TSTP Solution File: GRP654+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP654+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 11:20:18 EDT 2022
% Result : Theorem 252.80s 253.19s
% Output : Refutation 252.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP654+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.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 : Mon Jun 13 20:22:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 6.12/6.41 ============================== Prover9 ===============================
% 6.12/6.41 Prover9 (32) version 2009-11A, November 2009.
% 6.12/6.41 Process 27124 was started by sandbox on n018.cluster.edu,
% 6.12/6.41 Mon Jun 13 20:22:43 2022
% 6.12/6.41 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26961_n018.cluster.edu".
% 6.12/6.41 ============================== end of head ===========================
% 6.12/6.41
% 6.12/6.41 ============================== INPUT =================================
% 6.12/6.41
% 6.12/6.41 % Reading from file /tmp/Prover9_26961_n018.cluster.edu
% 6.12/6.41
% 6.12/6.41 set(prolog_style_variables).
% 6.12/6.41 set(auto2).
% 6.12/6.41 % set(auto2) -> set(auto).
% 6.12/6.41 % set(auto) -> set(auto_inference).
% 6.12/6.41 % set(auto) -> set(auto_setup).
% 6.12/6.41 % set(auto_setup) -> set(predicate_elim).
% 6.12/6.41 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.12/6.41 % set(auto) -> set(auto_limits).
% 6.12/6.41 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.12/6.41 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.12/6.41 % set(auto) -> set(auto_denials).
% 6.12/6.41 % set(auto) -> set(auto_process).
% 6.12/6.41 % set(auto2) -> assign(new_constants, 1).
% 6.12/6.41 % set(auto2) -> assign(fold_denial_max, 3).
% 6.12/6.41 % set(auto2) -> assign(max_weight, "200.000").
% 6.12/6.41 % set(auto2) -> assign(max_hours, 1).
% 6.12/6.41 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.12/6.41 % set(auto2) -> assign(max_seconds, 0).
% 6.12/6.41 % set(auto2) -> assign(max_minutes, 5).
% 6.12/6.41 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.12/6.41 % set(auto2) -> set(sort_initial_sos).
% 6.12/6.41 % set(auto2) -> assign(sos_limit, -1).
% 6.12/6.41 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.12/6.41 % set(auto2) -> assign(max_megs, 400).
% 6.12/6.41 % set(auto2) -> assign(stats, some).
% 6.12/6.41 % set(auto2) -> clear(echo_input).
% 6.12/6.41 % set(auto2) -> set(quiet).
% 6.12/6.41 % set(auto2) -> clear(print_initial_clauses).
% 6.12/6.41 % set(auto2) -> clear(print_given).
% 6.12/6.41 assign(lrs_ticks,-1).
% 6.12/6.41 assign(sos_limit,10000).
% 6.12/6.41 assign(order,kbo).
% 6.12/6.41 set(lex_order_vars).
% 6.12/6.41 clear(print_given).
% 6.12/6.41
% 6.12/6.41 % formulas(sos). % not echoed (6 formulas)
% 6.12/6.41
% 6.12/6.41 ============================== end of input ==========================
% 6.12/6.41
% 6.12/6.41 % From the command line: assign(max_seconds, 300).
% 6.12/6.41
% 6.12/6.41 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.12/6.41
% 6.12/6.41 % Formulas that are not ordinary clauses:
% 6.12/6.41 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 6.12/6.41 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 6.12/6.41 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 6.12/6.41 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 6.12/6.41 5 (all C all B all A mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 6.12/6.41 6 -(exists X0 all X1 (mult(X1,X0) = X1 & mult(X0,X1) = X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.12/6.41
% 6.12/6.41 ============================== end of process non-clausal formulas ===
% 6.12/6.41
% 6.12/6.41 ============================== PROCESS INITIAL CLAUSES ===============
% 6.12/6.41
% 6.12/6.41 ============================== PREDICATE ELIMINATION =================
% 6.12/6.41
% 6.12/6.41 ============================== end predicate elimination =============
% 6.12/6.41
% 6.12/6.41 Auto_denials:
% 6.12/6.41 % copying label goals to answer in negative clause
% 6.12/6.41
% 6.12/6.41 Term ordering decisions:
% 6.12/6.41
% 6.12/6.41 % Assigning unary symbol f1 kb_weight 0 and highest precedence (5).
% 6.12/6.41 Function symbol KB weights: mult=1. ld=1. rd=1. f1=0.
% 6.12/6.41
% 6.12/6.41 ============================== end of process initial clauses ========
% 6.12/6.41
% 6.12/6.41 ============================== CLAUSES FOR SEARCH ====================
% 6.12/6.41
% 6.12/6.41 ============================== end of clauses for search =============
% 6.12/6.41
% 6.12/6.41 ============================== SEARCH ================================
% 6.12/6.41
% 6.12/6.41 % Starting search at 0.01 seconds.
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=95.000, iters=3346
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=67.000, iters=3342
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=63.000, iters=3377
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=59.000, iters=3352
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=55.000, iters=3341
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=51.000, iters=3382
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=47.000, iters=3372
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=43.000, iters=3334
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=39.000, iters=3344
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=35.000, iters=3353
% 6.12/6.41
% 6.12/6.41 Low Water (keep): wt=31.000, iters=3386
% 6.12/6.41
% 6.12/6.41 Low Water (displace): id=4423, wt=135.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=9517, wt=134.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=7994, wt=130.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=5291, wt=126.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=7966, wt=122.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=9939, wt=118.000
% 252.80/253.19
% 252.80/253.19 Low Water (keep): wt=27.000, iters=3375
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=9960, wt=114.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=7990, wt=110.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=10051, wt=106.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=9979, wt=102.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=9977, wt=98.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=10427, wt=94.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=7047, wt=90.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=6994, wt=86.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=10459, wt=82.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=10461, wt=78.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=10460, wt=74.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=9980, wt=70.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=10823, wt=66.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=11232, wt=62.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=11239, wt=58.000
% 252.80/253.19
% 252.80/253.19 Low Water (keep): wt=23.000, iters=3369
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=12611, wt=54.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=12837, wt=50.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=14380, wt=48.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=15537, wt=46.000
% 252.80/253.19
% 252.80/253.19 Low Water (displace): id=16034, wt=42.000
% 252.80/253.19
% 252.80/253.19 ============================== PROOF =================================
% 252.80/253.19 % SZS status Theorem
% 252.80/253.19 % SZS output start Refutation
% 252.80/253.19
% 252.80/253.19 % Proof 1 at 247.23 (+ 4.78) seconds: goals.
