TSTP Solution File: GRP274-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP274-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 11:18:26 EDT 2022
% Result : Unsatisfiable 75.35s 75.63s
% Output : Refutation 75.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP274-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 04:16:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 75.35/75.63 ============================== Prover9 ===============================
% 75.35/75.63 Prover9 (32) version 2009-11A, November 2009.
% 75.35/75.63 Process 4147 was started by sandbox2 on n019.cluster.edu,
% 75.35/75.63 Mon Jun 13 04:16:40 2022
% 75.35/75.63 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3908_n019.cluster.edu".
% 75.35/75.63 ============================== end of head ===========================
% 75.35/75.63
% 75.35/75.63 ============================== INPUT =================================
% 75.35/75.63
% 75.35/75.63 % Reading from file /tmp/Prover9_3908_n019.cluster.edu
% 75.35/75.63
% 75.35/75.63 set(prolog_style_variables).
% 75.35/75.63 set(auto2).
% 75.35/75.63 % set(auto2) -> set(auto).
% 75.35/75.63 % set(auto) -> set(auto_inference).
% 75.35/75.63 % set(auto) -> set(auto_setup).
% 75.35/75.63 % set(auto_setup) -> set(predicate_elim).
% 75.35/75.63 % set(auto_setup) -> assign(eq_defs, unfold).
% 75.35/75.63 % set(auto) -> set(auto_limits).
% 75.35/75.63 % set(auto_limits) -> assign(max_weight, "100.000").
% 75.35/75.63 % set(auto_limits) -> assign(sos_limit, 20000).
% 75.35/75.63 % set(auto) -> set(auto_denials).
% 75.35/75.63 % set(auto) -> set(auto_process).
% 75.35/75.63 % set(auto2) -> assign(new_constants, 1).
% 75.35/75.63 % set(auto2) -> assign(fold_denial_max, 3).
% 75.35/75.63 % set(auto2) -> assign(max_weight, "200.000").
% 75.35/75.63 % set(auto2) -> assign(max_hours, 1).
% 75.35/75.63 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 75.35/75.63 % set(auto2) -> assign(max_seconds, 0).
% 75.35/75.63 % set(auto2) -> assign(max_minutes, 5).
% 75.35/75.63 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 75.35/75.63 % set(auto2) -> set(sort_initial_sos).
% 75.35/75.63 % set(auto2) -> assign(sos_limit, -1).
% 75.35/75.63 % set(auto2) -> assign(lrs_ticks, 3000).
% 75.35/75.63 % set(auto2) -> assign(max_megs, 400).
% 75.35/75.63 % set(auto2) -> assign(stats, some).
% 75.35/75.63 % set(auto2) -> clear(echo_input).
% 75.35/75.63 % set(auto2) -> set(quiet).
% 75.35/75.63 % set(auto2) -> clear(print_initial_clauses).
% 75.35/75.63 % set(auto2) -> clear(print_given).
% 75.35/75.63 assign(lrs_ticks,-1).
% 75.35/75.63 assign(sos_limit,10000).
% 75.35/75.63 assign(order,kbo).
% 75.35/75.63 set(lex_order_vars).
% 75.35/75.63 clear(print_given).
% 75.35/75.63
% 75.35/75.63 % formulas(sos). % not echoed (29 formulas)
% 75.35/75.63
% 75.35/75.63 ============================== end of input ==========================
% 75.35/75.63
% 75.35/75.63 % From the command line: assign(max_seconds, 300).
% 75.35/75.63
% 75.35/75.63 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 75.35/75.63
% 75.35/75.63 % Formulas that are not ordinary clauses:
% 75.35/75.63
% 75.35/75.63 ============================== end of process non-clausal formulas ===
% 75.35/75.63
% 75.35/75.63 ============================== PROCESS INITIAL CLAUSES ===============
% 75.35/75.63
% 75.35/75.63 ============================== PREDICATE ELIMINATION =================
% 75.35/75.63
% 75.35/75.63 ============================== end predicate elimination =============
% 75.35/75.63
% 75.35/75.63 Auto_denials: (non-Horn, no changes).
