TSTP Solution File: GRP282-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP282-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 11:18:28 EDT 2022
% Result : Unsatisfiable 124.22s 124.51s
% Output : Refutation 124.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP282-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 01:42:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.31/5.62 ============================== Prover9 ===============================
% 5.31/5.62 Prover9 (32) version 2009-11A, November 2009.
% 5.31/5.62 Process 24626 was started by sandbox2 on n014.cluster.edu,
% 5.31/5.62 Tue Jun 14 01:42:22 2022
% 5.31/5.62 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24393_n014.cluster.edu".
% 5.31/5.62 ============================== end of head ===========================
% 5.31/5.62
% 5.31/5.62 ============================== INPUT =================================
% 5.31/5.62
% 5.31/5.62 % Reading from file /tmp/Prover9_24393_n014.cluster.edu
% 5.31/5.62
% 5.31/5.62 set(prolog_style_variables).
% 5.31/5.62 set(auto2).
% 5.31/5.62 % set(auto2) -> set(auto).
% 5.31/5.62 % set(auto) -> set(auto_inference).
% 5.31/5.62 % set(auto) -> set(auto_setup).
% 5.31/5.62 % set(auto_setup) -> set(predicate_elim).
% 5.31/5.62 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.31/5.62 % set(auto) -> set(auto_limits).
% 5.31/5.62 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.31/5.62 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.31/5.62 % set(auto) -> set(auto_denials).
% 5.31/5.62 % set(auto) -> set(auto_process).
% 5.31/5.62 % set(auto2) -> assign(new_constants, 1).
% 5.31/5.62 % set(auto2) -> assign(fold_denial_max, 3).
% 5.31/5.62 % set(auto2) -> assign(max_weight, "200.000").
% 5.31/5.62 % set(auto2) -> assign(max_hours, 1).
% 5.31/5.62 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.31/5.62 % set(auto2) -> assign(max_seconds, 0).
% 5.31/5.62 % set(auto2) -> assign(max_minutes, 5).
% 5.31/5.62 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.31/5.62 % set(auto2) -> set(sort_initial_sos).
% 5.31/5.62 % set(auto2) -> assign(sos_limit, -1).
% 5.31/5.62 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.31/5.62 % set(auto2) -> assign(max_megs, 400).
% 5.31/5.62 % set(auto2) -> assign(stats, some).
% 5.31/5.62 % set(auto2) -> clear(echo_input).
% 5.31/5.62 % set(auto2) -> set(quiet).
% 5.31/5.62 % set(auto2) -> clear(print_initial_clauses).
% 5.31/5.62 % set(auto2) -> clear(print_given).
% 5.31/5.62 assign(lrs_ticks,-1).
% 5.31/5.62 assign(sos_limit,10000).
% 5.31/5.62 assign(order,kbo).
% 5.31/5.62 set(lex_order_vars).
% 5.31/5.62 clear(print_given).
% 5.31/5.62
% 5.31/5.62 % formulas(sos). % not echoed (52 formulas)
% 5.31/5.62
% 5.31/5.62 ============================== end of input ==========================
% 5.31/5.62
% 5.31/5.62 % From the command line: assign(max_seconds, 300).
% 5.31/5.62
% 5.31/5.62 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.31/5.62
% 5.31/5.62 % Formulas that are not ordinary clauses:
% 5.31/5.62
% 5.31/5.62 ============================== end of process non-clausal formulas ===
% 5.31/5.62
% 5.31/5.62 ============================== PROCESS INITIAL CLAUSES ===============
% 5.31/5.62
% 5.31/5.62 ============================== PREDICATE ELIMINATION =================
% 5.31/5.62
% 5.31/5.62 ============================== end predicate elimination =============
% 5.31/5.62
% 5.31/5.62 Auto_denials: (non-Horn, no changes).
% 5.31/5.62
% 5.31/5.62 Term ordering decisions:
% 5.31/5.62
% 5.31/5.62 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 5.31/5.62 Function symbol KB weights: sk_c9=1. sk_c7=1. sk_c8=1. sk_c6=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. identity=1. multiply=1. inverse=0.
% 5.31/5.62
% 5.31/5.62 ============================== end of process initial clauses ========
% 5.31/5.62
% 5.31/5.62 ============================== CLAUSES FOR SEARCH ====================
% 5.31/5.62
% 5.31/5.62 ============================== end of clauses for search =============
% 5.31/5.62
% 5.31/5.62 ============================== SEARCH ================================
% 5.31/5.62
% 5.31/5.62 % Starting search at 0.12 seconds.
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=60.000, iters=3586
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=59.000, iters=3342
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=58.000, iters=3390
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=57.000, iters=3384
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=56.000, iters=3415
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=55.000, iters=3367
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=54.000, iters=3468
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=53.000, iters=3371
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=52.000, iters=3443
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=51.000, iters=3333
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=50.000, iters=3354
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=49.000, iters=3341
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=47.000, iters=3355
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=46.000, iters=3375
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=45.000, iters=3341
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=44.000, iters=3346
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=43.000, iters=3355
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=42.000, iters=3345
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=41.000, iters=3351
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=40.000, iters=3346
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=39.000, iters=3461
% 5.31/5.62
% 5.31/5.62 Low Water (keep): wt=38.000, iters=3335
% 5.31/5.62
% 5.31/5.62 Low Water (displace): id=14743, wt=15.000
% 5.31/5.62
% 5.31/5.62 Low Water (displace): id=14750, wt=14.000
% 5.31/5.62
% 5.31/5.62 Low Water (displace): id=14752, wt=13.000
% 5.31/5.62
% 5.31/5.62 Low Water (displace): id=14822, wt=12.000
% 124.22/124.51
% 124.22/124.51 Low Water (displace): id=14825, wt=11.000
% 124.22/124.51
% 124.22/124.51 Low Water (displace): id=15473, wt=10.000
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=37.000, iters=3334
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=36.000, iters=3334
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=35.000, iters=3351
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=33.000, iters=3346
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=32.000, iters=3335
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=31.000, iters=3377
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=30.000, iters=3362
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=20.000, iters=3376
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=17.000, iters=3342
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=16.000, iters=3433
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=15.000, iters=3350
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=14.000, iters=3336
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=13.000, iters=3342
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=12.000, iters=3335
% 124.22/124.51
% 124.22/124.51 Low Water (keep): wt=11.000, iters=3450
% 124.22/124.51
% 124.22/124.51 ============================== PROOF =================================
% 124.22/124.51 % SZS status Unsatisfiable
% 124.22/124.51 % SZS output start Refutation
% 124.22/124.51
% 124.22/124.51 % Proof 1 at 120.72 (+ 2.78) seconds.
