TSTP Solution File: GRP308-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP308-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 11:18:34 EDT 2022
% Result : Unsatisfiable 103.97s 104.38s
% Output : Refutation 103.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP308-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 14 07:53:20 EDT 2022
% 0.12/0.32 % CPUTime :
% 19.35/19.68 ============================== Prover9 ===============================
% 19.35/19.68 Prover9 (32) version 2009-11A, November 2009.
% 19.35/19.68 Process 21767 was started by sandbox on n020.cluster.edu,
% 19.35/19.68 Tue Jun 14 07:53:20 2022
% 19.35/19.68 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21409_n020.cluster.edu".
% 19.35/19.68 ============================== end of head ===========================
% 19.35/19.68
% 19.35/19.68 ============================== INPUT =================================
% 19.35/19.68
% 19.35/19.68 % Reading from file /tmp/Prover9_21409_n020.cluster.edu
% 19.35/19.68
% 19.35/19.68 set(prolog_style_variables).
% 19.35/19.68 set(auto2).
% 19.35/19.68 % set(auto2) -> set(auto).
% 19.35/19.68 % set(auto) -> set(auto_inference).
% 19.35/19.68 % set(auto) -> set(auto_setup).
% 19.35/19.68 % set(auto_setup) -> set(predicate_elim).
% 19.35/19.68 % set(auto_setup) -> assign(eq_defs, unfold).
% 19.35/19.68 % set(auto) -> set(auto_limits).
% 19.35/19.68 % set(auto_limits) -> assign(max_weight, "100.000").
% 19.35/19.68 % set(auto_limits) -> assign(sos_limit, 20000).
% 19.35/19.68 % set(auto) -> set(auto_denials).
% 19.35/19.68 % set(auto) -> set(auto_process).
% 19.35/19.68 % set(auto2) -> assign(new_constants, 1).
% 19.35/19.68 % set(auto2) -> assign(fold_denial_max, 3).
% 19.35/19.68 % set(auto2) -> assign(max_weight, "200.000").
% 19.35/19.68 % set(auto2) -> assign(max_hours, 1).
% 19.35/19.68 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 19.35/19.68 % set(auto2) -> assign(max_seconds, 0).
% 19.35/19.68 % set(auto2) -> assign(max_minutes, 5).
% 19.35/19.68 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 19.35/19.68 % set(auto2) -> set(sort_initial_sos).
% 19.35/19.68 % set(auto2) -> assign(sos_limit, -1).
% 19.35/19.68 % set(auto2) -> assign(lrs_ticks, 3000).
% 19.35/19.68 % set(auto2) -> assign(max_megs, 400).
% 19.35/19.68 % set(auto2) -> assign(stats, some).
% 19.35/19.68 % set(auto2) -> clear(echo_input).
% 19.35/19.68 % set(auto2) -> set(quiet).
% 19.35/19.68 % set(auto2) -> clear(print_initial_clauses).
% 19.35/19.68 % set(auto2) -> clear(print_given).
% 19.35/19.68 assign(lrs_ticks,-1).
% 19.35/19.68 assign(sos_limit,10000).
% 19.35/19.68 assign(order,kbo).
% 19.35/19.68 set(lex_order_vars).
% 19.35/19.68 clear(print_given).
% 19.35/19.68
% 19.35/19.68 % formulas(sos). % not echoed (40 formulas)
% 19.35/19.68
% 19.35/19.68 ============================== end of input ==========================
% 19.35/19.68
% 19.35/19.68 % From the command line: assign(max_seconds, 300).
% 19.35/19.68
% 19.35/19.68 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 19.35/19.68
% 19.35/19.68 % Formulas that are not ordinary clauses:
% 19.35/19.68
% 19.35/19.68 ============================== end of process non-clausal formulas ===
% 19.35/19.68
% 19.35/19.68 ============================== PROCESS INITIAL CLAUSES ===============
% 19.35/19.68
% 19.35/19.68 ============================== PREDICATE ELIMINATION =================
% 19.35/19.68
% 19.35/19.68 ============================== end predicate elimination =============
% 19.35/19.68
% 19.35/19.68 Auto_denials: (non-Horn, no changes).
% 19.35/19.68
% 19.35/19.68 Term ordering decisions:
% 19.35/19.68
% 19.35/19.68 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 19.35/19.68 Function symbol KB weights: sk_c8=1. sk_c6=1. sk_c7=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. identity=1. multiply=1. inverse=0.
