TSTP Solution File: GRP362-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP362-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 11:18:46 EDT 2022
% Result : Unsatisfiable 11.63s 11.94s
% Output : Refutation 11.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP362-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 11:03:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.84/10.17 ============================== Prover9 ===============================
% 9.84/10.17 Prover9 (32) version 2009-11A, November 2009.
% 9.84/10.17 Process 24140 was started by sandbox on n022.cluster.edu,
% 9.84/10.17 Mon Jun 13 11:03:34 2022
% 9.84/10.17 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23986_n022.cluster.edu".
% 9.84/10.17 ============================== end of head ===========================
% 9.84/10.17
% 9.84/10.17 ============================== INPUT =================================
% 9.84/10.17
% 9.84/10.17 % Reading from file /tmp/Prover9_23986_n022.cluster.edu
% 9.84/10.17
% 9.84/10.17 set(prolog_style_variables).
% 9.84/10.17 set(auto2).
% 9.84/10.17 % set(auto2) -> set(auto).
% 9.84/10.17 % set(auto) -> set(auto_inference).
% 9.84/10.17 % set(auto) -> set(auto_setup).
% 9.84/10.17 % set(auto_setup) -> set(predicate_elim).
% 9.84/10.17 % set(auto_setup) -> assign(eq_defs, unfold).
% 9.84/10.17 % set(auto) -> set(auto_limits).
% 9.84/10.17 % set(auto_limits) -> assign(max_weight, "100.000").
% 9.84/10.17 % set(auto_limits) -> assign(sos_limit, 20000).
% 9.84/10.17 % set(auto) -> set(auto_denials).
% 9.84/10.17 % set(auto) -> set(auto_process).
% 9.84/10.17 % set(auto2) -> assign(new_constants, 1).
% 9.84/10.17 % set(auto2) -> assign(fold_denial_max, 3).
% 9.84/10.17 % set(auto2) -> assign(max_weight, "200.000").
% 9.84/10.17 % set(auto2) -> assign(max_hours, 1).
% 9.84/10.17 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 9.84/10.17 % set(auto2) -> assign(max_seconds, 0).
% 9.84/10.17 % set(auto2) -> assign(max_minutes, 5).
% 9.84/10.17 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 9.84/10.17 % set(auto2) -> set(sort_initial_sos).
% 9.84/10.17 % set(auto2) -> assign(sos_limit, -1).
% 9.84/10.17 % set(auto2) -> assign(lrs_ticks, 3000).
% 9.84/10.17 % set(auto2) -> assign(max_megs, 400).
% 9.84/10.17 % set(auto2) -> assign(stats, some).
% 9.84/10.17 % set(auto2) -> clear(echo_input).
% 9.84/10.17 % set(auto2) -> set(quiet).
% 9.84/10.17 % set(auto2) -> clear(print_initial_clauses).
% 9.84/10.17 % set(auto2) -> clear(print_given).
% 9.84/10.17 assign(lrs_ticks,-1).
% 9.84/10.17 assign(sos_limit,10000).
% 9.84/10.17 assign(order,kbo).
% 9.84/10.17 set(lex_order_vars).
% 9.84/10.17 clear(print_given).
% 9.84/10.17
% 9.84/10.17 % formulas(sos). % not echoed (58 formulas)
% 9.84/10.17
% 9.84/10.17 ============================== end of input ==========================
% 9.84/10.17
% 9.84/10.17 % From the command line: assign(max_seconds, 300).
% 9.84/10.17
% 9.84/10.17 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 9.84/10.17
% 9.84/10.17 % Formulas that are not ordinary clauses:
% 9.84/10.17
% 9.84/10.17 ============================== end of process non-clausal formulas ===
% 9.84/10.17
% 9.84/10.17 ============================== PROCESS INITIAL CLAUSES ===============
% 9.84/10.17
% 9.84/10.17 ============================== PREDICATE ELIMINATION =================
% 9.84/10.17
% 9.84/10.17 ============================== end predicate elimination =============
% 9.84/10.17
% 9.84/10.17 Auto_denials: (non-Horn, no changes).
% 9.84/10.17
% 9.84/10.17 Term ordering decisions:
% 9.84/10.17
% 9.84/10.17 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 9.84/10.17 Function symbol KB weights: sk_c10=1. sk_c9=1. sk_c8=1. sk_c1=1. sk_c2=1. sk_c6=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c7=1. identity=1. multiply=1. inverse=0.