% 124.22/124.51 % Length of proof is 234.
% 124.22/124.51 % Level of proof is 36.
% 124.22/124.51 % Maximum clause weight is 65.000.
% 124.22/124.51 % Given clauses 9019.
% 124.22/124.51
% 124.22/124.51 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 124.22/124.51 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 124.22/124.51 3 inverse(sk_c1) = sk_c9 | inverse(sk_c9) = sk_c7 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 124.22/124.51 4 inverse(sk_c1) = sk_c9 | inverse(sk_c4) = sk_c9 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 124.22/124.51 5 inverse(sk_c1) = sk_c9 | inverse(sk_c5) = sk_c6 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 124.22/124.51 6 inverse(sk_c2) = sk_c9 | inverse(sk_c9) = sk_c7 # label(prove_this_43) # label(negated_conjecture). [assumption].
% 124.22/124.51 7 inverse(sk_c2) = sk_c9 | inverse(sk_c4) = sk_c9 # label(prove_this_44) # label(negated_conjecture). [assumption].
% 124.22/124.51 8 inverse(sk_c2) = sk_c9 | inverse(sk_c5) = sk_c6 # label(prove_this_47) # label(negated_conjecture). [assumption].
% 124.22/124.51 9 multiply(sk_c9,sk_c8) = sk_c7 | inverse(sk_c9) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 124.22/124.51 12 multiply(sk_c1,sk_c9) = sk_c8 | inverse(sk_c9) = sk_c7 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 124.22/124.51 13 multiply(sk_c1,sk_c9) = sk_c8 | inverse(sk_c4) = sk_c9 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 124.22/124.51 15 inverse(sk_c1) = sk_c9 | multiply(sk_c8,sk_c9) = sk_c7 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 124.22/124.51 16 inverse(sk_c1) = sk_c9 | multiply(sk_c8,sk_c7) = sk_c9 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 124.22/124.51 17 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c7) = sk_c9 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 124.22/124.51 18 inverse(sk_c1) = sk_c9 | multiply(sk_c5,sk_c6) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 124.22/124.51 20 multiply(sk_c9,sk_c3) = sk_c8 | inverse(sk_c9) = sk_c7 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 124.22/124.51 21 multiply(sk_c9,sk_c3) = sk_c8 | inverse(sk_c4) = sk_c9 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 124.22/124.51 23 multiply(sk_c2,sk_c9) = sk_c3 | inverse(sk_c9) = sk_c7 # label(prove_this_35) # label(negated_conjecture). [assumption].
% 124.22/124.51 24 multiply(sk_c2,sk_c9) = sk_c3 | inverse(sk_c4) = sk_c9 # label(prove_this_36) # label(negated_conjecture). [assumption].
% 124.22/124.51 26 inverse(sk_c2) = sk_c9 | multiply(sk_c8,sk_c9) = sk_c7 # label(prove_this_41) # label(negated_conjecture). [assumption].
% 124.22/124.51 28 inverse(sk_c2) = sk_c9 | multiply(sk_c4,sk_c7) = sk_c9 # label(prove_this_45) # label(negated_conjecture). [assumption].
% 124.22/124.51 29 inverse(sk_c2) = sk_c9 | multiply(sk_c5,sk_c6) = sk_c7 # label(prove_this_46) # label(negated_conjecture). [assumption].
% 124.22/124.51 31 multiply(sk_c9,sk_c8) = sk_c7 | multiply(sk_c8,sk_c9) = sk_c7 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 124.22/124.51 37 multiply(sk_c1,sk_c9) = sk_c8 | multiply(sk_c8,sk_c7) = sk_c9 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 124.22/124.51 38 multiply(sk_c1,sk_c9) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c9 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 124.22/124.51 43 multiply(sk_c9,sk_c3) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c9 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 124.22/124.51 48 multiply(sk_c2,sk_c9) = sk_c3 | multiply(sk_c4,sk_c7) = sk_c9 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 124.22/124.51 51 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 124.22/124.51 52 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(D) != sk_c9 | multiply(D,sk_c7) != sk_c9 | multiply(E,F) != sk_c7 | inverse(E) != F | multiply(F,sk_c9) != sk_c7 # label(prove_this_49) # label(negated_conjecture). [assumption].
% 124.22/124.51 242 inverse(sk_c9) = sk_c7 | multiply(sk_c9,sk_c1) = identity. [para(3(a,1),2(a,1,1))].
% 124.22/124.51 243 inverse(sk_c1) = sk_c9 | multiply(sk_c9,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 124.22/124.51 245 inverse(sk_c9) = sk_c7 | multiply(sk_c9,sk_c2) = identity. [para(6(a,1),2(a,1,1))].
% 124.22/124.51 246 inverse(sk_c2) = sk_c9 | multiply(sk_c9,sk_c4) = identity. [para(7(b,1),2(a,1,1))].
% 124.22/124.51 248 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),51(a,1,1)),rewrite([1(2)]),flip(a)].
% 124.22/124.51 249 inverse(sk_c9) = sk_c7 | multiply(sk_c9,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(9(a,1),51(a,1,1)),flip(b)].
% 124.22/124.51 250 inverse(sk_c9) = sk_c7 | multiply(A,multiply(sk_c9,sk_c8)) = multiply(A,sk_c7). [para(9(a,1),51(a,2,2)),rewrite([51(8)])].
% 124.22/124.51 256 inverse(sk_c9) = sk_c7 | multiply(A,multiply(sk_c1,sk_c9)) = multiply(A,sk_c8). [para(12(a,1),51(a,2,2)),rewrite([51(8)])].
% 124.22/124.51 261 inverse(sk_c1) = sk_c9 | multiply(sk_c8,multiply(sk_c9,A)) = multiply(sk_c7,A). [para(15(b,1),51(a,1,1)),flip(b)].
% 124.22/124.51 265 inverse(sk_c1) = sk_c9 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c9,A). [para(17(b,1),51(a,1,1)),flip(b)].
% 124.22/124.51 268 inverse(sk_c1) = sk_c9 | multiply(A,multiply(sk_c5,sk_c6)) = multiply(A,sk_c7). [para(18(b,1),51(a,2,2)),rewrite([51(8)])].
