TSTP Solution File: GRP306-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP306-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:18:34 EDT 2022
% Result : Unsatisfiable 36.03s 36.30s
% Output : Refutation 36.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP306-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 15:04:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.30/3.61 ============================== Prover9 ===============================
% 3.30/3.61 Prover9 (32) version 2009-11A, November 2009.
% 3.30/3.61 Process 19677 was started by sandbox on n014.cluster.edu,
% 3.30/3.61 Mon Jun 13 15:04:52 2022
% 3.30/3.61 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19523_n014.cluster.edu".
% 3.30/3.61 ============================== end of head ===========================
% 3.30/3.61
% 3.30/3.61 ============================== INPUT =================================
% 3.30/3.61
% 3.30/3.61 % Reading from file /tmp/Prover9_19523_n014.cluster.edu
% 3.30/3.61
% 3.30/3.61 set(prolog_style_variables).
% 3.30/3.61 set(auto2).
% 3.30/3.61 % set(auto2) -> set(auto).
% 3.30/3.61 % set(auto) -> set(auto_inference).
% 3.30/3.61 % set(auto) -> set(auto_setup).
% 3.30/3.61 % set(auto_setup) -> set(predicate_elim).
% 3.30/3.61 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.30/3.61 % set(auto) -> set(auto_limits).
% 3.30/3.61 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.30/3.61 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.30/3.61 % set(auto) -> set(auto_denials).
% 3.30/3.61 % set(auto) -> set(auto_process).
% 3.30/3.61 % set(auto2) -> assign(new_constants, 1).
% 3.30/3.61 % set(auto2) -> assign(fold_denial_max, 3).
% 3.30/3.61 % set(auto2) -> assign(max_weight, "200.000").
% 3.30/3.61 % set(auto2) -> assign(max_hours, 1).
% 3.30/3.61 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.30/3.61 % set(auto2) -> assign(max_seconds, 0).
% 3.30/3.61 % set(auto2) -> assign(max_minutes, 5).
% 3.30/3.61 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.30/3.61 % set(auto2) -> set(sort_initial_sos).
% 3.30/3.61 % set(auto2) -> assign(sos_limit, -1).
% 3.30/3.61 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.30/3.61 % set(auto2) -> assign(max_megs, 400).
% 3.30/3.61 % set(auto2) -> assign(stats, some).
% 3.30/3.61 % set(auto2) -> clear(echo_input).
% 3.30/3.61 % set(auto2) -> set(quiet).
% 3.30/3.61 % set(auto2) -> clear(print_initial_clauses).
% 3.30/3.61 % set(auto2) -> clear(print_given).
% 3.30/3.61 assign(lrs_ticks,-1).
% 3.30/3.61 assign(sos_limit,10000).
% 3.30/3.61 assign(order,kbo).
% 3.30/3.61 set(lex_order_vars).
% 3.30/3.61 clear(print_given).
% 3.30/3.61
% 3.30/3.61 % formulas(sos). % not echoed (25 formulas)
% 3.30/3.61
% 3.30/3.61 ============================== end of input ==========================
% 3.30/3.61
% 3.30/3.61 % From the command line: assign(max_seconds, 300).
% 3.30/3.61
% 3.30/3.61 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.30/3.61
% 3.30/3.61 % Formulas that are not ordinary clauses:
% 3.30/3.61
% 3.30/3.61 ============================== end of process non-clausal formulas ===
% 3.30/3.61
% 3.30/3.61 ============================== PROCESS INITIAL CLAUSES ===============
% 3.30/3.61
% 3.30/3.61 ============================== PREDICATE ELIMINATION =================
% 3.30/3.61
% 3.30/3.61 ============================== end predicate elimination =============
% 3.30/3.61
% 3.30/3.61 Auto_denials: (non-Horn, no changes).
% 3.30/3.61
% 3.30/3.61 Term ordering decisions:
% 3.30/3.61
% 3.30/3.61 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 3.30/3.61 Function symbol KB weights: sk_c8=1. sk_c2=1. sk_c7=1. sk_c1=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c6=1. identity=1. multiply=1. inverse=0.
