TSTP Solution File: GRP347-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP347-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n010.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 11:18:43 EDT 2022

% Result   : Unsatisfiable 52.49s 52.79s
% Output   : Refutation 52.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP347-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 13 07:57:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 52.49/52.79  ============================== Prover9 ===============================
% 52.49/52.79  Prover9 (32) version 2009-11A, November 2009.
% 52.49/52.79  Process 32019 was started by sandbox on n010.cluster.edu,
% 52.49/52.79  Mon Jun 13 07:57:25 2022
% 52.49/52.79  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31866_n010.cluster.edu".
% 52.49/52.79  ============================== end of head ===========================
% 52.49/52.79  
% 52.49/52.79  ============================== INPUT =================================
% 52.49/52.79  
% 52.49/52.79  % Reading from file /tmp/Prover9_31866_n010.cluster.edu
% 52.49/52.79  
% 52.49/52.79  set(prolog_style_variables).
% 52.49/52.79  set(auto2).
% 52.49/52.79      % set(auto2) -> set(auto).
% 52.49/52.79      % set(auto) -> set(auto_inference).
% 52.49/52.79      % set(auto) -> set(auto_setup).
% 52.49/52.79      % set(auto_setup) -> set(predicate_elim).
% 52.49/52.79      % set(auto_setup) -> assign(eq_defs, unfold).
% 52.49/52.79      % set(auto) -> set(auto_limits).
% 52.49/52.79      % set(auto_limits) -> assign(max_weight, "100.000").
% 52.49/52.79      % set(auto_limits) -> assign(sos_limit, 20000).
% 52.49/52.79      % set(auto) -> set(auto_denials).
% 52.49/52.79      % set(auto) -> set(auto_process).
% 52.49/52.79      % set(auto2) -> assign(new_constants, 1).
% 52.49/52.79      % set(auto2) -> assign(fold_denial_max, 3).
% 52.49/52.79      % set(auto2) -> assign(max_weight, "200.000").
% 52.49/52.79      % set(auto2) -> assign(max_hours, 1).
% 52.49/52.79      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 52.49/52.79      % set(auto2) -> assign(max_seconds, 0).
% 52.49/52.79      % set(auto2) -> assign(max_minutes, 5).
% 52.49/52.79      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 52.49/52.79      % set(auto2) -> set(sort_initial_sos).
% 52.49/52.79      % set(auto2) -> assign(sos_limit, -1).
% 52.49/52.79      % set(auto2) -> assign(lrs_ticks, 3000).
% 52.49/52.79      % set(auto2) -> assign(max_megs, 400).
% 52.49/52.79      % set(auto2) -> assign(stats, some).
% 52.49/52.79      % set(auto2) -> clear(echo_input).
% 52.49/52.79      % set(auto2) -> set(quiet).
% 52.49/52.79      % set(auto2) -> clear(print_initial_clauses).
% 52.49/52.79      % set(auto2) -> clear(print_given).
% 52.49/52.79  assign(lrs_ticks,-1).
% 52.49/52.79  assign(sos_limit,10000).
% 52.49/52.79  assign(order,kbo).
% 52.49/52.79  set(lex_order_vars).
% 52.49/52.79  clear(print_given).
% 52.49/52.79  
% 52.49/52.79  % formulas(sos).  % not echoed (34 formulas)
% 52.49/52.79  
% 52.49/52.79  ============================== end of input ==========================
% 52.49/52.79  
% 52.49/52.79  % From the command line: assign(max_seconds, 300).
% 52.49/52.79  
% 52.49/52.79  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 52.49/52.79  
% 52.49/52.79  % Formulas that are not ordinary clauses:
% 52.49/52.79  
% 52.49/52.79  ============================== end of process non-clausal formulas ===
% 52.49/52.79  
% 52.49/52.79  ============================== PROCESS INITIAL CLAUSES ===============
% 52.49/52.79  
% 52.49/52.79  ============================== PREDICATE ELIMINATION =================
% 52.49/52.79  
% 52.49/52.79  ============================== end predicate elimination =============
% 52.49/52.79  
% 52.49/52.79  Auto_denials:  (non-Horn, no changes).
% 52.49/52.79  
% 52.49/52.79  Term ordering decisions:
% 52.49/52.79  
% 52.49/52.79  % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 52.49/52.79  Function symbol KB weights:  sk_c6=1. sk_c7=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 52.49/52.79  
% 52.49/52.79  ============================== end of process initial clauses ========
% 52.49/52.79  
% 52.49/52.79  ============================== CLAUSES FOR SEARCH ====================
% 52.49/52.79  
% 52.49/52.79  ============================== end of clauses for search =============
% 52.49/52.79  
% 52.49/52.79  ============================== SEARCH ================================
% 52.49/52.79  
% 52.49/52.79  % Starting search at 0.02 seconds.