% 75.35/75.63
% 75.35/75.63 Term ordering decisions:
% 75.35/75.63
% 75.35/75.63 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 75.35/75.63 Function symbol KB weights: sk_c7=1. sk_c6=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 75.35/75.63
% 75.35/75.63 ============================== end of process initial clauses ========
% 75.35/75.63
% 75.35/75.63 ============================== CLAUSES FOR SEARCH ====================
% 75.35/75.63
% 75.35/75.63 ============================== end of clauses for search =============
% 75.35/75.63
% 75.35/75.63 ============================== SEARCH ================================
% 75.35/75.63
% 75.35/75.63 % Starting search at 0.02 seconds.
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=40.000, iters=3353
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=39.000, iters=3364
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=38.000, iters=3345
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=37.000, iters=3367
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=36.000, iters=3357
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=35.000, iters=3417
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=34.000, iters=3414
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=33.000, iters=3345
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=32.000, iters=3344
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=31.000, iters=3368
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=30.000, iters=3391
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=29.000, iters=3351
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=27.000, iters=3355
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=26.000, iters=3334
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=23.000, iters=3337
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=19.000, iters=3459
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=17.000, iters=3594
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=16.000, iters=3340
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=15.000, iters=3346
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=14.000, iters=3354
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=13.000, iters=3358
% 75.35/75.63
% 75.35/75.63 Low Water (displace): id=3853, wt=49.000
% 75.35/75.63
% 75.35/75.63 Low Water (displace): id=4506, wt=48.000
% 75.35/75.63
% 75.35/75.63 Low Water (displace): id=2551, wt=47.000
% 75.35/75.63
% 75.35/75.63 Low Water (displace): id=14751, wt=11.000
% 75.35/75.63
% 75.35/75.63 Low Water (keep): wt=12.000, iters=3336
% 75.35/75.63
% 75.35/75.63 ============================== PROOF =================================
% 75.35/75.63 % SZS status Unsatisfiable
% 75.35/75.63 % SZS output start Refutation
% 75.35/75.63
% 75.35/75.63 % Proof 1 at 72.55 (+ 2.10) seconds.
% 75.35/75.63 % Length of proof is 159.
% 75.35/75.63 % Level of proof is 29.
% 75.35/75.63 % Maximum clause weight is 46.000.
% 75.35/75.63 % Given clauses 5486.
% 75.35/75.63
% 75.35/75.63 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 75.35/75.63 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 75.35/75.63 3 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 75.35/75.63 4 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 75.35/75.63 5 inverse(sk_c2) = sk_c5 | inverse(sk_c3) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 75.35/75.63 6 inverse(sk_c2) = sk_c5 | inverse(sk_c4) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 75.35/75.63 7 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 75.35/75.63 8 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 75.35/75.63 9 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 75.35/75.63 10 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 75.35/75.63 11 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 75.35/75.63 15 multiply(sk_c2,sk_c5) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 75.35/75.63 16 inverse(sk_c2) = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 75.35/75.63 17 inverse(sk_c2) = sk_c5 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 75.35/75.63 18 inverse(sk_c2) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 75.35/75.63 19 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 75.35/75.63 20 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 75.35/75.63 21 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 75.35/75.63 22 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 75.35/75.63 25 multiply(sk_c2,sk_c5) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 75.35/75.63 27 multiply(sk_c2,sk_c5) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 75.35/75.63 28 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 75.35/75.63 29 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(B,sk_c5) != sk_c7 | inverse(B) != sk_c5 | 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_26) # label(negated_conjecture). [assumption].
% 75.35/75.63 33 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 75.35/75.63 34 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 75.35/75.63 36 inverse(sk_c2) = sk_c5 | multiply(sk_c6,sk_c4) = identity. [para(6(b,1),2(a,1,1))].
% 75.35/75.63 37 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),28(a,1,1)),rewrite([1(2)]),flip(a)].