% 3.30/3.61
% 3.30/3.61 ============================== end of process initial clauses ========
% 3.30/3.61
% 3.30/3.61 ============================== CLAUSES FOR SEARCH ====================
% 3.30/3.61
% 3.30/3.61 ============================== end of clauses for search =============
% 3.30/3.61
% 3.30/3.61 ============================== SEARCH ================================
% 3.30/3.61
% 3.30/3.61 % Starting search at 0.02 seconds.
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=46.000, iters=3427
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=45.000, iters=3380
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=42.000, iters=3355
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=41.000, iters=3417
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=40.000, iters=3384
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=39.000, iters=3337
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=38.000, iters=3507
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=37.000, iters=3368
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=36.000, iters=3334
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=35.000, iters=3363
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=34.000, iters=3361
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=33.000, iters=3368
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=32.000, iters=3337
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=31.000, iters=3333
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=30.000, iters=3409
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=29.000, iters=3377
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=28.000, iters=3334
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=27.000, iters=3382
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=26.000, iters=3350
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=25.000, iters=3342
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=24.000, iters=3342
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=23.000, iters=3334
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=22.000, iters=3363
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=21.000, iters=3334
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=20.000, iters=3388
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=19.000, iters=3370
% 3.30/3.61
% 3.30/3.61 Low Water (keep): wt=18.000, iters=3352
% 36.03/36.30
% 36.03/36.30 Low Water (keep): wt=17.000, iters=3340
% 36.03/36.30
% 36.03/36.30 Low Water (keep): wt=16.000, iters=3340
% 36.03/36.30
% 36.03/36.30 Low Water (keep): wt=15.000, iters=3334
% 36.03/36.30
% 36.03/36.30 Low Water (displace): id=15627, wt=14.000
% 36.03/36.30
% 36.03/36.30 Low Water (displace): id=15751, wt=13.000
% 36.03/36.30
% 36.03/36.30 Low Water (displace): id=17242, wt=12.000
% 36.03/36.30
% 36.03/36.30 Low Water (displace): id=17250, wt=11.000
% 36.03/36.30
% 36.03/36.30 Low Water (keep): wt=14.000, iters=3353
% 36.03/36.30
% 36.03/36.30 ============================== PROOF =================================
% 36.03/36.30 % SZS status Unsatisfiable
% 36.03/36.30 % SZS output start Refutation
% 36.03/36.30
% 36.03/36.30 % Proof 1 at 34.37 (+ 0.99) seconds.
% 36.03/36.30 % Length of proof is 139.
% 36.03/36.30 % Level of proof is 31.
% 36.03/36.30 % Maximum clause weight is 43.000.
% 36.03/36.30 % Given clauses 3918.
% 36.03/36.30
% 36.03/36.30 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 36.03/36.30 2 multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 36.03/36.30 3 sk_c6 = multiply(sk_c8,sk_c7). [copy(2),flip(a)].
% 36.03/36.30 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 36.03/36.30 5 inverse(sk_c8) = sk_c6 | inverse(sk_c3) = sk_c8 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 36.03/36.30 6 multiply(sk_c8,sk_c7) = inverse(sk_c8) | inverse(sk_c3) = sk_c8. [copy(5),rewrite([3(3)]),flip(a)].
% 36.03/36.30 7 inverse(sk_c8) = sk_c6 | inverse(sk_c4) = sk_c8 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 36.03/36.30 8 multiply(sk_c8,sk_c7) = inverse(sk_c8) | inverse(sk_c4) = sk_c8. [copy(7),rewrite([3(3)]),flip(a)].
% 36.03/36.30 9 inverse(sk_c1) = sk_c2 | inverse(sk_c3) = sk_c8 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 36.03/36.30 10 inverse(sk_c1) = sk_c2 | inverse(sk_c4) = sk_c8 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 36.03/36.30 13 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 36.03/36.30 14 multiply(sk_c8,sk_c7) = inverse(sk_c8) | multiply(sk_c8,sk_c5) = sk_c7. [copy(13),rewrite([3(3)]),flip(a)].