% 19.35/19.68
% 19.35/19.68 ============================== end of process initial clauses ========
% 19.35/19.68
% 19.35/19.68 ============================== CLAUSES FOR SEARCH ====================
% 19.35/19.68
% 19.35/19.68 ============================== end of clauses for search =============
% 19.35/19.68
% 19.35/19.68 ============================== SEARCH ================================
% 19.35/19.68
% 19.35/19.68 % Starting search at 0.02 seconds.
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=53.000, iters=3344
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=52.000, iters=3345
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=51.000, iters=3552
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=50.000, iters=3513
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=49.000, iters=3443
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=48.000, iters=3421
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=47.000, iters=3511
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=46.000, iters=3368
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=44.000, iters=3438
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=43.000, iters=3339
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=42.000, iters=3354
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=41.000, iters=3349
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=40.000, iters=3337
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=39.000, iters=3336
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=38.000, iters=3373
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=37.000, iters=3342
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=36.000, iters=3345
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=35.000, iters=3350
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=34.000, iters=3355
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=33.000, iters=3348
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=32.000, iters=3375
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=31.000, iters=3611
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=16.000, iters=3350
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=15.000, iters=3367
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=14.000, iters=3495
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=13.000, iters=3346
% 19.35/19.68
% 19.35/19.68 Low Water (keep): wt=12.000, iters=3502
% 103.97/104.38
% 103.97/104.38 Low Water (displace): id=4030, wt=61.000
% 103.97/104.38
% 103.97/104.38 Low Water (displace): id=22256, wt=11.000
% 103.97/104.38
% 103.97/104.38 Low Water (displace): id=22822, wt=10.000
% 103.97/104.38
% 103.97/104.38 Low Water (keep): wt=11.000, iters=3357
% 103.97/104.38
% 103.97/104.38 ============================== PROOF =================================
% 103.97/104.38 % SZS status Unsatisfiable
% 103.97/104.38 % SZS output start Refutation
% 103.97/104.38
% 103.97/104.38 % Proof 1 at 100.94 (+ 2.38) seconds.
% 103.97/104.38 % Length of proof is 167.
% 103.97/104.38 % Level of proof is 43.
% 103.97/104.38 % Maximum clause weight is 59.000.
% 103.97/104.38 % Given clauses 9633.
% 103.97/104.38
% 103.97/104.38 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 103.97/104.38 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 103.97/104.38 3 inverse(sk_c8) = sk_c6 | inverse(sk_c3) = sk_c8 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 103.97/104.38 4 inverse(sk_c8) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 103.97/104.38 5 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = sk_c6 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 103.97/104.38 6 inverse(sk_c1) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_32) # label(negated_conjecture). [assumption].
% 103.97/104.38 7 inverse(sk_c1) = sk_c8 | inverse(sk_c4) = sk_c7 # label(prove_this_34) # label(negated_conjecture). [assumption].
% 103.97/104.38 9 multiply(sk_c8,sk_c7) = sk_c6 | inverse(sk_c3) = sk_c8 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 103.97/104.38 10 multiply(sk_c8,sk_c7) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 103.97/104.38 13 inverse(sk_c8) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 103.97/104.38 14 inverse(sk_c8) = sk_c6 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 103.97/104.38 15 multiply(sk_c6,sk_c7) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 103.97/104.38 16 multiply(sk_c6,sk_c7) = sk_c8 | inverse(sk_c4) = sk_c7 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 103.97/104.38 18 multiply(sk_c8,sk_c2) = sk_c7 | inverse(sk_c3) = sk_c8 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 103.97/104.38 19 multiply(sk_c8,sk_c2) = sk_c7 | inverse(sk_c4) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 103.97/104.38 21 multiply(sk_c1,sk_c8) = sk_c2 | inverse(sk_c3) = sk_c8 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 103.97/104.38 22 multiply(sk_c1,sk_c8) = sk_c2 | inverse(sk_c4) = sk_c7 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 103.97/104.38 24 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 103.97/104.38 25 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_33) # label(negated_conjecture). [assumption].
