TSTP Solution File: GRP252-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP252-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 11:18:21 EDT 2022
% Result : Unsatisfiable 3.48s 3.90s
% Output : Refutation 3.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : GRP252-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.09 % Command : tptp2X_and_run_prover9 %d %s
% 0.09/0.29 % Computer : n023.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jun 13 22:10:21 EDT 2022
% 0.09/0.29 % CPUTime :
% 3.48/3.90 ============================== Prover9 ===============================
% 3.48/3.90 Prover9 (32) version 2009-11A, November 2009.
% 3.48/3.90 Process 18124 was started by sandbox2 on n023.cluster.edu,
% 3.48/3.90 Mon Jun 13 22:10:21 2022
% 3.48/3.90 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17971_n023.cluster.edu".
% 3.48/3.90 ============================== end of head ===========================
% 3.48/3.90
% 3.48/3.90 ============================== INPUT =================================
% 3.48/3.90
% 3.48/3.90 % Reading from file /tmp/Prover9_17971_n023.cluster.edu
% 3.48/3.90
% 3.48/3.90 set(prolog_style_variables).
% 3.48/3.90 set(auto2).
% 3.48/3.90 % set(auto2) -> set(auto).
% 3.48/3.90 % set(auto) -> set(auto_inference).
% 3.48/3.90 % set(auto) -> set(auto_setup).
% 3.48/3.90 % set(auto_setup) -> set(predicate_elim).
% 3.48/3.90 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.48/3.90 % set(auto) -> set(auto_limits).
% 3.48/3.90 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.48/3.90 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.48/3.90 % set(auto) -> set(auto_denials).
% 3.48/3.90 % set(auto) -> set(auto_process).
% 3.48/3.90 % set(auto2) -> assign(new_constants, 1).
% 3.48/3.90 % set(auto2) -> assign(fold_denial_max, 3).
% 3.48/3.90 % set(auto2) -> assign(max_weight, "200.000").
% 3.48/3.90 % set(auto2) -> assign(max_hours, 1).
% 3.48/3.90 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.48/3.90 % set(auto2) -> assign(max_seconds, 0).
% 3.48/3.90 % set(auto2) -> assign(max_minutes, 5).
% 3.48/3.90 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.48/3.90 % set(auto2) -> set(sort_initial_sos).
% 3.48/3.90 % set(auto2) -> assign(sos_limit, -1).
% 3.48/3.90 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.48/3.90 % set(auto2) -> assign(max_megs, 400).
% 3.48/3.90 % set(auto2) -> assign(stats, some).
% 3.48/3.90 % set(auto2) -> clear(echo_input).
% 3.48/3.90 % set(auto2) -> set(quiet).
% 3.48/3.90 % set(auto2) -> clear(print_initial_clauses).
% 3.48/3.90 % set(auto2) -> clear(print_given).
% 3.48/3.90 assign(lrs_ticks,-1).
% 3.48/3.90 assign(sos_limit,10000).
% 3.48/3.90 assign(order,kbo).
% 3.48/3.90 set(lex_order_vars).
% 3.48/3.90 clear(print_given).
% 3.48/3.90
% 3.48/3.90 % formulas(sos). % not echoed (46 formulas)
% 3.48/3.90
% 3.48/3.90 ============================== end of input ==========================
% 3.48/3.90
% 3.48/3.90 % From the command line: assign(max_seconds, 300).
% 3.48/3.90
% 3.48/3.90 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.48/3.90
% 3.48/3.90 % Formulas that are not ordinary clauses:
% 3.48/3.90
% 3.48/3.90 ============================== end of process non-clausal formulas ===
% 3.48/3.90
% 3.48/3.90 ============================== PROCESS INITIAL CLAUSES ===============
% 3.48/3.90
% 3.48/3.90 ============================== PREDICATE ELIMINATION =================
% 3.48/3.90
% 3.48/3.90 ============================== end predicate elimination =============
% 3.48/3.90
% 3.48/3.90 Auto_denials: (non-Horn, no changes).