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=46.000, iters=3525
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=43.000, iters=3386
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=42.000, iters=3348
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=41.000, iters=3389
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=40.000, iters=3344
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=39.000, iters=3404
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=38.000, iters=3368
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=37.000, iters=3463
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=36.000, iters=3335
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=35.000, iters=3351
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=34.000, iters=3786
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=33.000, iters=3495
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=32.000, iters=3451
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=31.000, iters=3379
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=17.000, iters=3538
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=16.000, iters=3334
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=15.000, iters=3339
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=14.000, iters=3333
% 52.49/52.79  
% 52.49/52.79  Low Water (displace): id=4072, wt=52.000
% 52.49/52.79  
% 52.49/52.79  Low Water (displace): id=16556, wt=13.000
% 52.49/52.79  
% 52.49/52.79  Low Water (displace): id=16568, wt=12.000
% 52.49/52.79  
% 52.49/52.79  Low Water (displace): id=16785, wt=11.000
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=13.000, iters=3342
% 52.49/52.79  
% 52.49/52.79  Low Water (keep): wt=12.000, iters=3334
% 52.49/52.79  
% 52.49/52.79  ============================== PROOF =================================
% 52.49/52.79  % SZS status Unsatisfiable
% 52.49/52.79  % SZS output start Refutation
% 52.49/52.79  
% 52.49/52.79  % Proof 1 at 50.58 (+ 1.24) seconds.
% 52.49/52.79  % Length of proof is 172.
% 52.49/52.79  % Level of proof is 35.
% 52.49/52.79  % Maximum clause weight is 50.000.
% 52.49/52.79  % Given clauses 5644.
% 52.49/52.79  
% 52.49/52.79  1 multiply(identity,A) = A # label(left_identity) # label(axiom).  [assumption].
% 52.49/52.79  2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom).  [assumption].
% 52.49/52.79  3 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = sk_c5 # label(prove_this_8) # label(negated_conjecture).  [assumption].
% 52.49/52.79  4 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c6 # label(prove_this_10) # label(negated_conjecture).  [assumption].
% 52.49/52.79  6 inverse(sk_c2) = sk_c6 | inverse(sk_c6) = sk_c5 # label(prove_this_20) # label(negated_conjecture).  [assumption].
% 52.49/52.79  7 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = sk_c6 # label(prove_this_22) # label(negated_conjecture).  [assumption].
% 52.49/52.79  8 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_24) # label(negated_conjecture).  [assumption].
% 52.49/52.79  9 multiply(sk_c6,sk_c7) = sk_c5 | inverse(sk_c6) = sk_c5 # label(prove_this_2) # label(negated_conjecture).  [assumption].
% 52.49/52.79  11 multiply(sk_c6,sk_c7) = sk_c5 | inverse(sk_c4) = sk_c7 # label(prove_this_6) # label(negated_conjecture).  [assumption].
% 52.49/52.79  13 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_9) # label(negated_conjecture).  [assumption].
% 52.49/52.79  15 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c6) = sk_c5 # label(prove_this_14) # label(negated_conjecture).  [assumption].
% 52.49/52.79  18 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c5) = sk_c7 # label(prove_this_19) # label(negated_conjecture).  [assumption].
% 52.49/52.79  19 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_21) # label(negated_conjecture).  [assumption].
% 52.49/52.79  20 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_23) # label(negated_conjecture).  [assumption].
% 52.49/52.79  21 multiply(sk_c2,sk_c5) = sk_c6 | inverse(sk_c6) = sk_c5 # label(prove_this_26) # label(negated_conjecture).  [assumption].
% 52.49/52.79  23 multiply(sk_c2,sk_c5) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_30) # label(negated_conjecture).  [assumption].
% 52.49/52.79  24 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c6,sk_c5) = sk_c7 # label(prove_this_1) # label(negated_conjecture).  [assumption].
% 52.49/52.79  26 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_5) # label(negated_conjecture).  [assumption].
% 52.49/52.79  27 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c6,sk_c5) = sk_c7 # label(prove_this_13) # label(negated_conjecture).  [assumption].
% 52.49/52.79  30 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c6,sk_c5) = sk_c7 # label(prove_this_25) # label(negated_conjecture).  [assumption].
% 52.49/52.79  32 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_29) # label(negated_conjecture).  [assumption].