% 75.35/75.63 44 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(10(b,1),28(a,1,1)),flip(b)].
% 75.35/75.63 45 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(10(b,1),28(a,2,2)),rewrite([28(8)])].
% 75.35/75.63 68 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(22(b,1),28(a,1,1)),flip(b)].
% 75.35/75.63 98 identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(A,sk_c5) != sk_c7 | inverse(A) != sk_c5 | 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),29(a,1))].
% 75.35/75.63 146 identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(A,sk_c5) != sk_c7 | inverse(A) != sk_c5 | 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(98,b,g)].
% 75.35/75.63 234 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),37(a,1,2))].
% 75.35/75.63 247 inverse(sk_c2) = sk_c5 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(16(b,1),37(a,1,2))].
% 75.35/75.63 248 inverse(sk_c2) = sk_c5 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(17(b,1),37(a,1,2))].
% 75.35/75.63 249 inverse(sk_c2) = sk_c5 | multiply(inverse(sk_c4),sk_c6) = sk_c5. [para(18(b,1),37(a,1,2))].
% 75.35/75.63 260 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c7),identity) = sk_c3. [para(33(b,1),37(a,1,2))].
% 75.35/75.63 261 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(37(a,1),37(a,1,2))].
% 75.35/75.63 262 multiply(A,identity) = A. [back_rewrite(234),rewrite([261(4)])].
% 75.35/75.63 263 inverse(sk_c1) = sk_c7 | inverse(sk_c7) = sk_c3. [back_rewrite(260),rewrite([262(8)])].
% 75.35/75.63 266 inverse(identity) = identity. [para(262(a,1),2(a,1))].
% 75.35/75.63 306 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = sk_c4. [para(34(b,1),37(a,1,2)),rewrite([262(8)])].
% 75.35/75.63 322 inverse(sk_c2) = sk_c5 | multiply(A,multiply(sk_c6,sk_c4)) = A. [para(36(b,1),28(a,2,2)),rewrite([28(8),262(10)])].
% 75.35/75.63 323 inverse(sk_c2) = sk_c5 | inverse(sk_c6) = sk_c4. [para(36(b,1),37(a,1,2)),rewrite([262(8)])].
% 75.35/75.63 367 multiply(A,inverse(A)) = identity. [para(261(a,1),2(a,1))].
% 75.35/75.63 384 multiply(A,multiply(inverse(A),B)) = B. [para(261(a,1),37(a,1))].
% 75.35/75.63 385 inverse(inverse(A)) = A. [para(261(a,1),262(a,1)),rewrite([262(2)]),flip(a)].
% 75.35/75.63 402 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(A,sk_c5) != sk_c7 | inverse(A) != sk_c5 | 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(146),rewrite([385(6)]),xx(b)].
% 75.35/75.63 409 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c7) = identity. [para(3(b,1),367(a,1,2))].
% 75.35/75.63 411 inverse(sk_c2) = sk_c5 | multiply(sk_c3,sk_c7) = identity. [para(5(b,1),367(a,1,2))].
% 75.35/75.63 413 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(367(a,1),28(a,1)),flip(a)].
% 75.35/75.63 414 inverse(sk_c7) = sk_c3 | multiply(sk_c1,sk_c7) = identity. [para(263(a,1),367(a,1,2))].
% 75.35/75.63 415 inverse(sk_c6) = sk_c4 | multiply(sk_c1,sk_c7) = identity. [para(306(a,1),367(a,1,2))].
% 75.35/75.63 419 inverse(sk_c6) = sk_c4 | multiply(sk_c2,sk_c5) = identity. [para(323(a,1),367(a,1,2))].
% 75.35/75.63 444 inverse(sk_c1) = sk_c7 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(4(b,1),384(a,1,2,1))].
% 75.35/75.63 624 inverse(sk_c2) = sk_c5 | multiply(A,multiply(sk_c3,sk_c7)) = A. [para(411(b,1),28(a,2,2)),rewrite([28(8),262(10)])].
