TSTP Solution File: GRP312-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP312-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 11:18:35 EDT 2022
% Result : Unsatisfiable 25.28s 25.65s
% Output : Refutation 25.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08 % Problem : GRP312-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.09 % Command : tptp2X_and_run_prover9 %d %s
% 0.09/0.29 % Computer : n015.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 07:16:52 EDT 2022
% 0.09/0.29 % CPUTime :
% 19.43/19.79 ============================== Prover9 ===============================
% 19.43/19.79 Prover9 (32) version 2009-11A, November 2009.
% 19.43/19.79 Process 27143 was started by sandbox2 on n015.cluster.edu,
% 19.43/19.79 Mon Jun 13 07:16:53 2022
% 19.43/19.79 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26990_n015.cluster.edu".
% 19.43/19.79 ============================== end of head ===========================
% 19.43/19.79
% 19.43/19.79 ============================== INPUT =================================
% 19.43/19.79
% 19.43/19.79 % Reading from file /tmp/Prover9_26990_n015.cluster.edu
% 19.43/19.79
% 19.43/19.79 set(prolog_style_variables).
% 19.43/19.79 set(auto2).
% 19.43/19.79 % set(auto2) -> set(auto).
% 19.43/19.79 % set(auto) -> set(auto_inference).
% 19.43/19.79 % set(auto) -> set(auto_setup).
% 19.43/19.79 % set(auto_setup) -> set(predicate_elim).
% 19.43/19.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 19.43/19.79 % set(auto) -> set(auto_limits).
% 19.43/19.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 19.43/19.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 19.43/19.79 % set(auto) -> set(auto_denials).
% 19.43/19.79 % set(auto) -> set(auto_process).
% 19.43/19.79 % set(auto2) -> assign(new_constants, 1).
% 19.43/19.79 % set(auto2) -> assign(fold_denial_max, 3).
% 19.43/19.79 % set(auto2) -> assign(max_weight, "200.000").
% 19.43/19.79 % set(auto2) -> assign(max_hours, 1).
% 19.43/19.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 19.43/19.79 % set(auto2) -> assign(max_seconds, 0).
% 19.43/19.79 % set(auto2) -> assign(max_minutes, 5).
% 19.43/19.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 19.43/19.79 % set(auto2) -> set(sort_initial_sos).
% 19.43/19.79 % set(auto2) -> assign(sos_limit, -1).
% 19.43/19.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 19.43/19.79 % set(auto2) -> assign(max_megs, 400).
% 19.43/19.79 % set(auto2) -> assign(stats, some).
% 19.43/19.79 % set(auto2) -> clear(echo_input).
% 19.43/19.79 % set(auto2) -> set(quiet).
% 19.43/19.79 % set(auto2) -> clear(print_initial_clauses).
% 19.43/19.79 % set(auto2) -> clear(print_given).
% 19.43/19.79 assign(lrs_ticks,-1).
% 19.43/19.79 assign(sos_limit,10000).
% 19.43/19.79 assign(order,kbo).
% 19.43/19.79 set(lex_order_vars).
% 19.43/19.79 clear(print_given).
% 19.43/19.79
% 19.43/19.79 % formulas(sos). % not echoed (74 formulas)
% 19.43/19.79
% 19.43/19.79 ============================== end of input ==========================
% 19.43/19.79
% 19.43/19.79 % From the command line: assign(max_seconds, 300).
% 19.43/19.79
% 19.43/19.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 19.43/19.79
% 19.43/19.79 % Formulas that are not ordinary clauses:
% 19.43/19.79
% 19.43/19.79 ============================== end of process non-clausal formulas ===
% 19.43/19.79
% 19.43/19.79 ============================== PROCESS INITIAL CLAUSES ===============
% 19.43/19.79
% 19.43/19.79 ============================== PREDICATE ELIMINATION =================
% 19.43/19.79
% 19.43/19.79 ============================== end predicate elimination =============
% 19.43/19.79
% 19.43/19.79 Auto_denials: (non-Horn, no changes).
% 19.43/19.79
% 19.43/19.79 Term ordering decisions:
% 19.43/19.79
% 19.43/19.79 % Assigning unary symbol inverse kb_weight 0 and highest precedence (16).
% 19.43/19.79 Function symbol KB weights: sk_c11=1. sk_c12=1. sk_c9=1. sk_c10=1. sk_c7=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c6=1. sk_c8=1. identity=1. multiply=1. inverse=0.