% 103.97/104.38 29 multiply(sk_c8,sk_c7) = sk_c6 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 103.97/104.38 31 multiply(sk_c6,sk_c7) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 103.97/104.38 33 multiply(sk_c8,sk_c2) = sk_c7 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 103.97/104.38 34 multiply(sk_c8,sk_c2) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 103.97/104.38 36 multiply(sk_c1,sk_c8) = sk_c2 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 103.97/104.38 37 multiply(sk_c1,sk_c8) = sk_c2 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 103.97/104.38 39 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 103.97/104.38 40 multiply(sk_c8,sk_c7) != sk_c6 | inverse(sk_c8) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(D,sk_c7) != sk_c6 | inverse(D) != sk_c7 | inverse(E) != sk_c6 | multiply(E,sk_c8) != sk_c6 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 103.97/104.38 68 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 103.97/104.38 69 inverse(sk_c8) = sk_c6 | multiply(sk_c7,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 103.97/104.38 70 inverse(sk_c8) = sk_c6 | multiply(sk_c6,sk_c5) = identity. [para(5(b,1),2(a,1,1))].
% 103.97/104.38 74 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),39(a,1,1)),rewrite([1(2)]),flip(a)].
% 103.97/104.38 75 inverse(sk_c3) = sk_c8 | multiply(sk_c8,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(9(a,1),39(a,1,1)),flip(b)].
% 103.97/104.38 77 inverse(sk_c4) = sk_c7 | multiply(sk_c8,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(10(a,1),39(a,1,1)),flip(b)].
% 103.97/104.38 84 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c6). [para(13(b,1),39(a,2,2)),rewrite([39(8)])].
% 103.97/104.38 87 inverse(sk_c3) = sk_c8 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(15(a,1),39(a,1,1)),flip(b)].
% 103.97/104.38 89 inverse(sk_c4) = sk_c7 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(16(a,1),39(a,1,1)),flip(b)].
% 103.97/104.38 94 inverse(sk_c3) = sk_c8 | multiply(A,multiply(sk_c8,sk_c2)) = multiply(A,sk_c7). [para(18(a,1),39(a,2,2)),rewrite([39(8)])].
% 103.97/104.38 96 inverse(sk_c4) = sk_c7 | multiply(A,multiply(sk_c8,sk_c2)) = multiply(A,sk_c7). [para(19(a,1),39(a,2,2)),rewrite([39(8)])].
% 103.97/104.38 100 inverse(sk_c3) = sk_c8 | multiply(A,multiply(sk_c1,sk_c8)) = multiply(A,sk_c2). [para(21(a,1),39(a,2,2)),rewrite([39(8)])].
% 103.97/104.38 102 inverse(sk_c4) = sk_c7 | multiply(A,multiply(sk_c1,sk_c8)) = multiply(A,sk_c2). [para(22(a,1),39(a,2,2)),rewrite([39(8)])].
% 103.97/104.38 115 multiply(sk_c8,sk_c7) = sk_c6 | multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(29(b,1),39(a,1,1)),flip(b)].
% 103.97/104.38 197 multiply(sk_c8,sk_c7) != sk_c6 | inverse(sk_c8) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(D,multiply(E,sk_c7)) != sk_c6 | inverse(multiply(D,E)) != sk_c7 | inverse(F) != sk_c6 | multiply(F,sk_c8) != sk_c6. [para(39(a,1),40(i,1))].
% 103.97/104.38 992 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c8,sk_c3)) = multiply(A,identity). [para(68(b,1),39(a,2,2)),rewrite([39(8)])].
% 103.97/104.38 1006 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),74(a,1,2))].
% 103.97/104.38 1012 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c8),sk_c6) = sk_c7. [para(9(a,1),74(a,1,2))].
% 103.97/104.38 1017 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c5),sk_c6) = sk_c8. [para(14(b,1),74(a,1,2))].
% 103.97/104.38 1044 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(74(a,1),74(a,1,2))].
% 103.97/104.38 1045 multiply(A,identity) = A. [back_rewrite(1006),rewrite([1044(4)])].
% 103.97/104.38 1050 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c8,sk_c3)) = A. [back_rewrite(992),rewrite([1045(10)])].
% 103.97/104.38 1059 inverse(identity) = identity. [para(1045(a,1),2(a,1))].
% 103.97/104.38 1140 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = sk_c4. [para(69(b,1),74(a,1,2)),rewrite([1045(8)])].
% 103.97/104.38 1144 inverse(sk_c8) = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(1140(b,1),2(a,1,1))].
% 103.97/104.38 1147 inverse(sk_c8) = sk_c6 | inverse(sk_c6) = sk_c5. [para(70(b,1),74(a,1,2)),rewrite([1045(8)])].
% 103.97/104.38 1257 multiply(A,inverse(A)) = identity. [para(1044(a,1),2(a,1))].
% 103.97/104.38 1316 multiply(A,multiply(inverse(A),B)) = B. [para(1044(a,1),74(a,1))].