% 75.35/75.63 633 inverse(sk_c7) = sk_c3 | identity = sk_c6 | inverse(sk_c3) = sk_c7. [para(414(b,1),7(a,1))].
% 75.35/75.63 727 inverse(sk_c6) = sk_c4 | identity = sk_c6 | inverse(sk_c4) = sk_c6. [para(415(b,1),8(a,1))].
% 75.35/75.63 743 inverse(sk_c6) = sk_c4 | identity = sk_c7 | inverse(sk_c4) = sk_c6. [para(419(b,1),15(a,1))].
% 75.35/75.63 755 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c6,sk_c3)) = identity. [para(33(b,1),44(b,2)),merge(b)].
% 75.35/75.63 924 inverse(sk_c1) = sk_c7 | multiply(sk_c6,multiply(sk_c3,sk_c6)) = sk_c5. [para(9(b,1),45(b,2)),merge(b)].
% 75.35/75.63 926 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c3,sk_c6)) = identity. [para(409(b,1),45(b,2)),merge(b)].
% 75.35/75.63 1477 inverse(sk_c2) = sk_c5 | multiply(inverse(sk_c6),multiply(sk_c5,A)) = multiply(sk_c7,A). [para(247(b,1),28(a,1,1)),flip(b)].
% 75.35/75.63 1488 inverse(sk_c2) = sk_c5 | multiply(sk_c7,sk_c7) = sk_c6. [para(5(b,1),248(b,1,1)),merge(b)].
% 75.35/75.63 1496 inverse(sk_c2) = sk_c5 | multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(1488(b,1),28(a,1,1)),flip(b)].
% 75.35/75.63 1504 inverse(sk_c2) = sk_c5 | multiply(sk_c6,sk_c6) = sk_c5. [para(6(b,1),249(b,1,1)),merge(b)].
% 75.35/75.63 1643 inverse(sk_c2) = sk_c5 | multiply(sk_c6,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(1504(b,1),28(a,1,1)),flip(b)].
% 75.35/75.63 1677 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(413(a,1),37(a,1,2)),rewrite([262(3)]),flip(a)].
% 75.35/75.63 1721 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c6,inverse(sk_c7)) = inverse(sk_c3). [para(20(b,1),1677(a,1,2,1))].
% 75.35/75.63 1722 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4). [para(21(b,1),1677(a,1,2,1))].
% 75.35/75.63 1728 multiply(sk_c2,sk_c5) = sk_c7 | multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4). [para(27(b,1),1677(a,1,2,1))].
% 75.35/75.63 1732 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(1677(a,1),37(a,1,2)),flip(a)].
% 75.35/75.63 3542 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(A,multiply(B,sk_c5)) != sk_c7 | multiply(inverse(B),inverse(A)) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6. [para(28(a,1),402(c,1)),rewrite([1732(15)])].
% 75.35/75.63 4530 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c5,inverse(sk_c7)) = sk_c6. [para(367(a,1),68(b,1,2)),rewrite([262(8)]),flip(b)].
% 75.35/75.63 5952 inverse(sk_c7) = sk_c3 | identity = sk_c6. [para(633(c,1),385(a,1,1)),merge(c)].
% 75.35/75.63 5955 identity = sk_c6 | inverse(sk_c3) = sk_c7. [para(5952(a,1),385(a,1,1))].
% 75.35/75.63 6290 inverse(sk_c6) = sk_c4 | identity = sk_c6. [para(727(c,1),385(a,1,1)),merge(c)].
% 75.35/75.63 6292 identity = sk_c6 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(6290(a,1),37(a,1,1))].
% 75.35/75.63 6293 identity = sk_c6 | inverse(sk_c4) = sk_c6. [para(6290(a,1),385(a,1,1))].
% 75.35/75.63 6905 inverse(sk_c6) = sk_c4 | identity = sk_c7. [para(743(c,1),385(a,1,1)),merge(c)].
% 75.35/75.63 7253 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = inverse(sk_c3). [para(755(b,1),37(a,1,2)),rewrite([262(8)]),flip(b)].
