TSTP Solution File: GRP289-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP289-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 11:18:30 EDT 2022
% Result : Unsatisfiable 157.74s 158.06s
% Output : Refutation 157.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : GRP289-1 : TPTP v8.1.0. Released v2.5.0.
% 0.09/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n009.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 14:43:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 157.74/158.06 ============================== Prover9 ===============================
% 157.74/158.06 Prover9 (32) version 2009-11A, November 2009.
% 157.74/158.06 Process 19622 was started by sandbox on n009.cluster.edu,
% 157.74/158.06 Mon Jun 13 14:43:08 2022
% 157.74/158.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19468_n009.cluster.edu".
% 157.74/158.06 ============================== end of head ===========================
% 157.74/158.06
% 157.74/158.06 ============================== INPUT =================================
% 157.74/158.06
% 157.74/158.06 % Reading from file /tmp/Prover9_19468_n009.cluster.edu
% 157.74/158.06
% 157.74/158.06 set(prolog_style_variables).
% 157.74/158.06 set(auto2).
% 157.74/158.06 % set(auto2) -> set(auto).
% 157.74/158.06 % set(auto) -> set(auto_inference).
% 157.74/158.06 % set(auto) -> set(auto_setup).
% 157.74/158.06 % set(auto_setup) -> set(predicate_elim).
% 157.74/158.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 157.74/158.06 % set(auto) -> set(auto_limits).
% 157.74/158.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 157.74/158.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 157.74/158.06 % set(auto) -> set(auto_denials).
% 157.74/158.06 % set(auto) -> set(auto_process).
% 157.74/158.06 % set(auto2) -> assign(new_constants, 1).
% 157.74/158.06 % set(auto2) -> assign(fold_denial_max, 3).
% 157.74/158.06 % set(auto2) -> assign(max_weight, "200.000").
% 157.74/158.06 % set(auto2) -> assign(max_hours, 1).
% 157.74/158.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 157.74/158.06 % set(auto2) -> assign(max_seconds, 0).
% 157.74/158.06 % set(auto2) -> assign(max_minutes, 5).
% 157.74/158.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 157.74/158.06 % set(auto2) -> set(sort_initial_sos).
% 157.74/158.06 % set(auto2) -> assign(sos_limit, -1).
% 157.74/158.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 157.74/158.06 % set(auto2) -> assign(max_megs, 400).
% 157.74/158.06 % set(auto2) -> assign(stats, some).
% 157.74/158.06 % set(auto2) -> clear(echo_input).
% 157.74/158.06 % set(auto2) -> set(quiet).
% 157.74/158.06 % set(auto2) -> clear(print_initial_clauses).
% 157.74/158.06 % set(auto2) -> clear(print_given).
% 157.74/158.06 assign(lrs_ticks,-1).
% 157.74/158.06 assign(sos_limit,10000).
% 157.74/158.06 assign(order,kbo).
% 157.74/158.06 set(lex_order_vars).
% 157.74/158.06 clear(print_given).
% 157.74/158.06
% 157.74/158.06 % formulas(sos). % not echoed (29 formulas)
% 157.74/158.06
% 157.74/158.06 ============================== end of input ==========================
% 157.74/158.06
% 157.74/158.06 % From the command line: assign(max_seconds, 300).
% 157.74/158.06
% 157.74/158.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 157.74/158.06
% 157.74/158.06 % Formulas that are not ordinary clauses:
% 157.74/158.06
% 157.74/158.06 ============================== end of process non-clausal formulas ===
% 157.74/158.06
% 157.74/158.06 ============================== PROCESS INITIAL CLAUSES ===============
% 157.74/158.06
% 157.74/158.06 ============================== PREDICATE ELIMINATION =================
% 157.74/158.06
% 157.74/158.06 ============================== end predicate elimination =============
% 157.74/158.06
% 157.74/158.06 Auto_denials: (non-Horn, no changes).
% 157.74/158.06
% 157.74/158.06 Term ordering decisions:
% 157.74/158.06
% 157.74/158.06 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 157.74/158.06 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.
% 157.74/158.06
% 157.74/158.06 ============================== end of process initial clauses ========
% 157.74/158.06
% 157.74/158.06 ============================== CLAUSES FOR SEARCH ====================
% 157.74/158.06
% 157.74/158.06 ============================== end of clauses for search =============
% 157.74/158.06
% 157.74/158.06 ============================== SEARCH ================================
% 157.74/158.06
% 157.74/158.06 % Starting search at 0.01 seconds.