% 19.43/19.79
% 19.43/19.79 ============================== end of process initial clauses ========
% 19.43/19.79
% 19.43/19.79 ============================== CLAUSES FOR SEARCH ====================
% 19.43/19.79
% 19.43/19.79 ============================== end of clauses for search =============
% 19.43/19.79
% 19.43/19.79 ============================== SEARCH ================================
% 19.43/19.79
% 19.43/19.79 % Starting search at 0.14 seconds.
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=705, wt=62.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=10697, wt=45.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=11232, wt=44.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=11294, wt=43.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=11381, wt=42.000
% 19.43/19.79
% 19.43/19.79 Low Water (keep): wt=46.000, iters=3485
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=13739, wt=41.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=13955, wt=40.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=14523, wt=37.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=15879, wt=36.000
% 19.43/19.79
% 19.43/19.79 Low Water (keep): wt=45.000, iters=3574
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=27171, wt=32.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=27203, wt=30.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=27212, wt=29.000
% 19.43/19.79
% 19.43/19.79 Low Water (keep): wt=44.000, iters=3362
% 19.43/19.79
% 19.43/19.79 Low Water (keep): wt=43.000, iters=3376
% 19.43/19.79
% 19.43/19.79 Low Water (keep): wt=42.000, iters=3337
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=28217, wt=25.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=28273, wt=24.000
% 19.43/19.79
% 19.43/19.79 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 18.41 sec).
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=28317, wt=23.000
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=28894, wt=15.000
% 19.43/19.79
% 19.43/19.79 Low Water (keep): wt=41.000, iters=3480
% 19.43/19.79
% 19.43/19.79 Low Water (displace): id=29130, wt=14.000
% 25.28/25.65
% 25.28/25.65 Low Water (displace): id=29579, wt=12.000
% 25.28/25.65
% 25.28/25.65 Low Water (displace): id=30625, wt=11.000
% 25.28/25.65
% 25.28/25.65 Low Water (displace): id=34478, wt=10.000
% 25.28/25.65
% 25.28/25.65 Low Water (keep): wt=40.000, iters=3336
% 25.28/25.65
% 25.28/25.65 Low Water (keep): wt=39.000, iters=3818
% 25.28/25.65
% 25.28/25.65 Low Water (keep): wt=38.000, iters=3693
% 25.28/25.65
% 25.28/25.65 Low Water (keep): wt=37.000, iters=3607
% 25.28/25.65
% 25.28/25.65 Low Water (keep): wt=36.000, iters=3445
% 25.28/25.65
% 25.28/25.65 ============================== PROOF =================================
% 25.28/25.65 % SZS status Unsatisfiable
% 25.28/25.65 % SZS output start Refutation
% 25.28/25.65
% 25.28/25.65 % Proof 1 at 24.43 (+ 0.22) seconds.
% 25.28/25.65 % Length of proof is 135.
% 25.28/25.65 % Level of proof is 24.
% 25.28/25.65 % Maximum clause weight is 77.000.
% 25.28/25.65 % Given clauses 868.
% 25.28/25.65
% 25.28/25.65 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 25.28/25.65 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 25.28/25.65 3 inverse(sk_c1) = sk_c12 | inverse(sk_c4) = sk_c12 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 25.28/25.65 9 inverse(sk_c2) = sk_c11 | inverse(sk_c5) = sk_c11 # label(prove_this_44) # label(negated_conjecture). [assumption].
% 25.28/25.65 15 inverse(sk_c3) = sk_c11 | inverse(sk_c6) = sk_c9 # label(prove_this_66) # label(negated_conjecture). [assumption].
% 25.28/25.65 20 multiply(sk_c11,sk_c12) = sk_c10 | inverse(sk_c6) = sk_c9 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 25.28/25.65 21 multiply(sk_c11,sk_c12) = sk_c10 | inverse(sk_c8) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 25.28/25.65 22 multiply(sk_c11,sk_c12) = sk_c10 | inverse(sk_c7) = sk_c9 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 25.28/25.65 23 multiply(sk_c1,sk_c12) = sk_c11 | inverse(sk_c4) = sk_c12 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 25.28/25.65 28 inverse(sk_c1) = sk_c12 | multiply(sk_c4,sk_c12) = sk_c11 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 25.28/25.65 34 multiply(sk_c2,sk_c11) = sk_c10 | inverse(sk_c5) = sk_c11 # label(prove_this_34) # label(negated_conjecture). [assumption].