% 124.22/124.51 278 inverse(sk_c9) = sk_c7 | multiply(A,multiply(sk_c2,sk_c9)) = multiply(A,sk_c3). [para(23(a,1),51(a,2,2)),rewrite([51(8)])].
% 124.22/124.51 280 inverse(sk_c4) = sk_c9 | multiply(A,multiply(sk_c2,sk_c9)) = multiply(A,sk_c3). [para(24(a,1),51(a,2,2)),rewrite([51(8)])].
% 124.22/124.51 290 inverse(sk_c2) = sk_c9 | multiply(A,multiply(sk_c5,sk_c6)) = multiply(A,sk_c7). [para(29(b,1),51(a,2,2)),rewrite([51(8)])].
% 124.22/124.51 307 multiply(sk_c1,sk_c9) = sk_c8 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c9,A). [para(38(b,1),51(a,1,1)),flip(b)].
% 124.22/124.51 345 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,identity) != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(B) != sk_c9 | multiply(B,sk_c7) != sk_c9 | multiply(C,D) != sk_c7 | inverse(C) != D | multiply(D,sk_c9) != sk_c7. [resolve(52,e,2,a)].
% 124.22/124.51 570 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,identity) != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(B) != sk_c9 | multiply(B,sk_c7) != sk_c9 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8. [factor(345,f,m)].
% 124.22/124.51 1762 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,identity) != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(B,sk_c8) != sk_c7 | inverse(B) != sk_c8. [factor(570,g,j)].
% 124.22/124.51 5936 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),248(a,1,2))].
% 124.22/124.51 5942 inverse(sk_c9) = sk_c7 | multiply(inverse(sk_c9),sk_c7) = sk_c8. [para(9(a,1),248(a,1,2))].
% 124.22/124.51 5946 inverse(sk_c4) = sk_c9 | multiply(inverse(sk_c1),sk_c8) = sk_c9. [para(13(a,1),248(a,1,2))].
% 124.22/124.51 5948 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c8),sk_c7) = sk_c9. [para(15(b,1),248(a,1,2))].
% 124.22/124.51 5950 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c4),sk_c9) = sk_c7. [para(17(b,1),248(a,1,2))].
% 124.22/124.51 5953 inverse(sk_c9) = sk_c7 | multiply(inverse(sk_c9),sk_c8) = sk_c3. [para(20(a,1),248(a,1,2))].
% 124.22/124.51 5959 inverse(sk_c2) = sk_c9 | multiply(inverse(sk_c8),sk_c7) = sk_c9. [para(26(b,1),248(a,1,2))].
% 124.22/124.51 5964 multiply(sk_c9,sk_c8) = sk_c7 | multiply(inverse(sk_c8),sk_c7) = sk_c9. [para(31(b,1),248(a,1,2))].
% 124.22/124.51 5976 multiply(sk_c9,sk_c3) = sk_c8 | multiply(inverse(sk_c4),sk_c9) = sk_c7. [para(43(b,1),248(a,1,2))].
% 124.22/124.51 5981 multiply(sk_c2,sk_c9) = sk_c3 | multiply(inverse(sk_c4),sk_c9) = sk_c7. [para(48(b,1),248(a,1,2))].
% 124.22/124.51 6014 inverse(sk_c9) = sk_c7 | multiply(inverse(sk_c9),identity) = sk_c1. [para(242(b,1),248(a,1,2))].
% 124.22/124.51 6015 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(248(a,1),248(a,1,2))].
% 124.22/124.51 6028 multiply(A,identity) = A. [back_rewrite(5936),rewrite([6015(4)])].
% 124.22/124.51 6029 inverse(sk_c9) = sk_c7 | inverse(sk_c9) = sk_c1. [back_rewrite(6014),rewrite([6028(8)])].
% 124.22/124.51 6068 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | sk_c8 != sk_c9 | inverse(inverse(sk_c9)) != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(B,sk_c8) != sk_c7 | inverse(B) != sk_c8. [back_rewrite(1762),rewrite([6028(15)]),flip(d)].
% 124.22/124.51 6164 inverse(identity) = identity. [para(6028(a,1),2(a,1))].
% 124.22/124.51 6529 inverse(sk_c9) = sk_c7 | multiply(sk_c1,sk_c9) = identity. [para(6029(b,1),2(a,1,1))].
% 124.22/124.51 6602 inverse(sk_c1) = sk_c9 | inverse(sk_c9) = sk_c4. [para(243(b,1),248(a,1,2)),rewrite([6028(8)])].
% 124.22/124.51 6627 inverse(sk_c9) = sk_c7 | inverse(sk_c9) = sk_c2. [para(245(b,1),248(a,1,2)),rewrite([6028(8)])].
% 124.22/124.51 6676 inverse(sk_c2) = sk_c9 | inverse(sk_c9) = sk_c4. [para(246(b,1),248(a,1,2)),rewrite([6028(8)])].
% 124.22/124.51 6689 inverse(sk_c9) = sk_c7 | multiply(sk_c2,sk_c9) = identity. [para(6627(b,1),2(a,1,1))].
% 124.22/124.51 6691 inverse(sk_c9) = sk_c7 | sk_c2 = sk_c1. [para(6627(b,1),6029(b,1)),merge(b)].
% 124.22/124.51 6692 sk_c2 = sk_c1 | multiply(sk_c7,sk_c9) = identity. [para(6691(a,1),2(a,1,1))].
% 124.22/124.51 6750 sk_c2 = sk_c1 | multiply(A,multiply(sk_c7,sk_c9)) = A. [para(6692(b,1),51(a,2,2)),rewrite([51(7),6028(9)])].
% 124.22/124.51 6859 sk_c2 = sk_c1 | inverse(sk_c7) = sk_c9. [para(6692(b,1),248(a,1,2)),rewrite([6028(7)])].
% 124.22/124.51 7045 multiply(A,inverse(A)) = identity. [para(6015(a,1),2(a,1))].
% 124.22/124.51 7330 multiply(A,multiply(inverse(A),B)) = B. [para(6015(a,1),248(a,1))].
% 124.22/124.51 7331 inverse(inverse(A)) = A. [para(6015(a,1),6028(a,1)),rewrite([6028(2)]),flip(a)].