% 36.03/36.30 15 inverse(sk_c8) = sk_c6 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 36.03/36.30 16 multiply(sk_c8,sk_c7) = inverse(sk_c8) | multiply(sk_c4,sk_c8) = sk_c5. [copy(15),rewrite([3(3)]),flip(a)].
% 36.03/36.30 17 multiply(sk_c1,sk_c2) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 36.03/36.30 18 multiply(sk_c1,sk_c2) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 36.03/36.30 19 inverse(sk_c1) = sk_c2 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 36.03/36.30 20 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 36.03/36.30 21 inverse(sk_c1) = sk_c2 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 36.03/36.30 24 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 36.03/36.30 25 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 36.03/36.30 26 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 36.03/36.30 30 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 36.03/36.30 31 multiply(sk_c8,sk_c7) != sk_c6 | inverse(sk_c8) != sk_c6 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(sk_c8,D) != sk_c7 | multiply(E,sk_c8) != D | inverse(E) != sk_c8 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 36.03/36.30 32 multiply(sk_c8,sk_c7) != inverse(sk_c8) | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(sk_c8,D) != sk_c7 | multiply(E,sk_c8) != D | inverse(E) != sk_c8. [copy(31),rewrite([3(4),3(10)]),flip(b),xx(a)].
% 36.03/36.30 52 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),30(a,1,1)),rewrite([1(2)]),flip(a)].
% 36.03/36.30 56 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c8,sk_c7)) = multiply(A,inverse(sk_c8)). [para(8(a,1),30(a,2,2)),rewrite([30(8)])].
% 36.03/36.30 59 multiply(sk_c8,sk_c7) = inverse(sk_c8) | multiply(sk_c8,multiply(sk_c5,A)) = multiply(sk_c7,A). [para(14(b,1),30(a,1,1)),flip(b)].
% 36.03/36.30 67 inverse(sk_c1) = sk_c2 | multiply(sk_c3,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(19(b,1),30(a,1,1)),flip(b)].
% 36.03/36.30 68 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c3,sk_c8)) = multiply(A,sk_c7). [para(19(b,1),30(a,2,2)),rewrite([30(8)])].
% 36.03/36.30 72 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c5). [para(21(b,1),30(a,2,2)),rewrite([30(8)])].
% 36.03/36.30 77 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c3,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(24(b,1),30(a,1,1)),flip(b)].
% 36.03/36.30 82 multiply(sk_c1,sk_c2) = sk_c8 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c5). [para(26(b,1),30(a,2,2)),rewrite([30(9)])].
% 36.03/36.30 118 multiply(sk_c8,sk_c7) != inverse(sk_c8) | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,C) != sk_c7 | multiply(D,sk_c8) != C | inverse(D) != sk_c8. [para(4(a,1),32(e,1))].
% 36.03/36.30 258 multiply(sk_c8,sk_c7) != inverse(sk_c8) | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,C) != sk_c7 | identity != C. [factor(118,f,i),rewrite([4(31)])].
% 36.03/36.30 623 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),52(a,1,2))].
% 36.03/36.30 633 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c8),sk_c7) = sk_c5. [para(20(b,1),52(a,1,2))].
% 36.03/36.30 650 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(52(a,1),52(a,1,2))].
% 36.03/36.30 653 multiply(A,identity) = A. [back_rewrite(623),rewrite([650(4)])].
% 36.03/36.30 673 inverse(identity) = identity. [para(653(a,1),4(a,1))].
% 36.03/36.30 742 multiply(A,inverse(A)) = identity. [para(650(a,1),4(a,1))].
% 36.03/36.30 775 multiply(A,multiply(inverse(A),B)) = B. [para(650(a,1),52(a,1))].
% 36.03/36.30 776 inverse(inverse(A)) = A. [para(650(a,1),653(a,1)),rewrite([653(2)]),flip(a)].
% 36.03/36.30 805 multiply(sk_c8,sk_c7) != inverse(sk_c8) | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | identity != sk_c7 | multiply(sk_c8,C) != sk_c7 | identity != C. [back_rewrite(258),rewrite([776(21)]),xx(f)].