% 25.28/25.65 39 inverse(sk_c2) = sk_c11 | multiply(sk_c5,sk_c11) = sk_c10 # label(prove_this_43) # label(negated_conjecture). [assumption].
% 25.28/25.65 41 inverse(sk_c2) = sk_c11 | multiply(sk_c9,sk_c11) = sk_c12 # label(prove_this_47) # label(negated_conjecture). [assumption].
% 25.28/25.65 55 multiply(sk_c11,sk_c12) = sk_c10 | multiply(sk_c6,sk_c9) = sk_c12 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 25.28/25.65 56 multiply(sk_c11,sk_c12) = sk_c10 | multiply(sk_c9,sk_c11) = sk_c12 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 25.28/25.65 57 multiply(sk_c11,sk_c12) = sk_c10 | multiply(sk_c8,sk_c9) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 25.28/25.65 58 multiply(sk_c1,sk_c12) = sk_c11 | multiply(sk_c4,sk_c12) = sk_c11 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 25.28/25.65 64 multiply(sk_c2,sk_c11) = sk_c10 | multiply(sk_c5,sk_c11) = sk_c10 # label(prove_this_33) # label(negated_conjecture). [assumption].
% 25.28/25.65 66 multiply(sk_c2,sk_c11) = sk_c10 | multiply(sk_c9,sk_c11) = sk_c12 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 25.28/25.65 70 multiply(sk_c3,sk_c11) = sk_c12 | multiply(sk_c6,sk_c9) = sk_c12 # label(prove_this_55) # label(negated_conjecture). [assumption].
% 25.28/25.65 72 multiply(sk_c3,sk_c11) = sk_c12 | multiply(sk_c8,sk_c9) = sk_c7 # label(prove_this_60) # label(negated_conjecture). [assumption].
% 25.28/25.65 73 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 25.28/25.65 74 multiply(sk_c11,sk_c12) != sk_c10 | multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(C,sk_c11) != sk_c12 | inverse(C) != sk_c11 | multiply(D,sk_c12) != sk_c11 | inverse(D) != sk_c12 | multiply(E,sk_c11) != sk_c10 | inverse(E) != sk_c11 | multiply(F,V6) != sk_c12 | inverse(F) != V6 | multiply(V6,sk_c11) != sk_c12 | inverse(V7) != V8 | inverse(V8) != V6 | multiply(V7,V6) != V8 # label(prove_this_71) # label(negated_conjecture). [assumption].
% 25.28/25.65 76 multiply(sk_c11,sk_c12) != sk_c10 | multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(C,sk_c11) != sk_c12 | inverse(C) != sk_c11 | multiply(D,sk_c11) != sk_c10 | inverse(D) != sk_c11 | multiply(E,F) != sk_c12 | inverse(E) != F | multiply(F,sk_c11) != sk_c12 | inverse(V6) != V7 | inverse(V7) != F | multiply(V6,F) != V7. [factor(74,b,h),merge(h)].
% 25.28/25.65 84 multiply(sk_c11,sk_c12) != sk_c10 | multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(C,sk_c11) != sk_c12 | inverse(C) != sk_c11 | multiply(D,E) != sk_c12 | inverse(D) != E | multiply(E,sk_c11) != sk_c12 | inverse(F) != V6 | inverse(V6) != E | multiply(F,E) != V6. [factor(76,d,h),merge(h)].
% 25.28/25.65 100 multiply(sk_c11,sk_c12) != sk_c10 | multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(C,sk_c11) != sk_c12 | inverse(C) != sk_c11 | multiply(D,C) != sk_c12 | inverse(D) != C | inverse(E) != F | inverse(F) != C | multiply(E,C) != F. [factor(84,f,j)].
% 25.28/25.65 156 multiply(sk_c11,sk_c12) != sk_c10 | multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(C,sk_c11) != sk_c12 | inverse(C) != sk_c11 | multiply(D,C) != sk_c12 | inverse(D) != C | inverse(C) != C | multiply(D,C) != C. [factor(100,i,j)].
% 25.28/25.65 254 multiply(sk_c11,sk_c12) != sk_c10 | multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(C,sk_c11) != sk_c12 | inverse(C) != sk_c11 | multiply(C,C) != sk_c12 | inverse(C) != C | multiply(C,C) != C. [factor(156,i,j)].