% 52.49/52.79  33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom).  [assumption].
% 52.49/52.79  34 multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | multiply(C,sk_c6) != sk_c7 | inverse(C) != sk_c6 | multiply(D,sk_c7) != sk_c5 | inverse(D) != sk_c7 # label(prove_this_31) # label(negated_conjecture).  [assumption].
% 52.49/52.79  50 inverse(sk_c6) = sk_c5 | multiply(sk_c7,sk_c1) = identity.  [para(3(a,1),2(a,1,1))].
% 52.49/52.79  53 inverse(sk_c6) = sk_c5 | multiply(sk_c6,sk_c2) = identity.  [para(6(a,1),2(a,1,1))].
% 52.49/52.79  56 multiply(inverse(A),multiply(A,B)) = B.  [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 52.49/52.79  57 inverse(sk_c6) = sk_c5 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c5,A).  [para(9(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79  58 inverse(sk_c6) = sk_c5 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c5).  [para(9(a,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79  62 inverse(sk_c4) = sk_c7 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c5).  [para(11(a,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79  69 inverse(sk_c6) = sk_c5 | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c7,A).  [para(15(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79  70 inverse(sk_c6) = sk_c5 | multiply(A,multiply(sk_c1,sk_c6)) = multiply(A,sk_c7).  [para(15(a,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79  78 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7).  [para(19(b,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79  80 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c5).  [para(20(b,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79  85 inverse(sk_c4) = sk_c7 | multiply(sk_c2,multiply(sk_c5,A)) = multiply(sk_c6,A).  [para(23(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79  88 multiply(sk_c6,sk_c7) = sk_c5 | multiply(A,multiply(sk_c6,sk_c5)) = multiply(A,sk_c7).  [para(24(b,1),33(a,2,2)),rewrite([33(9)])].
% 52.49/52.79  93 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c7,A).  [para(27(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79  99 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c2,multiply(sk_c5,A)) = multiply(sk_c6,A).  [para(30(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79  103 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c5,A).  [para(32(b,1),33(a,1,1)),flip(b)].
% 52.49/52.79  131 multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | multiply(C,sk_c7) != sk_c5 | inverse(C) != sk_c7.  [para(2(a,1),34(h,1))].
% 52.49/52.79  459 multiply(inverse(inverse(A)),identity) = A.  [para(2(a,1),56(a,1,2))].
% 52.49/52.79  471 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c1),sk_c7) = sk_c6.  [para(15(a,1),56(a,1,2))].
% 52.49/52.79  490 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),identity) = sk_c1.  [para(50(b,1),56(a,1,2))].
% 52.49/52.79  491 multiply(inverse(inverse(A)),B) = multiply(A,B).  [para(56(a,1),56(a,1,2))].
% 52.49/52.79  492 multiply(A,identity) = A.  [back_rewrite(459),rewrite([491(4)])].
% 52.49/52.79  493 inverse(sk_c6) = sk_c5 | inverse(sk_c7) = sk_c1.  [back_rewrite(490),rewrite([492(8)])].
% 52.49/52.79  495 inverse(identity) = identity.  [para(492(a,1),2(a,1))].
% 52.49/52.79  537 inverse(sk_c6) = sk_c5 | multiply(sk_c1,multiply(sk_c7,A)) = A.  [para(493(b,1),56(a,1,1))].
% 52.49/52.79  546 inverse(sk_c6) = sk_c5 | multiply(A,multiply(sk_c6,sk_c2)) = A.  [para(53(b,1),33(a,2,2)),rewrite([33(8),492(10)])].
% 52.49/52.79  547 inverse(sk_c6) = sk_c5 | inverse(sk_c6) = sk_c2.  [para(53(b,1),56(a,1,2)),rewrite([492(8)])].
% 52.49/52.79  570 inverse(sk_c6) = sk_c5 | multiply(sk_c2,sk_c6) = identity.  [para(547(b,1),2(a,1,1))].
% 52.49/52.79  571 inverse(sk_c6) = sk_c5 | multiply(sk_c2,multiply(sk_c6,A)) = A.  [para(547(b,1),56(a,1,1))].
% 52.49/52.79  579 inverse(sk_c6) = sk_c5 | multiply(sk_c5,sk_c1) = sk_c6.  [para(50(b,1),57(b,1,2)),rewrite([492(11)]),flip(c),merge(b)].
% 52.49/52.79  602 multiply(A,inverse(A)) = identity.  [para(491(a,1),2(a,1))].
% 52.49/52.79  603 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),A) = multiply(sk_c1,A).  [para(3(a,1),491(a,1,1,1))].