% 9.84/10.17
% 9.84/10.17 ============================== end of process initial clauses ========
% 9.84/10.17
% 9.84/10.17 ============================== CLAUSES FOR SEARCH ====================
% 9.84/10.17
% 9.84/10.17 ============================== end of clauses for search =============
% 9.84/10.17
% 9.84/10.17 ============================== SEARCH ================================
% 9.84/10.17
% 9.84/10.17 % Starting search at 0.03 seconds.
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=34.000, iters=3484
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=33.000, iters=3359
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=32.000, iters=3335
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=31.000, iters=3380
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=30.000, iters=3353
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=29.000, iters=3339
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=28.000, iters=3333
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=27.000, iters=3340
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=26.000, iters=3333
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=25.000, iters=3357
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=24.000, iters=3386
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=22.000, iters=3379
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=21.000, iters=3341
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=20.000, iters=3375
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=19.000, iters=3402
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=17.000, iters=3438
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=16.000, iters=3343
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=15.000, iters=3348
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=14.000, iters=3339
% 9.84/10.17
% 9.84/10.17 Low Water (keep): wt=13.000, iters=3335
% 9.84/10.17
% 9.84/10.17 Low Water (displace): id=5989, wt=43.000
% 9.84/10.17
% 9.84/10.17 Low Water (displace): id=5992, wt=42.000
% 9.84/10.17
% 9.84/10.17 Low Water (displace): id=5831, wt=40.000
% 9.84/10.17
% 9.84/10.17 Low Water (displace): id=5854, wt=39.000
% 9.84/10.17
% 9.84/10.17 Low Water (displace): id=5098, wt=38.000
% 9.84/10.17
% 9.84/10.17 Low Water (displace): id=5816, wt=36.000
% 11.63/11.94
% 11.63/11.94 Low Water (displace): id=15495, wt=11.000
% 11.63/11.94
% 11.63/11.94 ============================== PROOF =================================
% 11.63/11.94 % SZS status Unsatisfiable
% 11.63/11.94 % SZS output start Refutation
% 11.63/11.94
% 11.63/11.94 % Proof 1 at 10.64 (+ 0.31) seconds.
% 11.63/11.94 % Length of proof is 147.
% 11.63/11.94 % Level of proof is 22.
% 11.63/11.94 % Maximum clause weight is 69.000.
% 11.63/11.94 % Given clauses 2182.
% 11.63/11.94
% 11.63/11.94 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 11.63/11.94 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 11.63/11.94 3 inverse(sk_c9) = sk_c10 | inverse(sk_c10) = sk_c9 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 11.63/11.94 8 inverse(sk_c1) = sk_c10 | inverse(sk_c3) = sk_c10 # label(prove_this_49) # label(negated_conjecture). [assumption].
% 11.63/11.94 9 inverse(sk_c1) = sk_c10 | inverse(sk_c5) = sk_c6 # label(prove_this_51) # label(negated_conjecture). [assumption].
% 11.63/11.94 10 inverse(sk_c1) = sk_c10 | inverse(sk_c7) = sk_c10 # label(prove_this_53) # label(negated_conjecture). [assumption].
% 11.63/11.94 12 multiply(sk_c9,sk_c8) = sk_c10 | inverse(sk_c3) = sk_c10 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 11.63/11.94 14 multiply(sk_c9,sk_c8) = sk_c10 | inverse(sk_c7) = sk_c10 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 11.63/11.94 21 multiply(sk_c10,sk_c8) = sk_c9 | inverse(sk_c3) = sk_c10 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 11.63/11.94 23 multiply(sk_c10,sk_c8) = sk_c9 | inverse(sk_c7) = sk_c10 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 11.63/11.94 25 multiply(sk_c10,sk_c2) = sk_c9 | inverse(sk_c3) = sk_c10 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 11.63/11.94 27 multiply(sk_c10,sk_c2) = sk_c9 | inverse(sk_c7) = sk_c10 # label(prove_this_35) # label(negated_conjecture). [assumption].
% 11.63/11.94 29 multiply(sk_c1,sk_c10) = sk_c2 | inverse(sk_c3) = sk_c10 # label(prove_this_40) # label(negated_conjecture). [assumption].
% 11.63/11.94 31 multiply(sk_c1,sk_c10) = sk_c2 | inverse(sk_c7) = sk_c10 # label(prove_this_44) # label(negated_conjecture). [assumption].