% 36.03/36.30 823 inverse(sk_c1) = sk_c2 | multiply(sk_c3,sk_c8) = identity. [para(9(b,1),742(a,1,2))].
% 36.03/36.30 824 inverse(sk_c1) = sk_c2 | multiply(sk_c4,sk_c8) = identity. [para(10(b,1),742(a,1,2))].
% 36.03/36.30 825 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(742(a,1),30(a,1)),flip(a)].
% 36.03/36.30 1495 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(825(a,1),52(a,1,2)),rewrite([653(3)]),flip(a)].
% 36.03/36.30 1521 multiply(sk_c8,sk_c7) = inverse(sk_c8) | multiply(sk_c5,inverse(sk_c7)) = inverse(sk_c8). [para(14(b,1),1495(a,1,2,1))].
% 36.03/36.30 1551 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(1495(a,1),52(a,1,2)),flip(a)].
% 36.03/36.30 1560 inverse(sk_c1) = sk_c2 | multiply(sk_c7,inverse(sk_c5)) = sk_c8. [para(633(b,1),1495(a,1,2,1)),rewrite([776(11)])].
% 36.03/36.30 3016 inverse(sk_c1) = sk_c2 | multiply(A,sk_c7) = A. [para(823(b,1),68(b,1,2)),rewrite([653(10)]),flip(c),merge(b)].
% 36.03/36.30 3931 inverse(sk_c1) = sk_c2 | multiply(A,sk_c5) = A. [para(824(b,1),72(b,1,2)),rewrite([653(10)]),flip(c),merge(b)].
% 36.03/36.30 4122 inverse(sk_c1) = sk_c2 | inverse(sk_c5) = identity. [para(3931(b,1),4(a,1))].
% 36.03/36.30 4138 inverse(sk_c1) = sk_c2 | multiply(sk_c5,A) = A. [para(4122(b,1),52(a,1,1)),rewrite([1(8)])].
% 36.03/36.30 4190 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c5),A) = A. [para(4138(b,1),52(a,1,2))].
% 36.03/36.30 5115 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c7,inverse(sk_c8)) = sk_c3. [para(742(a,1),77(b,1,2)),rewrite([653(8)]),flip(b)].
% 36.03/36.30 5492 multiply(sk_c8,sk_c7) != inverse(sk_c8) | multiply(A,multiply(B,C)) != sk_c8 | multiply(inverse(B),inverse(A)) != C | multiply(C,sk_c7) != sk_c8 | identity != sk_c7 | multiply(sk_c8,D) != sk_c7 | identity != D. [para(30(a,1),805(b,1)),rewrite([1551(12)])].
% 36.03/36.30 5706 inverse(sk_c1) = sk_c2 | inverse(sk_c5) = sk_c7. [para(4190(b,1),3016(b,1)),flip(c),merge(b)].
% 36.03/36.30 5711 inverse(sk_c1) = sk_c2 | inverse(sk_c5) = sk_c5. [para(4190(b,1),3931(b,1)),flip(c),merge(b)].
% 36.03/36.30 5735 inverse(sk_c1) = sk_c2 | multiply(sk_c7,A) = A. [para(5706(b,1),4190(b,1,1)),merge(b)].
% 36.03/36.30 5744 inverse(sk_c1) = sk_c2 | multiply(sk_c7,sk_c5) = sk_c8. [para(5711(b,1),1560(b,1,2)),merge(b)].
% 36.03/36.30 6082 inverse(sk_c1) = sk_c2 | inverse(sk_c5) = sk_c8. [para(5735(b,1),1560(b,1)),merge(b)].
% 36.03/36.30 6095 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c5) = identity. [para(6082(b,1),4(a,1,1))].
% 36.03/36.30 6112 inverse(sk_c1) = sk_c2 | identity = sk_c8. [para(6082(b,1),4122(b,1)),flip(c),merge(b)].