% 3.48/3.90
% 3.48/3.90 Term ordering decisions:
% 3.48/3.90
% 3.48/3.90 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 3.48/3.90 Function symbol KB weights: sk_c9=1. sk_c8=1. sk_c10=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c6=1. sk_c7=1. identity=1. multiply=1. inverse=0.
% 3.48/3.90
% 3.48/3.90 ============================== end of process initial clauses ========
% 3.48/3.90
% 3.48/3.90 ============================== CLAUSES FOR SEARCH ====================
% 3.48/3.90
% 3.48/3.90 ============================== end of clauses for search =============
% 3.48/3.90
% 3.48/3.90 ============================== SEARCH ================================
% 3.48/3.90
% 3.48/3.90 % Starting search at 0.02 seconds.
% 3.48/3.90
% 3.48/3.90 Low Water (keep): wt=51.000, iters=3459
% 3.48/3.90
% 3.48/3.90 Low Water (keep): wt=48.000, iters=3339
% 3.48/3.90
% 3.48/3.90 Low Water (keep): wt=47.000, iters=3359
% 3.48/3.90
% 3.48/3.90 Low Water (keep): wt=46.000, iters=3353
% 3.48/3.90
% 3.48/3.90 Low Water (keep): wt=44.000, iters=3357
% 3.48/3.90
% 3.48/3.90 Low Water (keep): wt=43.000, iters=3400
% 3.48/3.90
% 3.48/3.90 Low Water (keep): wt=42.000, iters=3454
% 3.48/3.90
% 3.48/3.90 Low Water (keep): wt=41.000, iters=3371
% 3.48/3.90
% 3.48/3.90 Low Water (keep): wt=39.000, iters=3351
% 3.48/3.90
% 3.48/3.90 ============================== PROOF =================================
% 3.48/3.90 % SZS status Unsatisfiable
% 3.48/3.90 % SZS output start Refutation
% 3.48/3.90
% 3.48/3.90 % Proof 1 at 2.83 (+ 0.03) seconds.
% 3.48/3.90 % Length of proof is 97.
% 3.48/3.90 % Level of proof is 23.
% 3.48/3.90 % Maximum clause weight is 59.000.
% 3.48/3.90 % Given clauses 506.
% 3.48/3.90
% 3.48/3.90 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 3.48/3.90 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 3.48/3.90 3 inverse(sk_c1) = sk_c10 | inverse(sk_c4) = sk_c10 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 3.48/3.90 7 inverse(sk_c2) = sk_c9 | inverse(sk_c5) = sk_c8 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 3.48/3.90 8 inverse(sk_c2) = sk_c9 | inverse(sk_c6) = sk_c8 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 3.48/3.90 12 multiply(sk_c1,sk_c10) = sk_c9 | inverse(sk_c4) = sk_c10 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 3.48/3.90 13 multiply(sk_c1,sk_c10) = sk_c9 | inverse(sk_c5) = sk_c8 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 3.48/3.90 14 multiply(sk_c1,sk_c10) = sk_c9 | inverse(sk_c6) = sk_c8 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 3.48/3.90 15 inverse(sk_c1) = sk_c10 | multiply(sk_c4,sk_c10) = sk_c9 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 3.48/3.90 20 multiply(sk_c2,sk_c9) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 3.48/3.90 21 multiply(sk_c2,sk_c9) = sk_c8 | inverse(sk_c6) = sk_c8 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 3.48/3.90 23 inverse(sk_c2) = sk_c9 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 3.48/3.90 24 inverse(sk_c2) = sk_c9 | multiply(sk_c8,sk_c7) = sk_c9 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 3.48/3.90 25 inverse(sk_c2) = sk_c9 | multiply(sk_c6,sk_c8) = sk_c7 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 3.48/3.90 33 multiply(sk_c1,sk_c10) = sk_c9 | multiply(sk_c4,sk_c10) = sk_c9 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 3.48/3.90 38 multiply(sk_c2,sk_c9) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 3.48/3.90 39 multiply(sk_c2,sk_c9) = sk_c8 | multiply(sk_c8,sk_c7) = sk_c9 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 3.48/3.90 40 multiply(sk_c2,sk_c9) = sk_c8 | multiply(sk_c6,sk_c8) = sk_c7 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 3.48/3.90 45 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 3.48/3.90 46 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(C) != sk_c9 | multiply(C,sk_c8) != sk_c9 | multiply(D,sk_c10) != sk_c9 | inverse(D) != sk_c10 | multiply(E,sk_c8) != sk_c9 | inverse(E) != sk_c8 | multiply(sk_c8,F) != sk_c9 | multiply(V6,sk_c8) != F | inverse(V6) != sk_c8 # label(prove_this_43) # label(negated_conjecture). [assumption].