% 25.28/25.65 328 inverse(sk_c2) = sk_c11 | multiply(sk_c11,sk_c5) = identity. [para(9(b,1),2(a,1,1))].
% 25.28/25.65 334 inverse(sk_c3) = sk_c11 | multiply(sk_c9,sk_c6) = identity. [para(15(b,1),2(a,1,1))].
% 25.28/25.65 337 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),73(a,1,1)),rewrite([1(2)]),flip(a)].
% 25.28/25.65 343 inverse(sk_c6) = sk_c9 | multiply(A,multiply(sk_c11,sk_c12)) = multiply(A,sk_c10). [para(20(a,1),73(a,2,2)),rewrite([73(8)])].
% 25.28/25.65 345 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c11,sk_c12)) = multiply(A,sk_c10). [para(21(a,1),73(a,2,2)),rewrite([73(8)])].
% 25.28/25.65 347 inverse(sk_c7) = sk_c9 | multiply(A,multiply(sk_c11,sk_c12)) = multiply(A,sk_c10). [para(22(a,1),73(a,2,2)),rewrite([73(8)])].
% 25.28/25.65 370 inverse(sk_c5) = sk_c11 | multiply(sk_c2,multiply(sk_c11,A)) = multiply(sk_c10,A). [para(34(a,1),73(a,1,1)),flip(b)].
% 25.28/25.65 380 inverse(sk_c2) = sk_c11 | multiply(sk_c5,multiply(sk_c11,A)) = multiply(sk_c10,A). [para(39(b,1),73(a,1,1)),flip(b)].
% 25.28/25.65 384 inverse(sk_c2) = sk_c11 | multiply(sk_c9,multiply(sk_c11,A)) = multiply(sk_c12,A). [para(41(b,1),73(a,1,1)),flip(b)].
% 25.28/25.65 415 multiply(sk_c11,sk_c12) = sk_c10 | multiply(A,multiply(sk_c9,sk_c11)) = multiply(A,sk_c12). [para(56(b,1),73(a,2,2)),rewrite([73(9)])].
% 25.28/25.65 446 multiply(sk_c3,sk_c11) = sk_c12 | multiply(sk_c8,multiply(sk_c9,A)) = multiply(sk_c7,A). [para(72(b,1),73(a,1,1)),flip(b)].
% 25.28/25.65 24162 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),337(a,1,2))].
% 25.28/25.65 24229 multiply(sk_c3,sk_c11) = sk_c12 | multiply(inverse(sk_c6),sk_c12) = sk_c9. [para(70(b,1),337(a,1,2))].
% 25.28/25.65 24292 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(337(a,1),337(a,1,2))].
% 25.28/25.65 24462 multiply(A,identity) = A. [back_rewrite(24162),rewrite([24292(4)])].
% 25.28/25.65 24647 inverse(identity) = identity. [para(24462(a,1),2(a,1))].
% 25.28/25.65 24682 multiply(sk_c11,sk_c12) != sk_c10 | multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | sk_c12 != sk_c11 | identity != sk_c11 | identity != sk_c12. [para(24462(a,1),254(h,1)),rewrite([1(22),24647(24),24647(30),24462(34)]),flip(f),xx(i),xx(j)].
% 25.28/25.65 25194 inverse(sk_c2) = sk_c11 | inverse(sk_c11) = sk_c5. [para(328(b,1),337(a,1,2)),rewrite([24462(8)])].
% 25.28/25.65 25257 inverse(sk_c11) = sk_c5 | multiply(sk_c11,sk_c2) = identity. [para(25194(a,1),2(a,1,1))].
% 25.28/25.65 25390 inverse(sk_c3) = sk_c11 | inverse(sk_c9) = sk_c6. [para(334(b,1),337(a,1,2)),rewrite([24462(8)])].
% 25.28/25.65 25486 multiply(A,inverse(A)) = identity. [para(24292(a,1),2(a,1))].
% 25.28/25.65 26028 multiply(A,multiply(inverse(A),B)) = B. [para(24292(a,1),337(a,1))].
% 25.28/25.65 26029 inverse(inverse(A)) = A. [para(24292(a,1),24462(a,1)),rewrite([24462(2)]),flip(a)].
% 25.28/25.65 26349 inverse(sk_c9) = sk_c6 | inverse(sk_c11) = sk_c3. [para(25390(a,1),26029(a,1,1))].