% 252.80/253.19 % Length of proof is 198.
% 252.80/253.19 % Level of proof is 36.
% 252.80/253.19 % Maximum clause weight is 39.000.
% 252.80/253.19 % Given clauses 2993.
% 252.80/253.19
% 252.80/253.19 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 252.80/253.19 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 252.80/253.19 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 252.80/253.19 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 252.80/253.19 5 (all C all B all A mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 252.80/253.19 6 -(exists X0 all X1 (mult(X1,X0) = X1 & mult(X0,X1) = X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 252.80/253.19 7 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 252.80/253.19 8 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 252.80/253.19 9 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 252.80/253.19 10 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 252.80/253.19 11 mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))) # label(f05) # label(axiom). [clausify(5)].
% 252.80/253.19 12 mult(f1(A),A) != f1(A) | mult(A,f1(A)) != f1(A) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(6)].
% 252.80/253.19 14 rd(A,ld(B,A)) = B. [para(7(a,1),10(a,1,1))].
% 252.80/253.19 15 mult(A,mult(B,mult(A,ld(mult(mult(A,B),A),C)))) = C. [para(11(a,1),7(a,1))].
% 252.80/253.19 16 mult(A,mult(ld(A,B),mult(A,C))) = mult(mult(B,A),C). [para(7(a,1),11(a,1,1,1)),flip(a)].
% 252.80/253.19 17 ld(mult(mult(A,B),A),mult(A,mult(B,mult(A,C)))) = C. [para(11(a,1),8(a,1,2))].
% 252.80/253.19 18 mult(rd(A,B),mult(B,mult(rd(A,B),C))) = mult(mult(A,rd(A,B)),C). [para(9(a,1),11(a,1,1,1)),flip(a)].
% 252.80/253.19 19 rd(mult(A,mult(B,mult(A,C))),C) = mult(mult(A,B),A). [para(11(a,1),10(a,1,1))].
% 252.80/253.19 22 mult(A,mult(B,ld(mult(mult(B,A),B),C))) = ld(B,C). [para(15(a,1),8(a,1,2)),flip(a)].
% 252.80/253.19 26 mult(mult(A,B),ld(B,C)) = mult(B,mult(ld(B,A),C)). [para(7(a,1),16(a,1,2,2)),flip(a)].
% 252.80/253.19 27 ld(A,mult(mult(B,A),C)) = mult(ld(A,B),mult(A,C)). [para(16(a,1),8(a,1,2))].
% 252.80/253.19 29 rd(mult(mult(A,B),C),mult(ld(B,A),mult(B,C))) = B. [para(16(a,1),10(a,1,1))].
% 252.80/253.19 39 ld(mult(A,mult(ld(A,ld(A,B)),B)),mult(ld(A,B),mult(mult(B,A),C))) = mult(A,C). [para(16(a,1),17(a,1,2,2)),rewrite([26(4)])].
% 252.80/253.19 40 mult(mult(A,rd(A,B)),B) = mult(rd(A,B),mult(B,A)). [para(9(a,1),18(a,1,2,2)),flip(a)].
% 252.80/253.19 42 mult(rd(A,B),mult(mult(B,mult(rd(A,B),C)),mult(rd(A,B),D))) = mult(mult(mult(mult(A,rd(A,B)),C),rd(A,B)),D). [para(18(a,1),11(a,1,1,1)),flip(a)].
% 252.80/253.19 46 rd(mult(A,mult(B,C)),ld(A,C)) = mult(mult(A,B),A). [para(7(a,1),19(a,1,1,2,2))].
% 252.80/253.19 48 mult(mult(A,rd(B,mult(A,C))),A) = rd(mult(A,B),C). [para(9(a,1),19(a,1,1,2)),flip(a)].
% 252.80/253.19 55 mult(ld(A,B),mult(A,ld(mult(B,A),C))) = ld(A,C). [para(7(a,1),22(a,1,2,2,1,1))].
% 252.80/253.19 56 mult(A,ld(mult(mult(A,B),A),C)) = ld(B,ld(A,C)). [para(22(a,1),8(a,1,2)),flip(a)].
% 252.80/253.19 63 ld(mult(A,B),mult(B,mult(ld(B,A),C))) = ld(B,C). [para(26(a,1),8(a,1,2))].
% 252.80/253.19 64 mult(A,mult(ld(A,rd(B,A)),C)) = mult(B,ld(A,C)). [para(9(a,1),26(a,1,1)),flip(a)].
% 252.80/253.19 74 mult(ld(A,rd(B,A)),mult(A,C)) = ld(A,mult(B,C)). [para(9(a,1),27(a,1,2,1)),flip(a)].
% 252.80/253.19 130 rd(mult(A,B),ld(A,C)) = mult(mult(A,rd(B,C)),A). [para(9(a,1),46(a,1,1,2))].
% 252.80/253.19 147 ld(mult(A,rd(B,mult(A,C))),rd(mult(A,B),C)) = A. [para(48(a,1),8(a,1,2))].
