TSTP Solution File: GRP358-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP358-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 11:18:45 EDT 2022
% Result : Unsatisfiable 29.37s 29.63s
% Output : Refutation 29.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP358-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 22:44:24 EDT 2022
% 0.15/0.37 % CPUTime :
% 29.37/29.63 ============================== Prover9 ===============================
% 29.37/29.63 Prover9 (32) version 2009-11A, November 2009.
% 29.37/29.63 Process 23448 was started by sandbox2 on n005.cluster.edu,
% 29.37/29.63 Mon Jun 13 22:44:24 2022
% 29.37/29.63 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23295_n005.cluster.edu".
% 29.37/29.63 ============================== end of head ===========================
% 29.37/29.63
% 29.37/29.63 ============================== INPUT =================================
% 29.37/29.63
% 29.37/29.63 % Reading from file /tmp/Prover9_23295_n005.cluster.edu
% 29.37/29.63
% 29.37/29.63 set(prolog_style_variables).
% 29.37/29.63 set(auto2).
% 29.37/29.63 % set(auto2) -> set(auto).
% 29.37/29.63 % set(auto) -> set(auto_inference).
% 29.37/29.63 % set(auto) -> set(auto_setup).
% 29.37/29.63 % set(auto_setup) -> set(predicate_elim).
% 29.37/29.63 % set(auto_setup) -> assign(eq_defs, unfold).
% 29.37/29.63 % set(auto) -> set(auto_limits).
% 29.37/29.63 % set(auto_limits) -> assign(max_weight, "100.000").
% 29.37/29.63 % set(auto_limits) -> assign(sos_limit, 20000).
% 29.37/29.63 % set(auto) -> set(auto_denials).
% 29.37/29.63 % set(auto) -> set(auto_process).
% 29.37/29.63 % set(auto2) -> assign(new_constants, 1).
% 29.37/29.63 % set(auto2) -> assign(fold_denial_max, 3).
% 29.37/29.63 % set(auto2) -> assign(max_weight, "200.000").
% 29.37/29.63 % set(auto2) -> assign(max_hours, 1).
% 29.37/29.63 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 29.37/29.63 % set(auto2) -> assign(max_seconds, 0).
% 29.37/29.63 % set(auto2) -> assign(max_minutes, 5).
% 29.37/29.63 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 29.37/29.63 % set(auto2) -> set(sort_initial_sos).
% 29.37/29.63 % set(auto2) -> assign(sos_limit, -1).
% 29.37/29.63 % set(auto2) -> assign(lrs_ticks, 3000).
% 29.37/29.63 % set(auto2) -> assign(max_megs, 400).
% 29.37/29.63 % set(auto2) -> assign(stats, some).
% 29.37/29.63 % set(auto2) -> clear(echo_input).
% 29.37/29.63 % set(auto2) -> set(quiet).
% 29.37/29.63 % set(auto2) -> clear(print_initial_clauses).
% 29.37/29.63 % set(auto2) -> clear(print_given).
% 29.37/29.63 assign(lrs_ticks,-1).
% 29.37/29.63 assign(sos_limit,10000).
% 29.37/29.63 assign(order,kbo).
% 29.37/29.63 set(lex_order_vars).
% 29.37/29.63 clear(print_given).
% 29.37/29.63
% 29.37/29.63 % formulas(sos). % not echoed (34 formulas)
% 29.37/29.63
% 29.37/29.63 ============================== end of input ==========================
% 29.37/29.63
% 29.37/29.63 % From the command line: assign(max_seconds, 300).
% 29.37/29.63
% 29.37/29.63 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 29.37/29.63
% 29.37/29.63 % Formulas that are not ordinary clauses:
% 29.37/29.63
% 29.37/29.63 ============================== end of process non-clausal formulas ===
% 29.37/29.63
% 29.37/29.63 ============================== PROCESS INITIAL CLAUSES ===============
% 29.37/29.63
% 29.37/29.63 ============================== PREDICATE ELIMINATION =================
% 29.37/29.63
% 29.37/29.63 ============================== end predicate elimination =============
% 29.37/29.63
% 29.37/29.63 Auto_denials: (non-Horn, no changes).
% 29.37/29.63
% 29.37/29.63 Term ordering decisions:
% 29.37/29.63
% 29.37/29.63 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 29.37/29.63 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.
