TSTP Solution File: GRP311-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP311-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 11:18:35 EDT 2022
% Result : Unsatisfiable 38.77s 39.09s
% Output : Refutation 38.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP311-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 06:28:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 9.67/9.92 ============================== Prover9 ===============================
% 9.67/9.92 Prover9 (32) version 2009-11A, November 2009.
% 9.67/9.92 Process 13760 was started by sandbox on n012.cluster.edu,
% 9.67/9.92 Tue Jun 14 06:28:41 2022
% 9.67/9.92 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13607_n012.cluster.edu".
% 9.67/9.92 ============================== end of head ===========================
% 9.67/9.92
% 9.67/9.92 ============================== INPUT =================================
% 9.67/9.92
% 9.67/9.92 % Reading from file /tmp/Prover9_13607_n012.cluster.edu
% 9.67/9.92
% 9.67/9.92 set(prolog_style_variables).
% 9.67/9.92 set(auto2).
% 9.67/9.92 % set(auto2) -> set(auto).
% 9.67/9.92 % set(auto) -> set(auto_inference).
% 9.67/9.92 % set(auto) -> set(auto_setup).
% 9.67/9.92 % set(auto_setup) -> set(predicate_elim).
% 9.67/9.92 % set(auto_setup) -> assign(eq_defs, unfold).
% 9.67/9.92 % set(auto) -> set(auto_limits).
% 9.67/9.92 % set(auto_limits) -> assign(max_weight, "100.000").
% 9.67/9.92 % set(auto_limits) -> assign(sos_limit, 20000).
% 9.67/9.92 % set(auto) -> set(auto_denials).
% 9.67/9.92 % set(auto) -> set(auto_process).
% 9.67/9.92 % set(auto2) -> assign(new_constants, 1).
% 9.67/9.92 % set(auto2) -> assign(fold_denial_max, 3).
% 9.67/9.92 % set(auto2) -> assign(max_weight, "200.000").
% 9.67/9.92 % set(auto2) -> assign(max_hours, 1).
% 9.67/9.92 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 9.67/9.92 % set(auto2) -> assign(max_seconds, 0).
% 9.67/9.92 % set(auto2) -> assign(max_minutes, 5).
% 9.67/9.92 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 9.67/9.92 % set(auto2) -> set(sort_initial_sos).
% 9.67/9.92 % set(auto2) -> assign(sos_limit, -1).
% 9.67/9.92 % set(auto2) -> assign(lrs_ticks, 3000).
% 9.67/9.92 % set(auto2) -> assign(max_megs, 400).
% 9.67/9.92 % set(auto2) -> assign(stats, some).
% 9.67/9.92 % set(auto2) -> clear(echo_input).
% 9.67/9.92 % set(auto2) -> set(quiet).
% 9.67/9.92 % set(auto2) -> clear(print_initial_clauses).
% 9.67/9.92 % set(auto2) -> clear(print_given).
% 9.67/9.92 assign(lrs_ticks,-1).
% 9.67/9.92 assign(sos_limit,10000).
% 9.67/9.92 assign(order,kbo).
% 9.67/9.92 set(lex_order_vars).
% 9.67/9.92 clear(print_given).
% 9.67/9.92
% 9.67/9.92 % formulas(sos). % not echoed (34 formulas)
% 9.67/9.92
% 9.67/9.92 ============================== end of input ==========================
% 9.67/9.92
% 9.67/9.92 % From the command line: assign(max_seconds, 300).
% 9.67/9.92
% 9.67/9.92 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 9.67/9.92
% 9.67/9.92 % Formulas that are not ordinary clauses:
% 9.67/9.92
% 9.67/9.92 ============================== end of process non-clausal formulas ===
% 9.67/9.92
% 9.67/9.92 ============================== PROCESS INITIAL CLAUSES ===============
% 9.67/9.92
% 9.67/9.92 ============================== PREDICATE ELIMINATION =================
% 9.67/9.92
% 9.67/9.92 ============================== end predicate elimination =============
% 9.67/9.92
% 9.67/9.92 Auto_denials: (non-Horn, no changes).
% 9.67/9.92
% 9.67/9.92 Term ordering decisions:
% 9.67/9.92
% 9.67/9.92 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 9.67/9.92 Function symbol KB weights: sk_c7=1. sk_c6=1. sk_c5=1. sk_c3=1. sk_c4=1. sk_c1=1. sk_c2=1. identity=1. multiply=1. inverse=0.
% 9.67/9.92
% 9.67/9.92 ============================== end of process initial clauses ========
% 9.67/9.92
% 9.67/9.92 ============================== CLAUSES FOR SEARCH ====================
% 9.67/9.92
% 9.67/9.92 ============================== end of clauses for search =============
% 9.67/9.92
% 9.67/9.92 ============================== SEARCH ================================
% 9.67/9.92
% 9.67/9.92 % Starting search at 0.01 seconds.
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=49.000, iters=3414
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=48.000, iters=3646
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=45.000, iters=3340
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=44.000, iters=3375
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=43.000, iters=3339
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=42.000, iters=3335
% 9.67/9.92
% 9.67/9.92 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 1.04 sec).
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=41.000, iters=3351
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=40.000, iters=3341
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=39.000, iters=3340
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=38.000, iters=3366
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=37.000, iters=3343
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=36.000, iters=3333
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=35.000, iters=3343
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=34.000, iters=3346
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=33.000, iters=3345
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=31.000, iters=3495
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=30.000, iters=3486
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=17.000, iters=3427
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=16.000, iters=3333
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=15.000, iters=3380
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=14.000, iters=3350
% 9.67/9.92
% 9.67/9.92 Low Water (keep): wt=13.000, iters=3364
% 9.67/9.92
% 9.67/9.92 Low Water (displace): id=2980, wt=57.000
% 9.67/9.92
% 9.67/9.92 Low Water (displace): id=12544, wt=12.000
% 9.67/9.92
% 9.67/9.92 Low Water (displace): id=12649, wt=11.000
% 38.77/39.09
% 38.77/39.09 Low Water (displace): id=13120, wt=10.000
% 38.77/39.09
% 38.77/39.09 Low Water (keep): wt=12.000, iters=3334
% 38.77/39.09
% 38.77/39.09 ============================== PROOF =================================
% 38.77/39.09 % SZS status Unsatisfiable
% 38.77/39.09 % SZS output start Refutation
% 38.77/39.09
% 38.77/39.09 % Proof 1 at 37.17 (+ 0.92) seconds.