% 11.63/11.94 33 inverse(sk_c1) = sk_c10 | multiply(sk_c3,sk_c10) = sk_c4 # label(prove_this_48) # label(negated_conjecture). [assumption].
% 11.63/11.94 34 inverse(sk_c1) = sk_c10 | multiply(sk_c5,sk_c6) = sk_c8 # label(prove_this_50) # label(negated_conjecture). [assumption].
% 11.63/11.94 41 multiply(sk_c9,sk_c8) = sk_c10 | multiply(sk_c7,sk_c8) = sk_c10 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 11.63/11.94 42 multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c10,sk_c4) = sk_c9 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 11.63/11.94 43 multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c3,sk_c10) = sk_c4 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 11.63/11.94 47 multiply(sk_c10,sk_c2) = sk_c9 | multiply(sk_c10,sk_c4) = sk_c9 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 11.63/11.94 48 multiply(sk_c10,sk_c2) = sk_c9 | multiply(sk_c3,sk_c10) = sk_c4 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 11.63/11.94 52 multiply(sk_c1,sk_c10) = sk_c2 | multiply(sk_c10,sk_c4) = sk_c9 # label(prove_this_38) # label(negated_conjecture). [assumption].
% 11.63/11.94 53 multiply(sk_c1,sk_c10) = sk_c2 | multiply(sk_c3,sk_c10) = sk_c4 # label(prove_this_39) # label(negated_conjecture). [assumption].
% 11.63/11.94 57 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 11.63/11.94 58 multiply(sk_c9,sk_c8) != sk_c10 | inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | multiply(sk_c10,A) != sk_c9 | multiply(B,sk_c10) != A | inverse(B) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(sk_c10,C) != sk_c9 | multiply(D,sk_c10) != C | inverse(D) != sk_c10 | multiply(E,F) != sk_c8 | inverse(E) != F | multiply(F,sk_c9) != sk_c8 | inverse(V6) != sk_c10 | multiply(V6,sk_c8) != sk_c10 # label(prove_this_55) # label(negated_conjecture). [assumption].
% 11.63/11.94 59 multiply(sk_c9,sk_c8) != sk_c10 | inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | multiply(sk_c10,A) != sk_c9 | multiply(B,sk_c10) != A | inverse(B) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(sk_c10,C) != sk_c9 | multiply(D,sk_c10) != C | inverse(D) != sk_c10 | multiply(E,F) != sk_c8 | inverse(E) != F | multiply(F,sk_c9) != sk_c8. [factor(58,a,o),merge(n)].
% 11.63/11.94 65 multiply(sk_c9,sk_c8) != sk_c10 | inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | multiply(sk_c10,A) != sk_c9 | multiply(B,sk_c10) != A | inverse(B) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(C,D) != sk_c8 | inverse(C) != D | multiply(D,sk_c9) != sk_c8. [factor(59,e,i),merge(h),merge(i)].
% 11.63/11.94 88 inverse(sk_c10) = sk_c9 | multiply(sk_c10,sk_c9) = identity. [para(3(a,1),2(a,1,1))].
% 11.63/11.94 93 inverse(sk_c1) = sk_c10 | multiply(sk_c10,sk_c3) = identity. [para(8(b,1),2(a,1,1))].
% 11.63/11.94 94 inverse(sk_c1) = sk_c10 | multiply(sk_c6,sk_c5) = identity. [para(9(b,1),2(a,1,1))].
% 11.63/11.94 95 inverse(sk_c1) = sk_c10 | multiply(sk_c10,sk_c7) = identity. [para(10(b,1),2(a,1,1))].
% 11.63/11.94 96 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),57(a,1,1)),rewrite([1(2)]),flip(a)].
% 11.63/11.94 99 inverse(sk_c3) = sk_c10 | multiply(sk_c9,multiply(sk_c8,A)) = multiply(sk_c10,A). [para(12(a,1),57(a,1,1)),flip(b)].
% 11.63/11.94 103 inverse(sk_c7) = sk_c10 | multiply(sk_c9,multiply(sk_c8,A)) = multiply(sk_c10,A). [para(14(a,1),57(a,1,1)),flip(b)].
% 11.63/11.94 161 multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c3,multiply(sk_c10,A)) = multiply(sk_c4,A). [para(43(b,1),57(a,1,1)),flip(b)].