% 36.03/36.30 6114 inverse(sk_c1) = sk_c2 | multiply(sk_c8,A) = A. [para(6082(b,1),4190(b,1,1)),merge(b)].
% 36.03/36.30 6119 identity = sk_c8 | multiply(sk_c1,sk_c2) = identity. [para(6112(a,1),742(a,1,2))].
% 36.03/36.30 6409 identity = sk_c8 | inverse(sk_c3) = sk_c8. [para(6119(b,1),17(a,1)),merge(b)].
% 36.03/36.30 6410 identity = sk_c8 | inverse(sk_c4) = sk_c8. [para(6119(b,1),18(a,1)),merge(b)].
% 36.03/36.30 6411 identity = sk_c8 | multiply(sk_c8,sk_c5) = sk_c7. [para(6119(b,1),25(a,1)),merge(b)].
% 36.03/36.30 6425 identity = sk_c8 | inverse(sk_c8) = sk_c3. [para(6409(b,1),776(a,1,1))].
% 36.03/36.30 6426 identity = sk_c8 | multiply(sk_c3,sk_c8) = identity. [para(6409(b,1),742(a,1,2))].
% 36.03/36.30 6443 identity = sk_c8 | multiply(sk_c8,sk_c4) = identity. [para(6410(b,1),4(a,1,1))].
% 36.03/36.30 6445 identity = sk_c8 | inverse(sk_c8) = sk_c4. [para(6410(b,1),776(a,1,1))].
% 36.03/36.30 6585 identity = sk_c8 | sk_c4 = sk_c3. [para(6445(b,1),6425(b,1)),merge(b)].
% 36.03/36.30 6595 sk_c4 = sk_c3 | inverse(sk_c8) = identity. [para(6585(a,1),673(a,1,1))].
% 36.03/36.30 6699 sk_c4 = sk_c3 | inverse(sk_c8) = sk_c8. [para(6585(a,1),6595(b,2)),merge(b)].
% 36.03/36.30 6705 sk_c4 = sk_c3 | multiply(sk_c8,sk_c8) = identity. [para(6699(b,1),4(a,1,1))].
% 36.03/36.30 6712 sk_c4 = sk_c3 | multiply(sk_c8,multiply(sk_c8,A)) = A. [para(6699(b,1),52(a,1,1))].
% 36.03/36.30 6869 identity = sk_c8 | multiply(inverse(sk_c8),sk_c7) = sk_c5. [para(6411(b,1),52(a,1,2))].
% 36.03/36.30 6989 identity = sk_c8 | multiply(inverse(sk_c4),inverse(sk_c8)) = identity. [para(6443(b,1),1551(a,1,1)),rewrite([673(5)]),flip(b)].
% 36.03/36.30 7245 sk_c4 = sk_c3 | multiply(A,multiply(sk_c8,sk_c8)) = A. [para(6705(b,1),30(a,2,2)),rewrite([30(7),653(9)])].
% 36.03/36.30 7606 inverse(sk_c1) = sk_c2 | multiply(sk_c7,sk_c5) = sk_c3. [para(6095(b,1),67(b,1,2)),rewrite([653(11)]),flip(c),merge(b)].
% 36.03/36.30 7744 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c8),A) = A. [para(6114(b,1),52(a,1,2))].
% 36.03/36.30 7941 identity = sk_c8 | multiply(inverse(sk_c7),sk_c8) = inverse(sk_c5). [para(6869(b,1),1551(a,1,1)),rewrite([776(10)]),flip(b)].
% 36.03/36.30 7948 identity = sk_c8 | multiply(sk_c4,sk_c7) = sk_c5. [para(6445(b,1),6869(b,1,1)),merge(b)].
% 36.03/36.30 7983 identity = sk_c8 | multiply(inverse(sk_c4),sk_c5) = sk_c7. [para(7948(b,1),52(a,1,2))].
% 36.03/36.30 8092 inverse(sk_c1) = sk_c2 | sk_c3 = sk_c7. [para(7606(b,1),3931(b,1)),merge(b)].