% 124.22/124.51 7387 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(B,sk_c8) != sk_c7 | inverse(B) != sk_c8. [back_rewrite(6068),rewrite([7331(18)]),xx(e)].
% 124.22/124.51 7719 inverse(sk_c9) = sk_c4 | inverse(sk_c9) = sk_c1. [para(6602(a,1),7331(a,1,1))].
% 124.22/124.51 7721 inverse(sk_c9) = sk_c4 | inverse(sk_c9) = sk_c2. [para(6676(a,1),7331(a,1,1))].
% 124.22/124.51 7724 inverse(sk_c1) = sk_c9 | multiply(sk_c5,sk_c6) = identity. [para(5(b,1),7045(a,1,2))].
% 124.22/124.51 7726 inverse(sk_c2) = sk_c9 | multiply(sk_c5,sk_c6) = identity. [para(8(b,1),7045(a,1,2))].
% 124.22/124.51 7727 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(7045(a,1),51(a,1)),flip(a)].
% 124.22/124.51 7807 inverse(sk_c9) = sk_c7 | multiply(sk_c7,inverse(sk_c8)) = sk_c9. [para(7045(a,1),249(b,1,2)),rewrite([6028(7)]),flip(b)].
% 124.22/124.51 8508 inverse(sk_c1) = sk_c9 | identity = sk_c7. [para(7724(b,1),18(b,1)),merge(b)].
% 124.22/124.51 8512 identity = sk_c7 | inverse(sk_c9) = sk_c1. [para(8508(a,1),7331(a,1,1))].
% 124.22/124.51 8521 inverse(sk_c9) = sk_c7 | multiply(A,sk_c8) = A. [para(6529(b,1),256(b,1,2)),rewrite([6028(10)]),flip(c),merge(b)].
% 124.22/124.51 8656 inverse(sk_c2) = sk_c9 | identity = sk_c7. [para(7726(b,1),29(b,1)),merge(b)].
% 124.22/124.51 8660 identity = sk_c7 | inverse(sk_c9) = sk_c2. [para(8656(a,1),7331(a,1,1))].
% 124.22/124.51 8669 identity = sk_c7 | sk_c2 = sk_c1. [para(8660(b,1),8512(b,1)),merge(b)].
% 124.22/124.51 8673 sk_c2 = sk_c1 | inverse(sk_c7) = identity. [para(8669(a,1),6164(a,1,1))].
% 124.22/124.51 8715 sk_c2 = sk_c1 | identity = sk_c9. [para(8673(b,1),6859(b,1)),merge(b)].
% 124.22/124.51 8717 sk_c2 = sk_c1 | multiply(sk_c9,A) = A. [para(8715(b,1),1(a,1,1))].
% 124.22/124.51 8719 sk_c2 = sk_c1 | inverse(sk_c9) = identity. [para(8715(b,1),6164(a,1,1))].
% 124.22/124.51 8809 sk_c2 = sk_c1 | identity = sk_c4 | inverse(sk_c9) = sk_c1. [para(8719(b,1),7719(a,1))].
% 124.22/124.51 8810 sk_c2 = sk_c1 | identity = sk_c4 | inverse(sk_c9) = sk_c2. [para(8719(b,1),7721(a,1))].
% 124.22/124.51 9536 sk_c2 = sk_c1 | multiply(inverse(sk_c9),A) = A. [para(8717(b,1),248(a,1,2))].
% 124.22/124.51 9696 inverse(sk_c1) = sk_c9 | multiply(sk_c7,inverse(sk_c9)) = sk_c8. [para(7045(a,1),261(b,1,2)),rewrite([6028(7)]),flip(b)].
% 124.22/124.51 10195 inverse(sk_c9) = sk_c7 | sk_c7 = sk_c9. [para(8521(b,1),9(a,1)),flip(b),merge(c)].
% 124.22/124.51 10212 sk_c7 = sk_c9 | identity = sk_c7 | sk_c1 = sk_c7. [para(10195(a,1),8512(b,1)),flip(c)].
% 124.22/124.51 10514 inverse(sk_c1) = sk_c9 | multiply(A,sk_c7) = A. [para(7724(b,1),268(b,1,2)),rewrite([6028(10)]),flip(c),merge(b)].
% 124.22/124.51 11193 inverse(sk_c1) = sk_c9 | inverse(sk_c7) = identity. [para(10514(b,1),2(a,1))].
% 124.22/124.51 11194 inverse(sk_c1) = sk_c9 | sk_c8 = sk_c9. [para(10514(b,1),16(b,1)),merge(b)].
% 124.22/124.51 11195 inverse(sk_c1) = sk_c9 | sk_c4 = sk_c9. [para(10514(b,1),17(b,1)),merge(b)].
% 124.22/124.51 11298 sk_c8 = sk_c9 | multiply(sk_c9,sk_c1) = identity. [para(11194(a,1),2(a,1,1))].
% 124.22/124.51 11305 sk_c4 = sk_c9 | inverse(sk_c9) = sk_c1. [para(11195(a,1),7331(a,1,1))].
% 124.22/124.51 11388 inverse(sk_c7) = identity | inverse(sk_c9) = sk_c1. [para(11193(a,1),7331(a,1,1))].
% 124.22/124.51 11391 sk_c8 = sk_c9 | multiply(A,multiply(sk_c9,sk_c1)) = A. [para(11298(b,1),51(a,2,2)),rewrite([51(7),6028(9)])].
% 124.22/124.51 12134 inverse(sk_c9) = sk_c7 | multiply(A,sk_c3) = A. [para(6689(b,1),278(b,1,2)),rewrite([6028(10)]),flip(c),merge(b)].
% 124.22/124.51 12418 inverse(sk_c4) = sk_c9 | multiply(sk_c9,multiply(sk_c2,sk_c9)) = sk_c8. [para(21(a,1),280(b,2)),merge(b)].
% 124.22/124.51 12638 inverse(sk_c9) = sk_c7 | inverse(sk_c3) = identity. [para(12134(b,1),2(a,1))].
% 124.22/124.51 12834 inverse(sk_c9) = sk_c7 | multiply(sk_c3,A) = A. [para(12638(b,1),248(a,1,1)),rewrite([1(8)])].
% 124.22/124.51 13158 inverse(sk_c9) = sk_c7 | multiply(inverse(sk_c3),A) = A. [para(12834(b,1),248(a,1,2))].