% 252.80/253.19 151 mult(A,mult(rd(B,mult(A,C)),mult(A,D))) = mult(rd(mult(A,B),C),D). [para(48(a,1),11(a,1,1)),flip(a)].
% 252.80/253.19 168 ld(ld(A,B),ld(A,C)) = mult(A,ld(mult(B,A),C)). [para(55(a,1),8(a,1,2))].
% 252.80/253.19 184 ld(mult(mult(A,B),A),C) = ld(A,ld(B,ld(A,C))). [para(56(a,1),8(a,1,2)),flip(a)].
% 252.80/253.19 189 mult(rd(A,B),ld(mult(mult(mult(A,rd(A,B)),C),rd(A,B)),D)) = ld(mult(B,mult(rd(A,B),C)),ld(rd(A,B),D)). [para(18(a,1),56(a,1,2,1,1))].
% 252.80/253.19 205 ld(mult(A,B),mult(B,C)) = ld(B,ld(ld(B,A),C)). [para(7(a,1),63(a,1,2,2))].
% 252.80/253.19 225 ld(A,mult(B,ld(A,C))) = mult(ld(A,rd(B,A)),C). [para(64(a,1),8(a,1,2))].
% 252.80/253.19 226 rd(mult(A,ld(B,C)),mult(ld(B,rd(A,B)),C)) = B. [para(64(a,1),10(a,1,1))].
% 252.80/253.19 229 mult(mult(A,B),mult(ld(B,rd(C,B)),D)) = mult(B,mult(ld(B,A),mult(C,ld(B,D)))). [para(64(a,1),16(a,1,2,2)),flip(a)].
% 252.80/253.19 264 mult(mult(A,rd(ld(A,B),C)),A) = rd(B,ld(A,C)). [para(7(a,1),130(a,1,1)),flip(a)].
% 252.80/253.19 284 ld(mult(A,rd(B,mult(A,B))),A) = A. [para(10(a,1),147(a,1,2))].
% 252.80/253.19 334 ld(mult(A,rd(ld(A,B),B)),A) = A. [para(7(a,1),284(a,1,1,2,2))].
% 252.80/253.19 337 mult(A,rd(B,mult(A,B))) = rd(A,A). [para(284(a,1),14(a,1,2)),flip(a)].
% 252.80/253.19 350 mult(A,rd(ld(A,B),B)) = rd(A,A). [para(334(a,1),14(a,1,2)),flip(a)].
% 252.80/253.19 353 rd(A,mult(B,A)) = ld(B,rd(B,B)). [para(337(a,1),8(a,1,2)),flip(a)].
% 252.80/253.19 354 rd(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [para(9(a,1),337(a,1,2,2)),flip(a)].
% 252.80/253.19 360 mult(rd(A,A),B) = mult(ld(A,A),B). [para(337(a,1),18(a,2,1)),rewrite([353(2),353(5),229(7),7(5),74(6),8(4)]),flip(a)].
% 252.80/253.19 363 mult(ld(A,A),A) = A. [para(337(a,1),19(a,2,1)),rewrite([151(5),10(2),10(2),360(2)]),flip(a)].
% 252.80/253.19 390 ld(ld(A,A),A) = A. [para(363(a,1),8(a,1,2))].
% 252.80/253.19 391 rd(A,A) = ld(A,A). [para(363(a,1),10(a,1,1))].
% 252.80/253.19 394 mult(mult(A,ld(mult(A,B),mult(A,B))),A) = rd(mult(A,mult(A,B)),B). [para(363(a,1),19(a,1,1,2)),flip(a)].
% 252.80/253.19 399 mult(ld(A,ld(A,A)),B) = ld(A,B). [para(363(a,1),55(a,1,2,2,1)),rewrite([7(4)])].
% 252.80/253.19 433 ld(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [back_rewrite(354),rewrite([391(3)])].
% 252.80/253.19 434 rd(A,mult(B,A)) = ld(B,ld(B,B)). [back_rewrite(353),rewrite([391(3)])].
% 252.80/253.19 435 mult(A,rd(ld(A,B),B)) = ld(A,A). [back_rewrite(350),rewrite([391(4)])].
% 252.80/253.19 464 mult(ld(A,A),mult(A,B)) = mult(A,ld(ld(A,A),B)). [para(390(a,1),26(a,2,2,1)),rewrite([7(2)]),flip(a)].
% 252.80/253.19 466 rd(mult(A,B),mult(A,mult(ld(A,A),B))) = ld(A,A). [para(390(a,1),29(a,1,2,1)),rewrite([7(2)])].
% 252.80/253.19 473 rd(ld(A,B),B) = ld(A,ld(A,A)). [para(399(a,1),10(a,1,1))].
% 252.80/253.19 477 mult(ld(A,B),ld(A,ld(A,A))) = ld(A,rd(B,A)). [para(399(a,1),19(a,1,1,2,2)),rewrite([399(5),225(3),10(4),399(5)]),flip(a)].
% 252.80/253.19 479 mult(A,mult(ld(A,ld(B,ld(B,B))),C)) = mult(ld(B,A),ld(A,C)). [para(399(a,1),26(a,1,1)),flip(a)].
% 252.80/253.19 489 rd(ld(A,B),ld(ld(A,ld(A,A)),C)) = ld(A,rd(rd(B,C),A)). [para(399(a,1),130(a,1,1)),rewrite([399(9),477(10)])].
% 252.80/253.19 523 ld(ld(A,ld(A,A)),B) = mult(A,B). [para(363(a,1),39(a,1,2,2,1)),rewrite([479(6),477(4),391(1),399(6),8(4)])].
% 252.80/253.19 526 ld(A,mult(ld(A,A),mult(mult(A,A),B))) = mult(A,B). [para(399(a,1),39(a,1,1,2)),rewrite([7(2)])].
% 252.80/253.19 530 rd(ld(A,B),mult(A,C)) = ld(A,rd(rd(B,C),A)). [back_rewrite(489),rewrite([523(4)])].