% 11.63/11.94 171 multiply(sk_c10,sk_c2) = sk_c9 | multiply(sk_c3,multiply(sk_c10,A)) = multiply(sk_c4,A). [para(48(b,1),57(a,1,1)),flip(b)].
% 11.63/11.94 180 multiply(sk_c10,sk_c4) = sk_c9 | multiply(A,multiply(sk_c1,sk_c10)) = multiply(A,sk_c2). [para(52(a,1),57(a,2,2)),rewrite([57(9)])].
% 11.63/11.94 182 multiply(sk_c1,sk_c10) = sk_c2 | multiply(A,multiply(sk_c3,sk_c10)) = multiply(A,sk_c4). [para(53(b,1),57(a,2,2)),rewrite([57(9)])].
% 11.63/11.94 206 multiply(sk_c9,sk_c8) != sk_c10 | inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | multiply(sk_c10,identity) != sk_c9 | inverse(inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c9) != sk_c8. [resolve(65,e,2,a)].
% 11.63/11.94 222 multiply(sk_c9,sk_c8) != sk_c10 | inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | multiply(sk_c10,A) != sk_c9 | identity != A | inverse(inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(B,C) != sk_c8 | inverse(B) != C | multiply(C,sk_c9) != sk_c8. [para(2(a,1),65(e,1))].
% 11.63/11.94 346 multiply(sk_c9,sk_c8) != sk_c10 | inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | inverse(inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c9) != sk_c8. [factor(222,c,d)].
% 11.63/11.94 479 multiply(sk_c9,sk_c8) != sk_c10 | inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | inverse(inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(sk_c10,sk_c9) != sk_c8. [factor(346,e,h),rewrite([2(30)]),merge(g)].
% 11.63/11.94 537 inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | inverse(inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(sk_c10,sk_c9) != sk_c8 | inverse(sk_c7) = sk_c10. [resolve(479,a,14,a)].
% 11.63/11.94 539 inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | inverse(inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(sk_c10,sk_c9) != sk_c8 | inverse(sk_c3) = sk_c10. [resolve(479,a,12,a)].
% 11.63/11.94 545 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),96(a,1,2))].
% 11.63/11.94 567 inverse(sk_c3) = sk_c10 | multiply(inverse(sk_c10),sk_c9) = sk_c2. [para(25(a,1),96(a,1,2))].
% 11.63/11.94 569 inverse(sk_c7) = sk_c10 | multiply(inverse(sk_c10),sk_c9) = sk_c2. [para(27(a,1),96(a,1,2))].
% 11.63/11.94 604 inverse(sk_c10) = sk_c9 | multiply(inverse(sk_c10),identity) = sk_c9. [para(88(b,1),96(a,1,2))].
% 11.63/11.94 605 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(96(a,1),96(a,1,2))].
% 11.63/11.94 608 multiply(A,identity) = A. [back_rewrite(545),rewrite([605(4)])].
% 11.63/11.94 609 inverse(sk_c10) = sk_c9. [back_rewrite(604),rewrite([608(8)]),merge(b)].
% 11.63/11.94 616 multiply(sk_c9,sk_c8) != sk_c10 | inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c9) != sk_c8. [back_rewrite(206),rewrite([608(17),609(19),609(23)]),flip(d),xx(f),merge(e)].
% 11.63/11.94 626 inverse(sk_c7) = sk_c10 | multiply(sk_c9,sk_c9) = sk_c2. [back_rewrite(569),rewrite([609(6)])].
% 11.63/11.94 628 inverse(sk_c3) = sk_c10 | multiply(sk_c9,sk_c9) = sk_c2. [back_rewrite(567),rewrite([609(6)])].
% 11.63/11.94 637 inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | multiply(sk_c10,sk_c9) != sk_c8 | inverse(sk_c3) = sk_c10. [back_rewrite(539),rewrite([609(14),609(18)]),xx(e),merge(d)].
% 11.63/11.94 639 inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | multiply(sk_c10,sk_c9) != sk_c8 | inverse(sk_c7) = sk_c10. [back_rewrite(537),rewrite([609(14),609(18)]),xx(e),merge(d)].
% 11.63/11.94 688 multiply(sk_c9,sk_c8) != sk_c10 | inverse(sk_c9) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | multiply(sk_c10,sk_c9) != sk_c8. [back_rewrite(479),rewrite([609(19),609(23)]),xx(f),merge(e)].
% 11.63/11.94 957 multiply(sk_c9,sk_c10) = identity. [para(609(a,1),2(a,1,1))].