% 38.77/39.09 % Length of proof is 252.
% 38.77/39.09 % Level of proof is 37.
% 38.77/39.09 % Maximum clause weight is 51.000.
% 38.77/39.09 % Given clauses 4041.
% 38.77/39.09
% 38.77/39.09 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 38.77/39.09 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 38.77/39.09 3 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 38.77/39.09 4 inverse(sk_c7) = sk_c5 | inverse(sk_c4) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 38.77/39.09 5 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 38.77/39.09 6 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 38.77/39.09 7 multiply(sk_c7,sk_c6) = sk_c5 | inverse(sk_c3) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 38.77/39.09 8 multiply(sk_c7,sk_c6) = sk_c5 | inverse(sk_c4) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 38.77/39.09 9 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 38.77/39.09 10 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 38.77/39.09 11 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 38.77/39.09 12 multiply(sk_c5,sk_c6) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 38.77/39.09 13 multiply(sk_c5,sk_c6) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 38.77/39.09 14 multiply(sk_c7,sk_c2) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 38.77/39.09 15 multiply(sk_c7,sk_c2) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 38.77/39.09 16 multiply(sk_c1,sk_c7) = sk_c2 | inverse(sk_c3) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 38.77/39.09 17 multiply(sk_c1,sk_c7) = sk_c2 | inverse(sk_c4) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 38.77/39.09 19 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 38.77/39.09 20 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 38.77/39.09 21 multiply(sk_c7,sk_c6) = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 38.77/39.09 25 multiply(sk_c5,sk_c6) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 38.77/39.09 29 multiply(sk_c7,sk_c2) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 38.77/39.09 32 multiply(sk_c1,sk_c7) = sk_c2 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 38.77/39.09 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 38.77/39.09 34 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,A) != sk_c6 | multiply(B,sk_c7) != A | inverse(B) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7 | inverse(D) != sk_c6 | multiply(D,sk_c5) != sk_c6 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 38.77/39.09 48 inverse(sk_c7) = sk_c5 | multiply(sk_c7,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 38.77/39.09 49 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 38.77/39.09 50 inverse(sk_c3) = sk_c7 | multiply(sk_c7,sk_c1) = identity. [para(5(a,1),2(a,1,1))].
% 38.77/39.09 51 inverse(sk_c4) = sk_c6 | multiply(sk_c7,sk_c1) = identity. [para(6(a,1),2(a,1,1))].
% 38.77/39.09 52 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 38.77/39.09 53 inverse(sk_c3) = sk_c7 | multiply(sk_c7,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(7(a,1),33(a,1,1)),flip(b)].
% 38.77/39.09 57 inverse(sk_c7) = sk_c5 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(9(b,1),33(a,1,1)),flip(b)].
% 38.77/39.09 59 inverse(sk_c7) = sk_c5 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(10(b,1),33(a,1,1)),flip(b)].
% 38.77/39.09 60 inverse(sk_c7) = sk_c5 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(10(b,1),33(a,2,2)),rewrite([33(8)])].
% 38.77/39.09 61 inverse(sk_c7) = sk_c5 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(11(b,1),33(a,1,1)),flip(b)].
% 38.77/39.09 62 inverse(sk_c7) = sk_c5 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c6). [para(11(b,1),33(a,2,2)),rewrite([33(8)])].
% 38.77/39.09 63 inverse(sk_c3) = sk_c7 | multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(12(a,1),33(a,1,1)),flip(b)].
% 38.77/39.09 65 inverse(sk_c4) = sk_c6 | multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(13(a,1),33(a,1,1)),flip(b)].
% 38.77/39.09 72 inverse(sk_c3) = sk_c7 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c2). [para(16(a,1),33(a,2,2)),rewrite([33(8)])].
% 38.77/39.09 74 inverse(sk_c4) = sk_c6 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c2). [para(17(a,1),33(a,2,2)),rewrite([33(8)])].
% 38.77/39.09 77 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(19(b,1),33(a,1,1)),flip(b)].
% 38.77/39.09 80 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c6). [para(20(b,1),33(a,2,2)),rewrite([33(8)])].
% 38.77/39.09 103 multiply(sk_c4,sk_c5) = sk_c6 | multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c2,A). [para(32(a,1),33(a,1,1)),flip(b)].
% 38.77/39.09 104 multiply(sk_c4,sk_c5) = sk_c6 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c2). [para(32(a,1),33(a,2,2)),rewrite([33(9)])].
% 38.77/39.09 116 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,multiply(A,sk_c7)) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6. [resolve(34,e,1,a(flip)),rewrite([1(19)])].
% 38.77/39.09 124 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,A) != sk_c6 | identity != A | inverse(inverse(sk_c7)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6. [para(2(a,1),34(e,1))].
% 38.77/39.09 164 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,multiply(A,sk_c7)) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [factor(116,c,h)].
% 38.77/39.09 188 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,A) != sk_c6 | identity != A | inverse(inverse(sk_c7)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [factor(124,f,h)].
% 38.77/39.09 299 inverse(sk_c7) = sk_c5 | multiply(sk_c7,multiply(sk_c3,A)) = A. [para(48(b,1),33(a,1,1)),rewrite([1(6)]),flip(b)].
% 38.77/39.09 309 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),52(a,1,2))].
% 38.77/39.09 313 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c7),sk_c5) = sk_c6. [para(7(a,1),52(a,1,2))].
% 38.77/39.09 315 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(9(b,1),52(a,1,2))].
% 38.77/39.09 316 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(10(b,1),52(a,1,2))].
% 38.77/39.09 322 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c1),sk_c2) = sk_c7. [para(16(a,1),52(a,1,2))].
% 38.77/39.09 323 inverse(sk_c4) = sk_c6 | multiply(inverse(sk_c1),sk_c2) = sk_c7. [para(17(a,1),52(a,1,2))].