% 124.22/124.51 13392 inverse(sk_c1) = sk_c9 | inverse(sk_c8) = sk_c9. [para(5948(b,1),10514(b,1)),flip(c),merge(b)].
% 124.22/124.51 13395 inverse(sk_c8) = sk_c9 | inverse(sk_c9) = sk_c1. [para(13392(a,1),7331(a,1,1))].
% 124.22/124.51 13396 inverse(sk_c8) = sk_c9 | multiply(sk_c1,sk_c9) = identity. [para(13392(a,1),7045(a,1,2))].
% 124.22/124.51 13453 inverse(sk_c9) = sk_c1 | inverse(sk_c9) = sk_c8. [para(13395(a,1),7331(a,1,1))].
% 124.22/124.51 13541 inverse(sk_c8) = sk_c9 | multiply(A,multiply(sk_c1,sk_c9)) = A. [para(13396(b,1),51(a,2,2)),rewrite([51(8),6028(10)])].
% 124.22/124.51 13606 inverse(sk_c2) = sk_c9 | multiply(A,sk_c7) = A. [para(7726(b,1),290(b,1,2)),rewrite([6028(10)]),flip(c),merge(b)].
% 124.22/124.51 13667 inverse(sk_c2) = sk_c9 | sk_c4 = sk_c9. [para(13606(b,1),28(b,1)),merge(b)].
% 124.22/124.51 13776 sk_c4 = sk_c9 | inverse(sk_c9) = sk_c2. [para(13667(a,1),7331(a,1,1))].
% 124.22/124.51 13900 sk_c4 = sk_c9 | sk_c2 = sk_c1. [para(13776(b,1),11305(b,1)),merge(b)].
% 124.22/124.51 14592 inverse(sk_c1) = sk_c9 | multiply(sk_c9,sk_c9) = sk_c7. [para(4(b,1),5950(b,1,1)),merge(b)].
% 124.22/124.51 14599 inverse(sk_c1) = sk_c9 | multiply(sk_c8,sk_c7) = multiply(sk_c7,sk_c9). [para(14592(b,1),261(b,1,2)),merge(b)].
% 124.22/124.51 15385 inverse(sk_c9) = sk_c7 | inverse(sk_c9) = sk_c3. [para(5953(b,1),8521(b,1)),flip(c),merge(b)].
% 124.22/124.51 15392 inverse(sk_c9) = sk_c7 | inverse(sk_c3) = sk_c9. [para(15385(b,1),7331(a,1,1))].
% 124.22/124.51 15395 inverse(sk_c9) = sk_c7 | multiply(sk_c3,sk_c7) = sk_c8. [para(15385(b,1),5942(b,1,1)),merge(b)].
% 124.22/124.51 15547 inverse(sk_c9) = sk_c7 | identity = sk_c9. [para(15392(b,1),12638(b,1)),flip(c),merge(b)].
% 124.22/124.51 15553 identity = sk_c9 | inverse(sk_c7) = sk_c9. [para(15547(a,1),7331(a,1,1))].
% 124.22/124.51 15574 identity = sk_c9 | inverse(sk_c9) = sk_c1. [para(15553(b,1),11388(a,1)),flip(b),merge(b)].
% 124.22/124.51 15595 identity = sk_c9 | sk_c1 = sk_c7. [para(15574(b,1),15547(a,1)),merge(c)].
% 124.22/124.51 15600 multiply(sk_c1,sk_c9) = sk_c8 | multiply(sk_c9,inverse(sk_c7)) = sk_c4. [para(7045(a,1),307(b,1,2)),rewrite([6028(8)]),flip(b)].
% 124.22/124.51 15709 sk_c1 = sk_c7 | sk_c7 = sk_c9. [para(15595(a,1),10212(b,1)),flip(c),merge(c),merge(d)].
% 124.22/124.51 15751 sk_c7 = sk_c9 | inverse(sk_c4) = sk_c9 | multiply(inverse(sk_c7),sk_c8) = sk_c9. [para(15709(a,1),5946(b,1,1,1))].
% 124.22/124.51 17130 inverse(sk_c9) = sk_c7 | multiply(inverse(sk_c3),sk_c8) = sk_c7. [para(15395(b,1),248(a,1,2))].
% 124.22/124.51 18523 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(B,multiply(C,sk_c8)) != sk_c7 | inverse(multiply(B,C)) != sk_c8. [para(51(a,1),7387(i,1))].
% 124.22/124.51 20692 inverse(sk_c2) = sk_c9 | inverse(sk_c8) = sk_c9. [para(5959(b,1),13606(b,1)),flip(c),merge(b)].
% 124.22/124.51 20696 inverse(sk_c8) = sk_c9 | inverse(sk_c9) = sk_c2. [para(20692(a,1),7331(a,1,1))].
% 124.22/124.51 20697 inverse(sk_c8) = sk_c9 | multiply(sk_c2,sk_c9) = identity. [para(20692(a,1),7045(a,1,2))].
% 124.22/124.51 20703 inverse(sk_c9) = sk_c2 | inverse(sk_c9) = sk_c8. [para(20696(a,1),7331(a,1,1))].
% 124.22/124.51 20721 inverse(sk_c9) = sk_c8 | sk_c2 = sk_c1. [para(20703(a,1),13453(a,1)),merge(c)].
% 124.22/124.51 20748 sk_c2 = sk_c1 | multiply(sk_c8,A) = A. [para(20721(a,1),9536(b,1,1)),merge(b)].
% 124.22/124.51 20876 sk_c2 = sk_c1 | multiply(inverse(sk_c8),A) = A. [para(20748(b,1),248(a,1,2))].
% 124.22/124.51 23383 sk_c2 = sk_c1 | multiply(sk_c7,sk_c9) = inverse(sk_c8). [para(6750(b,1),20876(b,1)),flip(c),merge(b)].
% 124.22/124.51 23459 sk_c2 = sk_c1 | multiply(A,inverse(sk_c8)) = A. [para(23383(b,1),6750(b,1,2)),merge(b)].
% 124.22/124.51 23986 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(7727(a,1),248(a,1,2)),rewrite([6028(3)]),flip(a)].
% 124.22/124.51 24370 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(23986(a,1),248(a,1,2)),flip(a)].
% 124.22/124.51 24904 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(B,multiply(C,sk_c8)) != sk_c7 | multiply(inverse(C),inverse(B)) != sk_c8. [back_rewrite(18523),rewrite([24370(40)])].