% 252.80/253.19 552 mult(rd(A,mult(B,A)),C) = ld(B,C). [para(434(a,2),55(a,1,1)),rewrite([363(4),7(4)])].
% 252.80/253.19 558 mult(A,rd(B,mult(C,B))) = mult(A,ld(C,ld(C,C))). [para(434(a,2),64(a,2,2)),rewrite([64(5)]),flip(a)].
% 252.80/253.19 566 rd(A,mult(B,A)) = rd(C,mult(B,C)). [para(434(a,2),434(a,2))].
% 252.80/253.19 612 mult(rd(ld(A,B),B),C) = ld(A,C). [para(473(a,2),55(a,1,1)),rewrite([363(4),7(4)])].
% 252.80/253.19 615 mult(A,rd(ld(B,C),C)) = mult(A,ld(B,ld(B,B))). [para(473(a,2),64(a,2,2)),rewrite([64(5)]),flip(a)].
% 252.80/253.19 618 rd(ld(A,B),B) = rd(C,mult(A,C)). [para(473(a,2),434(a,2)),flip(a)].
% 252.80/253.19 619 rd(ld(A,B),B) = rd(ld(A,C),C). [para(473(a,2),473(a,2))].
% 252.80/253.19 654 ld(rd(A,B),C) = mult(rd(B,A),C). [para(9(a,1),552(a,1,1,2)),flip(a)].
% 252.80/253.19 659 mult(ld(A,B),rd(C,mult(A,C))) = ld(A,rd(B,A)). [para(552(a,1),19(a,1,1,2,2)),rewrite([552(5),225(3),10(4),552(5)]),flip(a)].
% 252.80/253.19 678 ld(ld(A,A),B) = mult(ld(A,A),B). [para(363(a,1),552(a,1,1,2)),rewrite([391(1)]),flip(a)].
% 252.80/253.19 689 mult(rd(A,B),rd(B,A)) = mult(rd(B,A),rd(A,B)). [back_rewrite(433),rewrite([654(3)])].
% 252.80/253.19 713 mult(rd(A,B),ld(mult(mult(mult(A,rd(A,B)),C),rd(A,B)),D)) = ld(mult(B,mult(rd(A,B),C)),mult(rd(B,A),D)). [back_rewrite(189),rewrite([654(13)])].
% 252.80/253.19 757 mult(ld(A,A),mult(A,B)) = mult(A,mult(ld(A,A),B)). [back_rewrite(464),rewrite([678(5)])].
% 252.80/253.19 765 rd(A,mult(rd(B,C),A)) = rd(C,B). [para(9(a,1),566(a,1,2)),flip(a)].
% 252.80/253.19 773 rd(A,mult(ld(B,B),A)) = ld(B,B). [para(363(a,1),566(a,1,2)),rewrite([391(1)]),flip(a)].
% 252.80/253.19 778 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(7(a,1),42(a,2)),rewrite([713(12),7(11)])].
% 252.80/253.19 807 rd(mult(mult(A,mult(rd(B,A),C)),mult(rd(B,A),D)),mult(mult(mult(mult(B,rd(B,A)),C),rd(B,A)),D)) = mult(rd(A,B),mult(rd(A,B),rd(B,A))). [para(42(a,1),434(a,1,2)),rewrite([654(17),654(18)])].
% 252.80/253.19 817 mult(rd(A,B),mult(rd(A,B),rd(B,A))) = rd(A,B). [para(42(a,1),566(a,1,2)),rewrite([807(13),765(8)])].
% 252.80/253.19 826 mult(ld(A,B),rd(ld(A,C),C)) = ld(A,rd(B,A)). [para(612(a,1),19(a,1,1,2,2)),rewrite([612(5),225(3),10(4),612(5)]),flip(a)].
% 252.80/253.19 895 mult(ld(A,A),mult(ld(A,A),B)) = B. [para(678(a,1),7(a,1,2))].
% 252.80/253.19 899 mult(A,mult(ld(A,A),ld(mult(A,A),B))) = ld(A,B). [para(55(a,1),678(a,2)),rewrite([678(5),757(5)])].
% 252.80/253.19 964 mult(ld(A,A),ld(A,B)) = mult(A,ld(mult(A,A),B)). [para(55(a,1),895(a,1,2))].
% 252.80/253.19 1029 ld(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),ld(mult(B,ld(A,A)),C)). [para(678(a,1),168(a,1,1)),rewrite([678(4)])].
% 252.80/253.19 1046 mult(A,ld(mult(A,A),mult(ld(A,A),B))) = ld(A,B). [para(363(a,1),184(a,1,1,1)),rewrite([7(2),678(4),678(6),964(6)]),flip(a)].
% 252.80/253.19 1129 mult(ld(mult(A,A),ld(A,A)),B) = ld(mult(A,A),B). [para(205(a,1),399(a,1,1,2)),rewrite([678(3),363(3)])].
% 252.80/253.19 1139 rd(ld(mult(A,A),B),B) = ld(mult(A,A),ld(A,A)). [para(205(a,1),473(a,2,2)),rewrite([678(6),363(6)])].
% 252.80/253.19 1168 mult(ld(A,rd(ld(B,ld(B,B)),A)),C) = ld(A,ld(B,ld(A,C))). [para(399(a,1),225(a,1,2)),flip(a)].
% 252.80/253.19 1204 rd(mult(A,ld(mult(ld(B,B),A),C)),mult(ld(mult(ld(B,B),A),ld(B,B)),C)) = mult(ld(B,B),A). [para(773(a,1),226(a,1,2,1,2))].
% 252.80/253.19 1213 rd(rd(A,ld(B,C)),B) = mult(B,rd(ld(B,A),C)). [para(264(a,1),10(a,1,1))].