% 38.77/39.09 327 multiply(sk_c7,sk_c6) = sk_c5 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(21(b,1),52(a,1,2))].
% 38.77/39.09 340 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c7),identity) = sk_c3. [para(48(b,1),52(a,1,2))].
% 38.77/39.09 341 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(52(a,1),52(a,1,2))].
% 38.77/39.09 342 multiply(A,identity) = A. [back_rewrite(309),rewrite([341(4)])].
% 38.77/39.09 343 inverse(sk_c7) = sk_c5 | inverse(sk_c7) = sk_c3. [back_rewrite(340),rewrite([342(8)])].
% 38.77/39.09 348 inverse(identity) = identity. [para(342(a,1),2(a,1))].
% 38.77/39.09 376 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c7) = identity. [para(343(b,1),2(a,1,1))].
% 38.77/39.09 379 inverse(sk_c7) = sk_c5 | inverse(sk_c6) = sk_c4. [para(49(b,1),52(a,1,2)),rewrite([342(8)])].
% 38.77/39.09 384 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c6) = identity. [para(379(b,1),2(a,1,1))].
% 38.77/39.09 385 inverse(sk_c7) = sk_c5 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(379(b,1),52(a,1,1))].
% 38.77/39.09 386 inverse(sk_c3) = sk_c7 | multiply(A,multiply(sk_c7,sk_c1)) = A. [para(50(b,1),33(a,2,2)),rewrite([33(8),342(10)])].
% 38.77/39.09 394 inverse(sk_c4) = sk_c6 | multiply(A,multiply(sk_c7,sk_c1)) = A. [para(51(b,1),33(a,2,2)),rewrite([33(8),342(10)])].
% 38.77/39.09 401 inverse(sk_c3) = sk_c7 | multiply(sk_c7,multiply(sk_c6,sk_c6)) = sk_c7. [para(12(a,1),53(b,2)),merge(b)].
% 38.77/39.09 434 multiply(A,inverse(A)) = identity. [para(341(a,1),2(a,1))].
% 38.77/39.09 457 multiply(A,multiply(inverse(A),B)) = B. [para(341(a,1),52(a,1))].
% 38.77/39.09 458 inverse(inverse(A)) = A. [para(341(a,1),342(a,1)),rewrite([342(2)]),flip(a)].
% 38.77/39.09 470 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,A) != sk_c6 | identity != A | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [back_rewrite(188),rewrite([458(23)]),xx(f)].
% 38.77/39.09 476 inverse(sk_c3) = sk_c7 | multiply(sk_c1,sk_c7) = identity. [para(5(a,1),434(a,1,2))].
% 38.77/39.09 477 inverse(sk_c4) = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(6(a,1),434(a,1,2))].
% 38.77/39.09 478 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(434(a,1),33(a,1)),flip(a)].
% 38.77/39.09 519 inverse(sk_c3) = sk_c7 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(5(a,1),457(a,1,2,1))].
% 38.77/39.09 520 inverse(sk_c4) = sk_c6 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(6(a,1),457(a,1,2,1))].
% 38.77/39.09 563 inverse(sk_c7) = sk_c5 | multiply(A,multiply(sk_c4,sk_c6)) = A. [para(384(b,1),33(a,2,2)),rewrite([33(8),342(10)])].
% 38.77/39.09 619 inverse(sk_c7) = sk_c5 | multiply(sk_c5,sk_c3) = sk_c6. [para(48(b,1),57(b,1,2)),rewrite([342(11)]),flip(c),merge(b)].
% 38.77/39.09 654 inverse(sk_c4) = sk_c6 | identity = sk_c2. [para(477(b,1),17(a,1)),merge(c)].
% 38.77/39.09 659 identity = sk_c2 | multiply(sk_c4,sk_c6) = identity. [para(654(a,1),434(a,1,2))].
% 38.77/39.09 685 identity = sk_c2 | multiply(A,multiply(sk_c4,sk_c6)) = A. [para(659(b,1),33(a,2,2)),rewrite([33(7),342(9)])].
% 38.77/39.09 700 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c5) = multiply(sk_c7,sk_c7). [para(9(b,1),59(b,1,2)),merge(b)].
% 38.77/39.09 702 inverse(sk_c7) = sk_c5 | multiply(sk_c3,multiply(sk_c6,sk_c3)) = identity. [para(48(b,1),59(b,2)),merge(b)].
% 38.77/39.09 738 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c5),sk_c6) = sk_c3. [para(619(b,1),52(a,1,2))].
% 38.77/39.09 745 inverse(sk_c7) = sk_c5 | multiply(sk_c6,multiply(sk_c3,sk_c6)) = sk_c5. [para(9(b,1),60(b,2)),merge(b)].
% 38.77/39.09 747 inverse(sk_c7) = sk_c5 | multiply(sk_c3,multiply(sk_c3,sk_c6)) = identity. [para(376(b,1),60(b,2)),merge(b)].
% 38.77/39.09 818 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c7. [para(379(b,1),315(b,1,1)),merge(b)].
% 38.77/39.09 819 inverse(sk_c7) = sk_c5 | sk_c6 = sk_c7. [para(818(b,1),11(b,1)),flip(c),merge(b)].
% 38.77/39.09 827 inverse(sk_c7) = sk_c5 | multiply(sk_c6,inverse(sk_c5)) = sk_c4. [para(434(a,1),61(b,1,2)),rewrite([342(7)]),flip(b)].
% 38.77/39.09 852 sk_c6 = sk_c7 | inverse(sk_c5) = sk_c7. [para(819(a,1),458(a,1,1))].
% 38.77/39.09 936 inverse(sk_c7) = sk_c5 | multiply(sk_c7,sk_c7) = sk_c6. [para(3(b,1),316(b,1,1)),merge(b)].
% 38.77/39.09 1076 inverse(sk_c3) = sk_c7 | multiply(sk_c7,sk_c2) = sk_c7. [para(5(a,1),322(b,1,1)),merge(b)].
% 38.77/39.09 1079 inverse(sk_c3) = sk_c7 | sk_c6 = sk_c7. [para(1076(b,1),14(a,1)),flip(b),merge(c)].