% 124.22/124.51 26374 sk_c2 = sk_c1 | identity = sk_c4. [para(8810(c,1),8809(c,1)),merge(c),merge(d),merge(e)].
% 124.22/124.51 26375 sk_c2 = sk_c1 | multiply(sk_c4,A) = A. [para(26374(b,1),1(a,1,1))].
% 124.22/124.51 26485 sk_c2 = sk_c1 | multiply(inverse(sk_c4),A) = A. [para(26375(b,1),248(a,1,2))].
% 124.22/124.51 27019 sk_c2 = sk_c1 | inverse(sk_c4) = inverse(sk_c8). [para(26485(b,1),23459(b,1)),flip(c),merge(b)].
% 124.22/124.51 27037 sk_c2 = sk_c1 | multiply(sk_c4,inverse(sk_c8)) = identity. [para(27019(b,1),7045(a,1,2))].
% 124.22/124.51 27215 sk_c2 = sk_c1 | multiply(sk_c9,inverse(sk_c8)) = identity. [para(13900(a,1),27037(b,1,1)),merge(b)].
% 124.22/124.51 28397 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c8) = identity. [para(9696(b,1),265(b,1,2)),rewrite([7045(15)]),merge(b)].
% 124.22/124.51 28428 inverse(sk_c1) = sk_c9 | inverse(sk_c4) = sk_c8. [para(28397(b,1),248(a,1,2)),rewrite([6028(8)])].
% 124.22/124.51 28434 inverse(sk_c1) = sk_c9 | inverse(sk_c8) = sk_c4. [para(28428(b,1),7331(a,1,1))].
% 124.22/124.51 28438 inverse(sk_c8) = sk_c4 | multiply(sk_c1,sk_c9) = identity. [para(28434(a,1),7045(a,1,2))].
% 124.22/124.51 31015 inverse(sk_c9) = sk_c7 | multiply(sk_c9,A) = A. [para(15392(b,1),13158(b,1,1)),merge(b)].
% 124.22/124.51 31065 inverse(sk_c9) = sk_c7 | multiply(inverse(sk_c9),A) = A. [para(31015(b,1),248(a,1,2))].
% 124.22/124.51 39009 inverse(sk_c9) = sk_c7 | inverse(sk_c3) = sk_c7. [para(17130(b,1),8521(b,1)),flip(c),merge(b)].
% 124.22/124.51 39018 inverse(sk_c9) = sk_c7 | multiply(sk_c7,A) = A. [para(39009(b,1),13158(b,1,1)),merge(b)].
% 124.22/124.51 39070 inverse(sk_c9) = sk_c7 | inverse(sk_c8) = sk_c9. [para(39018(b,1),7807(b,1)),merge(b)].
% 124.22/124.51 39079 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | sk_c7 != B | multiply(sk_c8,inverse(B)) != sk_c8. [para(2(a,1),24904(i,1,2)),rewrite([6028(35),7331(38)]),flip(i)].
% 124.22/124.51 39082 multiply(sk_c9,sk_c8) != sk_c7 | multiply(A,multiply(B,sk_c9)) != sk_c8 | multiply(inverse(B),inverse(A)) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | sk_c7 != C | multiply(sk_c8,inverse(C)) != sk_c8. [para(51(a,1),39079(b,1)),rewrite([24370(12)])].
% 124.22/124.51 39088 inverse(sk_c9) = sk_c7 | multiply(sk_c9,sk_c8) = identity. [para(39070(b,1),2(a,1,1))].
% 124.22/124.51 39107 inverse(sk_c9) = sk_c7 | multiply(A,sk_c7) = A. [para(39088(b,1),250(b,1,2)),rewrite([6028(10)]),flip(c),merge(b)].
% 124.22/124.51 40676 multiply(sk_c9,sk_c8) != sk_c7 | sk_c8 != A | multiply(sk_c9,inverse(A)) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | sk_c7 != B | multiply(sk_c8,inverse(B)) != sk_c8. [para(2(a,1),39082(b,1,2)),rewrite([6028(7),7331(10)]),flip(b)].
% 124.22/124.51 40678 multiply(sk_c9,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c9,A) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | sk_c7 != B | multiply(sk_c8,inverse(B)) != sk_c8. [para(7331(a,1),40676(c,1,2)),flip(b)].
% 124.22/124.51 40680 multiply(sk_c9,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c9,A) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | inverse(B) != sk_c7 | multiply(sk_c8,B) != sk_c8. [para(7331(a,1),40678(j,1,2)),flip(i)].
% 124.22/124.51 40689 multiply(sk_c9,sk_c8) != sk_c7 | multiply(inverse(A),sk_c9) != sk_c8 | sk_c9 != A | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | inverse(B) != sk_c7 | multiply(sk_c8,B) != sk_c8. [para(7330(a,1),40680(c,1)),rewrite([24370(9),7331(9)]),flip(c)].
% 124.22/124.51 40703 multiply(sk_c9,sk_c8) != sk_c7 | multiply(inverse(A),sk_c9) != sk_c8 | sk_c9 != A | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(inverse(B),sk_c8) != sk_c7 | sk_c8 != B. [para(7330(a,1),40689(j,1)),rewrite([24370(37),7331(37)]),flip(j)].
% 124.22/124.51 43007 multiply(sk_c9,sk_c8) != sk_c7 | multiply(inverse(A),multiply(inverse(B),sk_c9)) != sk_c8 | multiply(B,A) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(inverse(C),sk_c8) != sk_c7 | sk_c8 != C. [para(24370(a,1),40703(b,1,1)),rewrite([51(10)]),flip(c)].
% 124.22/124.51 43397 multiply(sk_c9,sk_c8) != sk_c7 | multiply(inverse(sk_c7),multiply(inverse(sk_c8),sk_c9)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(inverse(A),sk_c8) != sk_c7 | sk_c8 != A. [factor(43007,c,f)].
% 124.22/124.51 43984 multiply(sk_c9,sk_c8) != sk_c7 | multiply(inverse(sk_c7),multiply(inverse(sk_c8),sk_c9)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | inverse(sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8. [para(24370(a,1),43397(h,1,1)),rewrite([51(40)]),flip(i)].
% 124.22/124.51 44762 inverse(sk_c9) = sk_c7. [para(31065(b,1),39107(b,1)),flip(c),merge(b),merge(c)].