% 25.28/25.65 26421 inverse(sk_c1) = sk_c12 | multiply(sk_c4,sk_c12) = identity. [para(3(b,1),25486(a,1,2))].
% 25.28/25.65 27108 inverse(sk_c6) = sk_c9 | multiply(inverse(sk_c10),multiply(sk_c11,sk_c12)) = identity. [para(2(a,1),343(b,2))].
% 25.28/25.65 27173 inverse(sk_c11) = sk_c3 | multiply(sk_c6,sk_c9) = identity. [para(26349(a,1),2(a,1,1))].
% 25.28/25.65 27255 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c10),multiply(sk_c11,sk_c12)) = identity. [para(2(a,1),345(b,2))].
% 25.28/25.65 27408 inverse(sk_c7) = sk_c9 | multiply(inverse(sk_c10),multiply(sk_c11,sk_c12)) = identity. [para(2(a,1),347(b,2))].
% 25.28/25.65 27757 multiply(sk_c11,sk_c12) != sk_c10 | sk_c12 != sk_c11 | identity != sk_c12 | multiply(A,sk_c11) != sk_c10 | inverse(A) != sk_c11 | identity != sk_c11. [para(1(a,1),24682(b,1)),rewrite([24647(10)]),merge(f),merge(h)].
% 25.28/25.65 27836 multiply(sk_c11,sk_c12) != sk_c10 | sk_c12 != sk_c11 | identity != sk_c12 | multiply(A,multiply(B,sk_c11)) != sk_c10 | inverse(multiply(A,B)) != sk_c11 | identity != sk_c11. [para(73(a,1),27757(d,1))].
% 25.28/25.65 27842 multiply(sk_c11,sk_c12) != sk_c10 | sk_c12 != sk_c11 | identity != sk_c12 | sk_c10 != A | inverse(multiply(A,inverse(sk_c11))) != sk_c11 | identity != sk_c11. [para(2(a,1),27836(d,1,2)),rewrite([24462(13)]),flip(d)].
% 25.28/25.65 27889 multiply(sk_c11,sk_c12) != sk_c10 | sk_c12 != sk_c11 | identity != sk_c12 | multiply(A,B) != sk_c10 | inverse(multiply(A,multiply(B,inverse(sk_c11)))) != sk_c11 | identity != sk_c11. [para(73(a,1),27842(e,1,1)),flip(d)].
% 25.28/25.65 27975 multiply(sk_c11,sk_c12) != sk_c10 | sk_c12 != sk_c11 | identity != sk_c12 | multiply(A,multiply(B,C)) != sk_c10 | inverse(multiply(A,multiply(B,multiply(C,inverse(sk_c11))))) != sk_c11 | identity != sk_c11. [para(73(a,1),27889(e,1,1,2))].
% 25.28/25.65 29022 inverse(sk_c1) = sk_c12 | identity = sk_c11. [para(26421(b,1),28(b,1)),merge(b)].
% 25.28/25.65 29033 identity = sk_c11 | multiply(sk_c1,sk_c12) = identity. [para(29022(a,1),25486(a,1,2))].
% 25.28/25.65 29099 identity = sk_c11 | inverse(sk_c4) = sk_c12. [para(29033(b,1),23(a,1)),merge(b)].
% 25.28/25.65 29110 identity = sk_c11 | multiply(sk_c4,sk_c12) = identity. [para(29099(b,1),25486(a,1,2))].
% 25.28/25.65 29544 multiply(sk_c11,sk_c12) != sk_c10 | sk_c12 != sk_c11 | identity != sk_c12 | multiply(A,multiply(inverse(multiply(B,inverse(sk_c11))),B)) != sk_c10 | inverse(A) != sk_c11 | identity != sk_c11. [para(2(a,1),27975(e,1,1,2)),rewrite([24462(21)])].
% 25.28/25.65 29657 multiply(sk_c11,sk_c12) != sk_c10 | sk_c12 != sk_c11 | identity != sk_c12 | inverse(multiply(sk_c10,inverse(sk_c11))) != sk_c11 | identity != sk_c11. [resolve(29544,d,26028,a)].
% 25.28/25.65 31438 identity = sk_c11 | multiply(sk_c1,sk_c12) = sk_c11. [para(29110(b,1),58(b,1)),merge(c)].
% 25.28/25.65 32849 inverse(sk_c5) = sk_c11 | multiply(sk_c10,inverse(sk_c11)) = sk_c2. [para(25486(a,1),370(b,1,2)),rewrite([24462(7)]),flip(b)].