% 75.35/75.63 7384 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = inverse(sk_c3). [para(926(b,1),37(a,1,2)),rewrite([262(8)]),flip(b)].
% 75.35/75.63 7391 inverse(sk_c1) = sk_c7 | multiply(sk_c6,inverse(sk_c3)) = sk_c5. [para(7384(b,1),924(b,1,2)),merge(b)].
% 75.35/75.63 7401 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = inverse(sk_c3). [para(7391(b,1),444(b,1,2)),merge(b)].
% 75.35/75.63 7409 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c6. [para(7401(b,1),11(b,1)),merge(b)].
% 75.35/75.63 7416 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = identity. [para(7409(b,1),2(a,1,1))].
% 75.35/75.63 7593 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = identity. [para(7416(b,1),7253(b,1)),flip(c),merge(b)].
% 75.35/75.63 7804 inverse(sk_c1) = sk_c7 | identity = sk_c6. [para(7593(b,1),7409(b,1)),merge(b)].
% 75.35/75.63 7821 identity = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(7804(a,1),367(a,1,2))].
% 75.35/75.63 8248 identity = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5. [para(7821(b,1),19(a,1)),merge(b)].
% 75.35/75.63 8530 identity = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(8248(b,1),37(a,1,2))].
% 75.35/75.63 9125 identity = sk_c6 | multiply(inverse(sk_c5),sk_c6) = inverse(sk_c7). [para(8530(b,1),1732(a,1,1)),rewrite([385(10)]),flip(b)].
% 75.35/75.63 14821 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | sk_c7 != A | multiply(sk_c5,inverse(A)) != sk_c5 | 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(2(a,1),3542(c,1,2)),rewrite([262(10),385(13)]),flip(c)].
% 75.35/75.63 14824 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | sk_c7 != A | multiply(sk_c5,inverse(A)) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(inverse(B),inverse(C)) != sk_c6 | multiply(C,multiply(B,sk_c5)) != sk_c6. [para(28(a,1),14821(h,1)),rewrite([1732(28)])].
% 75.35/75.63 15618 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | sk_c7 != A | multiply(sk_c5,inverse(A)) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(sk_c5,inverse(B)) != sk_c6 | sk_c6 != B. [para(2(a,1),14824(h,1,2)),rewrite([385(29),262(33)]),flip(h)].
% 75.35/75.63 15621 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c5,A) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(sk_c5,inverse(B)) != sk_c6 | sk_c6 != B. [para(385(a,1),15618(d,1,2)),flip(c)].
% 75.35/75.63 15625 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c5,A) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(sk_c5,B) != sk_c6 | inverse(B) != sk_c6. [para(385(a,1),15621(g,1,2)),flip(h)].
% 75.35/75.63 15637 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(A),sk_c5) != sk_c7 | sk_c5 != A | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(sk_c5,B) != sk_c6 | inverse(B) != sk_c6. [para(384(a,1),15625(d,1)),rewrite([1732(12),385(12)]),flip(d)].
% 75.35/75.63 15650 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(A),sk_c5) != sk_c7 | sk_c5 != A | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != B | multiply(inverse(B),sk_c5) != sk_c6. [para(384(a,1),15637(g,1)),rewrite([1732(32),385(32)]),flip(g)].
% 75.35/75.63 15671 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(A),sk_c5) != sk_c7 | sk_c5 != A | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(B,C) != sk_c6 | multiply(inverse(C),multiply(inverse(B),sk_c5)) != sk_c6. [para(1732(a,1),15650(h,1,1)),rewrite([28(34)]),flip(g)].
% 75.35/75.63 15673 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(A),sk_c5) != sk_c7 | sk_c5 != A | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(inverse(sk_c5),multiply(inverse(sk_c7),sk_c5)) != sk_c6. [factor(15671,b,g)].
% 75.35/75.63 15678 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(A),multiply(inverse(B),sk_c5)) != sk_c7 | multiply(B,A) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(inverse(sk_c5),multiply(inverse(sk_c7),sk_c5)) != sk_c6. [para(1732(a,1),15673(c,1,1)),rewrite([28(13)]),flip(d)].