% 103.97/104.38 1317 inverse(inverse(A)) = A. [para(1044(a,1),1045(a,1)),rewrite([1045(2)]),flip(a)].
% 103.97/104.38 1396 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c8) = identity. [para(6(b,1),1257(a,1,2))].
% 103.97/104.38 1397 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c7) = identity. [para(7(b,1),1257(a,1,2))].
% 103.97/104.38 1399 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1257(a,1),39(a,1)),flip(a)].
% 103.97/104.38 1785 inverse(sk_c1) = sk_c8 | identity = sk_c7. [para(1396(b,1),24(b,1)),merge(b)].
% 103.97/104.38 1807 identity = sk_c7 | multiply(sk_c1,sk_c8) = identity. [para(1785(a,1),1257(a,1,2))].
% 103.97/104.38 2161 inverse(sk_c1) = sk_c8 | identity = sk_c6. [para(1397(b,1),25(b,1)),merge(b)].
% 103.97/104.38 2167 inverse(sk_c8) = sk_c6 | multiply(A,sk_c6) = A. [para(1144(b,1),84(b,1,2)),rewrite([1045(10)]),flip(c),merge(b)].
% 103.97/104.38 2246 identity = sk_c6 | multiply(sk_c1,sk_c8) = identity. [para(2161(a,1),1257(a,1,2))].
% 103.97/104.38 2429 identity = sk_c6 | multiply(A,multiply(sk_c1,sk_c8)) = A. [para(2246(b,1),39(a,2,2)),rewrite([39(7),1045(9)])].
% 103.97/104.38 2598 inverse(sk_c3) = sk_c8 | multiply(A,multiply(sk_c6,multiply(sk_c7,B))) = multiply(A,multiply(sk_c8,B)). [para(87(b,1),39(a,2,2)),rewrite([39(9)])].
% 103.97/104.38 2602 inverse(sk_c3) = sk_c8 | multiply(sk_c8,inverse(sk_c7)) = sk_c6. [para(1257(a,1),87(b,1,2)),rewrite([1045(7)]),flip(b)].
% 103.97/104.38 2960 inverse(sk_c4) = sk_c7 | multiply(A,multiply(sk_c6,multiply(sk_c7,B))) = multiply(A,multiply(sk_c8,B)). [para(89(b,1),39(a,2,2)),rewrite([39(9)])].
% 103.97/104.38 3906 inverse(sk_c3) = sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c2)) = sk_c6. [para(9(a,1),94(b,2)),merge(b)].
% 103.97/104.38 3982 inverse(sk_c8) = sk_c6 | inverse(sk_c6) = identity. [para(2167(b,1),2(a,1))].
% 103.97/104.38 4020 inverse(sk_c8) = sk_c6 | multiply(sk_c6,A) = A. [para(3982(b,1),74(a,1,1)),rewrite([1(8)])].
% 103.97/104.38 4313 inverse(sk_c4) = sk_c7 | multiply(sk_c8,multiply(sk_c8,sk_c2)) = sk_c6. [para(10(a,1),96(b,2)),merge(b)].
% 103.97/104.38 5065 identity = sk_c6 | inverse(sk_c3) = sk_c8 | multiply(A,sk_c2) = A. [para(2246(b,1),100(b,1,2)),rewrite([1045(9)]),flip(c)].
% 103.97/104.38 5158 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c6),A) = A. [para(4020(b,1),74(a,1,2))].
% 103.97/104.38 5464 identity = sk_c6 | inverse(sk_c4) = sk_c7 | multiply(A,sk_c2) = A. [para(2246(b,1),102(b,1,2)),rewrite([1045(9)]),flip(c)].
% 103.97/104.38 7432 multiply(sk_c8,sk_c7) = sk_c6 | multiply(sk_c6,inverse(sk_c8)) = sk_c5. [para(1257(a,1),115(b,1,2)),rewrite([1045(8)]),flip(b)].
% 103.97/104.38 10429 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = sk_c8. [para(1017(b,1),2167(b,1)),flip(c),merge(b)].
% 103.97/104.38 12385 multiply(sk_c8,sk_c7) != sk_c6 | inverse(sk_c8) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | sk_c6 != D | inverse(multiply(D,inverse(sk_c7))) != sk_c7 | inverse(E) != sk_c6 | multiply(E,sk_c8) != sk_c6. [para(2(a,1),197(i,1,2)),rewrite([1045(33)]),flip(i)].