% 252.80/253.19 1243 rd(A,rd(ld(B,C),C)) = rd(A,ld(B,ld(B,B))). [para(473(a,2),264(a,2,2)),rewrite([264(5)]),flip(a)].
% 252.80/253.19 1381 rd(mult(A,mult(A,B)),mult(mult(A,A),B)) = ld(A,A). [para(16(a,1),466(a,1,2))].
% 252.80/253.19 1398 mult(A,ld(mult(A,A),A)) = ld(A,A). [para(435(a,1),466(a,1,1)),rewrite([826(5),391(2),7(4),391(3),678(3),964(3)])].
% 252.80/253.19 1415 ld(mult(A,A),A) = ld(A,ld(A,A)). [para(1398(a,1),8(a,1,2)),flip(a)].
% 252.80/253.19 1419 mult(rd(ld(A,ld(A,A)),A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [para(1398(a,1),40(a,2,2)),rewrite([1415(2),1415(4),399(6),1168(5),1415(5)]),flip(a)].
% 252.80/253.19 1428 rd(A,ld(A,ld(A,A))) = mult(A,A). [para(1415(a,1),14(a,1,2))].
% 252.80/253.19 1429 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(mult(A,mult(A,A)),B). [para(1415(a,1),16(a,1,2,1)),rewrite([399(6),27(4),757(4)])].
% 252.80/253.19 1438 rd(ld(A,ld(A,A)),A) = ld(mult(A,A),ld(A,A)). [para(1415(a,1),473(a,1,1)),rewrite([205(7),678(6),363(6)])].
% 252.80/253.19 1446 ld(mult(A,A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [back_rewrite(1419),rewrite([1438(3),1129(5)])].
% 252.80/253.19 1447 rd(ld(A,ld(A,A)),A) = ld(A,ld(A,ld(A,A))). [back_rewrite(1438),rewrite([1446(6)])].
% 252.80/253.19 1450 rd(ld(mult(A,A),B),B) = ld(A,ld(A,ld(A,A))). [back_rewrite(1139),rewrite([1446(6)])].
% 252.80/253.19 1504 rd(A,rd(B,mult(A,B))) = mult(A,A). [para(434(a,2),1428(a,1,2))].
% 252.80/253.19 1505 rd(A,rd(ld(A,B),B)) = mult(A,A). [para(473(a,2),1428(a,1,2))].
% 252.80/253.19 1512 mult(mult(A,mult(A,A)),B) = mult(A,mult(A,mult(A,B))). [para(1428(a,1),225(a,2,1,2)),rewrite([523(5),523(5),523(7)]),flip(a)].
% 252.80/253.19 1520 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(A,mult(A,mult(A,B))). [back_rewrite(1429),rewrite([1512(8)])].
% 252.80/253.19 1521 mult(mult(A,A),rd(B,mult(A,B))) = A. [para(1504(a,1),9(a,1,1))].
% 252.80/253.19 1537 mult(mult(A,A),rd(ld(A,B),B)) = A. [para(1505(a,1),9(a,1,1))].
% 252.80/253.19 1550 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(1521(a,1),19(a,2,1)),rewrite([552(6),27(4),757(4),1520(5),19(4)])].
% 252.80/253.19 1574 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(mult(A,mult(A,A)),B). [para(1521(a,1),184(a,1,1,1)),rewrite([654(9),10(6),225(8),434(6)]),flip(a)].
% 252.80/253.19 1689 ld(mult(A,mult(A,A)),B) = ld(A,ld(A,ld(A,B))). [para(1550(a,1),184(a,1,1))].
% 252.80/253.19 1699 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(1574),rewrite([1689(8)])].
% 252.80/253.19 1707 mult(A,ld(mult(B,A),rd(B,A))) = ld(A,ld(A,A)). [para(477(a,1),8(a,1,2)),rewrite([168(4)])].
% 252.80/253.19 1708 ld(A,rd(mult(A,B),A)) = mult(B,ld(A,ld(A,A))). [para(8(a,1),477(a,1,1)),flip(a)].
% 252.80/253.19 1719 mult(A,ld(B,ld(B,ld(B,B)))) = rd(rd(A,B),B). [para(477(a,1),64(a,1,2)),rewrite([7(4)]),flip(a)].
% 252.80/253.19 1732 mult(A,rd(B,ld(A,ld(A,A)))) = mult(mult(A,B),A). [para(523(a,1),477(a,1,1)),rewrite([168(8),363(5),7(6),168(5),363(3),7(3),523(8)]),flip(a)].
% 252.80/253.19 1754 mult(ld(A,rd(ld(A,B),A)),ld(A,A)) = ld(A,ld(A,rd(B,A))). [para(477(a,1),225(a,1,2)),flip(a)].
% 252.80/253.19 1757 rd(ld(A,ld(A,ld(A,A))),A) = ld(mult(A,A),ld(A,ld(A,A))). [para(1415(a,1),477(a,1,1)),rewrite([205(6),678(5),363(5),1446(5),1719(6),1447(3),434(7)])].
% 252.80/253.19 1765 ld(mult(A,A),ld(A,ld(A,A))) = ld(A,ld(A,ld(A,ld(A,A)))). [para(477(a,1),1550(a,1,1)),rewrite([473(2),477(6),1447(3),477(11),473(8),1719(10),1447(7),1757(8)]),flip(a)].
% 252.80/253.19 1839 mult(ld(A,ld(A,ld(A,ld(A,A)))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(1699),rewrite([1765(4)])].
% 252.80/253.19 1872 ld(A,mult(ld(A,A),B)) = mult(A,ld(mult(A,A),B)). [para(7(a,1),526(a,1,2,2))].
% 252.80/253.19 1903 ld(A,rd(rd(B,rd(ld(A,C),C)),A)) = rd(ld(A,B),ld(A,A)). [para(435(a,1),530(a,1,2)),flip(a)].