% 29.37/29.63
% 29.37/29.63 ============================== end of process initial clauses ========
% 29.37/29.63
% 29.37/29.63 ============================== CLAUSES FOR SEARCH ====================
% 29.37/29.63
% 29.37/29.63 ============================== end of clauses for search =============
% 29.37/29.63
% 29.37/29.63 ============================== SEARCH ================================
% 29.37/29.63
% 29.37/29.63 % Starting search at 0.02 seconds.
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=56.000, iters=3633
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=52.000, iters=3597
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=48.000, iters=3445
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=46.000, iters=3415
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=45.000, iters=3389
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=43.000, iters=3366
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=39.000, iters=3454
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=38.000, iters=3431
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=37.000, iters=3375
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=36.000, iters=3363
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=35.000, iters=3333
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=34.000, iters=3380
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=33.000, iters=3361
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=32.000, iters=3400
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=31.000, iters=3433
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=30.000, iters=3366
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=29.000, iters=3433
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=28.000, iters=3360
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=19.000, iters=3345
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=16.000, iters=3409
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=15.000, iters=3974
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=14.000, iters=3481
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=13.000, iters=3336
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=12.000, iters=3375
% 29.37/29.63
% 29.37/29.63 Low Water (keep): wt=11.000, iters=3606
% 29.37/29.63
% 29.37/29.63 ============================== PROOF =================================
% 29.37/29.63 % SZS status Unsatisfiable
% 29.37/29.63 % SZS output start Refutation
% 29.37/29.63
% 29.37/29.63 % Proof 1 at 27.79 (+ 0.78) seconds.
% 29.37/29.63 % Length of proof is 174.
% 29.37/29.63 % Level of proof is 40.
% 29.37/29.63 % Maximum clause weight is 50.000.
% 29.37/29.63 % Given clauses 5139.
% 29.37/29.63
% 29.37/29.63 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 29.37/29.63 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 29.37/29.63 3 inverse(sk_c8) = sk_c6 | inverse(sk_c3) = sk_c8 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 29.37/29.63 4 inverse(sk_c8) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 29.37/29.63 5 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = sk_c6 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 29.37/29.63 6 inverse(sk_c1) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 29.37/29.63 7 inverse(sk_c1) = sk_c8 | inverse(sk_c4) = sk_c7 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 29.37/29.63 8 inverse(sk_c1) = sk_c8 | inverse(sk_c5) = sk_c6 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 29.37/29.63 10 multiply(sk_c7,sk_c6) = sk_c8 | inverse(sk_c4) = sk_c7 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 29.37/29.63 12 inverse(sk_c8) = sk_c6 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 29.37/29.63 13 inverse(sk_c8) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 29.37/29.63 14 inverse(sk_c8) = sk_c6 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 29.37/29.63 15 multiply(sk_c8,sk_c2) = sk_c7 | inverse(sk_c3) = sk_c8 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 29.37/29.63 16 multiply(sk_c8,sk_c2) = sk_c7 | inverse(sk_c4) = sk_c7 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 29.37/29.63 17 multiply(sk_c8,sk_c2) = sk_c7 | inverse(sk_c5) = sk_c6 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 29.37/29.63 18 multiply(sk_c1,sk_c8) = sk_c2 | inverse(sk_c3) = sk_c8 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 29.37/29.63 19 multiply(sk_c1,sk_c8) = sk_c2 | inverse(sk_c4) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 29.37/29.63 20 multiply(sk_c1,sk_c8) = sk_c2 | inverse(sk_c5) = sk_c6 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 29.37/29.63 21 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 29.37/29.63 22 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 29.37/29.63 23 inverse(sk_c1) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 29.37/29.63 24 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 29.37/29.63 25 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 29.37/29.63 26 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 29.37/29.63 28 multiply(sk_c8,sk_c2) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 29.37/29.63 31 multiply(sk_c1,sk_c8) = sk_c2 | multiply(sk_c4,sk_c7) = sk_c6 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 29.37/29.63 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 29.37/29.63 34 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | 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_31) # label(negated_conjecture). [assumption].
% 29.37/29.63 48 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 29.37/29.63 49 inverse(sk_c8) = sk_c6 | multiply(sk_c7,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 29.37/29.63 50 inverse(sk_c8) = sk_c6 | multiply(sk_c6,sk_c5) = identity. [para(5(b,1),2(a,1,1))].
% 29.37/29.63 54 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 29.37/29.63 64 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c6). [para(13(b,1),33(a,2,2)),rewrite([33(8)])].
% 29.37/29.63 65 inverse(sk_c8) = sk_c6 | multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(14(b,1),33(a,1,1)),flip(b)].