% 124.22/124.51 45055 multiply(sk_c9,sk_c8) != sk_c7 | multiply(inverse(sk_c7),multiply(inverse(sk_c8),sk_c9)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8. [back_rewrite(43984),rewrite([44762(29)]),xx(f)].
% 124.22/124.51 49651 multiply(sk_c7,sk_c9) = identity. [para(44762(a,1),2(a,1,1))].
% 124.22/124.51 49653 inverse(sk_c7) = sk_c9. [para(44762(a,1),7331(a,1,1))].
% 124.22/124.51 49654 multiply(sk_c9,sk_c7) = identity. [para(44762(a,1),7045(a,1,2))].
% 124.22/124.51 49655 multiply(sk_c9,multiply(sk_c7,A)) = A. [para(44762(a,1),7330(a,1,2,1))].
% 124.22/124.51 49682 inverse(sk_c1) = sk_c9 | multiply(sk_c8,sk_c7) = identity. [back_rewrite(14599),rewrite([49651(10)])].
% 124.22/124.51 49884 multiply(sk_c9,sk_c8) != sk_c7 | multiply(sk_c9,multiply(inverse(sk_c8),sk_c9)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8. [back_rewrite(45055),rewrite([49653(7)])].
% 124.22/124.51 49936 sk_c7 = sk_c9 | inverse(sk_c4) = sk_c9 | multiply(sk_c9,sk_c8) = sk_c9. [back_rewrite(15751),rewrite([49653(9)])].
% 124.22/124.51 49937 multiply(sk_c1,sk_c9) = sk_c8 | multiply(sk_c9,sk_c9) = sk_c4. [back_rewrite(15600),rewrite([49653(8)])].
% 124.22/124.51 50357 multiply(sk_c9,sk_c8) = sk_c7. [para(5964(b,1),24370(a,1,1)),rewrite([44762(7),49653(8),7331(10)]),flip(b),merge(b)].
% 124.22/124.51 50414 sk_c7 = sk_c9 | inverse(sk_c4) = sk_c9. [back_rewrite(49936),rewrite([50357(10)]),merge(c)].
% 124.22/124.51 50422 multiply(sk_c9,multiply(inverse(sk_c8),sk_c9)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c9) != sk_c7 | inverse(sk_c8) != sk_c9 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8. [back_rewrite(49884),rewrite([50357(3)]),xx(a)].
% 124.22/124.51 52112 multiply(sk_c9,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(50357(a,1),51(a,1,1)),flip(a)].
% 124.22/124.51 52113 multiply(sk_c7,sk_c7) = sk_c8. [para(50357(a,1),248(a,1,2)),rewrite([44762(2)])].
% 124.22/124.51 52149 multiply(inverse(sk_c8),sk_c7) = sk_c9. [para(50357(a,1),24370(a,1,1)),rewrite([49653(2),44762(5)]),flip(a)].
% 124.22/124.51 52386 multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(52113(a,1),51(a,1,1)),flip(a)].
% 124.22/124.51 52396 multiply(sk_c9,sk_c9) = inverse(sk_c8). [para(52113(a,1),24370(a,1,1)),rewrite([49653(4),49653(5)]),flip(a)].
% 124.22/124.51 52599 multiply(sk_c1,sk_c9) = sk_c8 | inverse(sk_c8) = sk_c4. [back_rewrite(49937),rewrite([52396(8)])].
% 124.22/124.51 52639 multiply(sk_c8,sk_c9) = sk_c7. [para(52149(a,1),248(a,1,2)),rewrite([7331(3)])].
% 124.22/124.51 53318 multiply(sk_c9,multiply(inverse(sk_c8),sk_c9)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c9 | sk_c8 != sk_c9 | inverse(sk_c8) != sk_c9 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8. [back_rewrite(50422),rewrite([52639(19)]),xx(d)].
% 124.22/124.51 53351 multiply(sk_c8,multiply(sk_c9,A)) = multiply(sk_c7,A). [para(52639(a,1),51(a,1,1)),flip(a)].
% 124.22/124.51 53403 multiply(sk_c9,multiply(sk_c9,A)) = multiply(inverse(sk_c8),A). [para(52396(a,1),51(a,1,1)),flip(a)].
% 124.22/124.51 53538 sk_c7 = sk_c9 | multiply(sk_c9,sk_c4) = identity. [para(50414(b,1),2(a,1,1))].
% 124.22/124.51 53540 sk_c7 = sk_c9 | sk_c4 = sk_c7. [para(50414(b,1),7331(a,1,1)),rewrite([44762(5)]),flip(b)].
% 124.22/124.51 54929 inverse(sk_c1) = sk_c9 | identity = sk_c8. [para(49682(b,1),10514(b,1)),merge(b)].
% 124.22/124.51 54933 identity = sk_c8 | multiply(sk_c1,sk_c9) = identity. [para(54929(a,1),7045(a,1,2))].
% 124.22/124.51 54939 identity = sk_c8 | multiply(sk_c8,sk_c7) = sk_c9. [para(54933(b,1),37(a,1)),merge(b)].
% 124.22/124.51 56609 identity = sk_c8 | inverse(sk_c8) = sk_c8. [para(54939(b,1),52112(a,1,2)),rewrite([52396(6),52113(8)])].
% 124.22/124.51 56682 sk_c8 = sk_c9 | multiply(sk_c7,sk_c1) = sk_c8. [para(11391(b,1),52386(a,1,2)),rewrite([52113(6),53351(9)]),flip(b)].
% 124.22/124.51 56729 multiply(sk_c8,sk_c7) = multiply(sk_c7,sk_c8). [para(52113(a,1),52386(a,1,2)),flip(a)].
% 124.22/124.51 57181 multiply(sk_c9,multiply(inverse(sk_c8),sk_c9)) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c9 | sk_c8 != sk_c9 | inverse(sk_c8) != sk_c9 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8. [back_rewrite(53318),rewrite([56729(11)])].
% 124.22/124.51 57827 multiply(inverse(sk_c8),sk_c9) = multiply(sk_c9,inverse(sk_c8)). [para(56729(a,1),24370(a,1,1)),rewrite([24370(4),49653(4),49653(6)])].
% 124.22/124.51 57831 multiply(inverse(sk_c8),inverse(sk_c8)) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c9 | sk_c8 != sk_c9 | inverse(sk_c8) != sk_c9 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8. [back_rewrite(57181),rewrite([57827(5),53403(6)])].