% 103.97/104.38 12402 multiply(sk_c8,sk_c7) != sk_c6 | inverse(sk_c8) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | inverse(sk_c8) != sk_c8 | sk_c6 != B | inverse(multiply(B,inverse(sk_c7))) != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c8) != sk_c6. [factor(12385,d,g)].
% 103.97/104.38 13421 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1399(a,1),74(a,1,2)),rewrite([1045(3)]),flip(a)].
% 103.97/104.38 13852 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(13421(a,1),74(a,1,2)),flip(a)].
% 103.97/104.38 14495 multiply(sk_c8,sk_c7) != sk_c6 | inverse(sk_c8) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | inverse(sk_c8) != sk_c8 | sk_c6 != B | multiply(sk_c7,inverse(B)) != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c8) != sk_c6. [back_rewrite(12402),rewrite([13852(36),1317(35)])].
% 103.97/104.38 16498 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c8),sk_c6) = inverse(sk_c7). [para(2602(b,1),74(a,1,2))].
% 103.97/104.38 16769 inverse(sk_c8) = sk_c6 | multiply(sk_c5,A) = A. [para(1147(b,1),5158(b,1,1)),merge(b)].
% 103.97/104.38 16834 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c5),A) = A. [para(16769(b,1),74(a,1,2))].
% 103.97/104.38 20265 inverse(sk_c8) = sk_c6 | multiply(sk_c8,A) = A. [para(10429(b,1),16834(b,1,1)),merge(b)].
% 103.97/104.38 24421 inverse(sk_c8) = sk_c6 | multiply(A,sk_c3) = A. [para(20265(b,1),1050(b,1,2)),merge(b)].
% 103.97/104.38 24525 inverse(sk_c8) = sk_c6 | multiply(A,sk_c8) = A. [para(24421(b,1),1050(b,1,2)),merge(b)].
% 103.97/104.38 24683 inverse(sk_c8) = sk_c6 | inverse(sk_c6) = sk_c8. [para(24525(b,1),5158(b,1)),merge(b)].
% 103.97/104.38 24688 inverse(sk_c8) = sk_c6. [para(24683(b,1),1317(a,1,1)),merge(b)].
% 103.97/104.38 28097 inverse(sk_c3) = sk_c8 | multiply(sk_c6,sk_c6) = inverse(sk_c7). [back_rewrite(16498),rewrite([24688(6)])].
% 103.97/104.38 28652 multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | sk_c6 != sk_c8 | sk_c6 != B | multiply(sk_c7,inverse(B)) != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c8) != sk_c6. [back_rewrite(14495),rewrite([24688(7),24688(27)]),xx(b)].
% 103.97/104.38 28897 multiply(sk_c8,sk_c7) = sk_c6 | multiply(sk_c6,sk_c6) = sk_c5. [back_rewrite(7432),rewrite([24688(8)])].
% 103.97/104.38 28990 inverse(sk_c3) = sk_c8 | multiply(sk_c6,sk_c6) = sk_c7. [back_rewrite(1012),rewrite([24688(6)])].
% 103.97/104.38 29788 multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | sk_c6 != sk_c8 | multiply(sk_c7,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c8) != sk_c6. [factor(28652,f,g),rewrite([24688(28)])].
% 103.97/104.38 29815 inverse(sk_c6) = sk_c8. [para(24688(a,1),1317(a,1,1))].
% 103.97/104.38 29816 multiply(sk_c8,sk_c6) = identity. [para(24688(a,1),1257(a,1,2))].
% 103.97/104.38 29817 multiply(sk_c8,multiply(sk_c6,A)) = A. [para(24688(a,1),1316(a,1,2,1))].
% 103.97/104.38 31943 inverse(sk_c3) = sk_c8 | multiply(sk_c7,sk_c2) = sk_c6. [para(3906(b,1),2598(b,2)),rewrite([29817(15)]),merge(b)].
% 103.97/104.38 31951 inverse(sk_c3) = sk_c8 | multiply(sk_c6,sk_c2) = identity. [para(31943(b,1),75(b,1,2)),rewrite([29816(11)]),flip(c),merge(b)].
% 103.97/104.38 32006 inverse(sk_c4) = sk_c7 | multiply(sk_c7,sk_c2) = sk_c6. [para(4313(b,1),2960(b,2)),rewrite([29817(15)]),merge(b)].
% 103.97/104.38 32015 inverse(sk_c4) = sk_c7 | multiply(sk_c6,sk_c2) = identity. [para(32006(b,1),77(b,1,2)),rewrite([29816(11)]),flip(c),merge(b)].