% 29.37/29.63 69 inverse(sk_c4) = sk_c7 | multiply(sk_c8,multiply(sk_c2,A)) = multiply(sk_c7,A). [para(16(a,1),33(a,1,1)),flip(b)].
% 29.37/29.63 71 inverse(sk_c5) = sk_c6 | multiply(sk_c8,multiply(sk_c2,A)) = multiply(sk_c7,A). [para(17(a,1),33(a,1,1)),flip(b)].
% 29.37/29.63 74 inverse(sk_c3) = sk_c8 | multiply(A,multiply(sk_c1,sk_c8)) = multiply(A,sk_c2). [para(18(a,1),33(a,2,2)),rewrite([33(8)])].
% 29.37/29.63 75 inverse(sk_c4) = sk_c7 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c2,A). [para(19(a,1),33(a,1,1)),flip(b)].
% 29.37/29.63 80 inverse(sk_c1) = sk_c8 | multiply(A,multiply(sk_c3,sk_c8)) = multiply(A,sk_c7). [para(21(b,1),33(a,2,2)),rewrite([33(8)])].
% 29.37/29.63 82 inverse(sk_c1) = sk_c8 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c6). [para(22(b,1),33(a,2,2)),rewrite([33(8)])].
% 29.37/29.63 83 inverse(sk_c1) = sk_c8 | multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(23(b,1),33(a,1,1)),flip(b)].
% 29.37/29.63 85 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c3,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(24(b,1),33(a,1,1)),flip(b)].
% 29.37/29.63 89 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(26(b,1),33(a,1,1)),flip(b)].
% 29.37/29.63 118 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(A,sk_c8)) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c8) != sk_c7 | inverse(B) != sk_c8 | multiply(C,sk_c7) != sk_c6 | inverse(C) != sk_c7 | inverse(D) != sk_c6 | multiply(D,sk_c8) != sk_c6. [resolve(34,d,1,a(flip)),rewrite([1(14)])].
% 29.37/29.63 540 inverse(sk_c8) = sk_c6 | multiply(sk_c8,multiply(sk_c3,A)) = A. [para(48(b,1),33(a,1,1)),rewrite([1(6)]),flip(b)].
% 29.37/29.63 541 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c8,sk_c3)) = multiply(A,identity). [para(48(b,1),33(a,2,2)),rewrite([33(8)])].
% 29.37/29.63 573 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),54(a,1,2))].
% 29.37/29.63 578 inverse(sk_c1) = sk_c8 | multiply(sk_c6,multiply(sk_c5,A)) = A. [para(8(b,1),54(a,1,1))].
% 29.37/29.63 584 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c5),sk_c6) = sk_c8. [para(14(b,1),54(a,1,2))].
% 29.37/29.63 593 inverse(sk_c1) = sk_c8 | multiply(inverse(sk_c5),sk_c6) = sk_c8. [para(23(b,1),54(a,1,2))].
% 29.37/29.63 594 multiply(sk_c7,sk_c6) = sk_c8 | multiply(inverse(sk_c3),sk_c7) = sk_c8. [para(24(b,1),54(a,1,2))].
% 29.37/29.63 604 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c8),identity) = sk_c3. [para(48(b,1),54(a,1,2))].
% 29.37/29.63 605 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(54(a,1),54(a,1,2))].
% 29.37/29.63 606 multiply(A,identity) = A. [back_rewrite(573),rewrite([605(4)])].
% 29.37/29.63 607 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c3. [back_rewrite(604),rewrite([606(8)])].
% 29.37/29.63 608 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c8,sk_c3)) = A. [back_rewrite(541),rewrite([606(10)])].
% 29.37/29.63 613 inverse(identity) = identity. [para(606(a,1),2(a,1))].
% 29.37/29.63 685 inverse(sk_c8) = sk_c6 | multiply(sk_c3,sk_c8) = identity. [para(607(b,1),2(a,1,1))].
% 29.37/29.63 688 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = sk_c4. [para(49(b,1),54(a,1,2)),rewrite([606(8)])].
% 29.37/29.63 695 inverse(sk_c8) = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(688(b,1),2(a,1,1))].
% 29.37/29.63 698 inverse(sk_c8) = sk_c6 | inverse(sk_c6) = sk_c5. [para(50(b,1),54(a,1,2)),rewrite([606(8)])].