% 252.80/253.19 1950 mult(f1(rd(A,mult(B,A))),ld(B,ld(B,B))) != f1(rd(A,mult(B,A))) | ld(B,f1(rd(A,mult(B,A)))) != f1(rd(A,mult(B,A))) # answer(goals). [para(558(a,1),12(a,1)),rewrite([552(16)])].
% 252.80/253.19 2128 f1(rd(A,mult(B,A))) != mult(f1(ld(B,ld(B,B))),ld(B,ld(B,B))) | ld(B,f1(rd(A,mult(B,A)))) != f1(rd(A,mult(B,A))) # answer(goals). [para(434(a,1),1950(a,1,1,1)),flip(a)].
% 252.80/253.19 2301 mult(A,rd(B,rd(ld(A,C),C))) = mult(mult(A,B),A). [para(612(a,1),659(a,1,2,2)),rewrite([654(3),14(2),14(3),654(8),14(4)]),flip(a)].
% 252.80/253.19 2455 f1(rd(A,mult(B,A))) != mult(f1(ld(B,ld(B,B))),rd(C,mult(B,C))) | ld(B,f1(rd(A,mult(B,A)))) != f1(rd(A,mult(B,A))) # answer(goals). [para(434(a,2),2128(a,2,2))].
% 252.80/253.19 2892 rd(ld(A,rd(B,A)),rd(ld(A,C),C)) = ld(A,B). [para(826(a,1),10(a,1,1))].
% 252.80/253.19 2980 mult(ld(A,A),ld(mult(A,A),B)) = ld(A,ld(A,B)). [para(899(a,1),8(a,1,2)),flip(a)].
% 252.80/253.19 3512 ld(mult(A,A),ld(A,B)) = ld(A,ld(mult(A,A),B)). [para(1046(a,1),225(a,1,2)),rewrite([434(6),1765(7),1839(10),1872(6),8(7)])].
% 252.80/253.19 3779 rd(rd(A,ld(B,ld(B,B))),mult(B,B)) = mult(mult(B,B),rd(ld(mult(B,B),A),B)). [para(1415(a,1),1213(a,1,1,2))].
% 252.80/253.19 3985 rd(A,rd(ld(mult(B,B),C),C)) = rd(A,ld(B,ld(B,ld(B,B)))). [para(205(a,1),1243(a,2,2,2)),rewrite([678(7),363(7),3512(7),1415(6)])].
% 252.80/253.19 4207 f1(rd(A,mult(B,A))) != mult(f1(ld(B,ld(B,B))),rd(C,mult(B,C))) | f1(ld(B,ld(B,B))) != ld(B,f1(rd(A,mult(B,A)))) # answer(goals). [para(434(a,1),2455(b,2,1)),flip(b)].
% 252.80/253.19 4311 rd(mult(mult(A,mult(A,B)),ld(mult(mult(A,A),B),C)),mult(ld(mult(mult(A,A),B),ld(A,A)),C)) = mult(mult(A,A),B). [para(1381(a,1),226(a,1,2,1,2))].
% 252.80/253.19 4685 rd(A,rd(ld(mult(B,B),C),C)) = mult(mult(A,B),B). [para(1450(a,2),264(a,2,2)),rewrite([1732(5),7(2)]),flip(a)].
% 252.80/253.19 4712 rd(A,ld(B,ld(B,ld(B,B)))) = mult(mult(A,B),B). [back_rewrite(3985),rewrite([4685(4)]),flip(a)].
% 252.80/253.19 6361 ld(mult(A,B),rd(A,B)) = ld(B,ld(B,ld(B,B))). [para(1707(a,1),8(a,1,2)),flip(a)].
% 252.80/253.19 6369 mult(mult(A,B),ld(mult(C,B),rd(C,B))) = rd(A,B). [para(1707(a,1),16(a,1,2,2)),rewrite([477(4),7(3)]),flip(a)].
% 252.80/253.19 6370 mult(rd(A,B),mult(B,rd(B,A))) = rd(A,rd(A,B)). [para(1707(a,1),18(a,1,2,2)),rewrite([654(5),654(6),817(6),6369(12)])].
% 252.80/253.19 7109 rd(rd(ld(A,ld(A,A)),B),B) = ld(A,ld(B,ld(B,ld(B,B)))). [para(1719(a,1),399(a,1))].
% 252.80/253.19 7239 rd(A,ld(B,ld(B,B))) = ld(B,mult(mult(B,A),B)). [para(1732(a,1),8(a,1,2)),flip(a)].
% 252.80/253.19 7548 mult(mult(A,A),rd(ld(mult(A,A),B),A)) = mult(B,ld(A,ld(A,A))). [back_rewrite(3779),rewrite([7239(3),530(5),10(3),1708(3)]),flip(a)].
% 252.80/253.19 7568 rd(A,rd(ld(B,C),C)) = ld(B,mult(mult(B,A),B)). [back_rewrite(1243),rewrite([7239(6)])].
% 252.80/253.19 10542 rd(ld(A,B),rd(ld(A,C),C)) = ld(A,mult(B,A)). [para(10(a,1),2892(a,1,1,2))].
% 252.80/253.19 11972 f1(rd(A,mult(B,A))) != mult(f1(ld(B,ld(B,B))),rd(C,mult(B,C))) | f1(ld(B,ld(B,B))) != ld(B,f1(rd(ld(B,D),D))) # answer(goals). [para(618(a,2),4207(b,2,2,1))].
% 252.80/253.19 12044 mult(mult(A,ld(B,B)),ld(B,B)) = rd(A,ld(B,B)). [para(689(a,1),4685(a,1,2,1,1)),rewrite([391(1),391(2),964(3),1415(2),7(3),678(2),10(3),391(3),391(5)]),flip(a)].