% 103.97/104.38 32290 identity = sk_c6 | inverse(sk_c3) = sk_c8. [para(5065(c,1),31951(b,1)),flip(d),merge(c),merge(d)].
% 103.97/104.38 32293 identity = sk_c6 | multiply(sk_c8,sk_c3) = identity. [para(32290(b,1),2(a,1,1))].
% 103.97/104.38 32795 identity = sk_c6 | inverse(sk_c4) = sk_c7. [para(5464(c,1),32015(b,1)),flip(d),merge(c),merge(d)].
% 103.97/104.38 32805 identity = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(32795(b,1),1257(a,1,2))].
% 103.97/104.38 32811 identity = sk_c6 | multiply(sk_c6,sk_c7) = sk_c8. [para(32805(b,1),31(b,1)),merge(c)].
% 103.97/104.38 32812 identity = sk_c6 | multiply(sk_c8,sk_c2) = sk_c7. [para(32805(b,1),34(b,1)),merge(c)].
% 103.97/104.38 32813 identity = sk_c6 | multiply(sk_c1,sk_c8) = sk_c2. [para(32805(b,1),37(b,1)),merge(c)].
% 103.97/104.38 32823 identity = sk_c6 | multiply(sk_c8,sk_c8) = sk_c7. [para(32811(b,1),74(a,1,2)),rewrite([29815(5)])].
% 103.97/104.38 32826 identity = sk_c6 | multiply(sk_c6,sk_c7) = sk_c2. [para(32812(b,1),74(a,1,2)),rewrite([24688(5)])].
% 103.97/104.38 32832 identity = sk_c6 | identity = sk_c2. [para(32813(b,1),2246(b,1)),flip(c),merge(b)].
% 103.97/104.38 32834 identity = sk_c6 | multiply(A,sk_c2) = A. [para(32813(b,1),2429(b,1,2)),merge(b)].
% 103.97/104.38 32848 identity = sk_c6 | inverse(sk_c2) = identity. [para(32832(b,1),1059(a,1,1))].
% 103.97/104.38 32869 identity = sk_c6 | sk_c2 = sk_c8. [para(32826(b,1),32811(b,1)),merge(b)].
% 103.97/104.38 32873 sk_c2 = sk_c8 | identity = sk_c8. [para(32869(a,1),1059(a,1,1)),rewrite([29815(5)]),flip(b)].
% 103.97/104.38 32896 sk_c2 = sk_c8 | sk_c6 = sk_c8. [para(32873(b,1),32869(a,1)),flip(b),merge(c)].
% 103.97/104.38 32902 sk_c6 = sk_c8 | identity = sk_c6. [para(32896(a,1),32848(b,1,1)),rewrite([24688(8)]),flip(c),merge(c)].
% 103.97/104.38 32905 sk_c6 = sk_c8 | identity = sk_c8. [para(32902(b,1),1059(a,1,1)),rewrite([29815(5)]),flip(b)].
% 103.97/104.38 32917 sk_c6 = sk_c8. [para(32905(b,1),32902(b,1)),flip(c),merge(b),merge(c)].
% 103.97/104.38 32952 identity = sk_c8 | multiply(A,sk_c2) = A. [back_rewrite(32834),rewrite([32917(2)])].
% 103.97/104.38 32953 identity = sk_c8 | identity = sk_c2. [back_rewrite(32832),rewrite([32917(2)])].
% 103.97/104.38 32960 identity = sk_c8 | multiply(sk_c8,sk_c8) = sk_c7. [back_rewrite(32823),rewrite([32917(2)])].
% 103.97/104.38 32968 identity = sk_c8 | multiply(sk_c8,sk_c2) = sk_c7. [back_rewrite(32812),rewrite([32917(2)])].
% 103.97/104.38 33188 identity = sk_c8 | multiply(sk_c8,sk_c3) = identity. [back_rewrite(32293),rewrite([32917(2)])].
% 103.97/104.38 34508 multiply(sk_c8,sk_c8) = identity. [back_rewrite(29816),rewrite([32917(2)])].
% 103.97/104.38 34511 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c7 | inverse(B) != sk_c8 | multiply(B,sk_c8) != sk_c8. [back_rewrite(29788),rewrite([32917(4),32917(6),34508(13),32917(21),32917(25),32917(30),32917(34)]),xx(f),merge(b)].
% 103.97/104.38 34528 inverse(sk_c3) = sk_c8 | identity = sk_c7. [back_rewrite(28990),rewrite([32917(5),32917(6),34508(7)])].