% 11.63/11.94 958 multiply(sk_c9,multiply(sk_c10,A)) = A. [para(609(a,1),96(a,1,1))].
% 11.63/11.94 1065 inverse(identity) = identity. [para(608(a,1),2(a,1))].
% 11.63/11.94 1088 inverse(sk_c9) = sk_c10. [para(957(a,1),96(a,1,2)),rewrite([608(4)])].
% 11.63/11.94 1363 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | multiply(sk_c10,sk_c9) != sk_c8. [back_rewrite(688),rewrite([1088(7)]),xx(b)].
% 11.63/11.94 1383 multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | multiply(sk_c10,sk_c9) != sk_c8 | inverse(sk_c7) = sk_c10. [back_rewrite(639),rewrite([1088(2)]),xx(a)].
% 11.63/11.94 1385 multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | multiply(sk_c10,sk_c9) != sk_c8 | inverse(sk_c3) = sk_c10. [back_rewrite(637),rewrite([1088(2)]),xx(a)].
% 11.63/11.94 1391 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c9) != sk_c8. [back_rewrite(616),rewrite([1088(7)]),xx(b)].
% 11.63/11.94 1401 multiply(sk_c10,sk_c9) = identity. [para(1088(a,1),2(a,1,1))].
% 11.63/11.94 1402 multiply(sk_c10,multiply(sk_c9,A)) = A. [para(1088(a,1),96(a,1,1))].
% 11.63/11.94 1404 multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | inverse(sk_c3) = sk_c10. [back_rewrite(1385),rewrite([1401(11)]),merge(c)].
% 11.63/11.94 1406 multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8 | inverse(sk_c7) = sk_c10. [back_rewrite(1383),rewrite([1401(11)]),merge(c)].
% 11.63/11.94 1412 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8. [back_rewrite(1363),rewrite([1401(16)]),merge(d)].
% 11.63/11.94 1417 inverse(sk_c1) = sk_c10 | sk_c3 = sk_c9. [para(93(b,1),96(a,1,2)),rewrite([609(6),608(7)]),flip(b)].
% 11.63/11.94 1440 inverse(sk_c1) = sk_c10 | inverse(sk_c6) = sk_c5. [para(94(b,1),96(a,1,2)),rewrite([608(8)])].
% 11.63/11.94 1466 inverse(sk_c1) = sk_c10 | multiply(sk_c5,sk_c6) = identity. [para(1440(b,1),2(a,1,1))].
% 11.63/11.94 1469 inverse(sk_c1) = sk_c10 | sk_c7 = sk_c9. [para(95(b,1),96(a,1,2)),rewrite([609(6),608(7)]),flip(b)].
% 11.63/11.94 1544 multiply(A,inverse(A)) = identity. [para(605(a,1),2(a,1))].
% 11.63/11.94 1549 inverse(inverse(A)) = A. [para(605(a,1),608(a,1)),rewrite([608(2)]),flip(a)].
% 11.63/11.94 1610 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | multiply(A,multiply(B,C)) != sk_c8 | inverse(multiply(A,B)) != C | multiply(C,sk_c9) != sk_c8. [para(57(a,1),1391(d,1))].
% 11.63/11.94 1617 inverse(sk_c1) = sk_c10 | multiply(sk_c3,sk_c10) = identity. [para(8(b,1),1544(a,1,2))].
% 11.63/11.94 1619 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1544(a,1),57(a,1)),flip(a)].
% 11.63/11.94 1620 sk_c3 = sk_c9 | multiply(sk_c1,sk_c10) = identity. [para(1417(a,1),1544(a,1,2))].
% 11.63/11.94 1621 sk_c7 = sk_c9 | multiply(sk_c1,sk_c10) = identity. [para(1469(a,1),1544(a,1,2))].
% 11.63/11.94 1622 inverse(sk_c3) = sk_c10 | multiply(sk_c10,inverse(sk_c8)) = sk_c9. [para(1544(a,1),99(b,1,2)),rewrite([608(7)]),flip(b)].
% 11.63/11.94 1629 sk_c3 = sk_c9 | identity = sk_c2 | inverse(sk_c3) = sk_c10. [para(1620(b,1),29(a,1))].
% 11.63/11.94 1687 sk_c7 = sk_c9 | identity = sk_c2 | inverse(sk_c7) = sk_c10. [para(1621(b,1),31(a,1))].