% 25.28/25.65 39365 inverse(sk_c2) = sk_c11 | multiply(sk_c10,inverse(sk_c11)) = sk_c5. [para(25486(a,1),380(b,1,2)),rewrite([24462(7)]),flip(b)].
% 25.28/25.65 41913 inverse(sk_c2) = sk_c11 | multiply(sk_c12,inverse(sk_c11)) = sk_c9. [para(25486(a,1),384(b,1,2)),rewrite([24462(7)]),flip(b)].
% 25.28/25.65 43011 identity = sk_c11. [para(31438(b,1),29033(b,1)),flip(c),merge(b),merge(c)].
% 25.28/25.65 43905 multiply(sk_c11,sk_c12) != sk_c10 | sk_c12 != sk_c11 | inverse(multiply(sk_c10,inverse(sk_c11))) != sk_c11. [back_rewrite(29657),rewrite([43011(9),43011(19)]),flip(c),xx(e),merge(c)].
% 25.28/25.65 44335 inverse(sk_c7) = sk_c9 | multiply(inverse(sk_c10),multiply(sk_c11,sk_c12)) = sk_c11. [back_rewrite(27408),rewrite([43011(11)])].
% 25.28/25.65 44350 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c10),multiply(sk_c11,sk_c12)) = sk_c11. [back_rewrite(27255),rewrite([43011(11)])].
% 25.28/25.65 44359 inverse(sk_c11) = sk_c3 | multiply(sk_c6,sk_c9) = sk_c11. [back_rewrite(27173),rewrite([43011(8)])].
% 25.28/25.65 44374 inverse(sk_c6) = sk_c9 | multiply(inverse(sk_c10),multiply(sk_c11,sk_c12)) = sk_c11. [back_rewrite(27108),rewrite([43011(11)])].
% 25.28/25.65 44541 inverse(sk_c11) = sk_c5 | multiply(sk_c11,sk_c2) = sk_c11. [back_rewrite(25257),rewrite([43011(8)])].
% 25.28/25.65 44555 inverse(sk_c11) = sk_c11. [back_rewrite(24647),rewrite([43011(1),43011(3)])].
% 25.28/25.65 44556 multiply(A,sk_c11) = A. [back_rewrite(24462),rewrite([43011(1)])].
% 25.28/25.65 44573 multiply(inverse(A),A) = sk_c11. [back_rewrite(2),rewrite([43011(3)])].
% 25.28/25.65 44574 multiply(sk_c11,A) = A. [back_rewrite(1),rewrite([43011(1)])].
% 25.28/25.65 44613 sk_c5 = sk_c11 | sk_c2 = sk_c11. [back_rewrite(44541),rewrite([44555(2),44574(6)]),flip(a)].
% 25.28/25.65 44636 sk_c3 = sk_c11 | multiply(sk_c6,sk_c9) = sk_c11. [back_rewrite(44359),rewrite([44555(2)]),flip(a)].
% 25.28/25.65 44745 sk_c10 != sk_c12 | sk_c12 != sk_c11 | inverse(sk_c10) != sk_c11. [back_rewrite(43905),rewrite([44574(3),44555(9),44556(9)]),flip(a)].
% 25.28/25.65 44928 inverse(sk_c2) = sk_c11 | sk_c9 = sk_c12. [back_rewrite(41913),rewrite([44555(7),44556(7)]),flip(b)].
% 25.28/25.65 44930 inverse(sk_c2) = sk_c11 | sk_c5 = sk_c10. [back_rewrite(39365),rewrite([44555(7),44556(7)]),flip(b)].
% 25.28/25.65 44934 inverse(sk_c5) = sk_c11 | sk_c2 = sk_c10. [back_rewrite(32849),rewrite([44555(7),44556(7)]),flip(b)].
% 25.28/25.65 45829 sk_c3 = sk_c12 | multiply(inverse(sk_c6),sk_c12) = sk_c9. [back_rewrite(24229),rewrite([44556(3)])].
% 25.28/25.65 48007 sk_c3 = sk_c12 | multiply(sk_c8,multiply(sk_c9,A)) = multiply(sk_c7,A). [back_rewrite(446),rewrite([44556(3)])].
% 25.28/25.65 48030 sk_c10 = sk_c12 | multiply(A,sk_c9) = multiply(A,sk_c12). [back_rewrite(415),rewrite([44574(3),44556(6)]),flip(a)].