% 38.77/39.09 1085 sk_c6 = sk_c7 | inverse(sk_c7) = sk_c3. [para(1079(a,1),458(a,1,1))].
% 38.77/39.09 1171 sk_c6 = sk_c7 | sk_c3 = sk_c5. [para(1085(b,1),819(a,1)),merge(c)].
% 38.77/39.09 1178 sk_c6 = sk_c7 | multiply(sk_c5,sk_c6) = sk_c7. [para(1171(b,1),25(b,1,1)),merge(c)].
% 38.77/39.09 1303 sk_c6 = sk_c7 | multiply(inverse(sk_c5),sk_c7) = sk_c6. [para(1178(b,1),52(a,1,2))].
% 38.77/39.09 1314 sk_c6 = sk_c7 | multiply(sk_c7,sk_c7) = sk_c6. [para(852(b,1),1303(b,1,1)),merge(b)].
% 38.77/39.09 1335 sk_c6 = sk_c7 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(1314(b,1),52(a,1,2))].
% 38.77/39.09 1415 inverse(sk_c4) = sk_c6 | multiply(sk_c7,sk_c2) = sk_c7. [para(6(a,1),323(b,1,1)),merge(b)].
% 38.77/39.09 1418 inverse(sk_c4) = sk_c6 | sk_c6 = sk_c7. [para(1415(b,1),15(a,1)),flip(b),merge(c)].
% 38.77/39.09 1478 sk_c6 = sk_c7 | multiply(sk_c6,sk_c4) = identity. [para(1418(a,1),2(a,1,1))].
% 38.77/39.09 1480 sk_c6 = sk_c7 | inverse(sk_c6) = sk_c4. [para(1418(a,1),458(a,1,1))].
% 38.77/39.09 1631 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(478(a,1),52(a,1,2)),rewrite([342(3)]),flip(a)].
% 38.77/39.09 1758 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(1631(a,1),52(a,1,2)),flip(a)].
% 38.77/39.09 1772 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(inverse(sk_c7),inverse(A)) != identity | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [para(1631(a,1),470(d,1)),rewrite([1758(21)]),flip(e)].
% 38.77/39.09 1775 sk_c6 = sk_c7 | multiply(sk_c7,inverse(sk_c6)) = sk_c5. [para(1303(b,1),1631(a,1,2,1)),rewrite([458(10)])].
% 38.77/39.09 1777 sk_c6 = sk_c7 | multiply(sk_c6,inverse(sk_c7)) = sk_c7. [para(1335(b,1),1631(a,1,2,1)),rewrite([458(10)])].
% 38.77/39.09 2019 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(inverse(sk_c7),inverse(A)) != identity | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(A,sk_c5) != sk_c6. [factor(1772,d,h)].
% 38.77/39.09 2034 sk_c6 = sk_c7 | multiply(sk_c7,sk_c4) = sk_c5. [para(1480(b,1),1775(b,1,2)),merge(b)].
% 38.77/39.09 2041 sk_c6 = sk_c7 | multiply(inverse(sk_c7),sk_c5) = sk_c4. [para(2034(b,1),52(a,1,2))].
% 38.77/39.09 2051 sk_c6 = sk_c7 | multiply(sk_c6,sk_c5) = sk_c7. [para(819(a,1),1777(b,1,2)),merge(b)].
% 38.77/39.09 2085 sk_c6 = sk_c7 | multiply(inverse(sk_c6),sk_c7) = sk_c5. [para(2051(b,1),52(a,1,2))].
% 38.77/39.09 2120 inverse(sk_c3) = sk_c7 | multiply(A,sk_c2) = A. [para(476(b,1),72(b,1,2)),rewrite([342(10)]),flip(c),merge(b)].
% 38.77/39.09 2151 sk_c6 = sk_c7 | multiply(sk_c5,sk_c5) = sk_c4. [para(819(a,1),2041(b,1,1)),merge(b)].
% 38.77/39.09 2236 sk_c6 = sk_c7 | multiply(sk_c4,sk_c7) = sk_c5. [para(1480(b,1),2085(b,1,1)),merge(b)].
% 38.77/39.09 2247 sk_c6 = sk_c7 | multiply(inverse(sk_c4),sk_c5) = sk_c7. [para(2236(b,1),52(a,1,2))].
% 38.77/39.09 2273 inverse(sk_c4) = sk_c6 | multiply(A,sk_c2) = A. [para(477(b,1),74(b,1,2)),rewrite([342(10)]),flip(c),merge(b)].
% 38.77/39.09 2995 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c6,sk_c6)) = multiply(sk_c7,multiply(sk_c4,sk_c5)). [para(80(b,1),77(b,1,2)),merge(b)].
% 38.77/39.09 3310 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | sk_c6 != A | multiply(inverse(sk_c7),A) != identity | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(inverse(A),sk_c5) != sk_c6. [para(458(a,1),2019(e,1,2)),rewrite([458(16)]),flip(d)].
% 38.77/39.09 4201 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,multiply(A,sk_c7)) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | multiply(inverse(B),inverse(C)) != sk_c6 | multiply(C,multiply(B,sk_c5)) != sk_c6. [para(33(a,1),164(i,1)),rewrite([1758(34)])].
% 38.77/39.09 4488 sk_c6 = sk_c7 | multiply(inverse(sk_c5),sk_c7) = inverse(sk_c4). [para(2041(b,1),1758(a,1,1)),rewrite([458(10)]),flip(b)].
% 38.77/39.09 4543 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(A,B) != sk_c6 | multiply(inverse(sk_c7),multiply(A,B)) != identity | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(inverse(B),multiply(inverse(A),sk_c5)) != sk_c6. [para(1758(a,1),3310(h,1,1)),rewrite([33(39)]),flip(d)].
% 38.77/39.09 5824 multiply(sk_c4,sk_c5) = sk_c6 | multiply(sk_c1,multiply(sk_c7,multiply(inverse(sk_c2),A))) = A. [para(457(a,1),103(b,2))].
% 38.77/39.09 5842 identity = sk_c2 | multiply(sk_c4,sk_c5) = sk_c6 | multiply(sk_c1,multiply(sk_c7,multiply(sk_c4,sk_c6))) = sk_c2. [para(685(b,1),103(b,2))].
