(a,1,1,1)),rewrite([24001(3),23979(4),24001(4),23979(5),24001(5),24001(4),23979(6),24001(6),23979(9),24001(9),23979(10),24001(10)])].
% 18.27/18.55 24005 mult(mult(ld(A,A),mult(ld(B,B),C)),ld(A,A)) = mult(ld(A,A),mult(C,ld(A,A))). [para(23946(a,1),1180(a,1,2,1,1,1)),rewrite([23979(3),24001(3),23979(4),24001(4),24001(3),24001(4),23979(6),24001(6),474(5),5302(6),23979(9),24001(9),23979(11),24001(11),474(10),1072(10)])].
% 18.27/18.55 24007 mult(mult(ld(A,A),ld(B,B)),ld(A,A)) = ld(A,A). [para(23946(a,1),1393(a,1,1,1,1)),rewrite([23979(5),24001(5),5302(5),11(7),24000(6),24001(4),1637(3),23979(4),24001(4),474(4),5341(5),24001(3),23979(5),24001(5),474(6)]),flip(a)].
% 18.27/18.55 24008 mult(ld(A,A),ld(B,B)) = ld(A,A). [para(23946(a,1),1393(a,2,1)),rewrite([23979(4),24001(4),23979(7),24001(7),4428(7),23979(5),24001(4),24001(3),24007(5),23979(4),24001(4),474(4),24000(5),24001(3),474(4)]),flip(a)].
% 18.27/18.55 24010 mult(mult(ld(A,A),rd(ld(B,B),C)),ld(B,B)) = ld(B,mult(rd(B,C),ld(B,B))). [para(23946(a,1),1463(a,1,1)),rewrite([23979(6),24001(6),474(5),1426(6),23979(8),24001(8),23979(11),24001(11),474(10)]),flip(a)].
% 18.27/18.55 24016 mult(ld(A,A),B) = B. [para(23946(a,1),1649(a,2,1)),rewrite([23979(5),24001(5),1649(6),24008(3),1381(2)]),flip(a)].
% 18.27/18.55 24030 mult(A,ld(B,B)) = A. [para(23946(a,1),2517(a,2,2)),rewrite([24016(2),1341(1),24016(3),474(2),7(2),7(2),474(2)]),flip(a)].
% 18.27/18.55 24072 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(23946(a,1),299(a,1,1,2,1,2,2)),rewrite([24016(2),1341(1),24030(3),24030(2),24016(2),1341(1),24016(4),1341(3),24016(5),1341(4),24030(5),24016(4),24030(4),24016(3),24016(3),1341(2),24030(3),24016(2),24016(4),1341(3),24016(6),1341(5),24030(6),24030(5),24030(4),24016(4),1341(3),24016(6),1341(5),24030(6),24030(5),24030(4),24016(5),1341(4),24016(7),1341(6),24016(8),1341(7),24016(10),1341(9),24030(10),24030(9),24030(8),24016(8),1341(7),24030(8),24016(7),24030(7),24016(6),24016(6),1341(5),24030(6),24016(5)]),flip(a)].
% 18.27/18.55 24093 mult(mult(A,B),A) = mult(A,mult(B,A)). [back_rewrite(7272),rewrite([24016(2),1341(1),24030(3),24030(3),24030(3),24016(4),24030(5),24030(5)]),flip(a)].
% 18.27/18.55 24095 ld(A,A) = c_0. [new_symbol(23996)].
% 18.27/18.55 24104 mult(c_0,mult(A,c_0)) = mult(c_0,A). [back_rewrite(2444),rewrite([24095(3),24072(4),8(5),1496(4),24095(3),24093(4),24095(7)])].
% 18.27/18.55 24105 rd(c_0,A) = ld(A,c_0). [back_rewrite(1386),rewrite([24095(1),24095(3)])].
% 18.27/18.55 24109 mult(c_0,mult(c_0,A)) = mult(c_0,A). [back_rewrite(24005),rewrite([24095(1),24095(2),24095(5),24093(6),24093(5),24104(5),24095(5),24095(6),24104(8)])].