% 25.28/25.65 48116 sk_c2 = sk_c10 | sk_c9 = sk_c12. [back_rewrite(66),rewrite([44556(3),44556(6)])].
% 25.28/25.65 48118 sk_c2 = sk_c10 | sk_c5 = sk_c10. [back_rewrite(64),rewrite([44556(3),44556(6)])].
% 25.28/25.65 48122 sk_c10 = sk_c12 | sk_c9 = sk_c12. [back_rewrite(56),rewrite([44574(3),44556(6)]),flip(a)].
% 25.28/25.65 48140 inverse(sk_c6) = sk_c9 | multiply(inverse(sk_c10),sk_c12) = sk_c11. [back_rewrite(44374),rewrite([44574(9)])].
% 25.28/25.65 48143 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c10),sk_c12) = sk_c11. [back_rewrite(44350),rewrite([44574(9)])].
% 25.28/25.65 48146 inverse(sk_c7) = sk_c9 | multiply(inverse(sk_c10),sk_c12) = sk_c11. [back_rewrite(44335),rewrite([44574(9)])].
% 25.28/25.65 48309 sk_c10 = sk_c12 | multiply(sk_c8,sk_c9) = sk_c7. [back_rewrite(57),rewrite([44574(3)]),flip(a)].
% 25.28/25.65 48310 sk_c10 = sk_c12 | multiply(sk_c6,sk_c9) = sk_c12. [back_rewrite(55),rewrite([44574(3)]),flip(a)].
% 25.28/25.65 49968 sk_c9 = sk_c12 | sk_c2 = sk_c12. [para(48122(a,1),48116(a,2)),merge(c)].
% 25.28/25.65 49977 sk_c9 = sk_c12 | sk_c2 = sk_c11. [para(44928(a,1),26029(a,1,1)),rewrite([44555(5)]),flip(b)].
% 25.28/25.65 50017 sk_c9 = sk_c12 | sk_c12 = sk_c11. [para(49977(b,1),49968(b,1)),flip(c),merge(b)].
% 25.28/25.65 50047 sk_c5 = sk_c10 | sk_c2 = sk_c11. [para(44930(a,1),26029(a,1,1)),rewrite([44555(5)]),flip(b)].
% 25.28/25.65 50146 sk_c2 = sk_c11 | sk_c10 = sk_c11. [para(50047(a,1),44613(a,1)),merge(c)].
% 25.28/25.65 50160 sk_c2 = sk_c10 | sk_c5 = sk_c11. [para(44934(a,1),26029(a,1,1)),rewrite([44555(5)]),flip(b)].
% 25.28/25.65 50216 sk_c2 = sk_c10 | sk_c10 = sk_c11. [para(50160(b,1),48118(b,1)),flip(c),merge(b)].
% 25.28/25.65 50242 sk_c10 = sk_c11. [para(50216(a,1),50146(a,1)),merge(b),merge(c)].
% 25.28/25.65 50918 sk_c12 = sk_c11 | multiply(sk_c6,sk_c9) = sk_c12. [back_rewrite(48310),rewrite([50242(1)]),flip(a)].
% 25.28/25.65 50919 sk_c12 = sk_c11 | multiply(sk_c8,sk_c9) = sk_c7. [back_rewrite(48309),rewrite([50242(1)]),flip(a)].
% 25.28/25.65 51020 inverse(sk_c7) = sk_c9 | sk_c12 = sk_c11. [back_rewrite(48146),rewrite([50242(5),44555(6),44574(7)])].
% 25.28/25.65 51022 inverse(sk_c8) = sk_c7 | sk_c12 = sk_c11. [back_rewrite(48143),rewrite([50242(5),44555(6),44574(7)])].
% 25.28/25.65 51024 inverse(sk_c6) = sk_c9 | sk_c12 = sk_c11. [back_rewrite(48140),rewrite([50242(5),44555(6),44574(7)])].
% 25.28/25.65 51042 sk_c12 = sk_c11 | multiply(A,sk_c9) = multiply(A,sk_c12). [back_rewrite(48030),rewrite([50242(1)]),flip(a)].
% 25.28/25.65 51571 sk_c12 != sk_c11. [back_rewrite(44745),rewrite([50242(1),50242(7),44555(8)]),flip(a),xx(c),merge(b)].