% 75.35/75.63 16018 identity != sk_c6 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(A),multiply(B,sk_c5)) != sk_c7 | multiply(inverse(B),A) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(inverse(sk_c5),multiply(inverse(sk_c7),sk_c5)) != sk_c6. [para(385(a,1),15678(c,1,2,1))].
% 75.35/75.63 20739 inverse(sk_c2) = sk_c5 | multiply(sk_c5,sk_c4) = sk_c6. [para(36(b,1),1643(b,1,2)),rewrite([262(11)]),flip(c),merge(b)].
% 75.35/75.63 20757 inverse(sk_c2) = sk_c5 | multiply(sk_c7,sk_c4) = identity. [para(20739(b,1),1477(b,1,2)),rewrite([2(12)]),flip(c),merge(b)].
% 75.35/75.63 20778 inverse(sk_c2) = sk_c5 | multiply(sk_c6,sk_c4) = sk_c7. [para(20757(b,1),1496(b,1,2)),rewrite([262(11)]),flip(c),merge(b)].
% 75.35/75.63 20870 inverse(sk_c2) = sk_c5 | identity = sk_c7. [para(20778(b,1),36(b,1)),flip(c),merge(b)].
% 75.35/75.63 20873 inverse(sk_c2) = sk_c5 | multiply(A,sk_c7) = A. [para(20778(b,1),322(b,1,2)),merge(b)].
% 75.35/75.63 20878 identity = sk_c7 | multiply(sk_c2,sk_c5) = identity. [para(20870(a,1),367(a,1,2))].
% 75.35/75.63 20902 identity = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5. [para(20878(b,1),25(a,1)),merge(b)].
% 75.35/75.63 20905 identity = sk_c7 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(20902(b,1),37(a,1,2))].
% 75.35/75.63 20934 inverse(sk_c2) = sk_c5 | inverse(sk_c3) = sk_c6. [para(20873(b,1),248(b,1)),merge(b)].
% 75.35/75.63 20946 inverse(sk_c2) = sk_c5 | multiply(A,sk_c3) = A. [para(20873(b,1),624(b,1,2)),merge(b)].
% 75.35/75.63 21102 inverse(sk_c2) = sk_c5 | inverse(sk_c3) = identity. [para(20946(b,1),2(a,1))].
% 75.35/75.63 21132 inverse(sk_c2) = sk_c5 | identity = sk_c6. [para(21102(b,1),20934(b,1)),merge(b)].
% 75.35/75.63 21135 identity = sk_c6 | inverse(sk_c5) = sk_c2. [para(21132(a,1),385(a,1,1))].
% 75.35/75.63 21137 identity = sk_c6 | multiply(sk_c2,multiply(sk_c5,A)) = A. [para(21132(a,1),384(a,1,2,1))].
% 75.35/75.63 21138 identity = sk_c6 | multiply(sk_c2,sk_c6) = inverse(sk_c7). [para(21135(b,1),9125(b,1,1)),merge(b)].
% 75.35/75.63 21987 multiply(sk_c6,inverse(sk_c7)) = inverse(sk_c3) | identity = sk_c6. [para(1721(a,1),7821(b,1)),flip(c),merge(c)].
% 75.35/75.63 22004 multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4) | identity = sk_c6. [para(1722(a,1),7821(b,1)),flip(c),merge(c)].
% 75.35/75.63 22122 multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4) | identity = sk_c7. [para(1728(a,1),20878(b,1)),flip(c),merge(c)].
% 75.35/75.63 24211 identity = sk_c6 | multiply(sk_c6,sk_c3) = inverse(sk_c3). [para(5952(a,1),21987(a,1,2)),merge(c)].
% 75.35/75.63 24212 identity = sk_c6 | multiply(sk_c6,inverse(sk_c7)) = sk_c7. [para(5955(b,1),21987(a,2)),merge(c)].