% 3.48/3.90 47 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(C) != sk_c9 | multiply(C,sk_c8) != sk_c9 | multiply(D,sk_c8) != sk_c9 | inverse(D) != sk_c8 | multiply(sk_c8,E) != sk_c9 | multiply(F,sk_c8) != E | inverse(F) != sk_c8. [factor(46,a,g),merge(g)].
% 3.48/3.90 88 inverse(sk_c2) = sk_c9 | multiply(sk_c8,sk_c5) = identity. [para(7(b,1),2(a,1,1))].
% 3.48/3.90 89 inverse(sk_c2) = sk_c9 | multiply(sk_c8,sk_c6) = identity. [para(8(b,1),2(a,1,1))].
% 3.48/3.90 93 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),45(a,1,1)),rewrite([1(2)]),flip(a)].
% 3.48/3.90 110 inverse(sk_c5) = sk_c8 | multiply(sk_c2,multiply(sk_c9,A)) = multiply(sk_c8,A). [para(20(a,1),45(a,1,1)),flip(b)].
% 3.48/3.90 116 inverse(sk_c2) = sk_c9 | multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c9,A). [para(23(b,1),45(a,1,1)),flip(b)].
% 3.48/3.90 121 inverse(sk_c2) = sk_c9 | multiply(A,multiply(sk_c6,sk_c8)) = multiply(A,sk_c7). [para(25(b,1),45(a,2,2)),rewrite([45(8)])].
% 3.48/3.90 204 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(C) != sk_c9 | multiply(C,sk_c8) != sk_c9 | multiply(D,sk_c8) != sk_c9 | inverse(D) != sk_c8 | multiply(sk_c8,identity) != sk_c9 | inverse(inverse(sk_c8)) != sk_c8. [resolve(47,j,2,a)].
% 3.48/3.90 459 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(C) != sk_c9 | multiply(C,sk_c8) != sk_c9 | inverse(C) != sk_c8 | multiply(sk_c8,identity) != sk_c9 | inverse(inverse(sk_c8)) != sk_c8. [factor(204,f,g)].
% 3.48/3.90 982 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(inverse(sk_c8)) != sk_c9 | identity != sk_c9 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,identity) != sk_c9. [factor(459,g,i),rewrite([2(23)])].
% 3.48/3.90 1913 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),93(a,1,2))].
% 3.48/3.90 1934 inverse(sk_c2) = sk_c9 | multiply(inverse(sk_c8),sk_c9) = sk_c7. [para(24(b,1),93(a,1,2))].
% 3.48/3.90 1957 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(93(a,1),93(a,1,2))].
% 3.48/3.90 1958 multiply(A,identity) = A. [back_rewrite(1913),rewrite([1957(4)])].
% 3.48/3.90 1962 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(inverse(sk_c8)) != sk_c9 | identity != sk_c9 | inverse(inverse(sk_c8)) != sk_c8 | sk_c8 != sk_c9. [back_rewrite(982),rewrite([1958(30)])].
% 3.48/3.90 1969 inverse(identity) = identity. [para(1958(a,1),2(a,1))].
% 3.48/3.90 2110 inverse(sk_c2) = sk_c9 | inverse(sk_c8) = sk_c5. [para(88(b,1),93(a,1,2)),rewrite([1958(8)])].