% 52.49/52.79  641 multiply(A,multiply(inverse(A),B)) = B.  [para(491(a,1),56(a,1))].
% 52.49/52.79  642 inverse(inverse(A)) = A.  [para(491(a,1),492(a,1)),rewrite([492(2)]),flip(a)].
% 52.49/52.79  680 multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(C,sk_c7) != sk_c5 | inverse(C) != sk_c7.  [back_rewrite(131),rewrite([642(34)]),xx(i)].
% 52.49/52.79  685 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = identity.  [para(4(b,1),602(a,1,2))].
% 52.49/52.79  687 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = identity.  [para(7(b,1),602(a,1,2))].
% 52.49/52.79  688 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c7) = identity.  [para(8(b,1),602(a,1,2))].
% 52.49/52.79  689 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity.  [para(602(a,1),33(a,1)),flip(a)].
% 52.49/52.79  709 inverse(sk_c6) = sk_c5 | multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6.  [para(21(a,1),58(b,2)),merge(b)].
% 52.49/52.79  776 inverse(sk_c6) = sk_c5 | multiply(A,multiply(sk_c2,sk_c6)) = A.  [para(570(b,1),33(a,2,2)),rewrite([33(8),492(10)])].
% 52.49/52.79  793 inverse(sk_c6) = sk_c5 | multiply(sk_c5,multiply(sk_c1,A)) = multiply(sk_c6,A).  [para(579(b,1),33(a,1,1)),flip(b)].
% 52.49/52.79  795 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c5),sk_c6) = sk_c1.  [para(579(b,1),56(a,1,2))].
% 52.49/52.79  796 inverse(sk_c1) = sk_c7 | identity = sk_c7.  [para(685(b,1),13(b,1)),merge(b)].
% 52.49/52.79  805 inverse(sk_c4) = sk_c7 | multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6.  [para(23(a,1),62(b,2)),merge(b)].
% 52.49/52.79  916 inverse(sk_c2) = sk_c6 | identity = sk_c7.  [para(687(b,1),19(b,1)),merge(b)].
% 52.49/52.79  918 identity = sk_c7 | multiply(sk_c6,sk_c2) = identity.  [para(916(a,1),2(a,1,1))].
% 52.49/52.79  965 inverse(sk_c2) = sk_c6 | identity = sk_c5.  [para(688(b,1),20(b,1)),merge(b)].
% 52.49/52.79  967 identity = sk_c5 | multiply(sk_c6,sk_c2) = identity.  [para(965(a,1),2(a,1,1))].
% 52.49/52.79  1014 identity = sk_c5 | multiply(A,multiply(sk_c6,sk_c2)) = A.  [para(967(b,1),33(a,2,2)),rewrite([33(7),492(9)])].
% 52.49/52.79  1185 inverse(sk_c6) = sk_c5 | multiply(sk_c7,sk_c2) = sk_c1.  [para(53(b,1),69(b,1,2)),rewrite([492(11)]),flip(c),merge(b)].
% 52.49/52.79  1766 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),sk_c1) = sk_c2.  [para(1185(b,1),56(a,1,2))].
% 52.49/52.79  2546 inverse(sk_c2) = sk_c6 | multiply(A,sk_c7) = A.  [para(687(b,1),78(b,1,2)),rewrite([492(10)]),flip(c),merge(b)].
% 52.49/52.79  2646 inverse(sk_c2) = sk_c6 | sk_c4 = sk_c5.  [para(2546(b,1),20(b,1)),merge(b)].
% 52.49/52.79  2698 sk_c4 = sk_c5 | multiply(sk_c2,multiply(sk_c6,A)) = A.  [para(2646(a,1),641(a,1,2,1))].
% 52.49/52.79  2845 inverse(sk_c2) = sk_c6 | multiply(A,sk_c5) = A.  [para(688(b,1),80(b,1,2)),rewrite([492(10)]),flip(c),merge(b)].
% 52.49/52.79  3313 inverse(sk_c2) = sk_c6 | sk_c7 = sk_c6.  [para(2845(b,1),18(b,1)),flip(c),merge(b)].
% 52.49/52.79  3374 sk_c7 = sk_c6 | multiply(sk_c2,multiply(sk_c6,A)) = A.  [para(3313(a,1),641(a,1,2,1))].
% 52.49/52.79  3948 inverse(sk_c4) = sk_c7 | multiply(sk_c2,multiply(sk_c5,multiply(sk_c6,sk_c7))) = multiply(sk_c6,sk_c5).  [para(62(b,1),85(b,2)),merge(b)].