% 38.77/39.09 5939 multiply(sk_c4,sk_c5) = sk_c6 | multiply(sk_c2,multiply(sk_c1,sk_c7)) = multiply(sk_c1,multiply(sk_c7,sk_c2)). [para(104(b,1),103(b,1,2)),flip(c),merge(b)].
% 38.77/39.09 6048 sk_c6 = sk_c7 | multiply(sk_c7,sk_c7) = inverse(sk_c4). [para(852(b,1),4488(b,1,1)),merge(b)].
% 38.77/39.09 6658 multiply(sk_c7,sk_c6) = sk_c5 | multiply(inverse(sk_c5),sk_c6) = inverse(sk_c7). [para(327(b,1),1758(a,1,1)),rewrite([458(12)]),flip(b)].
% 38.77/39.09 6868 inverse(sk_c3) = sk_c7 | multiply(sk_c6,sk_c6) = identity. [para(401(b,1),52(a,1,2)),rewrite([2(8)]),flip(b)].
% 38.77/39.09 7007 inverse(sk_c3) = sk_c7 | multiply(sk_c1,sk_c5) = sk_c6. [para(7(a,1),519(b,1,2)),merge(b)].
% 38.77/39.09 7008 inverse(sk_c3) = sk_c7 | multiply(sk_c1,sk_c6) = sk_c2. [para(14(a,1),519(b,1,2)),merge(b)].
% 38.77/39.09 7022 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c1),sk_c6) = sk_c5. [para(7007(b,1),52(a,1,2))].
% 38.77/39.09 7025 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c1),sk_c2) = sk_c6. [para(7008(b,1),52(a,1,2))].
% 38.77/39.09 7048 inverse(sk_c3) = sk_c7 | inverse(sk_c1) = sk_c6. [para(7025(b,1),2120(b,1)),flip(c),merge(b)].
% 38.77/39.09 7056 inverse(sk_c3) = sk_c7 | multiply(sk_c6,sk_c1) = identity. [para(7048(b,1),2(a,1,1))].
% 38.77/39.09 7063 inverse(sk_c3) = sk_c7 | multiply(sk_c6,sk_c6) = sk_c5. [para(7048(b,1),7022(b,1,1)),merge(b)].
% 38.77/39.09 7179 inverse(sk_c3) = sk_c7 | multiply(sk_c7,sk_c1) = sk_c5. [para(7056(b,1),63(b,1,2)),rewrite([342(11)]),flip(c),merge(b)].
% 38.77/39.09 7193 inverse(sk_c3) = sk_c7 | identity = sk_c5. [para(7063(b,1),6868(b,1)),flip(c),merge(b)].
% 38.77/39.09 7196 identity = sk_c5 | inverse(sk_c7) = sk_c3. [para(7193(a,1),458(a,1,1))].
% 38.77/39.09 7308 inverse(sk_c3) = sk_c7 | multiply(A,sk_c5) = A. [para(7179(b,1),386(b,1,2)),merge(b)].
% 38.77/39.09 7413 inverse(sk_c3) = sk_c7 | inverse(sk_c5) = identity. [para(7308(b,1),2(a,1))].
% 38.77/39.09 7418 inverse(sk_c3) = sk_c7 | inverse(sk_c7) = sk_c6. [para(7308(b,1),313(b,1)),merge(b)].
% 38.77/39.09 7425 inverse(sk_c5) = identity | inverse(sk_c7) = sk_c3. [para(7413(a,1),458(a,1,1))].
% 38.77/39.09 7446 inverse(sk_c7) = sk_c6 | inverse(sk_c7) = sk_c3. [para(7418(a,1),458(a,1,1))].
% 38.77/39.09 8609 inverse(sk_c4) = sk_c6 | multiply(sk_c1,sk_c5) = sk_c6. [para(8(a,1),520(b,1,2)),merge(b)].
% 38.77/39.09 8610 inverse(sk_c4) = sk_c6 | multiply(sk_c1,sk_c6) = sk_c2. [para(15(a,1),520(b,1,2)),merge(b)].
% 38.77/39.09 8637 inverse(sk_c4) = sk_c6 | multiply(inverse(sk_c1),sk_c2) = sk_c6. [para(8610(b,1),52(a,1,2))].
% 38.77/39.09 8710 inverse(sk_c4) = sk_c6 | inverse(sk_c1) = sk_c6. [para(8637(b,1),2273(b,1)),flip(c),merge(b)].
% 38.77/39.09 8712 inverse(sk_c4) = sk_c6 | multiply(sk_c6,sk_c1) = identity. [para(8710(b,1),2(a,1,1))].
% 38.77/39.09 8764 inverse(sk_c4) = sk_c6 | multiply(sk_c7,sk_c1) = sk_c5. [para(8712(b,1),65(b,1,2)),rewrite([342(11)]),flip(c),merge(b)].
% 38.77/39.09 8835 inverse(sk_c4) = sk_c6 | multiply(A,sk_c5) = A. [para(8764(b,1),394(b,1,2)),merge(b)].
% 38.77/39.09 8999 inverse(sk_c4) = sk_c6 | sk_c1 = sk_c6. [para(8835(b,1),8609(b,1)),merge(b)].
% 38.77/39.09 9002 sk_c1 = sk_c6 | inverse(sk_c6) = sk_c4. [para(8999(a,1),458(a,1,1))].
% 38.77/39.09 9924 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c5) = sk_c6. [para(936(b,1),700(b,2)),merge(b)].
% 38.77/39.09 9938 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c3),sk_c6) = sk_c5. [para(9924(b,1),52(a,1,2))].
% 38.77/39.09 9966 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c3) = inverse(sk_c3). [para(702(b,1),52(a,1,2)),rewrite([342(8)]),flip(b)].
% 38.77/39.09 9969 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c3) = sk_c7. [para(702(b,1),299(b,1,2)),rewrite([342(11)]),flip(c),merge(b)].
% 38.77/39.09 10286 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c6) = inverse(sk_c3). [para(747(b,1),52(a,1,2)),rewrite([342(8)]),flip(b)].