% 36.03/36.30 8094 inverse(sk_c1) = sk_c2 | sk_c3 = sk_c8. [para(7606(b,1),5744(b,1)),merge(b)].
% 36.03/36.30 8098 sk_c3 = sk_c7 | multiply(sk_c1,sk_c2) = identity. [para(8092(a,1),742(a,1,2))].
% 36.03/36.30 8153 sk_c3 = sk_c8 | multiply(sk_c1,multiply(sk_c2,A)) = A. [para(8094(a,1),775(a,1,2,1))].
% 36.03/36.30 8243 sk_c3 = sk_c7 | multiply(A,multiply(sk_c1,sk_c2)) = A. [para(8098(b,1),30(a,2,2)),rewrite([30(7),653(9)])].
% 36.03/36.30 8683 identity = sk_c8 | multiply(inverse(sk_c5),sk_c4) = inverse(sk_c7). [para(7983(b,1),1551(a,1,1)),rewrite([776(10)]),flip(b)].
% 36.03/36.30 9661 inverse(sk_c3) = sk_c8 | sk_c4 = sk_c3 | identity = sk_c7. [para(6(a,1),6712(b,1,2)),rewrite([742(11)])].
% 36.03/36.30 9662 inverse(sk_c4) = sk_c8 | sk_c4 = sk_c3 | identity = sk_c7. [para(8(a,1),6712(b,1,2)),rewrite([742(11)])].
% 36.03/36.30 10209 inverse(sk_c1) = sk_c2 | inverse(sk_c8) = sk_c7. [para(7744(b,1),3016(b,1)),flip(c),merge(b)].
% 36.03/36.30 10216 inverse(sk_c8) = sk_c7 | multiply(sk_c1,sk_c2) = identity. [para(10209(a,1),742(a,1,2))].
% 36.03/36.30 10385 identity = sk_c8 | multiply(sk_c7,inverse(sk_c5)) = sk_c8. [para(7941(b,1),52(a,1,2)),rewrite([776(6)])].
% 36.03/36.30 10391 identity = sk_c8 | multiply(sk_c5,inverse(sk_c7)) = inverse(sk_c8). [para(10385(b,1),1551(a,1,1)),rewrite([776(8)]),flip(b)].
% 36.03/36.30 10627 inverse(sk_c4) = sk_c8 | sk_c3 = sk_c8 | multiply(sk_c1,multiply(sk_c2,inverse(sk_c8))) = multiply(sk_c8,sk_c7). [para(56(b,1),8153(b,1,2))].
% 36.03/36.30 10700 sk_c3 = sk_c7 | multiply(sk_c8,sk_c7) = inverse(sk_c8) | multiply(sk_c8,multiply(sk_c5,multiply(sk_c1,sk_c2))) = sk_c7. [para(8243(b,1),59(b,2))].
% 36.03/36.30 11120 identity = sk_c8 | multiply(sk_c5,inverse(sk_c7)) = sk_c4. [para(8683(b,1),52(a,1,2)),rewrite([776(6)])].
% 36.03/36.30 11317 sk_c4 = sk_c3 | identity = sk_c7 | inverse(sk_c8) = sk_c3. [para(9661(a,1),776(a,1,1))].
% 36.03/36.30 11324 sk_c4 = sk_c3 | identity = sk_c7 | inverse(sk_c8) = sk_c4. [para(9662(a,1),776(a,1,1))].
% 36.03/36.30 11953 sk_c4 = sk_c3 | identity = sk_c7. [para(11324(c,1),11317(c,1)),merge(c),merge(d),merge(e)].
% 36.03/36.30 11976 sk_c4 = sk_c3 | inverse(sk_c8) = sk_c7. [para(11953(b,1),6595(b,2)),merge(b)].
% 36.03/36.30 12000 sk_c4 = sk_c3 | multiply(sk_c7,multiply(sk_c8,A)) = A. [para(11976(b,1),52(a,1,1))].
% 36.03/36.30 12620 sk_c4 = sk_c3 | multiply(sk_c7,A) = multiply(sk_c8,A). [para(6712(b,1),12000(b,1,2)),merge(b)].