% 252.80/253.19 12158 mult(mult(mult(ld(A,ld(B,ld(B,ld(B,B)))),B),B),C) = ld(A,C). [para(4712(a,1),612(a,1,1))].
% 252.80/253.19 12159 rd(A,mult(B,A)) = mult(mult(ld(B,ld(C,ld(C,ld(C,C)))),C),C). [para(4712(a,1),618(a,1)),flip(a)].
% 252.80/253.19 12160 rd(ld(A,B),B) = mult(mult(ld(A,ld(C,ld(C,ld(C,C)))),C),C). [para(4712(a,1),619(a,1)),flip(a)].
% 252.80/253.19 12780 ld(mult(mult(A,B),B),A) = ld(B,ld(B,ld(B,B))). [para(10(a,1),6361(a,1,2))].
% 252.80/253.19 12902 mult(A,mult(B,rd(ld(A,C),C))) = rd(mult(A,B),A). [para(618(a,2),6370(a,1,2,2)),rewrite([10(2),10(7)])].
% 252.80/253.19 13307 mult(mult(A,A),ld(B,mult(mult(B,ld(A,ld(B,ld(B,B)))),B))) = A. [para(7239(a,1),1537(a,1,2))].
% 252.80/253.19 13311 mult(A,ld(B,mult(mult(B,ld(C,ld(B,ld(B,B)))),B))) = mult(A,ld(C,ld(C,C))). [para(7239(a,1),615(a,1,2))].
% 252.80/253.19 13582 rd(A,mult(mult(ld(B,ld(C,ld(C,ld(C,C)))),C),C)) = ld(B,mult(mult(B,A),B)). [para(4712(a,1),7568(a,1,2))].
% 252.80/253.19 14660 rd(ld(A,ld(A,A)),ld(B,B)) = mult(ld(A,ld(B,B)),ld(B,B)). [para(399(a,1),12044(a,1,1)),flip(a)].
% 252.80/253.19 14666 mult(ld(A,rd(mult(B,ld(A,A)),A)),A) = ld(A,rd(B,ld(A,A))). [para(12044(a,1),225(a,1,2)),flip(a)].
% 252.80/253.19 14842 mult(A,mult(mult(B,ld(A,rd(ld(B,C),C))),B)) = rd(mult(A,B),A). [para(2301(a,1),12902(a,1,2))].
% 252.80/253.19 15046 mult(ld(mult(A,ld(B,B)),A),ld(B,B)) = ld(A,A). [para(778(a,1),394(a,2,1)),rewrite([391(1),391(2),391(4),1029(6),895(7),391(4),391(6)])].
% 252.80/253.19 15047 rd(ld(mult(A,ld(B,B)),A),ld(B,B)) = mult(ld(A,A),ld(B,B)). [para(394(a,1),12044(a,1,1)),rewrite([895(4),391(1),1029(9),895(10)]),flip(a)].
% 252.80/253.19 15049 rd(ld(A,A),ld(B,B)) = ld(mult(A,ld(B,B)),A). [para(15046(a,1),10(a,1,1))].
% 252.80/253.19 15051 ld(ld(mult(A,ld(B,B)),A),C) = mult(ld(mult(B,ld(A,A)),B),C). [para(15046(a,1),552(a,1,1,2)),rewrite([15049(3)]),flip(a)].
% 252.80/253.19 15056 ld(mult(ld(A,A),ld(B,B)),ld(mult(A,ld(B,B)),A)) = ld(B,B). [para(15046(a,1),12780(a,1,1,1)),rewrite([678(12),964(12),1415(11),7(12),678(11),964(11),1415(10),7(11),678(10),964(10),1415(9),7(10)])].
% 252.80/253.19 15060 ld(mult(ld(A,A),ld(B,B)),ld(A,A)) = ld(mult(A,ld(B,B)),A). [para(678(a,1),15049(a,1,1)),rewrite([964(3),1415(2),7(3),15049(3)]),flip(a)].
% 252.80/253.19 15393 rd(ld(A,ld(A,B)),ld(A,A)) = ld(A,rd(ld(A,mult(B,A)),A)). [para(10542(a,1),1903(a,1,2,1)),flip(a)].
% 252.80/253.19 15807 rd(ld(A,ld(A,A)),B) = mult(ld(A,ld(B,ld(B,ld(B,B)))),B). [para(7109(a,1),9(a,1,1)),flip(a)].
% 252.80/253.19 20239 rd(ld(A,rd(B,ld(A,A))),A) = ld(A,rd(mult(B,ld(A,A)),A)). [para(14666(a,1),10(a,1,1))].
% 252.80/253.19 20509 mult(ld(A,A),mult(ld(mult(A,A),B),ld(A,A))) = ld(A,rd(ld(A,mult(B,A)),A)). [para(2980(a,1),14842(a,2,1)),rewrite([678(9),12902(10),9(11),15393(10)])].
% 252.80/253.19 20782 mult(ld(mult(A,ld(B,B)),A),ld(A,A)) = ld(A,A). [para(14660(a,2),15051(a,2)),rewrite([678(3),964(3),1415(2),7(3),15051(5),1029(15),15060(14),1029(14),15056(13),964(8),1415(7),7(8),391(8),678(8),964(8),1415(7),7(8)])].
% 252.80/253.19 20785 ld(A,A) = ld(B,B). [para(20782(a,1),8(a,1,2)),rewrite([15051(5),15046(5)])].
% 252.80/253.19 20801 ld(A,A) = c_0. [new_symbol(20785)].
% 252.80/253.19 20811 ld(mult(A,c_0),A) = c_0. [back_rewrite(15060),rewrite([20801(1),20801(2),20801(4),1415(5),20801(4),20801(3),20801(2)]),flip(a)].
% 252.80/253.19 20815 ld(c_0,A) = mult(c_0,A). [back_rewrite(15051),rewrite([20801(1),20811(3),20801(3),20811(5)])].