% 29.37/29.63 699 inverse(sk_c8) = sk_c6 | multiply(sk_c5,sk_c6) = identity. [para(698(b,1),2(a,1,1))].
% 29.37/29.63 760 multiply(A,inverse(A)) = identity. [para(605(a,1),2(a,1))].
% 29.37/29.63 800 multiply(A,multiply(inverse(A),B)) = B. [para(605(a,1),54(a,1))].
% 29.37/29.63 801 inverse(inverse(A)) = A. [para(605(a,1),606(a,1)),rewrite([606(2)]),flip(a)].
% 29.37/29.63 868 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c8) = identity. [para(6(b,1),760(a,1,2))].
% 29.37/29.63 869 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c7) = identity. [para(7(b,1),760(a,1,2))].
% 29.37/29.63 870 inverse(sk_c1) = sk_c8 | multiply(sk_c5,sk_c6) = identity. [para(8(b,1),760(a,1,2))].
% 29.37/29.63 871 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(760(a,1),33(a,1)),flip(a)].
% 29.37/29.63 948 inverse(sk_c8) = sk_c6 | identity = sk_c7. [para(685(b,1),12(b,1)),merge(b)].
% 29.37/29.63 1022 inverse(sk_c8) = sk_c6 | identity = sk_c6. [para(695(b,1),13(b,1)),merge(b)].
% 29.37/29.63 1215 inverse(sk_c1) = sk_c8 | identity = sk_c7. [para(868(b,1),21(b,1)),merge(b)].
% 29.37/29.63 1229 identity = sk_c7 | inverse(sk_c8) = sk_c1. [para(1215(a,1),801(a,1,1))].
% 29.37/29.63 1232 identity = sk_c7 | sk_c1 = sk_c6. [para(1229(b,1),948(a,1)),merge(c)].
% 29.37/29.63 1569 inverse(sk_c1) = sk_c8 | identity = sk_c6. [para(869(b,1),22(b,1)),merge(b)].
% 29.37/29.63 1577 inverse(sk_c8) = sk_c6 | multiply(A,sk_c6) = A. [para(695(b,1),64(b,1,2)),rewrite([606(10)]),flip(c),merge(b)].
% 29.37/29.63 1656 identity = sk_c6 | inverse(sk_c8) = sk_c1. [para(1569(a,1),801(a,1,1))].
% 29.37/29.63 1657 identity = sk_c6 | multiply(sk_c1,sk_c8) = identity. [para(1569(a,1),760(a,1,2))].
% 29.37/29.63 1659 identity = sk_c6 | sk_c1 = sk_c6. [para(1656(b,1),1022(a,1)),merge(c)].
% 29.37/29.63 1665 sk_c1 = sk_c6 | inverse(sk_c6) = identity. [para(1659(a,1),613(a,1,1))].
% 29.37/29.63 1690 inverse(sk_c8) = sk_c6 | multiply(sk_c6,sk_c3) = sk_c5. [para(48(b,1),65(b,1,2)),rewrite([606(11)]),flip(c),merge(b)].
% 29.37/29.63 1737 sk_c1 = sk_c6 | inverse(sk_c6) = sk_c7. [para(1232(a,1),1665(b,2)),merge(b)].
% 29.37/29.63 1817 identity = sk_c6 | multiply(A,multiply(sk_c1,sk_c8)) = A. [para(1657(b,1),33(a,2,2)),rewrite([33(7),606(9)])].
% 29.37/29.63 2280 inverse(sk_c4) = sk_c7 | multiply(sk_c8,multiply(sk_c2,sk_c6)) = sk_c8. [para(10(a,1),69(b,2)),merge(b)].
% 29.37/29.63 2506 inverse(sk_c5) = sk_c6 | multiply(sk_c7,inverse(sk_c2)) = sk_c8. [para(760(a,1),71(b,1,2)),rewrite([606(7)]),flip(b)].
% 29.37/29.63 3000 inverse(sk_c3) = sk_c8 | multiply(sk_c8,multiply(sk_c1,sk_c8)) = sk_c7. [para(15(a,1),74(b,2)),merge(b)].
% 29.37/29.63 3098 inverse(sk_c8) = sk_c6 | inverse(sk_c6) = identity. [para(1577(b,1),2(a,1))].
% 29.37/29.63 3101 inverse(sk_c8) = sk_c6 | identity = sk_c5. [para(1577(b,1),699(b,1)),flip(c),merge(b)].
% 29.37/29.63 3133 inverse(sk_c8) = sk_c6 | multiply(sk_c6,A) = A. [para(3098(b,1),54(a,1,1)),rewrite([1(8)])].