% 3.48/3.90 2142 inverse(sk_c2) = sk_c9 | inverse(sk_c8) = sk_c6. [para(89(b,1),93(a,1,2)),rewrite([1958(8)])].
% 3.48/3.90 2286 multiply(A,inverse(A)) = identity. [para(1957(a,1),2(a,1))].
% 3.48/3.90 2389 inverse(inverse(A)) = A. [para(1957(a,1),1958(a,1)),rewrite([1958(2)]),flip(a)].
% 3.48/3.90 2415 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | sk_c8 != sk_c9 | identity != sk_c9. [back_rewrite(1962),rewrite([2389(17),2389(23)]),xx(g),merge(g)].
% 3.48/3.90 2495 inverse(sk_c8) = sk_c5 | inverse(sk_c9) = sk_c2. [para(2110(a,1),2389(a,1,1))].
% 3.48/3.90 2496 inverse(sk_c8) = sk_c6 | inverse(sk_c9) = sk_c2. [para(2142(a,1),2389(a,1,1))].
% 3.48/3.90 2500 inverse(sk_c1) = sk_c10 | multiply(sk_c4,sk_c10) = identity. [para(3(b,1),2286(a,1,2))].
% 3.48/3.90 2562 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | sk_c8 != sk_c9 | identity != sk_c9. [para(1(a,1),2415(c,1)),rewrite([1969(12)]),flip(c),merge(e),merge(f)].
% 3.48/3.90 2631 identity != sk_c9 | sk_c8 != sk_c9. [para(2(a,1),2562(a,1)),rewrite([2389(6)]),xx(b),merge(c)].
% 3.48/3.90 2649 inverse(sk_c9) = sk_c2 | multiply(sk_c5,sk_c8) = identity. [para(2495(a,1),2(a,1,1))].
% 3.48/3.90 2659 inverse(sk_c9) = sk_c2 | sk_c6 = sk_c5. [para(2496(a,1),2495(a,1)),merge(c)].
% 3.48/3.90 3142 inverse(sk_c1) = sk_c10 | identity = sk_c9. [para(2500(b,1),15(b,1)),merge(b)].
% 3.48/3.90 3248 identity = sk_c9 | multiply(sk_c1,sk_c10) = identity. [para(3142(a,1),2286(a,1,2))].
% 3.48/3.90 3259 identity = sk_c9 | inverse(sk_c4) = sk_c10. [para(3248(b,1),12(a,1)),merge(b)].
% 3.48/3.90 3260 identity = sk_c9 | inverse(sk_c5) = sk_c8. [para(3248(b,1),13(a,1)),merge(b)].
% 3.48/3.90 3261 identity = sk_c9 | inverse(sk_c6) = sk_c8. [para(3248(b,1),14(a,1)),merge(b)].
% 3.48/3.90 3346 identity = sk_c9 | multiply(sk_c4,sk_c10) = identity. [para(3259(b,1),2286(a,1,2))].
% 3.48/3.90 3350 identity = sk_c9 | inverse(sk_c8) = sk_c5. [para(3260(b,1),2389(a,1,1))].
% 3.48/3.90 3355 identity = sk_c9 | inverse(sk_c8) = sk_c6. [para(3261(b,1),2389(a,1,1))].
% 3.48/3.90 3504 identity = sk_c9 | sk_c6 = sk_c5. [para(3355(b,1),3350(b,1)),merge(b)].
% 3.48/3.90 3571 sk_c6 = sk_c5 | inverse(sk_c9) = identity. [para(3504(a,1),1969(a,1,1))].
% 3.48/3.90 3586 sk_c6 = sk_c5 | identity = sk_c2. [para(3571(b,1),2659(a,1)),merge(c)].
% 3.48/3.90 3728 sk_c6 = sk_c5 | multiply(sk_c2,A) = A. [para(3586(b,1),1(a,1,1))].