% 252.80/253.19 20816 mult(c_0,c_0) = c_0. [back_rewrite(15047),rewrite([20801(1),20811(3),20801(2),391(3),20801(3),20801(2),20801(3)]),flip(a)].
% 252.80/253.19 20949 mult(c_0,mult(ld(mult(A,A),B),c_0)) = ld(A,rd(ld(A,mult(B,A)),A)). [back_rewrite(20509),rewrite([20801(1),20801(4)])].
% 252.80/253.19 21049 rd(ld(A,rd(B,c_0)),A) = ld(A,rd(mult(B,c_0),A)). [back_rewrite(20239),rewrite([20801(1),20801(5)])].
% 252.80/253.19 22216 mult(ld(A,ld(B,ld(B,c_0))),B) = rd(ld(A,c_0),B). [back_rewrite(15807),rewrite([20801(1),20801(4)]),flip(a)].
% 252.80/253.19 22489 ld(A,mult(mult(A,B),A)) = rd(B,ld(A,c_0)). [back_rewrite(13582),rewrite([20801(1),22216(5),9(4)]),flip(a)].
% 252.80/253.19 22505 mult(A,rd(ld(B,ld(C,c_0)),ld(C,c_0))) = mult(A,ld(B,c_0)). [back_rewrite(13311),rewrite([20801(1),22489(6),20801(8)])].
% 252.80/253.19 22507 mult(A,c_0) = A. [back_rewrite(13307),rewrite([20801(2),22489(7),22505(8),26(4),20801(1),20816(3)])].
% 252.80/253.19 22629 rd(ld(A,B),B) = ld(A,c_0). [back_rewrite(12160),rewrite([20801(3),22216(7),9(6)])].
% 252.80/253.19 22630 rd(A,mult(B,A)) = ld(B,c_0). [back_rewrite(12159),rewrite([20801(3),22216(7),9(6)])].
% 252.80/253.19 22631 mult(ld(A,c_0),B) = ld(A,B). [back_rewrite(12158),rewrite([20801(1),22216(5),9(4)])].
% 252.80/253.19 22636 rd(A,c_0) = A. [back_rewrite(12044),rewrite([20801(1),22507(2),20801(1),22507(2),20801(1)]),flip(a)].
% 252.80/253.19 22638 mult(f1(ld(A,c_0)),ld(A,c_0)) != f1(ld(A,c_0)) | ld(A,f1(ld(A,c_0))) != f1(ld(A,c_0)) # answer(goals). [back_rewrite(11972),rewrite([22630(2),20801(4),22630(8),20801(11),22629(15)]),flip(a),flip(b)].
% 252.80/253.19 22808 mult(mult(A,A),rd(ld(mult(A,A),B),A)) = mult(B,ld(A,c_0)). [back_rewrite(7548),rewrite([20801(6)])].
% 252.80/253.19 22943 mult(mult(A,A),B) = mult(A,mult(A,B)). [back_rewrite(4311),rewrite([20801(9),22631(11),10(10)]),flip(a)].
% 252.80/253.19 23096 ld(A,rd(ld(A,B),A)) = ld(A,ld(A,rd(B,A))). [back_rewrite(1754),rewrite([20801(4),22507(5)])].
% 252.80/253.19 23129 mult(c_0,A) = A. [back_rewrite(1204),rewrite([20801(1),20801(5),20801(7),22631(9),10(8),20801(1)]),flip(a)].
% 252.80/253.19 23221 ld(mult(A,A),B) = ld(A,ld(A,B)). [back_rewrite(20949),rewrite([22507(5),23129(4),23096(6),10(4)])].
% 252.80/253.19 23373 rd(ld(A,B),A) = ld(A,rd(B,A)). [back_rewrite(21049),rewrite([22636(2),22507(4)])].
% 252.80/253.19 23623 mult(A,ld(B,c_0)) = rd(A,B). [back_rewrite(22808),rewrite([23221(3),23373(4),23373(3),22943(5),7(4),7(3)]),flip(a)].
% 252.80/253.19 23896 ld(c_0,A) = A. [back_rewrite(20815),rewrite([23129(4)])].
% 252.80/253.19 24653 rd(f1(ld(A,c_0)),A) != f1(ld(A,c_0)) | ld(A,f1(ld(A,c_0))) != f1(ld(A,c_0)) # answer(goals). [back_rewrite(22638),rewrite([23623(6)])].
% 252.80/253.19 25478 $F # answer(goals). [para(20801(a,1),24653(a,1,1,1)),rewrite([22636(4),20801(5),20801(9),23896(9),20801(10)]),xx(a),xx(b)].
% 252.80/253.19
% 252.80/253.19 % SZS output end Refutation
% 252.80/253.19 ============================== end of proof ==========================
% 252.80/253.19
% 252.80/253.19 ============================== STATISTICS ============================
% 252.80/253.19
% 252.80/253.19 Given=2993. Generated=8004701. Kept=25471. proofs=1.
% 252.80/253.19 Usable=198. Sos=1885. Demods=1941. Limbo=3, Disabled=23391. Hints=0.
% 252.80/253.19 Megabytes=32.63.
% 252.80/253.19 User_CPU=247.23, System_CPU=4.78, Wall_clock=252.
% 252.80/253.19
% 252.80/253.19 ============================== end of statistics =====================
% 252.80/253.19
% 252.80/253.19 ============================== end of search =========================
% 252.80/253.19
% 252.80/253.19 THEOREM PROVED
% 252.80/253.19 % SZS status Theorem
% 252.80/253.19
% 252.80/253.19 Exiting with 1 proof.
% 252.80/253.19
% 252.80/253.19 Process 27124 exit (max_proofs) Mon Jun 13 20:26:55 2022
% 252.85/253.19 Prover9 interrupted
%------------------------------------------------------------------------------