% 25.28/25.65 51619 multiply(A,sk_c9) = multiply(A,sk_c12). [back_unit_del(51042),unit_del(a,51571)].
% 25.28/25.65 51624 inverse(sk_c6) = sk_c9. [back_unit_del(51024),unit_del(b,51571)].
% 25.28/25.65 51625 inverse(sk_c8) = sk_c7. [back_unit_del(51022),unit_del(b,51571)].
% 25.28/25.65 51626 inverse(sk_c7) = sk_c9. [back_unit_del(51020),unit_del(b,51571)].
% 25.28/25.65 51638 multiply(sk_c8,sk_c12) = sk_c7. [back_unit_del(50919),rewrite([51619(6)]),unit_del(a,51571)].
% 25.28/25.65 51639 multiply(sk_c6,sk_c12) = sk_c12. [back_unit_del(50918),rewrite([51619(6)]),unit_del(a,51571)].
% 25.28/25.65 51650 sk_c9 = sk_c12. [back_unit_del(50017),unit_del(b,51571)].
% 25.28/25.65 51667 sk_c3 = sk_c11. [back_rewrite(44636),rewrite([51650(5),51639(6)]),unit_del(b,51571)].
% 25.28/25.65 51673 multiply(sk_c12,sk_c12) = sk_c12. [back_rewrite(45829),rewrite([51667(1),51624(5),51650(4),51650(7)]),flip(a),unit_del(a,51571)].
% 25.28/25.65 51679 multiply(sk_c8,multiply(sk_c12,A)) = multiply(sk_c7,A). [back_rewrite(48007),rewrite([51667(1),51650(5)]),flip(a),unit_del(a,51571)].
% 25.28/25.65 51684 inverse(sk_c7) = sk_c12. [back_rewrite(51626),rewrite([51650(3)])].
% 25.28/25.65 51707 multiply(sk_c7,multiply(sk_c8,A)) = A. [para(51625(a,1),337(a,1,1))].
% 25.28/25.65 51708 sk_c8 = sk_c12. [para(51625(a,1),26029(a,1,1)),rewrite([51684(2)]),flip(a)].
% 25.28/25.65 51711 multiply(sk_c7,sk_c12) = sk_c11. [para(51625(a,1),44573(a,1,1)),rewrite([51708(2)])].
% 25.28/25.65 51712 multiply(sk_c7,multiply(sk_c12,A)) = A. [back_rewrite(51707),rewrite([51708(2)])].
% 25.28/25.65 51713 multiply(sk_c12,multiply(sk_c12,A)) = multiply(sk_c7,A). [back_rewrite(51679),rewrite([51708(1)])].
% 25.28/25.65 51714 sk_c7 = sk_c12. [back_rewrite(51638),rewrite([51708(1),51673(3)]),flip(a)].
% 25.28/25.65 51716 multiply(sk_c12,multiply(sk_c12,A)) = multiply(sk_c12,A). [back_rewrite(51713),rewrite([51714(5)])].
% 25.28/25.65 51717 multiply(sk_c12,A) = A. [back_rewrite(51712),rewrite([51714(1),51716(4)])].
% 25.28/25.65 51718 $F. [back_rewrite(51711),rewrite([51714(1),51717(3)]),unit_del(a,51571)].
% 25.28/25.65
% 25.28/25.65 % SZS output end Refutation
% 25.28/25.65 ============================== end of proof ==========================
% 25.28/25.65
% 25.28/25.65 ============================== STATISTICS ============================
% 25.28/25.65
% 25.28/25.65 Given=868. Generated=205996. Kept=51717. proofs=1.
% 25.28/25.65 Usable=24. Sos=23. Demods=41. Limbo=4, Disabled=51740. Hints=0.
% 25.28/25.65 Megabytes=59.86.
% 25.28/25.65 User_CPU=24.43, System_CPU=0.22, Wall_clock=25.
% 25.28/25.65
% 25.28/25.65 ============================== end of statistics =====================
% 25.28/25.65
% 25.28/25.65 ============================== end of search =========================
% 25.28/25.65
% 25.28/25.65 THEOREM PROVED
% 25.28/25.65 % SZS status Unsatisfiable
% 25.28/25.65
% 25.28/25.65 Exiting with 1 proof.
% 25.28/25.65
% 25.28/25.65 Process 27143 exit (max_proofs) Mon Jun 13 07:17:18 2022
% 25.28/25.65 Prover9 interrupted
%------------------------------------------------------------------------------