% 11.63/11.94 1773 inverse(sk_c7) = sk_c10 | multiply(sk_c10,inverse(sk_c8)) = sk_c9. [para(1544(a,1),103(b,1,2)),rewrite([608(7)]),flip(b)].
% 11.63/11.94 2241 inverse(sk_c1) = sk_c10 | identity = sk_c8. [para(1466(b,1),34(b,1)),merge(b)].
% 11.63/11.94 2245 identity = sk_c8 | sk_c1 = sk_c9. [para(2241(a,1),1549(a,1,1)),rewrite([609(5)]),flip(b)].
% 11.63/11.94 2590 inverse(sk_c1) = sk_c10 | identity = sk_c4. [para(1617(b,1),33(b,1)),merge(b)].
% 11.63/11.94 2599 identity = sk_c4 | sk_c1 = sk_c9. [para(2590(a,1),1549(a,1,1)),rewrite([609(5)]),flip(b)].
% 11.63/11.94 2624 sk_c1 = sk_c9 | sk_c4 = sk_c8. [para(2599(a,1),2245(a,1)),merge(c)].
% 11.63/11.94 2629 sk_c1 = sk_c9 | multiply(sk_c10,sk_c8) = sk_c9. [para(2624(b,1),42(b,1,2)),merge(c)].
% 11.63/11.94 3910 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | sk_c8 != A | inverse(multiply(A,inverse(B))) != B | multiply(B,sk_c9) != sk_c8. [para(2(a,1),1610(d,1,2)),rewrite([608(15)]),flip(d)].
% 11.63/11.94 4107 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | sk_c8 != A | inverse(multiply(A,inverse(multiply(B,C)))) != multiply(B,C) | multiply(B,multiply(C,sk_c9)) != sk_c8. [para(57(a,1),3910(f,1))].
% 11.63/11.94 5307 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1619(a,1),96(a,1,2)),rewrite([608(3)]),flip(a)].
% 11.63/11.94 5527 multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c4,sk_c10) = sk_c9. [para(42(b,1),5307(a,1,2,1)),rewrite([1088(8),609(10)])].
% 11.63/11.94 5532 multiply(sk_c10,sk_c2) = sk_c9 | multiply(sk_c4,sk_c10) = sk_c9. [para(47(b,1),5307(a,1,2,1)),rewrite([1088(8),609(10)])].
% 11.63/11.94 5545 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(5307(a,1),96(a,1,2)),flip(a)].
% 11.63/11.94 5748 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | sk_c8 != A | multiply(B,multiply(C,inverse(A))) != multiply(B,C) | multiply(B,multiply(C,sk_c9)) != sk_c8. [back_rewrite(4107),rewrite([5545(17),5545(20),5545(19),1549(17),1549(17),57(18)])].
% 11.63/11.94 9086 inverse(sk_c3) = sk_c10 | multiply(sk_c9,sk_c9) = inverse(sk_c8). [para(1622(b,1),96(a,1,2)),rewrite([609(6)])].
% 11.63/11.94 9185 sk_c3 = sk_c9 | identity = sk_c2. [para(1629(c,1),1549(a,1,1)),rewrite([609(8)]),flip(c),merge(c)].
% 11.63/11.94 9190 sk_c3 = sk_c9 | inverse(sk_c2) = identity. [para(9185(b,1),1065(a,1,1))].
% 11.63/11.94 9875 sk_c7 = sk_c9 | identity = sk_c2. [para(1687(c,1),1549(a,1,1)),rewrite([609(8)]),flip(c),merge(c)].
% 11.63/11.94 9878 sk_c7 = sk_c9 | inverse(sk_c2) = identity. [para(9875(b,1),1065(a,1,1))].
% 11.63/11.94 10327 multiply(sk_c10,sk_c4) = sk_c9 | multiply(sk_c9,multiply(inverse(sk_c1),sk_c2)) = identity. [para(180(b,1),2(a,1)),rewrite([5545(9),609(7),57(11)])].
% 11.63/11.94 11105 inverse(sk_c7) = sk_c10 | multiply(sk_c9,sk_c9) = inverse(sk_c8). [para(1773(b,1),96(a,1,2)),rewrite([609(6)])].
% 11.63/11.94 11461 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | sk_c8 != A | multiply(B,multiply(sk_c10,inverse(A))) != multiply(B,sk_c10) | sk_c8 != B. [para(2(a,1),5748(f,1,2)),rewrite([1088(17),1088(21),608(24)]),flip(f)].