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=39.000, iters=3382
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=38.000, iters=3342
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=37.000, iters=3350
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=36.000, iters=3386
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=35.000, iters=3336
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=34.000, iters=3354
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=33.000, iters=3336
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=32.000, iters=3358
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=31.000, iters=3352
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=30.000, iters=3340
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=29.000, iters=3348
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=28.000, iters=3333
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=27.000, iters=3447
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=24.000, iters=3406
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=19.000, iters=3628
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=17.000, iters=3525
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=16.000, iters=3381
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=15.000, iters=3354
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=14.000, iters=3359
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=13.000, iters=3333
% 157.74/158.06
% 157.74/158.06 Low Water (displace): id=15450, wt=12.000
% 157.74/158.06
% 157.74/158.06 Low Water (displace): id=15452, wt=11.000
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=12.000, iters=3333
% 157.74/158.06
% 157.74/158.06 Low Water (keep): wt=11.000, iters=3333
% 157.74/158.06
% 157.74/158.06 Low Water (displace): id=35328, wt=10.000
% 157.74/158.06
% 157.74/158.06 Low Water (displace): id=36464, wt=9.000
% 157.74/158.06
% 157.74/158.06 ============================== PROOF =================================
% 157.74/158.06 % SZS status Unsatisfiable
% 157.74/158.06 % SZS output start Refutation
% 157.74/158.06
% 157.74/158.06 % Proof 1 at 152.77 (+ 4.33) seconds.
% 157.74/158.06 % Length of proof is 191.
% 157.74/158.06 % Level of proof is 27.
% 157.74/158.06 % Maximum clause weight is 46.000.
% 157.74/158.06 % Given clauses 7442.
% 157.74/158.06
% 157.74/158.06 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 157.74/158.06 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 157.74/158.06 3 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 157.74/158.06 4 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 157.74/158.06 5 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 157.74/158.06 6 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 157.74/158.06 8 multiply(sk_c7,sk_c6) = sk_c5 | inverse(sk_c4) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 157.74/158.06 9 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 157.74/158.06 10 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 157.74/158.06 11 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 157.74/158.06 12 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 157.74/158.06 13 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 157.74/158.06 15 multiply(sk_c2,sk_c6) = sk_c5 | inverse(sk_c4) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 157.74/158.06 16 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 157.74/158.06 17 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 157.74/158.06 18 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 157.74/158.06 19 multiply(sk_c7,sk_c6) = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 157.74/158.06 22 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 157.74/158.06 23 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 157.74/158.06 24 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 157.74/158.06 27 multiply(sk_c2,sk_c6) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 157.74/158.06 28 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 157.74/158.06 29 multiply(sk_c7,sk_c6) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c5 | inverse(B) != sk_c6 | 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].
% 157.74/158.06 37 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 157.74/158.06 38 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 157.74/158.06 40 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c4) = identity. [para(6(b,1),2(a,1,1))].
% 157.74/158.06 41 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),28(a,1,1)),rewrite([1(2)]),flip(a)].
% 157.74/158.06 49 inverse(sk_c4) = sk_c6 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6). [para(10(a,1),28(a,2,2)),rewrite([28(8)])].
% 157.74/158.06 52 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(12(b,1),28(a,1,1)),flip(b)].
% 157.74/158.06 65 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c6). [para(18(b,1),28(a,2,2)),rewrite([28(8)])].
% 157.74/158.06 66 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c7,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(19(a,1),28(a,1,1)),flip(b)].
% 157.74/158.06 99 multiply(sk_c7,sk_c6) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | sk_c5 != sk_c6 | inverse(identity) != sk_c6 | 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(1(a,1),29(d,1)),flip(d)].
% 157.74/158.06 160 multiply(sk_c7,sk_c6) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | sk_c5 != sk_c6 | inverse(identity) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [factor(99,c,g)].
% 157.74/158.06 242 multiply(sk_c7,sk_c6) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | sk_c5 != sk_c6 | inverse(identity) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(A,sk_c6) != sk_c7. [factor(160,e,h),rewrite([1(31)]),merge(h)].
% 157.74/158.06 304 inverse(sk_c1) = sk_c7 | multiply(sk_c7,multiply(sk_c3,A)) = A. [para(37(b,1),28(a,1,1)),rewrite([1(6)]),flip(b)].