% 75.35/75.63 24256 identity = sk_c6 | multiply(sk_c6,sk_c3) = sk_c7. [para(5955(b,1),24211(b,2)),merge(b)].
% 75.35/75.63 24270 identity = sk_c6 | multiply(sk_c4,sk_c7) = sk_c3. [para(24256(b,1),6292(b,1,2)),merge(b)].
% 75.35/75.63 24281 identity = sk_c6 | multiply(sk_c4,sk_c7) = inverse(sk_c7). [para(24212(b,1),6292(b,1,2)),merge(b)].
% 75.35/75.63 24363 identity = sk_c6 | multiply(sk_c5,sk_c4) = inverse(sk_c4). [para(6290(a,1),22004(a,1,2)),merge(c)].
% 75.35/75.63 24392 identity = sk_c6 | multiply(sk_c5,sk_c4) = sk_c6. [para(6293(b,1),24363(b,2)),merge(b)].
% 75.35/75.63 24402 identity = sk_c6 | multiply(sk_c2,sk_c6) = sk_c4. [para(24392(b,1),21137(b,1,2)),merge(b)].
% 75.35/75.63 24413 identity = sk_c6 | inverse(sk_c7) = sk_c4. [para(24402(b,1),21138(b,1)),flip(c),merge(b)].
% 75.35/75.63 24495 identity = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(24413(b,1),2(a,1,1))].
% 75.35/75.63 24497 identity = sk_c6 | inverse(sk_c4) = sk_c7. [para(24413(b,1),385(a,1,1))].
% 75.35/75.63 24534 identity = sk_c6 | sk_c6 = sk_c7. [para(24497(b,1),6293(b,1)),flip(c),merge(b)].
% 75.35/75.63 24556 sk_c6 = sk_c7 | inverse(sk_c6) = identity. [para(24534(a,1),266(a,1,1))].
% 75.35/75.63 24593 sk_c6 = sk_c7 | identity = sk_c7 | sk_c5 = sk_c7. [para(24556(b,1),20905(b,1,1)),rewrite([1(9)])].
% 75.35/75.63 24595 sk_c6 = sk_c7 | inverse(sk_c6) = sk_c6. [para(24534(a,1),24556(b,2)),merge(b)].
% 75.35/75.63 24598 sk_c6 = sk_c7 | sk_c4 = sk_c6 | identity = sk_c7. [para(24595(b,1),6905(a,1)),flip(b)].
% 75.35/75.63 24787 identity = sk_c6 | identity = sk_c3. [para(24495(b,1),24270(b,1)),merge(b)].
% 75.35/75.63 24789 identity = sk_c6 | inverse(sk_c7) = identity. [para(24495(b,1),24281(b,1)),flip(c),merge(b)].
% 75.35/75.63 24792 identity = sk_c6 | inverse(sk_c3) = identity. [para(24787(b,1),266(a,1,1))].
% 75.35/75.63 24868 identity = sk_c6 | inverse(sk_c3) = sk_c6. [para(24789(b,1),21987(a,1,2)),rewrite([262(6)]),flip(b),merge(c)].
% 75.35/75.63 25123 identity = sk_c6. [para(24868(b,1),24792(b,1)),flip(c),merge(b),merge(c)].
% 75.35/75.63 25170 sk_c6 = sk_c7 | sk_c4 = sk_c6. [back_rewrite(24598),rewrite([25123(7)]),merge(c)].
% 75.35/75.63 25171 sk_c6 = sk_c7 | sk_c5 = sk_c7. [back_rewrite(24593),rewrite([25123(4)]),merge(b)].
% 75.35/75.63 26023 multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4) | sk_c6 = sk_c7. [back_rewrite(22122),rewrite([25123(8)])].
% 75.35/75.63 26652 multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(A),multiply(B,sk_c5)) != sk_c7 | multiply(inverse(B),A) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(inverse(sk_c5),multiply(inverse(sk_c7),sk_c5)) != sk_c6. [back_rewrite(16018),rewrite([25123(1)]),xx(a)].