% 103.97/104.38 34548 multiply(sk_c8,sk_c7) = sk_c8 | identity = sk_c5. [back_rewrite(28897),rewrite([32917(4),32917(6),32917(7),34508(8)])].
% 103.97/104.38 34604 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | sk_c8 != B | multiply(sk_c7,inverse(B)) != sk_c7 | inverse(C) != sk_c8 | multiply(C,sk_c8) != sk_c8. [back_rewrite(28652),rewrite([32917(4),32917(6),34508(13),32917(21),32917(24),32917(32),32917(36)]),xx(f),merge(b)].
% 103.97/104.38 34694 inverse(sk_c3) = sk_c8 | inverse(sk_c7) = identity. [back_rewrite(28097),rewrite([32917(5),32917(6),34508(7)]),flip(b)].
% 103.97/104.38 35018 inverse(sk_c8) = sk_c8. [back_rewrite(24688),rewrite([32917(3)])].
% 103.97/104.38 37656 identity = sk_c8 | identity = sk_c7. [back_rewrite(32960),rewrite([34508(6)])].
% 103.97/104.38 37661 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c7. [factor(34511,c,g),merge(f)].
% 103.97/104.38 37676 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | sk_c8 != B | multiply(sk_c7,inverse(B)) != sk_c7. [factor(34604,c,h),merge(g)].
% 103.97/104.38 37731 identity = sk_c8 | sk_c2 = sk_c7. [para(37656(b,1),32953(b,1)),flip(c),merge(b)].
% 103.97/104.38 37732 sk_c2 = sk_c7 | multiply(sk_c8,A) = A. [para(37731(a,1),1(a,1,1))].
% 103.97/104.38 37743 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,multiply(B,sk_c8)) != sk_c8 | multiply(inverse(B),inverse(A)) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c7. [para(39(a,1),37661(c,1)),rewrite([13852(15)])].
% 103.97/104.38 37752 identity = sk_c7 | multiply(sk_c3,sk_c8) = identity. [para(34528(a,1),1257(a,1,2))].
% 103.97/104.38 38015 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | inverse(B) != sk_c8 | multiply(sk_c7,B) != sk_c7. [para(1317(a,1),37676(f,1,2)),flip(e)].
% 103.97/104.38 38017 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,sk_c8) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c7,A) != sk_c7. [factor(38015,d,e)].
% 103.97/104.38 38020 identity = sk_c8 | sk_c7 = sk_c8. [para(32968(b,1),32952(b,1)),merge(b)].
% 103.97/104.38 38023 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,multiply(B,sk_c8)) != sk_c8 | multiply(inverse(B),inverse(A)) != sk_c8 | multiply(sk_c7,multiply(A,B)) != sk_c7. [para(39(a,1),38017(c,1)),rewrite([13852(15)])].
% 103.97/104.38 38083 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | sk_c8 != A | multiply(sk_c8,inverse(A)) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c7. [para(2(a,1),37743(c,1,2)),rewrite([1045(10),35018(12),35018(12)]),flip(c)].
% 103.97/104.38 38086 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,B) != sk_c8 | multiply(sk_c8,multiply(inverse(B),inverse(A))) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c7. [para(13852(a,1),38083(d,1,2)),flip(c)].
% 103.97/104.38 38088 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(sk_c8,multiply(inverse(sk_c7),sk_c8)) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c7. [factor(38086,a,c),rewrite([35018(13)])].
% 103.97/104.38 38095 identity = sk_c8 | multiply(sk_c8,sk_c3) = sk_c7. [para(37656(b,1),33188(b,2)),merge(b)].
% 103.97/104.38 38135 identity = sk_c5 | identity = sk_c7. [para(34548(a,1),74(a,1,2)),rewrite([35018(5),34508(6)])].
% 103.97/104.38 38148 identity = sk_c7 | inverse(sk_c5) = identity. [para(38135(a,1),1059(a,1,1))].
% 103.97/104.38 38154 identity = sk_c7 | inverse(sk_c5) = sk_c5. [para(38135(a,1),38148(b,2)),merge(b)].
% 103.97/104.38 38194 inverse(sk_c7) = identity | multiply(sk_c8,sk_c3) = identity. [para(34694(a,1),2(a,1,1))].
% 103.97/104.38 38262 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | sk_c8 != A | multiply(sk_c8,inverse(A)) != sk_c8 | multiply(sk_c7,multiply(A,sk_c8)) != sk_c7. [para(2(a,1),38023(c,1,2)),rewrite([1045(10),35018(12),35018(12),35018(18)]),flip(c)].