% 157.74/158.06 322 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),41(a,1,2))].
% 157.74/158.06 324 inverse(sk_c2) = sk_c6 | multiply(sk_c7,multiply(sk_c3,A)) = A. [para(5(b,1),41(a,1,1))].
% 157.74/158.06 331 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(12(b,1),41(a,1,2))].
% 157.74/158.06 332 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c4),sk_c6) = sk_c5. [para(13(b,1),41(a,1,2))].
% 157.74/158.06 334 inverse(sk_c4) = sk_c6 | multiply(inverse(sk_c2),sk_c5) = sk_c6. [para(15(a,1),41(a,1,2))].
% 157.74/158.06 335 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(16(b,1),41(a,1,2))].
% 157.74/158.06 336 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(17(b,1),41(a,1,2))].
% 157.74/158.06 337 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c4),sk_c6) = sk_c5. [para(18(b,1),41(a,1,2))].
% 157.74/158.06 346 multiply(sk_c2,sk_c6) = sk_c5 | multiply(inverse(sk_c4),sk_c6) = sk_c5. [para(27(b,1),41(a,1,2))].
% 157.74/158.06 348 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c7),identity) = sk_c3. [para(37(b,1),41(a,1,2))].
% 157.74/158.06 349 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(41(a,1),41(a,1,2))].
% 157.74/158.06 350 multiply(A,identity) = A. [back_rewrite(322),rewrite([349(4)])].
% 157.74/158.06 351 inverse(sk_c1) = sk_c7 | inverse(sk_c7) = sk_c3. [back_rewrite(348),rewrite([350(8)])].
% 157.74/158.06 353 inverse(identity) = identity. [para(350(a,1),2(a,1))].
% 157.74/158.06 370 multiply(sk_c7,sk_c6) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | sk_c5 != sk_c6 | identity != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(A,sk_c6) != sk_c7. [back_rewrite(242),rewrite([353(17)])].
% 157.74/158.06 378 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = sk_c4. [para(38(b,1),41(a,1,2)),rewrite([350(8)])].
% 157.74/158.06 385 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c6,sk_c4)) = A. [para(40(b,1),28(a,2,2)),rewrite([28(8),350(10)])].
% 157.74/158.06 386 inverse(sk_c2) = sk_c6 | inverse(sk_c6) = sk_c4. [para(40(b,1),41(a,1,2)),rewrite([350(8)])].
% 157.74/158.06 393 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | sk_c5 != sk_c6 | identity != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5. [para(1(a,1),370(b,1)),rewrite([353(10),1(25)]),flip(g),merge(g)].
% 157.74/158.06 408 inverse(sk_c6) = sk_c4 | multiply(sk_c6,sk_c2) = identity. [para(386(a,1),2(a,1,1))].
% 157.74/158.06 410 multiply(A,inverse(A)) = identity. [para(349(a,1),2(a,1))].
% 157.74/158.06 435 multiply(A,multiply(inverse(A),B)) = B. [para(349(a,1),41(a,1))].
% 157.74/158.06 436 inverse(inverse(A)) = A. [para(349(a,1),350(a,1)),rewrite([350(2)]),flip(a)].
% 157.74/158.06 440 inverse(sk_c6) = sk_c4 | multiply(inverse(sk_c6),A) = multiply(sk_c2,A). [para(386(a,1),349(a,1,1,1))].
% 157.74/158.06 457 inverse(sk_c6) = sk_c4 | inverse(sk_c6) = sk_c2. [para(386(a,1),436(a,1,1))].
% 157.74/158.06 458 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c7) = identity. [para(3(b,1),410(a,1,2))].
% 157.74/158.06 460 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c7) = identity. [para(5(b,1),410(a,1,2))].
% 157.74/158.06 462 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(410(a,1),28(a,1)),flip(a)].
% 157.74/158.06 463 inverse(sk_c7) = sk_c3 | multiply(sk_c1,sk_c7) = identity. [para(351(a,1),410(a,1,2))].
% 157.74/158.06 464 inverse(sk_c6) = sk_c4 | multiply(sk_c1,sk_c7) = identity. [para(378(a,1),410(a,1,2))].
% 157.74/158.06 468 inverse(sk_c6) = sk_c4 | multiply(sk_c2,sk_c6) = identity. [para(386(a,1),410(a,1,2))].