% 38.77/39.09 10294 inverse(sk_c7) = sk_c5 | multiply(sk_c6,inverse(sk_c3)) = sk_c5. [para(10286(b,1),745(b,1,2)),merge(b)].
% 38.77/39.09 10308 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c5) = inverse(sk_c3). [para(10294(b,1),385(b,1,2)),merge(b)].
% 38.77/39.09 10309 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c6. [para(10308(b,1),11(b,1)),merge(b)].
% 38.77/39.09 10316 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c3) = identity. [para(10309(b,1),2(a,1,1))].
% 38.77/39.09 10472 inverse(sk_c7) = sk_c5 | identity = sk_c7. [para(10316(b,1),9969(b,1)),merge(b)].
% 38.77/39.09 10473 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = identity. [para(10316(b,1),9966(b,1)),flip(c),merge(b)].
% 38.77/39.09 10517 identity = sk_c7 | inverse(sk_c5) = sk_c7. [para(10472(a,1),458(a,1,1))].
% 38.77/39.09 10614 identity = sk_c7 | inverse(sk_c7) = sk_c3. [para(10517(b,1),7425(a,1)),flip(b),merge(b)].
% 38.77/39.09 10654 identity = sk_c7 | sk_c3 = sk_c5. [para(10614(b,1),10472(a,1)),merge(c)].
% 38.77/39.09 10658 sk_c3 = sk_c5 | inverse(sk_c7) = identity. [para(10654(a,1),348(a,1,1))].
% 38.77/39.09 10885 inverse(sk_c7) = sk_c5 | multiply(sk_c3,A) = A. [para(10473(b,1),52(a,1,1)),rewrite([1(8)])].
% 38.77/39.09 10894 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c5) = identity. [para(10473(b,1),10308(b,2)),merge(b)].
% 38.77/39.09 11495 inverse(sk_c7) = sk_c5 | multiply(sk_c7,A) = A. [para(10885(b,1),299(b,1,2)),merge(b)].
% 38.77/39.09 11730 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(A,inverse(B)) != sk_c6 | multiply(inverse(sk_c7),multiply(A,inverse(B))) != identity | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(B,multiply(inverse(A),sk_c5)) != sk_c6. [para(458(a,1),4543(h,1,1))].
% 38.77/39.09 11792 inverse(sk_c7) = sk_c5 | multiply(A,sk_c6) = A. [para(10894(b,1),62(b,1,2)),rewrite([342(10)]),flip(c),merge(b)].
% 38.77/39.09 12187 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c7),A) = A. [para(11495(b,1),52(a,1,2))].
% 38.77/39.09 12253 inverse(sk_c7) = sk_c5 | inverse(sk_c5) = sk_c3. [para(11792(b,1),738(b,1)),merge(b)].
% 38.77/39.09 12258 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c5. [para(11792(b,1),9938(b,1)),merge(b)].
% 38.77/39.09 12442 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c3) = sk_c4. [para(12253(b,1),827(b,1,2)),merge(b)].
% 38.77/39.09 12469 inverse(sk_c7) = sk_c5 | identity = sk_c5. [para(12258(b,1),10473(b,1)),flip(c),merge(b)].
% 38.77/39.09 12480 identity = sk_c5 | sk_c3 = sk_c5. [para(12469(a,1),7196(b,1)),flip(c),merge(b)].
% 38.77/39.09 12488 sk_c3 = sk_c5 | inverse(sk_c5) = identity. [para(12480(a,1),348(a,1,1))].
% 38.77/39.09 12552 sk_c3 = sk_c5 | inverse(sk_c7) = sk_c5. [para(12480(a,1),10658(b,2)),merge(b)].
% 38.77/39.09 12676 sk_c3 = sk_c5 | inverse(sk_c7) = sk_c6. [para(12552(b,1),7446(b,1)),flip(c),merge(c)].
% 38.77/39.09 12775 sk_c3 = sk_c5 | identity = sk_c6. [para(12676(b,1),10658(b,1)),flip(c),merge(b)].
% 38.77/39.09 12779 sk_c3 = sk_c5 | inverse(sk_c6) = identity. [para(12775(b,1),348(a,1,1))].
% 38.77/39.09 12837 sk_c3 = sk_c5 | inverse(sk_c5) = sk_c6. [para(12775(b,1),12488(b,2)),merge(b)].
% 38.77/39.09 12937 sk_c3 = sk_c5 | inverse(sk_c6) = sk_c5. [para(12480(a,1),12779(b,2)),merge(b)].
% 38.77/39.09 12943 sk_c3 = sk_c5 | multiply(sk_c5,sk_c6) = identity. [para(12837(b,1),434(a,1,2))].
% 38.77/39.09 13439 sk_c3 = sk_c5 | multiply(sk_c5,sk_c6) = sk_c7. [para(10654(a,1),12943(b,2)),merge(b)].
% 38.77/39.09 13797 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,multiply(A,sk_c7)) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | multiply(sk_c5,inverse(B)) != sk_c6 | sk_c6 != B. [para(2(a,1),4201(i,1,2)),rewrite([458(35),342(39)]),flip(i)].
% 38.77/39.09 13801 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,multiply(A,sk_c7)) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | multiply(sk_c5,B) != sk_c6 | inverse(B) != sk_c6. [para(458(a,1),13797(h,1,2)),flip(i)].
% 38.77/39.09 13812 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,multiply(A,sk_c7)) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6. [resolve(13801,h,457,a),rewrite([1758(37),458(37)])].
% 38.77/39.09 13815 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,multiply(A,multiply(B,sk_c7))) != sk_c6 | multiply(inverse(B),inverse(A)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6. [para(33(a,1),13812(d,1,2)),rewrite([1758(23)])].
% 38.77/39.09 13818 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,A) != sk_c6 | multiply(sk_c7,inverse(A)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6. [para(2(a,1),13815(d,1,2,2)),rewrite([342(17),458(21)])].
% 38.77/39.09 13830 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c7,multiply(A,B)) != sk_c6 | multiply(sk_c7,multiply(inverse(B),inverse(A))) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6. [para(1758(a,1),13818(e,1,2))].