% 36.03/36.30 13044 sk_c4 = sk_c3 | multiply(sk_c8,multiply(sk_c8,sk_c8)) = sk_c7. [para(12620(b,1),7245(b,1)),merge(b)].
% 36.03/36.30 14988 sk_c4 = sk_c3 | multiply(inverse(sk_c8),sk_c7) = multiply(sk_c8,sk_c8). [para(13044(b,1),52(a,1,2))].
% 36.03/36.30 21240 multiply(sk_c7,inverse(sk_c8)) = sk_c3 | identity = sk_c8. [para(5115(a,1),6119(b,1)),flip(c),merge(c)].
% 36.03/36.30 21243 identity = sk_c8 | multiply(inverse(sk_c7),sk_c3) = inverse(sk_c8). [para(21240(a,1),52(a,1,2))].
% 36.03/36.30 21282 identity = sk_c8 | multiply(inverse(sk_c3),sk_c7) = sk_c8. [para(21243(b,1),1551(a,1,1)),rewrite([776(6),776(9)]),flip(b)].
% 36.03/36.30 21285 identity = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7. [para(21282(b,1),52(a,1,2)),rewrite([776(6)])].
% 36.03/36.30 21290 identity = sk_c8 | identity = sk_c7. [para(21285(b,1),6426(b,1)),flip(c),merge(b)].
% 36.03/36.30 21300 identity = sk_c8 | inverse(sk_c7) = identity. [para(21290(b,1),673(a,1,1))].
% 36.03/36.30 21334 identity = sk_c8 | sk_c5 = sk_c4. [para(21300(b,1),11120(b,1,2)),rewrite([653(9)]),merge(b)].
% 36.03/36.30 21335 identity = sk_c8 | inverse(sk_c8) = sk_c5. [para(21300(b,1),10391(b,1,2)),rewrite([653(9)]),flip(c),merge(b)].
% 36.03/36.30 21395 sk_c5 = sk_c4 | multiply(A,sk_c8) = A. [para(21334(a,1),653(a,1,2))].
% 36.03/36.30 21477 identity = sk_c8 | multiply(inverse(sk_c4),sk_c5) = identity. [para(21335(b,1),6989(b,1,2)),merge(b)].
% 36.03/36.30 21746 sk_c5 = sk_c4 | multiply(sk_c8,sk_c7) = inverse(sk_c8). [para(21395(b,1),16(b,1)),flip(c),merge(c)].
% 36.03/36.30 21835 multiply(sk_c8,sk_c7) != inverse(sk_c8) | sk_c8 != A | multiply(B,inverse(A)) != B | multiply(B,sk_c7) != sk_c8 | identity != sk_c7 | multiply(sk_c8,C) != sk_c7 | identity != C. [para(4(a,1),5492(b,1,2)),rewrite([653(8),776(10)]),flip(b)].
% 36.03/36.30 21839 multiply(sk_c8,sk_c7) != inverse(sk_c8) | inverse(A) != sk_c8 | multiply(B,A) != B | multiply(B,sk_c7) != sk_c8 | identity != sk_c7 | multiply(sk_c8,C) != sk_c7 | identity != C. [para(776(a,1),21835(c,1,2)),flip(b)].
% 36.03/36.30 21879 multiply(sk_c8,sk_c7) != inverse(sk_c8) | inverse(A) != sk_c8 | inverse(A) != identity | multiply(inverse(A),sk_c7) != sk_c8 | identity != sk_c7 | multiply(sk_c8,B) != sk_c7 | identity != B. [para(4(a,1),21839(c,1)),flip(c)].
% 36.03/36.30 21920 multiply(sk_c8,sk_c7) != inverse(sk_c8) | inverse(A) != sk_c8 | inverse(A) != identity | multiply(inverse(A),sk_c7) != sk_c8 | identity != sk_c7 | sk_c7 != B | multiply(inverse(sk_c8),B) != identity. [para(775(a,1),21879(f,1)),flip(f),flip(g)].