% 11.63/11.94 11464 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | inverse(A) != sk_c8 | multiply(B,multiply(sk_c10,A)) != multiply(B,sk_c10) | sk_c8 != B. [para(1549(a,1),11461(e,1,2,2)),flip(d)].
% 11.63/11.94 11466 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | multiply(inverse(A),sk_c10) != sk_c8 | multiply(B,sk_c10) != multiply(B,A) | sk_c8 != B. [para(1402(a,1),11464(e,1,2)),rewrite([5545(16),1088(16)]),flip(e)].
% 11.63/11.94 11469 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | multiply(sk_c10,sk_c10) != sk_c8 | multiply(A,sk_c9) != multiply(A,sk_c10) | sk_c8 != A. [para(1088(a,1),11466(d,1,1)),flip(e)].
% 11.63/11.94 12006 multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c3,multiply(sk_c10,sk_c10)) = sk_c9. [para(5527(b,1),161(b,2)),merge(b)].
% 11.63/11.94 12011 multiply(sk_c10,sk_c2) = sk_c9 | multiply(sk_c3,multiply(sk_c10,sk_c10)) = sk_c9. [para(5532(b,1),171(b,2)),merge(b)].
% 11.63/11.94 14274 inverse(sk_c3) = sk_c10 | inverse(sk_c8) = sk_c2. [para(9086(b,1),628(b,1)),merge(b)].
% 11.63/11.94 14282 inverse(sk_c8) = sk_c2 | sk_c3 = sk_c9. [para(14274(a,1),1549(a,1,1)),rewrite([609(6)]),flip(b)].
% 11.63/11.94 14288 sk_c3 = sk_c9 | inverse(sk_c2) = sk_c8. [para(14282(a,1),1549(a,1,1))].
% 11.63/11.94 14297 sk_c3 = sk_c9 | identity = sk_c8. [para(14288(b,1),9190(b,1)),flip(c),merge(b)].
% 11.63/11.94 15242 inverse(sk_c7) = sk_c10 | inverse(sk_c8) = sk_c2. [para(11105(b,1),626(b,1)),merge(b)].
% 11.63/11.94 15249 inverse(sk_c8) = sk_c2 | sk_c7 = sk_c9. [para(15242(a,1),1549(a,1,1)),rewrite([609(6)]),flip(b)].
% 11.63/11.94 15271 sk_c7 = sk_c9 | inverse(sk_c2) = sk_c8. [para(15249(a,1),1549(a,1,1))].
% 11.63/11.94 15274 sk_c7 = sk_c9 | identity = sk_c8. [para(15271(b,1),9878(b,1)),flip(c),merge(b)].
% 11.63/11.94 15553 identity != sk_c8 | inverse(sk_c3) = sk_c10. [resolve(1404,a,21,a),merge(c)].
% 11.63/11.94 15565 inverse(sk_c3) = sk_c10 | sk_c3 = sk_c9. [resolve(15553,a,14297,b)].
% 11.63/11.94 15575 sk_c3 = sk_c9. [para(15565(a,1),1549(a,1,1)),rewrite([609(5)]),flip(b),merge(b)].
% 11.63/11.94 15617 multiply(sk_c10,sk_c2) = sk_c9 | sk_c9 = sk_c10. [back_rewrite(12011),rewrite([15575(6),958(10)]),flip(b)].
% 11.63/11.94 15618 multiply(sk_c10,sk_c8) = sk_c9 | sk_c9 = sk_c10. [back_rewrite(12006),rewrite([15575(6),958(10)]),flip(b)].
% 11.63/11.94 15791 multiply(sk_c1,sk_c10) = sk_c2 | multiply(A,sk_c4) = A. [back_rewrite(182),rewrite([15575(6),957(8),608(7)]),flip(b)].
% 11.63/11.94 15828 identity != sk_c8 | inverse(sk_c7) = sk_c10. [resolve(1406,a,23,a),merge(c)].
% 11.63/11.94 15870 inverse(sk_c7) = sk_c10 | sk_c7 = sk_c9. [resolve(15828,a,15274,b)].
% 11.63/11.94 15903 sk_c7 = sk_c9. [para(15870(a,1),1549(a,1,1)),rewrite([609(5)]),flip(b),merge(b)].
% 11.63/11.94 16202 multiply(sk_c9,sk_c8) = sk_c10. [back_rewrite(41),rewrite([15903(6)]),merge(b)].