% 52.49/52.79  4457 inverse(sk_c6) = sk_c5 | multiply(sk_c7,sk_c7) = sk_c6.  [para(3(a,1),471(b,1,1)),merge(b)].
% 52.49/52.79  4461 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),sk_c6) = sk_c7.  [para(4457(b,1),56(a,1,2))].
% 52.49/52.79  4615 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c4,multiply(sk_c6,sk_c5)) = sk_c5.  [para(26(b,1),88(b,2)),merge(b)].
% 52.49/52.79  5095 multiply(A,inverse(multiply(B,A))) = inverse(B).  [para(689(a,1),56(a,1,2)),rewrite([492(3)]),flip(a)].
% 52.49/52.79  5184 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)).  [para(5095(a,1),56(a,1,2)),flip(a)].
% 52.49/52.79  6729 identity = sk_c7 | multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c7,sk_c2) = sk_c1.  [para(918(b,1),93(b,1,2)),rewrite([492(11)]),flip(c)].
% 52.49/52.79  7544 identity = sk_c5 | multiply(inverse(sk_c2),inverse(sk_c6)) = identity.  [para(1014(b,1),2(a,1)),rewrite([5184(7)])].
% 52.49/52.79  7725 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c6,inverse(sk_c5)) = sk_c2.  [para(602(a,1),99(b,1,2)),rewrite([492(8)]),flip(b)].
% 52.49/52.79  8297 inverse(sk_c6) = sk_c5 | multiply(sk_c1,sk_c1) = sk_c2.  [para(493(b,1),1766(b,1,1)),merge(b)].
% 52.49/52.79  8300 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c5,inverse(sk_c7)) = sk_c4.  [para(602(a,1),103(b,1,2)),rewrite([492(8)]),flip(b)].
% 52.49/52.79  8368 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c1),sk_c2) = sk_c1.  [para(8297(b,1),56(a,1,2))].
% 52.49/52.79  13870 multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(B,sk_c7) != sk_c5 | inverse(B) != sk_c7.  [para(1(a,1),680(e,1)),rewrite([495(14)])].
% 52.49/52.79  14012 multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(A),inverse(B)) != sk_c7 | multiply(B,multiply(A,sk_c6)) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(C,sk_c7) != sk_c5 | inverse(C) != sk_c7.  [para(33(a,1),13870(c,1)),rewrite([5184(7)])].
% 52.49/52.79  18363 inverse(sk_c4) = sk_c7 | sk_c7 = sk_c6.  [para(805(b,1),3374(b,1)),flip(c),merge(c)].
% 52.49/52.79  18561 inverse(sk_c6) = sk_c5 | multiply(sk_c6,inverse(sk_c1)) = sk_c5.  [para(602(a,1),793(b,1,2)),rewrite([492(7)]),flip(b)].
% 52.49/52.79  18632 inverse(sk_c6) = sk_c5 | multiply(sk_c2,sk_c5) = inverse(sk_c1).  [para(18561(b,1),571(b,1,2)),merge(b)].
% 52.49/52.79  18633 inverse(sk_c6) = sk_c5 | inverse(sk_c1) = sk_c6.  [para(18632(b,1),21(a,1)),merge(c)].
% 52.49/52.79  18647 inverse(sk_c6) = sk_c5 | multiply(sk_c1,sk_c6) = identity.  [para(18633(b,1),602(a,1,2))].
% 52.49/52.79  18650 inverse(sk_c6) = sk_c5 | multiply(sk_c6,sk_c2) = sk_c1.  [para(18633(b,1),8368(b,1,1)),merge(b)].
% 52.49/52.79  18745 inverse(sk_c6) = sk_c5 | identity = sk_c7.  [para(18647(b,1),15(a,1)),merge(c)].
% 52.49/52.79  18748 inverse(sk_c6) = sk_c5 | multiply(A,sk_c7) = A.  [para(18647(b,1),70(b,1,2)),rewrite([492(10)]),flip(c),merge(b)].
% 52.49/52.79  18751 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),sk_c6) = identity.  [para(18647(b,1),603(b,2)),merge(b)].
% 52.49/52.79  18765 identity = sk_c7 | multiply(sk_c6,sk_c5) = identity.  [para(18745(a,1),602(a,1,2))].
% 52.49/52.79  19054 identity = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5.  [para(18765(b,1),24(b,1)),merge(c)].
% 52.49/52.79  19268 identity = sk_c7 | multiply(inverse(sk_c6),sk_c5) = sk_c7.  [para(19054(b,1),56(a,1,2))].