% 75.35/75.63 28990 inverse(sk_c6) = sk_c6. [back_rewrite(266),rewrite([25123(1),25123(3)])].
% 75.35/75.63 28991 multiply(A,sk_c6) = A. [back_rewrite(262),rewrite([25123(1)])].
% 75.35/75.63 28993 multiply(sk_c6,A) = A. [back_rewrite(1),rewrite([25123(1)])].
% 75.35/75.63 29277 inverse(sk_c4) = sk_c5 | sk_c6 = sk_c7. [back_rewrite(26023),rewrite([28990(3),28991(3)]),flip(a)].
% 75.35/75.63 29559 multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(A),multiply(B,sk_c5)) != sk_c7 | multiply(inverse(B),A) != sk_c5 | sk_c5 != sk_c7 | inverse(sk_c7) != sk_c7 | multiply(inverse(sk_c5),multiply(inverse(sk_c7),sk_c5)) != sk_c6. [back_rewrite(26652),rewrite([28993(18),28991(22)]),flip(d)].
% 75.35/75.63 30775 sk_c6 = sk_c7 | sk_c5 = sk_c6. [para(25170(b,1),29277(a,1,1)),rewrite([28990(5)]),flip(b),merge(c)].
% 75.35/75.63 30787 sk_c6 = sk_c7. [para(30775(b,1),25171(b,1)),merge(b),merge(c)].
% 75.35/75.63 31467 multiply(sk_c7,sk_c5) != sk_c7 | multiply(inverse(A),multiply(B,sk_c5)) != sk_c7 | multiply(inverse(B),A) != sk_c5 | sk_c5 != sk_c7 | inverse(sk_c7) != sk_c7 | multiply(inverse(sk_c5),multiply(inverse(sk_c7),sk_c5)) != sk_c7. [back_rewrite(29559),rewrite([30787(4),30787(30)])].
% 75.35/75.63 31747 multiply(sk_c7,A) = A. [back_rewrite(28993),rewrite([30787(1)])].
% 75.35/75.63 31749 multiply(A,sk_c7) = A. [back_rewrite(28991),rewrite([30787(1)])].
% 75.35/75.63 31750 inverse(sk_c7) = sk_c7. [back_rewrite(28990),rewrite([30787(1),30787(3)])].
% 75.35/75.63 31949 sk_c5 = sk_c7. [back_rewrite(4530),rewrite([31747(3),30787(2),31750(6),31749(6),30787(5)]),merge(b)].
% 75.35/75.63 31974 $F. [factor(31467,b,f),rewrite([31949(2),31749(3),31949(4),31750(5),31750(6),31949(6),31749(7),31749(6),31750(8),31750(8),31949(8),31749(9),31949(8),31949(10),31750(14)]),xx(a),xx(b),xx(c),xx(d),xx(e)].
% 75.35/75.63
% 75.35/75.63 % SZS output end Refutation
% 75.35/75.63 ============================== end of proof ==========================
% 75.35/75.64
% 75.35/75.64 ============================== STATISTICS ============================
% 75.35/75.64
% 75.35/75.64 Given=5486. Generated=4070905. Kept=31973. proofs=1.
% 75.35/75.64 Usable=642. Sos=1907. Demods=14. Limbo=507, Disabled=28946. Hints=0.
% 75.35/75.64 Megabytes=27.98.
% 75.35/75.64 User_CPU=72.56, System_CPU=2.10, Wall_clock=75.
% 75.35/75.64
% 75.35/75.64 ============================== end of statistics =====================
% 75.35/75.64
% 75.35/75.64 ============================== end of search =========================
% 75.35/75.64
% 75.35/75.64 THEOREM PROVED
% 75.35/75.64 % SZS status Unsatisfiable
% 75.35/75.64
% 75.35/75.64 Exiting with 1 proof.
% 75.35/75.64
% 75.35/75.64 Process 4147 exit (max_proofs) Mon Jun 13 04:17:55 2022
% 75.35/75.64 Prover9 interrupted
%------------------------------------------------------------------------------