% 11.63/11.94 17424 multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | multiply(sk_c10,sk_c10) != sk_c8 | multiply(A,sk_c9) != multiply(A,sk_c10) | sk_c8 != A. [back_rewrite(11469),rewrite([16202(3)]),xx(a)].
% 11.63/11.94 19108 multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c8. [back_rewrite(1412),rewrite([16202(3)]),xx(a)].
% 11.63/11.94 19190 multiply(sk_c10,sk_c10) = sk_c8. [para(16202(a,1),96(a,1,2)),rewrite([1088(2)])].
% 11.63/11.94 19266 multiply(sk_c10,sk_c8) != sk_c9 | sk_c9 != sk_c10 | multiply(A,sk_c9) != multiply(A,sk_c10) | sk_c8 != A. [back_rewrite(17424),rewrite([19190(11)]),xx(c)].
% 11.63/11.94 19435 multiply(sk_c9,sk_c9) = inverse(sk_c8). [para(19190(a,1),5545(a,1,1)),rewrite([609(4),609(5)]),flip(a)].
% 11.63/11.94 19822 identity != sk_c8 | sk_c1 = sk_c9. [resolve(19108,a,2629,b)].
% 11.63/11.94 19969 sk_c1 = sk_c9. [resolve(19822,a,2245,a),merge(b)].
% 11.63/11.94 20048 identity = sk_c2 | multiply(A,sk_c4) = A. [back_rewrite(15791),rewrite([19969(1),957(3)])].
% 11.63/11.94 20085 multiply(sk_c10,sk_c4) = sk_c9 | identity = sk_c2. [back_rewrite(10327),rewrite([19969(7),1088(8),958(10)]),flip(b)].
% 11.63/11.94 20224 sk_c9 = sk_c10 | inverse(sk_c8) = sk_c2. [para(15617(a,1),96(a,1,2)),rewrite([609(5),19435(6)])].
% 11.63/11.94 20273 sk_c9 = sk_c10 | identity != sk_c8. [resolve(15618,a,19108,a)].
% 11.63/11.94 20277 sk_c9 = sk_c10 | inverse(sk_c8) = sk_c8. [para(15618(a,1),96(a,1,2)),rewrite([609(5),19435(6)])].
% 11.63/11.94 20285 sk_c9 = sk_c10 | sk_c2 = sk_c8. [para(20277(b,1),20224(b,1)),flip(c),merge(b)].
% 11.63/11.94 20555 identity = sk_c2 | sk_c9 = sk_c10. [para(20085(a,1),20048(b,1)),merge(b)].
% 11.63/11.94 20608 sk_c9 = sk_c10 | sk_c2 != sk_c8. [para(20555(a,1),20273(b,1)),merge(b)].
% 11.63/11.94 20613 sk_c9 = sk_c10. [resolve(20608,b,20285,b),merge(b)].
% 11.63/11.94 21000 multiply(sk_c10,sk_c8) != sk_c10. [back_rewrite(19266),rewrite([20613(4),20613(6),20613(9)]),xx(b),xx(c),xx(d)].
% 11.63/11.94 21010 $F. [back_rewrite(16202),rewrite([20613(1)]),unit_del(a,21000)].
% 11.63/11.94
% 11.63/11.94 % SZS output end Refutation
% 11.63/11.94 ============================== end of proof ==========================
% 11.63/11.94
% 11.63/11.94 ============================== STATISTICS ============================
% 11.63/11.94
% 11.63/11.94 Given=2182. Generated=584333. Kept=21009. proofs=1.
% 11.63/11.94 Usable=102. Sos=367. Demods=37. Limbo=397, Disabled=20201. Hints=0.
% 11.63/11.94 Megabytes=18.91.
% 11.63/11.94 User_CPU=10.64, System_CPU=0.31, Wall_clock=11.
% 11.63/11.94
% 11.63/11.94 ============================== end of statistics =====================
% 11.63/11.94
% 11.63/11.94 ============================== end of search =========================
% 11.63/11.94
% 11.63/11.94 THEOREM PROVED
% 11.63/11.94 % SZS status Unsatisfiable
% 11.63/11.94
% 11.63/11.94 Exiting with 1 proof.
% 11.63/11.94
% 11.63/11.94 Process 24140 exit (max_proofs) Mon Jun 13 11:03:45 2022
% 11.63/11.94 Prover9 interrupted
%------------------------------------------------------------------------------