% 52.49/52.79  19316 inverse(sk_c6) = sk_c5 | multiply(A,sk_c1) = A.  [para(18650(b,1),546(b,1,2)),merge(b)].
% 52.49/52.79  19538 inverse(sk_c6) = sk_c5 | multiply(sk_c1,sk_c7) = inverse(sk_c7).  [para(18748(b,1),603(b,1)),flip(c),merge(b)].
% 52.49/52.79  19548 inverse(sk_c6) = sk_c5 | multiply(sk_c2,sk_c6) = sk_c6.  [para(18748(b,1),709(b,1,2)),merge(b)].
% 52.49/52.79  19901 identity = sk_c7 | multiply(sk_c5,sk_c5) = sk_c7.  [para(18745(a,1),19268(b,1,1)),merge(b)].
% 52.49/52.79  19905 identity = sk_c7 | multiply(inverse(sk_c5),inverse(sk_c5)) = inverse(sk_c7).  [para(19901(b,1),5184(a,1,1)),flip(b)].
% 52.49/52.79  19917 inverse(sk_c6) = sk_c5 | inverse(sk_c1) = identity.  [para(19316(b,1),2(a,1))].
% 52.49/52.79  21839 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,inverse(A)) != sk_c7 | sk_c7 != A | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(B,sk_c7) != sk_c5 | inverse(B) != sk_c7.  [para(2(a,1),14012(c,1,2)),rewrite([642(8),492(12)]),flip(c)].
% 52.49/52.79  21842 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,inverse(A)) != sk_c7 | sk_c7 != A | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(B,multiply(C,sk_c7)) != sk_c5 | multiply(inverse(C),inverse(B)) != sk_c7.  [para(33(a,1),21839(i,1)),rewrite([5184(37)])].
% 52.49/52.79  22090 inverse(sk_c6) = sk_c5 | multiply(A,sk_c6) = A.  [para(19548(b,1),776(b,1,2)),merge(b)].
% 52.49/52.79  22735 inverse(sk_c6) = sk_c5 | inverse(sk_c5) = sk_c1.  [para(22090(b,1),795(b,1)),merge(b)].
% 52.49/52.79  22742 inverse(sk_c6) = sk_c5 | inverse(sk_c7) = sk_c7.  [para(22090(b,1),4461(b,1)),merge(b)].
% 52.49/52.79  22848 inverse(sk_c6) = sk_c5 | inverse(sk_c1) = sk_c5.  [para(22735(b,1),642(a,1,1))].
% 52.49/52.79  22877 inverse(sk_c6) = sk_c5 | identity = sk_c5.  [para(22848(b,1),19917(b,1)),flip(c),merge(b)].
% 52.49/52.79  22887 identity = sk_c5 | multiply(inverse(sk_c2),sk_c5) = identity.  [para(22877(a,1),7544(b,1,2)),merge(b)].
% 52.49/52.79  23363 inverse(sk_c6) = sk_c5 | multiply(sk_c7,sk_c6) = identity.  [para(22742(b,1),18751(b,1,1)),merge(b)].
% 52.49/52.79  23366 inverse(sk_c6) = sk_c5 | inverse(sk_c7) = sk_c6.  [para(23363(b,1),56(a,1,2)),rewrite([492(8)])].
% 52.49/52.79  23374 inverse(sk_c6) = sk_c5 | multiply(sk_c6,sk_c7) = identity.  [para(23366(b,1),2(a,1,1))].
% 52.49/52.79  23401 inverse(sk_c6) = sk_c5 | multiply(A,sk_c5) = A.  [para(23374(b,1),58(b,1,2)),rewrite([492(10)]),flip(c),merge(b)].
% 52.49/52.79  23493 inverse(sk_c6) = sk_c5 | multiply(sk_c1,sk_c7) = sk_c5.  [para(23401(b,1),537(b,1,2)),merge(b)].
% 52.49/52.79  24262 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,inverse(A)) != sk_c7 | sk_c7 != A | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | sk_c5 != B | multiply(sk_c7,inverse(B)) != sk_c7.  [para(2(a,1),21842(i,1,2)),rewrite([492(32),642(35)]),flip(i)].
% 52.49/52.79  24265 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,A) != sk_c7 | inverse(A) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | sk_c5 != B | multiply(sk_c7,inverse(B)) != sk_c7.  [para(642(a,1),24262(b,1,2)),flip(c)].
% 52.49/52.79  24270 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,A) != sk_c7 | inverse(A) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | inverse(B) != sk_c5 | multiply(sk_c7,B) != sk_c7.  [para(642(a,1),24265(j,1,2)),flip(i)].