% 124.22/124.51 57853 sk_c8 = sk_c9 | multiply(sk_c8,sk_c1) = multiply(sk_c7,sk_c8). [para(56682(b,1),52386(a,1,2)),flip(b)].
% 124.22/124.51 57900 inverse(sk_c8) = sk_c4 | identity = sk_c8. [para(52599(a,1),28438(b,1)),flip(c),merge(b)].
% 124.22/124.51 57922 identity = sk_c8 | sk_c4 = sk_c8. [para(57900(a,1),56609(b,1)),merge(b)].
% 124.22/124.51 57925 sk_c4 = sk_c8 | inverse(sk_c8) = identity. [para(57922(a,1),6164(a,1,1))].
% 124.22/124.51 57951 sk_c4 = sk_c8 | sk_c7 = sk_c9. [para(57925(b,1),52149(a,1,1)),rewrite([1(6)])].
% 124.22/124.51 57957 sk_c7 = sk_c9 | sk_c8 = sk_c7. [para(57951(a,1),53540(b,1)),merge(b)].
% 124.22/124.51 57958 sk_c7 = sk_c9 | identity = sk_c7. [para(57951(a,1),53538(b,1,2)),rewrite([50357(9)]),flip(c),merge(b)].
% 124.22/124.51 57959 sk_c7 = sk_c9 | identity = sk_c9. [para(57957(b,1),52149(a,1,1,1)),rewrite([49653(5),49654(6)])].
% 124.22/124.51 57989 sk_c7 = sk_c9. [para(57959(b,1),57958(b,1)),flip(c),merge(b),merge(c)].
% 124.22/124.51 58019 sk_c8 = sk_c9 | multiply(sk_c8,sk_c1) = sk_c9. [back_rewrite(57853),rewrite([57989(7),50357(9),57989(7)])].
% 124.22/124.51 58029 multiply(inverse(sk_c8),inverse(sk_c8)) != sk_c8 | sk_c8 != sk_c9 | inverse(sk_c8) != sk_c9 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c9 | multiply(B,A) != sk_c8. [back_rewrite(57831),rewrite([57989(8),50357(10),57989(8),57989(23)]),xx(b)].
% 124.22/124.51 59152 inverse(sk_c8) = sk_c8. [back_rewrite(52113),rewrite([57989(1),57989(2),52396(3)])].
% 124.22/124.51 59165 multiply(sk_c9,sk_c8) = sk_c9. [back_rewrite(50357),rewrite([57989(4)])].
% 124.22/124.51 59323 multiply(sk_c8,A) = A. [back_rewrite(49655),rewrite([57989(2),53403(4),59152(2)])].
% 124.22/124.51 59324 identity = sk_c8. [back_rewrite(49654),rewrite([57989(2),52396(3),59152(2)]),flip(a)].
% 124.22/124.51 60139 multiply(sk_c2,sk_c9) = sk_c3 | multiply(inverse(sk_c4),sk_c9) = sk_c9. [back_rewrite(5981),rewrite([57989(10)])].
% 124.22/124.51 60142 multiply(sk_c9,sk_c3) = sk_c8 | multiply(inverse(sk_c4),sk_c9) = sk_c9. [back_rewrite(5976),rewrite([57989(10)])].
% 124.22/124.51 60186 sk_c8 != sk_c9. [factor(58029,a,e),rewrite([59152(2),59152(3),59323(3),59152(8),59152(11),59152(11),59152(12),59152(12),59323(13),59323(12)]),xx(a),merge(b),merge(c)].
% 124.22/124.51 60193 sk_c2 = sk_c1. [back_rewrite(27215),rewrite([59152(6),59165(6),59324(5)]),flip(b),unit_del(b,60186)].
% 124.22/124.51 60231 multiply(sk_c9,sk_c9) = sk_c8. [back_rewrite(52396),rewrite([59152(5)])].
% 124.22/124.51 60237 multiply(sk_c1,sk_c9) = sk_c8. [back_rewrite(20697),rewrite([59152(2),60193(4),59324(7)]),unit_del(a,60186)].
% 124.22/124.51 60242 multiply(A,sk_c8) = A. [back_rewrite(13541),rewrite([59152(2),60237(6)]),unit_del(a,60186)].
% 124.22/124.51 60248 sk_c1 = sk_c9. [back_rewrite(58019),rewrite([59323(6)]),unit_del(a,60186)].
% 124.22/124.51 60314 sk_c3 = sk_c8 | multiply(inverse(sk_c4),sk_c9) = sk_c9. [back_rewrite(60139),rewrite([60193(1),60248(1),60231(3)]),flip(a)].
% 124.22/124.51 60329 inverse(sk_c4) = sk_c9. [back_rewrite(12418),rewrite([60193(6),60248(6),60231(8),60242(7)]),flip(b),unit_del(b,60186)].
% 124.22/124.51 60336 sk_c3 = sk_c8. [back_rewrite(60314),rewrite([60329(5),60231(6)]),unit_del(b,60186)].
% 124.22/124.51 60337 $F. [back_rewrite(60142),rewrite([60336(2),60242(3),60329(5),60231(6)]),flip(a),merge(b),unit_del(a,60186)].
% 124.22/124.51
% 124.22/124.51 % SZS output end Refutation
% 124.22/124.51 ============================== end of proof ==========================
% 124.22/124.51
% 124.22/124.51 ============================== STATISTICS ============================
% 124.22/124.51
% 124.22/124.51 Given=9019. Generated=5226067. Kept=60336. proofs=1.
% 124.22/124.51 Usable=6. Sos=78. Demods=20. Limbo=8, Disabled=60296. Hints=0.
% 124.22/124.51 Megabytes=54.38.
% 124.22/124.51 User_CPU=120.73, System_CPU=2.78, Wall_clock=124.
% 124.22/124.51
% 124.22/124.51 ============================== end of statistics =====================
% 124.22/124.51
% 124.22/124.51 ============================== end of search =========================
% 124.22/124.51
% 124.22/124.51 THEOREM PROVED
% 124.22/124.51 % SZS status Unsatisfiable
% 124.22/124.51
% 124.22/124.51 Exiting with 1 proof.
% 124.22/124.51
% 124.22/124.51 Process 24626 exit (max_proofs) Tue Jun 14 01:44:26 2022
% 124.22/124.51 Prover9 interrupted
%------------------------------------------------------------------------------