% 18.27/18.55 24110 ld(c_0,A) = mult(c_0,A). [back_rewrite(5341),rewrite([24095(1),24095(2),24109(4),24095(3)]),flip(a)].
% 18.27/18.55 24111 ld(A,mult(rd(A,B),c_0)) = mult(c_0,ld(B,c_0)). [back_rewrite(24010),rewrite([24095(1),24095(2),24105(3),24095(5),24093(6),24104(6),24095(6)]),flip(a)].
% 18.27/18.55 24116 mult(c_0,A) = A. [back_rewrite(24002),rewrite([24095(1),24095(2),24095(4),24093(5),24104(5),8(4),24095(1),24095(2),24104(4)]),flip(a)].
% 18.27/18.55 24159 rd(A,mult(ld(B,A),A)) = ld(A,B). [back_rewrite(20415),rewrite([24095(1),24116(5),24095(4),24110(6),24116(6)])].
% 18.27/18.55 24168 ld(mult(A,c_0),B) = mult(ld(A,B),c_0). [back_rewrite(20388),rewrite([24159(3),24095(2),24095(4),24095(5),24116(8)]),flip(a)].
% 18.27/18.55 24212 mult(A,ld(B,c_0)) = rd(A,B). [back_rewrite(18325),rewrite([24095(1),24116(2),8(2),24095(2),24105(3)]),flip(a)].
% 18.27/18.55 24222 mult(ld(A,c_0),c_0) = ld(A,c_0). [back_rewrite(17743),rewrite([24095(1),24116(2),24095(1),24095(3),24168(4),24095(6),24111(8),24212(8),24105(6)])].
% 18.27/18.55 24266 ld(A,rd(A,B)) = ld(B,c_0). [back_rewrite(11605),rewrite([24095(1),24110(2),24116(2),24095(1),24095(3),24116(4)]),flip(a)].
% 18.27/18.55 24390 rd(A,mult(B,c_0)) = rd(A,B). [back_rewrite(8156),rewrite([24095(1),24116(2),24095(1),24095(4),24095(6),24168(7),24222(7),24212(6)])].
% 18.27/18.55 24399 mult(rd(ld(A,c_0),B),c_0) = rd(ld(A,c_0),B). [back_rewrite(7806),rewrite([24266(2),24095(3),24390(5),24095(4),24095(6),24095(8),24116(9)])].
% 18.27/18.55 24407 mult(A,c_0) = A. [back_rewrite(7655),rewrite([24095(1),24095(4),24399(5),24095(4),13(6),24095(1),24095(2),24116(4)]),flip(a)].
% 18.27/18.55 24462 $F # answer(goals). [back_rewrite(1368),rewrite([24095(4),24407(3),24095(6),24116(6)]),xx(a),xx(b)].
% 18.27/18.55
% 18.27/18.55 % SZS output end Refutation
% 18.27/18.55 ============================== end of proof ==========================
% 18.27/18.55
% 18.27/18.55 ============================== STATISTICS ============================
% 18.27/18.55
% 18.27/18.55 Given=736. Generated=745962. Kept=24455. proofs=1.
% 18.27/18.55 Usable=667. Sos=9273. Demods=8331. Limbo=446, Disabled=14075. Hints=0.
% 18.27/18.55 Megabytes=27.81.
% 18.27/18.55 User_CPU=17.06, System_CPU=0.46, Wall_clock=17.
% 18.27/18.55
% 18.27/18.55 ============================== end of statistics =====================
% 18.27/18.55
% 18.27/18.55 ============================== end of search =========================
% 18.27/18.55
% 18.27/18.55 THEOREM PROVED
% 18.27/18.55 % SZS status Theorem
% 18.27/18.55
% 18.27/18.55 Exiting with 1 proof.
% 18.27/18.55
% 18.27/18.55 Process 16488 exit (max_proofs) Tue Jun 14 06:14:27 2022
% 18.27/18.55 Prover9 interrupted
%------------------------------------------------------------------------------