% 157.74/158.06 488 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c7,A)) = A. [para(3(b,1),435(a,1,2,1))].
% 157.74/158.06 491 inverse(sk_c2) = sk_c6 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(6(b,1),435(a,1,2,1))].
% 157.74/158.06 552 inverse(sk_c6) = sk_c2 | multiply(sk_c6,sk_c4) = identity. [para(457(a,1),410(a,1,2))].
% 157.74/158.06 600 inverse(sk_c6) = sk_c4 | multiply(A,multiply(sk_c6,sk_c2)) = A. [para(408(b,1),28(a,2,2)),rewrite([28(8),350(10)])].
% 157.74/158.06 658 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c3,sk_c7)) = A. [para(458(b,1),28(a,2,2)),rewrite([28(8),350(10)])].
% 157.74/158.06 672 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c3,sk_c7)) = A. [para(460(b,1),28(a,2,2)),rewrite([28(8),350(10)])].
% 157.74/158.06 784 inverse(sk_c7) = sk_c3 | identity = sk_c6 | inverse(sk_c3) = sk_c7. [para(463(b,1),9(a,1))].
% 157.74/158.06 793 inverse(sk_c6) = sk_c4 | identity = sk_c6 | inverse(sk_c4) = sk_c6. [para(464(b,1),10(a,1))].
% 157.74/158.06 817 inverse(sk_c6) = sk_c4 | identity = sk_c5 | inverse(sk_c4) = sk_c6. [para(468(b,1),15(a,1))].
% 157.74/158.06 930 inverse(sk_c4) = sk_c6 | multiply(inverse(sk_c6),multiply(sk_c1,sk_c7)) = identity. [para(2(a,1),49(b,2))].
% 157.74/158.06 987 inverse(sk_c6) = sk_c2 | multiply(A,multiply(sk_c6,sk_c4)) = A. [para(552(b,1),28(a,2,2)),rewrite([28(8),350(10)])].
% 157.74/158.06 1228 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c7) = sk_c6. [para(3(b,1),331(b,1,1)),merge(b)].
% 157.74/158.06 1253 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c6) = sk_c5. [para(4(b,1),332(b,1,1)),merge(b)].
% 157.74/158.06 1301 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = multiply(sk_c7,sk_c7). [para(11(b,1),52(b,1,2)),merge(b)].
% 157.74/158.06 1325 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = multiply(sk_c7,sk_c6). [para(1253(b,1),52(b,1,2)),merge(b)].
% 157.74/158.06 1469 inverse(sk_c4) = sk_c6 | multiply(inverse(sk_c2),multiply(sk_c5,A)) = multiply(sk_c6,A). [para(334(b,1),28(a,1,1)),flip(b)].
% 157.74/158.06 1477 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c6),multiply(sk_c5,A)) = multiply(sk_c7,A). [para(335(b,1),28(a,1,1)),flip(b)].
% 157.74/158.06 1581 inverse(sk_c2) = sk_c6 | multiply(sk_c7,sk_c7) = sk_c6. [para(5(b,1),336(b,1,1)),merge(b)].
% 157.74/158.06 1596 inverse(sk_c2) = sk_c6 | multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(1581(b,1),28(a,1,1)),flip(b)].
% 157.74/158.06 1605 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c6) = sk_c5. [para(6(b,1),337(b,1,1)),merge(b)].
% 157.74/158.06 1632 inverse(sk_c2) = sk_c6 | multiply(sk_c6,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(1605(b,1),28(a,1,1)),flip(b)].
% 157.74/158.06 1638 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c6. [para(1605(b,1),41(a,1,2))].
% 157.74/158.06 1807 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(462(a,1),41(a,1,2)),rewrite([350(3)]),flip(a)].
% 157.74/158.06 1840 inverse(sk_c4) = sk_c6 | multiply(sk_c6,inverse(sk_c5)) = inverse(sk_c7). [para(8(a,1),1807(a,1,2,1))].
% 157.74/158.06 1848 inverse(sk_c2) = sk_c6 | multiply(sk_c7,inverse(sk_c5)) = inverse(sk_c6). [para(16(b,1),1807(a,1,2,1))].
% 157.74/158.06 1855 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c6,inverse(sk_c7)) = inverse(sk_c3). [para(23(b,1),1807(a,1,2,1))].
% 157.74/158.06 1856 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4). [para(24(b,1),1807(a,1,2,1))].