% 29.37/29.63 3140 inverse(sk_c4) = sk_c7 | multiply(inverse(sk_c1),multiply(sk_c2,A)) = multiply(sk_c8,A). [para(75(b,1),54(a,1,2))].
% 29.37/29.63 3284 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c3. [para(1690(b,1),54(a,1,2))].
% 29.38/29.63 4306 inverse(sk_c1) = sk_c8 | multiply(A,sk_c7) = A. [para(868(b,1),80(b,1,2)),rewrite([606(10)]),flip(c),merge(b)].
% 29.38/29.63 4400 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c6),A) = A. [para(3133(b,1),54(a,1,2))].
% 29.38/29.63 4628 inverse(sk_c1) = sk_c8 | multiply(A,sk_c6) = A. [para(869(b,1),82(b,1,2)),rewrite([606(10)]),flip(c),merge(b)].
% 29.38/29.63 5229 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c7,inverse(sk_c8)) = sk_c3. [para(760(a,1),85(b,1,2)),rewrite([606(8)]),flip(b)].
% 29.38/29.63 5828 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c6,inverse(sk_c8)) = sk_c5. [para(760(a,1),89(b,1,2)),rewrite([606(8)]),flip(b)].
% 29.38/29.63 6775 inverse(sk_c1) = sk_c8 | identity = sk_c5. [para(4628(b,1),870(b,1)),flip(c),merge(b)].
% 29.38/29.63 6869 identity = sk_c5 | inverse(sk_c8) = sk_c1. [para(6775(a,1),801(a,1,1))].
% 29.38/29.63 6878 identity = sk_c5 | sk_c1 = sk_c6. [para(6869(b,1),3101(a,1)),merge(c)].
% 29.38/29.63 6901 sk_c1 = sk_c6 | sk_c5 = sk_c6. [para(6878(a,1),1659(a,1)),merge(c)].
% 29.38/29.63 8667 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(A,sk_c8)) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c8) != sk_c7 | inverse(B) != sk_c8 | identity != sk_c6 | inverse(C) != sk_c6 | multiply(C,sk_c8) != sk_c6. [para(2(a,1),118(g,1)),rewrite([801(31)]),xx(h)].
% 29.38/29.63 8676 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(A,sk_c8)) != sk_c7 | inverse(A) != sk_c8 | multiply(A,sk_c8) != sk_c7 | identity != sk_c6 | inverse(B) != sk_c6 | multiply(B,sk_c8) != sk_c6. [factor(8667,d,f)].
% 29.38/29.63 9195 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(A,sk_c8)) != sk_c7 | inverse(A) != sk_c8 | multiply(A,sk_c8) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [para(1(a,1),8676(h,1)),rewrite([613(27)]),flip(h),merge(g)].
% 29.38/29.63 9197 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(A,multiply(B,sk_c8))) != sk_c7 | inverse(multiply(A,B)) != sk_c8 | multiply(A,multiply(B,sk_c8)) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [para(33(a,1),9195(c,1,2)),rewrite([33(23)])].
% 29.38/29.63 9363 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,A) != sk_c7 | inverse(multiply(A,inverse(sk_c8))) != sk_c8 | sk_c7 != A | identity != sk_c6 | sk_c6 != sk_c8. [para(2(a,1),9197(c,1,2,2)),rewrite([606(12),2(23),606(21)]),flip(e)].
% 29.38/29.63 9403 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(A,B)) != sk_c7 | inverse(multiply(A,multiply(B,inverse(sk_c8)))) != sk_c8 | multiply(A,B) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [para(33(a,1),9363(d,1,1)),flip(e)].
% 29.38/29.63 9434 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = sk_c8. [para(584(b,1),1577(b,1)),flip(c),merge(b)].
% 29.38/29.63 9444 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c5. [para(9434(b,1),801(a,1,1))].
% 29.38/29.63 9485 sk_c1 = sk_c6 | inverse(sk_c8) = sk_c6. [para(6901(b,1),9444(b,2)),merge(c)].
% 29.38/29.63 9488 sk_c1 = sk_c6 | inverse(sk_c6) = sk_c8. [para(9485(b,1),801(a,1,1))].
% 29.38/29.63 9494 sk_c1 = sk_c6 | sk_c7 = sk_c8. [para(9488(b,1),1737(b,1)),flip(c),merge(b)].