% 103.97/104.38 38264 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(A,B) != sk_c8 | multiply(sk_c8,multiply(inverse(B),inverse(A))) != sk_c8 | multiply(sk_c7,multiply(A,multiply(B,sk_c8))) != sk_c7. [para(39(a,1),38262(e,1,2)),rewrite([13852(14)]),flip(c)].
% 103.97/104.38 38265 multiply(sk_c8,sk_c7) != sk_c8 | identity != sk_c7 | multiply(sk_c8,multiply(inverse(sk_c7),sk_c8)) != sk_c8 | multiply(sk_c7,multiply(sk_c8,multiply(sk_c7,sk_c8))) != sk_c7. [factor(38264,a,c),rewrite([35018(13)])].
% 103.97/104.38 38543 identity = sk_c7 | multiply(sk_c8,sk_c2) = sk_c7. [para(37752(b,1),33(b,1)),merge(c)].
% 103.97/104.38 38544 identity = sk_c7 | multiply(sk_c1,sk_c8) = sk_c2. [para(37752(b,1),36(b,1)),merge(c)].
% 103.97/104.38 39614 identity = sk_c7 | sk_c2 = sk_c7. [para(38543(b,1),37732(b,1)),flip(c),merge(c)].
% 103.97/104.38 39620 sk_c2 = sk_c7 | sk_c7 = sk_c8. [para(39614(a,1),37731(a,1)),merge(c)].
% 103.97/104.38 39772 identity = sk_c7 | identity = sk_c2. [para(38544(b,1),1807(b,1)),flip(c),merge(b)].
% 103.97/104.38 39801 sk_c7 = sk_c8 | identity = sk_c7. [para(39620(a,1),39772(b,2)),merge(c)].
% 103.97/104.38 39888 sk_c7 = sk_c8. [para(39801(b,1),38020(a,1)),merge(b),merge(c)].
% 103.97/104.38 40213 identity != sk_c8. [back_rewrite(38265),rewrite([39888(2),34508(3),39888(5),39888(8),35018(9),34508(10),1045(9),39888(10),39888(12),34508(14),1045(13),34508(12),39888(11)]),xx(c),merge(b),merge(c)].
% 103.97/104.38 40219 multiply(sk_c8,sk_c3) = identity. [back_rewrite(38194),rewrite([39888(1),35018(2)]),flip(a),unit_del(a,40213)].
% 103.97/104.38 40223 inverse(sk_c5) = sk_c5. [back_rewrite(38154),rewrite([39888(2)]),unit_del(a,40213)].
% 103.97/104.38 40226 identity = sk_c5. [back_rewrite(38148),rewrite([39888(2),40223(5)]),flip(b),unit_del(a,40213)].
% 103.97/104.38 40259 sk_c5 = sk_c8. [back_rewrite(38095),rewrite([40226(1),40219(6),40226(4),39888(5)]),merge(b)].
% 103.97/104.38 40264 $F. [back_rewrite(38088),rewrite([39888(2),34508(3),40226(1),40259(1),40226(4),40259(4),39888(5),39888(8),35018(9),34508(10),40226(8),40259(8),34508(9),40226(7),40259(7),39888(10),34508(12),40226(10),40259(10),39888(11)]),xx(a),xx(b),xx(c),xx(d)].
% 103.97/104.38
% 103.97/104.38 % SZS output end Refutation
% 103.97/104.38 ============================== end of proof ==========================
% 103.97/104.38
% 103.97/104.38 ============================== STATISTICS ============================
% 103.97/104.38
% 103.97/104.38 Given=9633. Generated=3935622. Kept=40263. proofs=1.
% 103.97/104.38 Usable=1052. Sos=4104. Demods=29. Limbo=376, Disabled=34771. Hints=0.
% 103.97/104.38 Megabytes=35.60.
% 103.97/104.38 User_CPU=100.94, System_CPU=2.38, Wall_clock=104.
% 103.97/104.38
% 103.97/104.38 ============================== end of statistics =====================
% 103.97/104.38
% 103.97/104.38 ============================== end of search =========================
% 103.97/104.38
% 103.97/104.38 THEOREM PROVED
% 103.97/104.38 % SZS status Unsatisfiable
% 103.97/104.38
% 103.97/104.38 Exiting with 1 proof.
% 103.97/104.38
% 103.97/104.38 Process 21767 exit (max_proofs) Tue Jun 14 07:55:04 2022
% 103.97/104.38 Prover9 interrupted
%------------------------------------------------------------------------------