% 157.74/158.06 1863 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(1807(a,1),41(a,1,2)),flip(a)].
% 157.74/158.06 2922 inverse(sk_c2) = sk_c6 | sk_c7 = sk_c6. [para(1638(b,1),335(b,1)),flip(c),merge(b)].
% 157.74/158.06 3003 sk_c7 = sk_c6 | inverse(sk_c6) = sk_c2. [para(2922(a,1),436(a,1,1))].
% 157.74/158.06 3863 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c5,inverse(sk_c6)) = sk_c7. [para(410(a,1),66(b,1,2)),rewrite([350(8)]),flip(b)].
% 157.74/158.06 7011 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c7. [para(16(b,1),491(b,1,2)),merge(b)].
% 157.74/158.06 7021 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c4),sk_c7) = sk_c5. [para(7011(b,1),41(a,1,2))].
% 157.74/158.06 7591 inverse(sk_c7) = sk_c3 | identity = sk_c6. [para(784(c,1),436(a,1,1)),merge(c)].
% 157.74/158.06 7594 identity = sk_c6 | inverse(sk_c3) = sk_c7. [para(7591(a,1),436(a,1,1))].
% 157.74/158.06 7837 inverse(sk_c6) = sk_c4 | identity = sk_c6. [para(793(c,1),436(a,1,1)),merge(c)].
% 157.74/158.06 7839 identity = sk_c6 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(7837(a,1),41(a,1,1))].
% 157.74/158.06 7840 identity = sk_c6 | inverse(sk_c4) = sk_c6. [para(7837(a,1),436(a,1,1))].
% 157.74/158.06 8326 inverse(sk_c6) = sk_c4 | identity = sk_c5. [para(817(c,1),436(a,1,1)),merge(c)].
% 157.74/158.06 8327 identity = sk_c5 | multiply(sk_c4,sk_c6) = identity. [para(8326(a,1),2(a,1,1))].
% 157.74/158.06 10158 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = sk_c6. [para(1228(b,1),1301(b,2)),merge(b)].
% 157.74/158.06 10167 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c6) = sk_c5. [para(10158(b,1),304(b,1,2)),merge(b)].
% 157.74/158.06 10268 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = sk_c5. [para(10167(b,1),1325(b,2)),merge(b)].
% 157.74/158.06 10364 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c7) = sk_c5. [para(10268(b,1),1301(b,1)),flip(c),merge(b)].
% 157.74/158.06 10475 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = sk_c7. [para(10364(b,1),488(b,1,2)),merge(b)].
% 157.74/158.06 10490 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c6) = sk_c7. [para(10475(b,1),1325(b,1)),flip(c),merge(b)].
% 157.74/158.06 10668 inverse(sk_c1) = sk_c7 | identity = sk_c6. [para(10490(b,1),41(a,1,2)),rewrite([2(8)])].
% 157.74/158.06 10674 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c7) = sk_c6. [para(10490(b,1),488(b,1,2)),merge(b)].
% 157.74/158.06 10687 identity = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(10668(a,1),410(a,1,2))].
% 157.74/158.06 10809 identity = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5. [para(10687(b,1),22(a,1)),merge(b)].
% 157.74/158.06 11007 identity = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(10809(b,1),41(a,1,2))].
% 157.74/158.06 11059 inverse(sk_c1) = sk_c7 | multiply(A,sk_c6) = A. [para(10674(b,1),658(b,1,2)),merge(b)].
% 157.74/158.06 11310 identity = sk_c6 | multiply(inverse(sk_c5),sk_c6) = inverse(sk_c7). [para(11007(b,1),1863(a,1,1)),rewrite([436(10)]),flip(b)].
% 157.74/158.06 11727 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = identity. [para(11059(b,1),2(a,1))].
% 157.74/158.06 11789 inverse(sk_c6) = identity | multiply(sk_c1,sk_c7) = identity. [para(11727(a,1),410(a,1,2))].
% 157.74/158.06 18819 inverse(sk_c6) = identity | inverse(sk_c4) = sk_c6. [para(11789(b,1),930(b,1,2)),rewrite([350(12)]),merge(c)].
% 157.74/158.06 18893 inverse(sk_c6) = identity | inverse(sk_c6) = sk_c4. [para(18819(b,1),436(a,1,1))].