% 3.48/3.90 3892 inverse(sk_c5) = sk_c8 | multiply(sk_c2,multiply(sk_c9,inverse(sk_c8))) = identity. [para(2286(a,1),110(b,2))].
% 3.48/3.90 4067 identity = sk_c9 | multiply(sk_c1,sk_c10) = sk_c9. [para(3346(b,1),33(b,1)),merge(c)].
% 3.48/3.90 4918 sk_c6 = sk_c5 | sk_c8 = sk_c9 | inverse(sk_c5) = sk_c8. [para(3728(b,1),20(a,1)),flip(b)].
% 3.48/3.90 4919 sk_c6 = sk_c5 | sk_c8 = sk_c9 | inverse(sk_c6) = sk_c8. [para(3728(b,1),21(a,1)),flip(b)].
% 3.48/3.90 4999 inverse(sk_c2) = sk_c9 | multiply(sk_c5,sk_c9) = multiply(sk_c9,sk_c7). [para(24(b,1),116(b,1,2)),merge(b)].
% 3.48/3.90 5724 identity = sk_c9. [para(4067(b,1),3248(b,1)),flip(c),merge(b),merge(c)].
% 3.48/3.90 6383 inverse(sk_c5) = sk_c8 | multiply(sk_c2,multiply(sk_c9,inverse(sk_c8))) = sk_c9. [back_rewrite(3892),rewrite([5724(11)])].
% 3.48/3.90 6894 inverse(sk_c9) = sk_c2 | multiply(sk_c5,sk_c8) = sk_c9. [back_rewrite(2649),rewrite([5724(8)])].
% 3.48/3.90 6897 sk_c8 != sk_c9. [back_rewrite(2631),rewrite([5724(1)]),xx(a)].
% 3.48/3.90 7011 inverse(sk_c9) = sk_c9. [back_rewrite(1969),rewrite([5724(1),5724(3)])].
% 3.48/3.90 7012 multiply(A,sk_c9) = A. [back_rewrite(1958),rewrite([5724(1)])].
% 3.48/3.90 7023 multiply(sk_c9,A) = A. [back_rewrite(1),rewrite([5724(1)])].
% 3.48/3.90 7030 sk_c6 = sk_c5 | inverse(sk_c6) = sk_c8. [back_unit_del(4919),unit_del(b,6897)].
% 3.48/3.90 7031 sk_c6 = sk_c5 | inverse(sk_c5) = sk_c8. [back_unit_del(4918),unit_del(b,6897)].
% 3.48/3.90 7112 sk_c2 = sk_c9 | multiply(sk_c5,sk_c8) = sk_c9. [back_rewrite(6894),rewrite([7011(2)]),flip(a)].
% 3.48/3.90 7398 inverse(sk_c2) = sk_c9 | sk_c7 = sk_c5. [back_rewrite(4999),rewrite([7012(7),7023(8)]),flip(b)].
% 3.48/3.90 7598 inverse(sk_c2) = sk_c9 | inverse(sk_c8) = sk_c7. [back_rewrite(1934),rewrite([7012(8)])].
% 3.48/3.90 8132 sk_c2 = sk_c8 | multiply(sk_c6,sk_c8) = sk_c7. [back_rewrite(40),rewrite([7012(3)])].
% 3.48/3.90 8133 sk_c2 = sk_c8 | multiply(sk_c8,sk_c7) = sk_c9. [back_rewrite(39),rewrite([7012(3)])].
% 3.48/3.90 8134 sk_c2 = sk_c8 | multiply(sk_c5,sk_c8) = sk_c9. [back_rewrite(38),rewrite([7012(3)])].
% 3.48/3.90 8137 inverse(sk_c5) = sk_c8 | multiply(sk_c2,inverse(sk_c8)) = sk_c9. [back_rewrite(6383),rewrite([7023(9)])].
% 3.48/3.90 8237 inverse(sk_c2) = sk_c9 | multiply(sk_c8,multiply(sk_c6,sk_c8)) = sk_c9. [para(24(b,1),121(b,2)),merge(b)].