% 29.38/29.63 11230 inverse(sk_c1) = sk_c8 | inverse(sk_c5) = sk_c8. [para(593(b,1),4628(b,1)),flip(c),merge(b)].
% 29.38/29.63 11231 inverse(sk_c1) = sk_c8 | multiply(sk_c8,sk_c5) = identity. [para(11230(b,1),2(a,1,1))].
% 29.38/29.63 12188 inverse(sk_c1) = sk_c8 | multiply(sk_c6,sk_c5) = sk_c5. [para(11231(b,1),83(b,1,2)),rewrite([606(11)]),flip(c),merge(b)].
% 29.38/29.63 12542 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(871(a,1),54(a,1,2)),rewrite([606(3)]),flip(a)].
% 29.38/29.63 12945 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(12542(a,1),54(a,1,2)),flip(a)].
% 29.38/29.63 13773 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(A,B)) != sk_c7 | multiply(sk_c8,multiply(inverse(B),inverse(A))) != sk_c8 | multiply(A,B) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [back_rewrite(9403),rewrite([12945(19),12945(18),801(17),33(19)])].
% 29.38/29.63 15365 identity = sk_c6 | multiply(inverse(sk_c8),inverse(sk_c1)) = identity. [para(1817(b,1),2(a,1)),rewrite([12945(7)])].
% 29.38/29.63 15372 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(inverse(A),B)) != sk_c7 | multiply(sk_c8,multiply(inverse(B),A)) != sk_c8 | multiply(inverse(A),B) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [para(801(a,1),13773(d,1,2,2))].
% 29.38/29.63 15379 inverse(sk_c5) = sk_c6 | multiply(inverse(sk_c7),sk_c8) = inverse(sk_c2). [para(2506(b,1),54(a,1,2))].
% 29.38/29.63 15648 inverse(sk_c8) = sk_c6 | multiply(sk_c5,A) = A. [para(698(b,1),4400(b,1,1)),merge(b)].
% 29.38/29.63 16010 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(inverse(A),sk_c8)) != sk_c7 | sk_c8 != A | multiply(inverse(A),sk_c8) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [para(800(a,1),15372(d,1)),flip(d)].
% 29.38/29.63 17638 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(inverse(A),multiply(inverse(B),sk_c8))) != sk_c7 | multiply(B,A) != sk_c8 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [para(12945(a,1),16010(c,1,2,1)),rewrite([33(15),12945(23),33(26)]),flip(d)].
% 29.38/29.63 17828 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8))) != sk_c7 | multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8)) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [factor(17638,a,d)].
% 29.38/29.63 18304 inverse(sk_c1) = sk_c8 | multiply(sk_c6,sk_c5) = sk_c7. [para(4306(b,1),578(b,1,2)),merge(b)].
% 29.38/29.63 18333 multiply(sk_c7,sk_c6) = sk_c8 | multiply(inverse(sk_c7),sk_c3) = inverse(sk_c8). [para(594(b,1),12945(a,1,1)),rewrite([801(12)]),flip(b)].
% 29.38/29.63 18378 inverse(sk_c1) = sk_c8 | sk_c5 = sk_c7. [para(18304(b,1),12188(b,1)),flip(c),merge(b)].
% 29.38/29.63 18383 sk_c5 = sk_c7 | multiply(sk_c1,sk_c8) = identity. [para(18378(a,1),760(a,1,2))].
% 29.38/29.63 18411 sk_c5 = sk_c7 | identity = sk_c2 | inverse(sk_c5) = sk_c6. [para(18383(b,1),20(a,1))].
% 29.38/29.63 18488 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c3) = sk_c5. [para(608(b,1),15648(b,1)),flip(c),merge(b)].
% 29.38/29.63 18508 inverse(sk_c8) = sk_c6 | multiply(A,sk_c5) = A. [para(18488(b,1),608(b,1,2)),merge(b)].
% 29.38/29.63 18576 inverse(sk_c8) = sk_c6 | inverse(sk_c6) = sk_c3. [para(18508(b,1),3284(b,1)),merge(b)].
% 29.38/29.63 18584 inverse(sk_c8) = sk_c6 | multiply(sk_c3,A) = A. [para(18576(b,1),4400(b,1,1)),merge(b)].
% 29.38/29.63 18713 inverse(sk_c8) = sk_c6 | multiply(sk_c8,A) = A. [para(18584(b,1),540(b,1,2)),merge(b)].