% 157.74/158.06 18931 inverse(sk_c6) = sk_c4 | multiply(sk_c6,A) = A. [para(18893(a,1),41(a,1,1)),rewrite([1(8)])].
% 157.74/158.06 18936 inverse(sk_c6) = sk_c4 | multiply(sk_c2,A) = A. [para(18893(a,1),440(b,1,1)),rewrite([1(10)]),flip(c),merge(b)].
% 157.74/158.06 19924 inverse(sk_c6) = sk_c4 | multiply(A,sk_c2) = A. [para(18931(b,1),600(b,1,2)),merge(b)].
% 157.74/158.06 19976 inverse(sk_c6) = sk_c4 | multiply(inverse(sk_c2),A) = A. [para(18936(b,1),41(a,1,2))].
% 157.74/158.06 25471 inverse(sk_c6) = sk_c4 | inverse(sk_c2) = sk_c2. [para(19976(b,1),19924(b,1)),flip(c),merge(b)].
% 157.74/158.06 27694 inverse(sk_c4) = sk_c6 | inverse(sk_c2) = inverse(sk_c7). [para(1840(b,1),1469(b,2)),rewrite([410(14),350(12)]),merge(b)].
% 157.74/158.06 27696 inverse(sk_c2) = inverse(sk_c7) | inverse(sk_c6) = sk_c4. [para(27694(a,1),436(a,1,1))].
% 157.74/158.06 27713 inverse(sk_c6) = sk_c4 | inverse(sk_c7) = sk_c2. [para(27696(a,1),25471(b,1)),merge(b)].
% 157.74/158.06 27869 inverse(sk_c6) = sk_c4 | inverse(sk_c2) = sk_c7. [para(27713(b,1),436(a,1,1))].
% 157.74/158.06 27969 inverse(sk_c6) = sk_c4 | sk_c7 = sk_c6. [para(27869(b,1),386(a,1)),merge(c)].
% 157.74/158.06 27975 sk_c7 = sk_c6 | multiply(sk_c4,sk_c6) = identity. [para(27969(a,1),2(a,1,1))].
% 157.74/158.06 28030 sk_c7 = sk_c6 | multiply(inverse(sk_c6),inverse(sk_c4)) = identity. [para(27975(b,1),1863(a,1,1)),rewrite([353(5)]),flip(b)].
% 157.74/158.06 28454 inverse(sk_c2) = sk_c6 | multiply(sk_c5,sk_c4) = sk_c6. [para(40(b,1),1632(b,1,2)),rewrite([350(11)]),flip(c),merge(b)].
% 157.74/158.06 28466 inverse(sk_c2) = sk_c6 | multiply(sk_c7,sk_c4) = identity. [para(28454(b,1),1477(b,1,2)),rewrite([2(12)]),flip(c),merge(b)].
% 157.74/158.06 28488 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c4) = sk_c7. [para(28466(b,1),1596(b,1,2)),rewrite([350(11)]),flip(c),merge(b)].
% 157.74/158.06 28618 inverse(sk_c2) = sk_c6 | multiply(A,sk_c7) = A. [para(28488(b,1),385(b,1,2)),merge(b)].
% 157.74/158.06 29176 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c5. [para(28618(b,1),7021(b,1)),merge(b)].
% 157.74/158.06 29177 inverse(sk_c2) = sk_c6 | multiply(A,sk_c3) = A. [para(28618(b,1),672(b,1,2)),merge(b)].
% 157.74/158.06 29266 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c5) = identity. [para(29176(b,1),410(a,1,2))].
% 157.74/158.06 29721 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = identity. [para(29177(b,1),2(a,1))].
% 157.74/158.06 29739 inverse(sk_c2) = sk_c6 | multiply(sk_c3,A) = A. [para(29721(b,1),41(a,1,1)),rewrite([1(8)])].
% 157.74/158.06 30145 inverse(sk_c2) = sk_c6 | multiply(A,sk_c6) = A. [para(29266(b,1),65(b,1,2)),rewrite([350(10)]),flip(c),merge(b)].
% 157.74/158.06 30310 inverse(sk_c2) = sk_c6 | multiply(sk_c7,A) = A. [para(29739(b,1),324(b,1,2)),merge(b)].
% 157.74/158.06 30646 inverse(sk_c2) = sk_c6 | inverse(sk_c6) = identity. [para(30145(b,1),2(a,1))].