% 36.03/36.30 21987 identity = sk_c8 | multiply(sk_c1,sk_c2) = sk_c8. [para(21477(b,1),82(b,2)),rewrite([52(14)]),flip(c),merge(c)].
% 36.03/36.30 21997 identity = sk_c8. [para(21987(b,1),6119(b,1)),flip(c),merge(b),merge(c)].
% 36.03/36.30 22020 multiply(sk_c8,sk_c7) != inverse(sk_c8) | inverse(A) != sk_c8 | multiply(inverse(A),sk_c7) != sk_c8 | sk_c7 != sk_c8 | sk_c7 != B | multiply(inverse(sk_c8),B) != sk_c8. [back_rewrite(21920),rewrite([21997(11),21997(18),21997(26)]),flip(e),merge(c)].
% 36.03/36.30 23817 inverse(sk_c8) = sk_c7 | multiply(sk_c1,sk_c2) = sk_c8. [back_rewrite(10216),rewrite([21997(8)])].
% 36.03/36.30 24050 inverse(sk_c8) = sk_c8. [back_rewrite(673),rewrite([21997(1),21997(3)])].
% 36.03/36.30 24051 multiply(A,sk_c8) = A. [back_rewrite(653),rewrite([21997(1)])].
% 36.03/36.30 24053 multiply(sk_c8,A) = A. [back_rewrite(1),rewrite([21997(1)])].
% 36.03/36.30 24078 sk_c7 != sk_c8. [factor(22020,c,f),rewrite([24053(3),24050(3),24050(5),24050(8),24053(9)]),xx(b),xx(e),merge(b),merge(c)].
% 36.03/36.30 24081 multiply(sk_c1,sk_c2) = sk_c8. [back_rewrite(23817),rewrite([24050(2)]),flip(a),unit_del(a,24078)].
% 36.03/36.30 24090 sk_c5 = sk_c4. [back_rewrite(21746),rewrite([24053(6),24050(6)]),unit_del(b,24078)].
% 36.03/36.30 24127 sk_c4 = sk_c3. [back_rewrite(14988),rewrite([24050(5),24053(6),24051(7)]),unit_del(b,24078)].
% 36.03/36.30 24130 sk_c3 = sk_c7. [back_rewrite(10700),rewrite([24053(6),24050(6),24090(8),24127(8),24081(11),24051(10),24053(9)]),merge(c),unit_del(b,24078)].
% 36.03/36.30 24132 inverse(sk_c7) = sk_c8. [back_rewrite(10627),rewrite([24127(1),24130(1),24130(5),24050(11),24051(11),24081(10),24053(11)]),flip(c),merge(c),unit_del(b,24078)].
% 36.03/36.30 24137 $F. [back_rewrite(1521),rewrite([24053(3),24050(3),24090(4),24127(4),24130(4),24132(6),24051(6),24050(6)]),merge(b),unit_del(a,24078)].
% 36.03/36.30
% 36.03/36.30 % SZS output end Refutation
% 36.03/36.30 ============================== end of proof ==========================
% 36.03/36.30
% 36.03/36.30 ============================== STATISTICS ============================
% 36.03/36.30
% 36.03/36.30 Given=3918. Generated=1947241. Kept=24129. proofs=1.
% 36.03/36.30 Usable=1277. Sos=3256. Demods=29. Limbo=87, Disabled=19534. Hints=0.
% 36.03/36.30 Megabytes=21.82.
% 36.03/36.30 User_CPU=34.37, System_CPU=0.99, Wall_clock=36.
% 36.03/36.30
% 36.03/36.30 ============================== end of statistics =====================
% 36.03/36.30
% 36.03/36.30 ============================== end of search =========================
% 36.03/36.30
% 36.03/36.30 THEOREM PROVED
% 36.03/36.30 % SZS status Unsatisfiable
% 36.03/36.30
% 36.03/36.30 Exiting with 1 proof.
% 36.03/36.30
% 36.03/36.30 Process 19677 exit (max_proofs) Mon Jun 13 15:05:28 2022
% 36.03/36.30 Prover9 interrupted
%------------------------------------------------------------------------------