% 38.77/39.09 13850 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | sk_c6 != A | multiply(sk_c7,multiply(inverse(A),sk_c7)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6. [para(457(a,1),13830(d,1)),rewrite([458(21)]),flip(d)].
% 38.77/39.09 13852 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(A,B) != sk_c6 | multiply(sk_c7,multiply(inverse(B),multiply(inverse(A),sk_c7))) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6. [para(1758(a,1),13850(e,1,2,1)),rewrite([33(23)]),flip(d)].
% 38.77/39.09 13853 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6 | multiply(sk_c7,multiply(inverse(sk_c5),multiply(sk_c6,sk_c7))) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7. [factor(13852,d,h),rewrite([458(26)])].
% 38.77/39.09 14057 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c4. [para(12442(b,1),9966(b,1)),flip(c),merge(b)].
% 38.77/39.09 14085 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c6) = sk_c5. [para(14057(b,1),9938(b,1,1)),merge(b)].
% 38.77/39.09 14462 multiply(sk_c7,sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c5,inverse(A)) != sk_c6 | multiply(inverse(sk_c7),multiply(sk_c5,inverse(A))) != identity | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != A. [para(2(a,1),11730(h,1,2)),rewrite([342(40)]),flip(h)].
% 38.77/39.09 14507 inverse(sk_c7) = sk_c5 | multiply(A,sk_c5) = A. [para(14085(b,1),563(b,1,2)),merge(b)].
% 38.77/39.09 16652 inverse(sk_c7) = sk_c5. [para(12187(b,1),14507(b,1)),flip(c),merge(b),merge(c)].
% 38.77/39.09 17227 multiply(sk_c7,sk_c6) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c5,inverse(A)) != sk_c6 | multiply(sk_c5,multiply(sk_c5,inverse(A))) != identity | multiply(sk_c6,sk_c7) != sk_c5 | sk_c6 != A. [back_rewrite(14462),rewrite([16652(7),16652(20),16652(32)]),xx(b),merge(f)].
% 38.77/39.09 17466 multiply(sk_c7,sk_c6) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6 | multiply(sk_c7,multiply(inverse(sk_c5),multiply(sk_c6,sk_c7))) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(sk_c5) != sk_c7. [back_rewrite(13853),rewrite([16652(7)]),xx(b)].
% 38.77/39.09 18530 multiply(sk_c7,sk_c6) = sk_c5 | multiply(inverse(sk_c5),sk_c6) = sk_c5. [back_rewrite(6658),rewrite([16652(11)])].
% 38.77/39.09 19547 multiply(sk_c5,sk_c7) = identity. [para(16652(a,1),2(a,1,1))].
% 38.77/39.09 19549 inverse(sk_c5) = sk_c7. [para(16652(a,1),458(a,1,1))].
% 38.77/39.09 19551 multiply(sk_c7,multiply(sk_c5,A)) = A. [para(16652(a,1),457(a,1,2,1))].
% 38.77/39.09 19694 multiply(sk_c7,sk_c6) = sk_c5. [back_rewrite(18530),rewrite([19549(7)]),merge(b)].
% 38.77/39.09 19975 multiply(sk_c5,sk_c6) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6 | multiply(sk_c7,multiply(sk_c7,multiply(sk_c6,sk_c7))) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5. [back_rewrite(17466),rewrite([19694(3),19549(17),19549(30)]),xx(a),xx(f)].
% 38.77/39.09 20905 multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c5,inverse(A)) != sk_c6 | multiply(sk_c5,multiply(sk_c5,inverse(A))) != identity | multiply(sk_c6,sk_c7) != sk_c5 | sk_c6 != A. [back_rewrite(17227),rewrite([19694(3)]),xx(a)].
% 38.77/39.09 20978 multiply(sk_c7,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(19694(a,1),33(a,1,1)),flip(a)].
% 38.77/39.09 20979 multiply(sk_c5,sk_c5) = sk_c6. [para(19694(a,1),52(a,1,2)),rewrite([16652(2)])].
% 38.77/39.09 20986 multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(19694(a,1),1758(a,1,1)),rewrite([19549(2),16652(5)]),flip(a)].
% 38.77/39.09 21001 multiply(sk_c5,sk_c6) != sk_c7 | sk_c6 != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5. [back_rewrite(19975),rewrite([20986(9),20978(14),19547(12),342(11)]),flip(b),xx(c)].
% 38.77/39.09 21040 sk_c6 = sk_c7 | sk_c4 = sk_c6. [back_rewrite(2151),rewrite([20979(6)]),flip(b)].
% 38.77/39.09 21041 multiply(sk_c5,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(20979(a,1),33(a,1,1)),flip(a)].
% 38.77/39.09 21042 multiply(sk_c7,sk_c7) = inverse(sk_c6). [para(20979(a,1),1758(a,1,1)),rewrite([19549(4),19549(5)]),flip(a)].
% 38.77/39.09 21046 multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c5,inverse(A)) != sk_c6 | multiply(sk_c6,inverse(A)) != identity | multiply(sk_c6,sk_c7) != sk_c5 | sk_c6 != A. [back_rewrite(20905),rewrite([21041(15)])].
% 38.77/39.09 21159 sk_c6 = sk_c7 | inverse(sk_c4) = inverse(sk_c6). [back_rewrite(6048),rewrite([21042(6)]),flip(b)].
% 38.77/39.09 21178 multiply(sk_c6,sk_c7) = sk_c5. [para(20986(a,1),52(a,1,2)),rewrite([458(3)])].
% 38.77/39.09 21180 sk_c6 = sk_c7 | multiply(sk_c4,sk_c5) = sk_c7. [para(1480(b,1),20986(a,1,1))].
% 38.77/39.09 21252 multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c5,inverse(A)) != sk_c6 | multiply(sk_c6,inverse(A)) != identity | sk_c6 != A. [back_rewrite(21046),rewrite([21178(18)]),xx(d)].
% 38.77/39.09 21273 multiply(sk_c5,sk_c6) != sk_c7 | sk_c6 != sk_c7. [back_rewrite(21001),rewrite([21178(11)]),xx(c)].