% 157.74/158.06 30694 inverse(sk_c6) = identity | inverse(sk_c6) = sk_c2. [para(30646(a,1),436(a,1,1))].
% 157.74/158.06 30736 inverse(sk_c6) = sk_c2 | multiply(sk_c6,A) = A. [para(30694(a,1),41(a,1,1)),rewrite([1(8)])].
% 157.74/158.06 31274 multiply(sk_c6,inverse(sk_c7)) = inverse(sk_c3) | identity = sk_c6. [para(1855(a,1),10687(b,1)),flip(c),merge(c)].
% 157.74/158.06 31309 inverse(sk_c2) = sk_c6 | inverse(sk_c5) = inverse(sk_c6). [para(30310(b,1),1848(b,1)),merge(b)].
% 157.74/158.06 31314 multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4) | identity = sk_c6. [para(1856(a,1),10687(b,1)),flip(c),merge(c)].
% 157.74/158.06 31449 inverse(sk_c6) = sk_c2 | multiply(A,sk_c4) = A. [para(30736(b,1),987(b,1,2)),merge(b)].
% 157.74/158.06 31757 inverse(sk_c5) = inverse(sk_c6) | inverse(sk_c6) = sk_c2. [para(31309(a,1),436(a,1,1))].
% 157.74/158.06 31829 inverse(sk_c6) = sk_c2 | inverse(sk_c5) = identity. [para(30694(a,1),31757(a,2)),merge(c)].
% 157.74/158.06 31842 inverse(sk_c6) = sk_c2 | multiply(sk_c5,A) = A. [para(31829(b,1),41(a,1,1)),rewrite([1(8)])].
% 157.74/158.06 31891 inverse(sk_c6) = sk_c2 | sk_c4 = sk_c5. [para(31842(b,1),31449(b,1)),merge(b)].
% 157.74/158.06 31908 sk_c4 = sk_c5 | multiply(sk_c2,sk_c6) = identity. [para(31891(a,1),2(a,1,1))].
% 157.74/158.06 34938 identity = sk_c6 | multiply(sk_c6,sk_c3) = inverse(sk_c3). [para(7591(a,1),31274(a,1,2)),merge(c)].
% 157.74/158.06 34939 identity = sk_c6 | multiply(sk_c6,inverse(sk_c7)) = sk_c7. [para(7594(b,1),31274(a,2)),merge(c)].
% 157.74/158.06 34987 identity = sk_c6 | multiply(sk_c6,sk_c3) = sk_c7. [para(7594(b,1),34938(b,2)),merge(b)].
% 157.74/158.06 34992 identity = sk_c6 | multiply(sk_c4,sk_c7) = sk_c3. [para(34987(b,1),7839(b,1,2)),merge(b)].
% 157.74/158.06 35011 identity = sk_c6 | multiply(sk_c4,sk_c7) = inverse(sk_c7). [para(34939(b,1),7839(b,1,2)),merge(b)].
% 157.74/158.06 35165 identity = sk_c6 | multiply(sk_c5,sk_c4) = inverse(sk_c4). [para(7837(a,1),31314(a,1,2)),merge(c)].
% 157.74/158.06 35184 identity = sk_c6 | multiply(sk_c5,sk_c4) = sk_c6. [para(7840(b,1),35165(b,2)),merge(b)].
% 157.74/158.06 35186 identity = sk_c6 | multiply(inverse(sk_c5),sk_c6) = sk_c4. [para(35184(b,1),41(a,1,2))].
% 157.74/158.06 35229 identity = sk_c6 | inverse(sk_c7) = sk_c4. [para(35186(b,1),11310(b,1)),flip(c),merge(b)].
% 157.74/158.06 35246 identity = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(35229(b,1),2(a,1,1))].
% 157.74/158.06 35248 identity = sk_c6 | inverse(sk_c4) = sk_c7. [para(35229(b,1),436(a,1,1))].
% 157.74/158.06 35439 identity = sk_c6 | sk_c7 = sk_c6. [para(35248(b,1),7840(b,1)),merge(b)].
% 157.74/158.06 35462 sk_c7 = sk_c6 | inverse(sk_c6) = identity. [para(35439(a,1),353(a,1,1))].
% 157.74/158.06 35594 sk_c7 = sk_c6 | identity = sk_c2. [para(35462(b,1),3003(b,1)),merge(b)].
% 157.74/158.06 35618 sk_c7 = sk_c6 | inverse(sk_c4) = identity. [para(35462(b,1),28030(b,1,1)),rewrite([1(10)]),merge(b)].