% 3.48/3.90 8249 sk_c6 = sk_c5 | inverse(sk_c8) = sk_c6. [para(7030(b,1),2389(a,1,1))].
% 3.48/3.90 8254 sk_c6 = sk_c5 | inverse(sk_c8) = sk_c5. [para(7031(b,1),2389(a,1,1))].
% 3.48/3.90 8567 sk_c7 = sk_c5 | sk_c2 = sk_c9. [para(7398(a,1),2389(a,1,1)),rewrite([7011(5)]),flip(b)].
% 3.48/3.90 8733 sk_c6 = sk_c5. [para(8254(b,1),8249(b,1)),flip(c),merge(b),merge(c)].
% 3.48/3.90 8897 inverse(sk_c2) = sk_c9 | multiply(sk_c8,multiply(sk_c5,sk_c8)) = sk_c9. [back_rewrite(8237),rewrite([8733(6)])].
% 3.48/3.90 8912 sk_c2 = sk_c8 | multiply(sk_c5,sk_c8) = sk_c7. [back_rewrite(8132),rewrite([8733(4)])].
% 3.48/3.90 9460 sk_c2 = sk_c9 | multiply(A,multiply(sk_c5,sk_c8)) = A. [para(7112(b,1),45(a,2,2)),rewrite([45(7),7012(9)])].
% 3.48/3.90 9753 inverse(sk_c8) = sk_c7 | sk_c2 = sk_c9. [para(7598(a,1),2389(a,1,1)),rewrite([7011(6)]),flip(b)].
% 3.48/3.90 10259 sk_c2 = sk_c8 | sk_c7 = sk_c9. [para(8912(b,1),8134(b,1)),merge(b)].
% 3.48/3.90 10471 sk_c2 = sk_c8. [para(10259(b,1),8133(b,1,2)),rewrite([7012(9)]),merge(b),unit_del(b,6897)].
% 3.48/3.90 10607 inverse(sk_c8) = sk_c7. [back_rewrite(9753),rewrite([10471(5)]),unit_del(b,6897)].
% 3.48/3.90 10709 multiply(A,multiply(sk_c5,sk_c8)) = A. [back_rewrite(9460),rewrite([10471(1)]),unit_del(a,6897)].
% 3.48/3.90 10834 sk_c7 = sk_c9. [back_rewrite(8897),rewrite([10471(1),10607(2),10709(8)]),unit_del(b,6897)].
% 3.48/3.90 10851 sk_c5 = sk_c9. [back_rewrite(8567),rewrite([10834(1),10471(4)]),flip(a),unit_del(b,6897)].
% 3.48/3.90 10855 $F. [back_rewrite(8137),rewrite([10851(1),7011(2),10471(4),10607(6),10834(5),7012(6)]),flip(a),merge(b),unit_del(a,6897)].
% 3.48/3.90
% 3.48/3.90 % SZS output end Refutation
% 3.48/3.90 ============================== end of proof ==========================
% 3.48/3.90
% 3.48/3.90 ============================== STATISTICS ============================
% 3.48/3.90
% 3.48/3.90 Given=506. Generated=28387. Kept=10854. proofs=1.
% 3.48/3.90 Usable=132. Sos=1237. Demods=28. Limbo=384, Disabled=9147. Hints=0.
% 3.48/3.90 Megabytes=11.42.
% 3.48/3.90 User_CPU=2.83, System_CPU=0.03, Wall_clock=3.
% 3.48/3.90
% 3.48/3.90 ============================== end of statistics =====================
% 3.48/3.90
% 3.48/3.90 ============================== end of search =========================
% 3.48/3.90
% 3.48/3.90 THEOREM PROVED
% 3.48/3.90 % SZS status Unsatisfiable
% 3.48/3.90
% 3.48/3.90 Exiting with 1 proof.
% 3.48/3.90
% 3.48/3.90 Process 18124 exit (max_proofs) Mon Jun 13 22:10:24 2022
% 3.48/3.90 Prover9 interrupted
%------------------------------------------------------------------------------