% 29.38/29.63 18762 inverse(sk_c8) = sk_c6 | multiply(A,sk_c3) = A. [para(18713(b,1),608(b,1,2)),merge(b)].
% 29.38/29.63 18829 inverse(sk_c8) = sk_c6 | multiply(A,sk_c8) = A. [para(18762(b,1),608(b,1,2)),merge(b)].
% 29.38/29.63 18906 inverse(sk_c8) = sk_c6 | inverse(sk_c6) = sk_c8. [para(18829(b,1),4400(b,1)),merge(b)].
% 29.38/29.63 18917 inverse(sk_c8) = sk_c6. [para(18906(b,1),801(a,1,1)),merge(b)].
% 29.38/29.63 19158 multiply(sk_c7,sk_c6) = sk_c8 | multiply(inverse(sk_c7),sk_c3) = sk_c6. [back_rewrite(18333),rewrite([18917(11)])].
% 29.38/29.63 19501 multiply(sk_c7,sk_c6) != sk_c8 | multiply(sk_c8,multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8))) != sk_c7 | multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8)) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [back_rewrite(17828),rewrite([18917(7)]),xx(b)].
% 29.38/29.63 20276 identity = sk_c6 | multiply(sk_c6,inverse(sk_c1)) = identity. [back_rewrite(15365),rewrite([18917(5)])].
% 29.38/29.63 21304 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c6,sk_c6) = sk_c5. [back_rewrite(5828),rewrite([18917(8)])].
% 29.38/29.63 21309 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c7,sk_c6) = sk_c3. [back_rewrite(5229),rewrite([18917(8)])].
% 29.38/29.63 21785 multiply(sk_c6,sk_c8) = identity. [para(18917(a,1),2(a,1,1))].
% 29.38/29.63 21787 inverse(sk_c6) = sk_c8. [para(18917(a,1),801(a,1,1))].
% 29.38/29.63 21788 multiply(sk_c8,sk_c6) = identity. [para(18917(a,1),760(a,1,2))].
% 29.38/29.63 21837 multiply(sk_c7,sk_c6) != sk_c8 | multiply(sk_c8,multiply(sk_c8,multiply(inverse(sk_c7),sk_c8))) != sk_c7 | multiply(sk_c8,multiply(inverse(sk_c7),sk_c8)) != sk_c7 | identity != sk_c6 | sk_c6 != sk_c8. [back_rewrite(19501),rewrite([21787(8),21787(17)])].
% 29.38/29.63 25200 inverse(sk_c4) = sk_c7 | multiply(sk_c2,sk_c6) = identity. [para(2280(b,1),54(a,1,2)),rewrite([18917(6),21785(7)]),flip(b)].
% 29.38/29.63 25695 sk_c7 = sk_c8 | inverse(sk_c3) = sk_c8. [para(9494(a,1),3000(b,1,2,1)),rewrite([21785(11),606(10)]),flip(c),merge(c)].
% 29.38/29.63 25700 sk_c7 = sk_c8 | multiply(sk_c8,sk_c3) = identity. [para(25695(b,1),2(a,1,1))].
% 29.38/29.63 25894 inverse(sk_c4) = sk_c7 | inverse(sk_c1) = identity. [para(25200(b,1),3140(b,1,2)),rewrite([606(12),21788(13)]),merge(b)].
% 29.38/29.63 25972 inverse(sk_c1) = identity | inverse(sk_c7) = sk_c4. [para(25894(a,1),801(a,1,1))].
% 29.38/29.63 26067 inverse(sk_c7) = sk_c4 | identity = sk_c6. [para(25972(a,1),20276(b,1,2)),rewrite([606(10)]),flip(c),merge(c)].
% 29.38/29.63 26068 identity = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(26067(a,1),2(a,1,1))].
% 29.38/29.63 26087 identity = sk_c6 | multiply(sk_c7,sk_c6) = sk_c8. [para(26068(b,1),25(b,1)),merge(c)].
% 29.38/29.63 26088 identity = sk_c6 | multiply(sk_c8,sk_c2) = sk_c7. [para(26068(b,1),28(b,1)),merge(c)].
% 29.38/29.63 26089 identity = sk_c6 | multiply(sk_c1,sk_c8) = sk_c2. [para(26068(b,1),31(b,1)),merge(c)].
% 29.38/29.63 26106 identity = sk_c6 | multiply(sk_c8,inverse(sk_c7)) = sk_c6. [para(26087(b,1),12945(a,1,1)),rewrite([18917(5),21787(6)]),flip(b)].