% 38.77/39.09 21826 sk_c6 = sk_c7 | multiply(sk_c6,sk_c6) = identity. [para(21040(b,1),1478(b,1,2)),merge(b)].
% 38.77/39.09 22020 sk_c1 = sk_c6 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c5,sk_c4) != sk_c6. [para(9002(b,1),21252(b,1,2)),rewrite([434(17)]),xx(d),xx(e)].
% 38.77/39.09 22024 sk_c3 = sk_c5 | multiply(sk_c5,sk_c6) != sk_c7. [para(12937(b,1),21252(b,1,2)),rewrite([20979(11),434(15)]),xx(c),xx(d),xx(e)].
% 38.77/39.09 22517 sk_c6 = sk_c7 | inverse(sk_c4) = sk_c4. [para(1480(b,1),21159(b,2)),merge(b)].
% 38.77/39.09 22539 sk_c6 = sk_c7 | inverse(sk_c1) = sk_c7. [para(21180(b,1),20(b,1)),flip(c),merge(c)].
% 38.77/39.09 22540 sk_c6 = sk_c7 | multiply(sk_c7,sk_c2) = sk_c6. [para(21180(b,1),29(b,1)),flip(c),merge(c)].
% 38.77/39.09 22547 sk_c6 = sk_c7 | sk_c1 = sk_c5. [para(22539(b,1),458(a,1,1)),rewrite([16652(5)]),flip(b)].
% 38.77/39.09 22549 sk_c6 = sk_c7 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(22539(b,1),457(a,1,2,1))].
% 38.77/39.09 22765 sk_c3 = sk_c5. [resolve(22024,b,13439,b),merge(b)].
% 38.77/39.09 22901 inverse(sk_c1) = sk_c7 | multiply(sk_c5,multiply(sk_c6,sk_c6)) = multiply(sk_c7,multiply(sk_c4,sk_c5)). [back_rewrite(2995),rewrite([22765(5)])].
% 38.77/39.09 22925 multiply(sk_c5,sk_c6) = sk_c7. [back_rewrite(25),rewrite([22765(6)]),merge(b)].
% 38.77/39.09 22975 sk_c1 = sk_c6 | multiply(sk_c5,sk_c4) != sk_c6. [back_rewrite(22020),rewrite([22925(6)]),xx(b)].
% 38.77/39.09 23434 sk_c6 != sk_c7. [back_rewrite(21273),rewrite([22925(3)]),xx(a)].
% 38.77/39.09 23508 multiply(sk_c1,multiply(sk_c7,A)) = A. [back_unit_del(22549),unit_del(a,23434)].
% 38.77/39.09 23510 sk_c1 = sk_c5. [back_unit_del(22547),unit_del(a,23434)].
% 38.77/39.09 23515 multiply(sk_c7,sk_c2) = sk_c6. [back_unit_del(22540),unit_del(a,23434)].
% 38.77/39.09 23518 inverse(sk_c4) = sk_c4. [back_unit_del(22517),unit_del(a,23434)].
% 38.77/39.09 23529 multiply(sk_c6,sk_c6) = identity. [back_unit_del(21826),unit_del(a,23434)].
% 38.77/39.09 23531 inverse(sk_c6) = sk_c4. [back_unit_del(21159),rewrite([23518(5)]),flip(b),unit_del(a,23434)].
% 38.77/39.09 23533 sk_c4 = sk_c6. [back_unit_del(21040),unit_del(a,23434)].
% 38.77/39.09 23543 multiply(sk_c6,sk_c5) = sk_c7. [back_unit_del(2247),rewrite([23533(4),23531(5),23533(4)]),unit_del(a,23434)].
% 38.77/39.09 23545 sk_c2 = sk_c7. [back_rewrite(5939),rewrite([23533(1),23543(3),23510(5),19547(7),342(6),23510(5),23515(8),22925(7)]),flip(a),unit_del(a,23434)].
% 38.77/39.09 23546 identity = sk_c7. [back_rewrite(5842),rewrite([23545(2),23533(4),23543(6),23510(7),23533(9),23529(11),342(10),19547(9),23545(8)]),flip(b),merge(c),unit_del(b,23434)].
% 38.77/39.09 23547 multiply(sk_c5,A) = A. [back_rewrite(5824),rewrite([23533(1),23543(3),23510(4),23545(6),16652(7),19551(8)]),flip(a),unit_del(a,23434)].
% 38.77/39.09 23549 multiply(sk_c7,A) = A. [back_rewrite(23508),rewrite([23510(1),23547(4)])].
% 38.77/39.09 23550 sk_c5 = sk_c6. [back_rewrite(22975),rewrite([23510(1),23533(5),23547(6)]),xx(b)].
% 38.77/39.09 23551 $F. [back_rewrite(22901),rewrite([23510(1),23550(1),23531(2),23533(1),23550(4),23529(7),23546(5),21178(6),23550(4),23533(6),23550(7),23529(8),23546(6),23549(7)]),merge(b),unit_del(a,23434)].
% 38.77/39.09
% 38.77/39.09 % SZS output end Refutation
% 38.77/39.09 ============================== end of proof ==========================
% 38.77/39.09
% 38.77/39.09 ============================== STATISTICS ============================
% 38.77/39.09
% 38.77/39.09 Given=4041. Generated=1756107. Kept=23550. proofs=1.
% 38.77/39.09 Usable=265. Sos=1725. Demods=70. Limbo=41, Disabled=21553. Hints=0.
% 38.77/39.09 Megabytes=22.96.
% 38.77/39.09 User_CPU=37.17, System_CPU=0.92, Wall_clock=38.
% 38.77/39.09
% 38.77/39.09 ============================== end of statistics =====================
% 38.77/39.09
% 38.77/39.09 ============================== end of search =========================
% 38.77/39.09
% 38.77/39.09 THEOREM PROVED
% 38.77/39.09 % SZS status Unsatisfiable
% 38.77/39.09
% 38.77/39.09 Exiting with 1 proof.
% 38.77/39.09
% 38.77/39.09 Process 13760 exit (max_proofs) Tue Jun 14 06:29:19 2022
% 38.77/39.09 Prover9 interrupted
%------------------------------------------------------------------------------