% 157.74/158.06 35753 sk_c7 = sk_c6 | inverse(sk_c4) = sk_c2. [para(35594(b,1),35618(b,2)),merge(b)].
% 157.74/158.06 35921 sk_c7 = sk_c6 | multiply(sk_c2,sk_c6) = sk_c5. [para(35753(b,1),346(b,1,1)),merge(c)].
% 157.74/158.06 36066 identity = sk_c6 | identity = sk_c3. [para(35246(b,1),34992(b,1)),merge(b)].
% 157.74/158.06 36068 identity = sk_c6 | inverse(sk_c7) = identity. [para(35246(b,1),35011(b,1)),flip(c),merge(b)].
% 157.74/158.06 36071 identity = sk_c6 | inverse(sk_c3) = identity. [para(36066(b,1),353(a,1,1))].
% 157.74/158.06 36146 identity = sk_c6 | inverse(sk_c3) = sk_c6. [para(36068(b,1),31274(a,1,2)),rewrite([350(6)]),flip(b),merge(c)].
% 157.74/158.06 36469 identity = sk_c6. [para(36146(b,1),36071(b,1)),flip(c),merge(b),merge(c)].
% 157.74/158.06 37301 sk_c4 = sk_c5 | multiply(sk_c2,sk_c6) = sk_c6. [back_rewrite(31908),rewrite([36469(7)])].
% 157.74/158.06 39980 sk_c5 = sk_c6 | multiply(sk_c4,sk_c6) = sk_c6. [back_rewrite(8327),rewrite([36469(1),36469(7)]),flip(a)].
% 157.74/158.06 40500 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5. [back_rewrite(393),rewrite([36469(9),36469(15)]),flip(c),xx(e),merge(c)].
% 157.74/158.06 40507 inverse(sk_c6) = sk_c6. [back_rewrite(353),rewrite([36469(1),36469(3)])].
% 157.74/158.06 40508 multiply(A,sk_c6) = A. [back_rewrite(350),rewrite([36469(1)])].
% 157.74/158.06 40510 multiply(sk_c6,A) = A. [back_rewrite(1),rewrite([36469(1)])].
% 157.74/158.06 41098 sk_c5 = sk_c7. [back_rewrite(3863),rewrite([40510(3),40507(6),40508(6)]),flip(a),merge(b)].
% 157.74/158.06 41123 sk_c7 != sk_c6. [back_rewrite(40500),rewrite([40508(3),41098(2),41098(7),40510(12),41098(11)]),xx(a),xx(d),merge(b)].
% 157.74/158.07 41167 sk_c4 = sk_c6. [back_rewrite(39980),rewrite([41098(1),40508(6)]),unit_del(a,41123)].
% 157.74/158.07 41369 sk_c2 = sk_c6. [back_rewrite(37301),rewrite([41167(1),41098(2),40508(6)]),flip(a),unit_del(a,41123)].
% 157.74/158.07 41429 $F. [back_rewrite(35921),rewrite([41369(4),40508(6),41098(5)]),flip(b),merge(b),unit_del(a,41123)].
% 157.74/158.07
% 157.74/158.07 % SZS output end Refutation
% 157.74/158.07 ============================== end of proof ==========================
% 157.74/158.07
% 157.74/158.07 ============================== STATISTICS ============================
% 157.74/158.07
% 157.74/158.07 Given=7442. Generated=8025139. Kept=41428. proofs=1.
% 157.74/158.07 Usable=1774. Sos=3906. Demods=21. Limbo=921, Disabled=34856. Hints=0.
% 157.74/158.07 Megabytes=34.98.
% 157.74/158.07 User_CPU=152.77, System_CPU=4.33, Wall_clock=157.
% 157.74/158.07
% 157.74/158.07 ============================== end of statistics =====================
% 157.74/158.07
% 157.74/158.07 ============================== end of search =========================
% 157.74/158.07
% 157.74/158.07 THEOREM PROVED
% 157.74/158.07 % SZS status Unsatisfiable
% 157.74/158.07
% 157.74/158.07 Exiting with 1 proof.
% 157.74/158.07
% 157.74/158.07 Process 19622 exit (max_proofs) Mon Jun 13 14:45:45 2022
% 157.82/158.07 Prover9 interrupted
%------------------------------------------------------------------------------