% 29.38/29.63 26115 identity = sk_c6 | multiply(A,sk_c2) = A. [para(26089(b,1),1817(b,1,2)),merge(b)].
% 29.38/29.63 26147 identity = sk_c6 | sk_c7 = sk_c8. [para(26115(b,1),26088(b,1)),flip(c),merge(b)].
% 29.38/29.63 26149 sk_c7 = sk_c8 | multiply(A,sk_c6) = A. [para(26147(a,1),606(a,1,2))].
% 29.38/29.63 26150 sk_c7 = sk_c8 | identity = sk_c8. [para(26147(a,1),613(a,1,1)),rewrite([21787(5)]),flip(b)].
% 29.38/29.63 26159 sk_c7 = sk_c8 | multiply(sk_c8,A) = A. [para(26150(b,1),1(a,1,1))].
% 29.38/29.63 26295 sk_c7 = sk_c8 | identity = sk_c3. [para(26159(b,1),25700(b,1)),flip(c),merge(b)].
% 29.38/29.63 26305 sk_c7 = sk_c8 | inverse(sk_c3) = identity. [para(26295(b,1),613(a,1,1))].
% 29.38/29.63 26324 sk_c7 = sk_c8 | multiply(sk_c7,sk_c6) = sk_c8. [para(26305(b,1),594(b,1,1)),rewrite([1(11)]),merge(c)].
% 29.38/29.63 26504 sk_c7 = sk_c8. [para(26324(b,1),26149(b,1)),flip(c),merge(b),merge(c)].
% 29.38/29.63 26599 identity = sk_c6. [back_rewrite(26106),rewrite([26504(5),18917(6),21788(6)]),merge(b)].
% 29.38/29.63 27412 sk_c6 != sk_c8. [back_rewrite(21837),rewrite([26504(1),21788(3),26599(1),26504(6),18917(7),21785(8),26599(6),21788(7),26599(5),21788(6),26599(4),26504(5),26504(8),18917(9),21785(10),26599(8),21788(9),26599(7),26504(8),26599(10)]),xx(d),merge(b),merge(c),merge(d)].
% 29.38/29.63 27416 sk_c3 = sk_c6. [back_rewrite(21309),rewrite([26504(1),21788(3),26599(1),26504(4),21788(6),26599(4)]),flip(b),unit_del(a,27412)].
% 29.38/29.63 27417 multiply(sk_c6,sk_c6) = sk_c5. [back_rewrite(21304),rewrite([26504(1),21788(3),26599(1)]),unit_del(a,27412)].
% 29.38/29.63 27419 sk_c5 = sk_c6. [back_rewrite(19158),rewrite([26504(1),21788(3),26599(1),26504(4),18917(5),27416(5),27417(6)]),unit_del(a,27412)].
% 29.38/29.63 27422 sk_c2 = sk_c6. [back_rewrite(18411),rewrite([27419(1),26504(2),26599(4),27419(7),21787(8)]),flip(b),flip(c),merge(c),unit_del(a,27412)].
% 29.38/29.63 27431 $F. [back_rewrite(15379),rewrite([27419(1),21787(2),26504(4),18917(5),21785(6),26599(4),27422(5),21787(6)]),flip(a),merge(b),unit_del(a,27412)].
% 29.38/29.63
% 29.38/29.63 % SZS output end Refutation
% 29.38/29.63 ============================== end of proof ==========================
% 29.38/29.63
% 29.38/29.63 ============================== STATISTICS ============================
% 29.38/29.63
% 29.38/29.63 Given=5139. Generated=1396082. Kept=27430. proofs=1.
% 29.38/29.63 Usable=1462. Sos=3113. Demods=36. Limbo=927, Disabled=21962. Hints=0.
% 29.38/29.63 Megabytes=23.08.
% 29.38/29.63 User_CPU=27.79, System_CPU=0.78, Wall_clock=29.
% 29.38/29.63
% 29.38/29.63 ============================== end of statistics =====================
% 29.38/29.63
% 29.38/29.63 ============================== end of search =========================
% 29.38/29.63
% 29.38/29.63 THEOREM PROVED
% 29.38/29.63 % SZS status Unsatisfiable
% 29.38/29.63
% 29.38/29.63 Exiting with 1 proof.
% 29.38/29.63
% 29.38/29.63 Process 23448 exit (max_proofs) Mon Jun 13 22:44:53 2022
% 29.38/29.63 Prover9 interrupted
%------------------------------------------------------------------------------