% 52.49/52.79  24288 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | inverse(B) != sk_c5 | multiply(sk_c7,B) != sk_c7.  [para(641(a,1),24270(b,1)),rewrite([5184(11),642(11)]),flip(b)].
% 52.49/52.79  24312 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(inverse(B),sk_c7) != sk_c5 | sk_c7 != B.  [para(641(a,1),24288(j,1)),rewrite([5184(34),642(34)]),flip(j)].
% 52.49/52.79  24314 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(inverse(A),sk_c7) != sk_c5.  [factor(24312,b,j)].
% 52.49/52.79  24498 inverse(sk_c6) = sk_c5 | inverse(sk_c7) = sk_c5.  [para(19538(b,1),23493(b,1)),merge(b)].
% 52.49/52.79  24519 inverse(sk_c6) = sk_c5 | multiply(sk_c5,sk_c6) = identity.  [para(24498(b,1),18751(b,1,1)),merge(b)].
% 52.49/52.79  24569 inverse(sk_c6) = sk_c5 | inverse(sk_c5) = sk_c6.  [para(24519(b,1),56(a,1,2)),rewrite([492(8)])].
% 52.49/52.79  24591 inverse(sk_c6) = sk_c5.  [para(24569(b,1),642(a,1,1)),merge(b)].
% 52.49/52.79  24647 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c7 | multiply(inverse(A),sk_c7) != sk_c5.  [back_rewrite(24314),rewrite([24591(25)]),xx(g)].
% 52.49/52.79  28497 multiply(sk_c5,sk_c6) = identity.  [para(24591(a,1),2(a,1,1))].
% 52.49/52.79  28498 multiply(sk_c5,multiply(sk_c6,A)) = A.  [para(24591(a,1),56(a,1,1))].
% 52.49/52.79  28499 inverse(sk_c5) = sk_c6.  [para(24591(a,1),642(a,1,1))].
% 52.49/52.79  28500 multiply(sk_c6,sk_c5) = identity.  [para(24591(a,1),602(a,1,2))].
% 52.49/52.79  28558 inverse(sk_c4) = sk_c7 | multiply(sk_c2,sk_c7) = identity.  [back_rewrite(3948),rewrite([28498(10),28500(10)])].
% 52.49/52.79  28777 identity = sk_c7 | multiply(sk_c6,sk_c6) = inverse(sk_c7).  [back_rewrite(19905),rewrite([28499(5),28499(6)])].
% 52.49/52.79  28867 identity = sk_c7 | multiply(sk_c6,sk_c6) = sk_c2.  [back_rewrite(7725),rewrite([28500(3),28499(6)])].
% 52.49/52.79  29929 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | identity != sk_c7 | multiply(inverse(A),sk_c7) != sk_c5.  [back_rewrite(24647),rewrite([28500(21)]),merge(g)].
% 52.49/52.79  30194 identity = sk_c7 | multiply(sk_c7,sk_c2) = sk_c1.  [back_rewrite(6729),rewrite([28500(6)]),merge(b)].
% 52.49/52.79  30213 multiply(sk_c6,sk_c7) = sk_c5 | sk_c4 = sk_c5.  [back_rewrite(4615),rewrite([28500(9),492(8)])].
% 52.49/52.79  30579 sk_c4 = sk_c5 | multiply(sk_c2,sk_c5) = sk_c7.  [para(30213(a,1),2698(b,1,2)),merge(b)].
% 52.49/52.79  30580 sk_c4 = sk_c5 | multiply(inverse(sk_c7),sk_c5) = sk_c6.  [para(30213(a,1),5184(a,1,1)),rewrite([28499(5),24591(8)]),flip(b)].
% 52.49/52.79  31196 inverse(sk_c4) = sk_c7 | inverse(sk_c2) = sk_c7.  [para(28558(b,1),56(a,1,2)),rewrite([492(8)])].
% 52.49/52.79  31203 inverse(sk_c2) = sk_c7 | inverse(sk_c7) = sk_c4.  [para(31196(a,1),642(a,1,1))].
% 52.49/52.79  31220 inverse(sk_c7) = sk_c4 | identity = sk_c5 | multiply(sk_c7,sk_c5) = identity.  [para(31203(a,1),22887(b,1,1))].
% 52.49/52.79  31643 identity = sk_c7 | inverse(sk_c7) = sk_c2.  [para(28777(b,1),28867(b,1)),merge(b)].
% 52.49/52.79  31648 identity = sk_c7 | multiply(sk_c7,sk_c2) = identity.  [para(31643(b,1),602(a,1,2))].
% 52.49/52.79  31996 identity = sk_c7 | identity = sk_c1.  [para(31648(b,1),30194(b,1)),merge(b)].
% 52.49/52.79  31999 identity = sk_c7 | inverse(sk_c1) = identity.  [para(31996(b,1),495(a,1,1))].
% 52.49/52.79  32012 identity = sk_c7.  [para(31999(b,1),796(a,1)),merge(b),merge(c)].
% 52.49/52.79  32084 inverse(sk_c7) = sk_c4 | sk_c5 = sk_c7 | multiply(sk_c7,sk_c5) = sk_c7.  [back_rewrite(31220),rewrite([32012(5),32012(11)]),flip(b)].
% 52.49/52.79  32186 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | sk_c7 != sk_c6 | sk_c5 != sk_c6 | multiply(inverse(A),sk_c7) != sk_c5.  [back_rewrite(29929),rewrite([32012(13),32012(19)]),xx(f)].
% 52.49/52.79  33094 multiply(sk_c5,sk_c6) = sk_c7.  [back_rewrite(28497),rewrite([32012(4)])].
% 52.49/52.79  33869 inverse(sk_c7) = sk_c7.  [back_rewrite(495),rewrite([32012(1),32012(3)])].
% 52.49/52.79  33870 multiply(A,sk_c7) = A.  [back_rewrite(492),rewrite([32012(1)])].
% 52.49/52.79  33872 multiply(sk_c7,A) = A.  [back_rewrite(1),rewrite([32012(1)])].
% 52.49/52.79  33882 sk_c5 != sk_c6 | sk_c7 != sk_c6.  [factor(32186,b,d),rewrite([33870(3),24591(8),33094(9),24591(14),33870(15)]),flip(a),xx(c),xx(e),merge(c)].
% 52.49/52.79  33953 sk_c4 = sk_c7 | sk_c5 = sk_c7.  [back_rewrite(32084),rewrite([33869(2),33872(9)]),flip(a),merge(c)].
% 52.49/52.79  33970 sk_c4 = sk_c5 | sk_c5 = sk_c6.  [back_rewrite(30580),rewrite([33869(5),33872(6)])].
% 52.49/52.79  34148 multiply(sk_c2,sk_c5) = sk_c6 | sk_c4 = sk_c5.  [back_rewrite(8300),rewrite([33869(8),33870(8)]),flip(b)].
% 52.49/52.79  35374 sk_c5 = sk_c6 | sk_c5 = sk_c7.  [para(33970(a,1),33953(a,1)),merge(c)].
% 52.49/52.79  35970 sk_c5 = sk_c6 | sk_c7 != sk_c6.  [para(35374(b,1),33882(a,1)),merge(c)].
% 52.49/52.79  37860 sk_c4 = sk_c5 | sk_c7 = sk_c6.  [para(34148(a,1),30579(b,1)),flip(c),merge(b)].
% 52.49/52.79  37901 sk_c7 = sk_c6.  [para(37860(a,1),18363(a,1,1)),rewrite([28499(5)]),flip(b),merge(b),merge(c)].
% 52.49/52.79  38839 sk_c5 = sk_c6.  [back_rewrite(35970),rewrite([37901(4)]),xx(b)].
% 52.49/52.79  39328 $F.  [back_rewrite(33882),rewrite([38839(1),37901(4)]),xx(a),xx(b)].
% 52.49/52.79  
% 52.49/52.79  % SZS output end Refutation
% 52.49/52.79  ============================== end of proof ==========================
% 52.49/52.79  
% 52.49/52.79  ============================== STATISTICS ============================
% 52.49/52.79  
% 52.49/52.79  Given=5644. Generated=2452782. Kept=39327. proofs=1.
% 52.49/52.79  Usable=518. Sos=1623. Demods=19. Limbo=1427, Disabled=35793. Hints=0.
% 52.49/52.79  Megabytes=32.75.
% 52.49/52.79  User_CPU=50.59, System_CPU=1.24, Wall_clock=52.
% 52.49/52.79  
% 52.49/52.79  ============================== end of statistics =====================
% 52.49/52.79  
% 52.49/52.79  ============================== end of search =========================
% 52.49/52.79  
% 52.49/52.79  THEOREM PROVED
% 52.49/52.79  % SZS status Unsatisfiable
% 52.49/52.79  
% 52.49/52.79  Exiting with 1 proof.
% 52.49/52.79  
% 52.49/52.79  Process 32019 exit (max_proofs) Mon Jun 13 07:58:17 2022
% 52.49/52.79  Prover9 interrupted
%------------------------------------------------------------------------------