TSTP Solution File: GRP303-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP303-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 11:18:33 EDT 2022
% Result : Unsatisfiable 2.64s 2.92s
% Output : Refutation 2.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP303-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 20:41:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.64/2.92 ============================== Prover9 ===============================
% 2.64/2.92 Prover9 (32) version 2009-11A, November 2009.
% 2.64/2.92 Process 12656 was started by sandbox2 on n013.cluster.edu,
% 2.64/2.92 Mon Jun 13 20:41:14 2022
% 2.64/2.92 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12500_n013.cluster.edu".
% 2.64/2.92 ============================== end of head ===========================
% 2.64/2.92
% 2.64/2.92 ============================== INPUT =================================
% 2.64/2.92
% 2.64/2.92 % Reading from file /tmp/Prover9_12500_n013.cluster.edu
% 2.64/2.92
% 2.64/2.92 set(prolog_style_variables).
% 2.64/2.92 set(auto2).
% 2.64/2.92 % set(auto2) -> set(auto).
% 2.64/2.92 % set(auto) -> set(auto_inference).
% 2.64/2.92 % set(auto) -> set(auto_setup).
% 2.64/2.92 % set(auto_setup) -> set(predicate_elim).
% 2.64/2.92 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.64/2.92 % set(auto) -> set(auto_limits).
% 2.64/2.92 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.64/2.92 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.64/2.92 % set(auto) -> set(auto_denials).
% 2.64/2.92 % set(auto) -> set(auto_process).
% 2.64/2.92 % set(auto2) -> assign(new_constants, 1).
% 2.64/2.92 % set(auto2) -> assign(fold_denial_max, 3).
% 2.64/2.92 % set(auto2) -> assign(max_weight, "200.000").
% 2.64/2.92 % set(auto2) -> assign(max_hours, 1).
% 2.64/2.92 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.64/2.92 % set(auto2) -> assign(max_seconds, 0).
% 2.64/2.92 % set(auto2) -> assign(max_minutes, 5).
% 2.64/2.92 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.64/2.92 % set(auto2) -> set(sort_initial_sos).
% 2.64/2.92 % set(auto2) -> assign(sos_limit, -1).
% 2.64/2.92 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.64/2.92 % set(auto2) -> assign(max_megs, 400).
% 2.64/2.92 % set(auto2) -> assign(stats, some).
% 2.64/2.92 % set(auto2) -> clear(echo_input).
% 2.64/2.92 % set(auto2) -> set(quiet).
% 2.64/2.92 % set(auto2) -> clear(print_initial_clauses).
% 2.64/2.92 % set(auto2) -> clear(print_given).
% 2.64/2.92 assign(lrs_ticks,-1).
% 2.64/2.92 assign(sos_limit,10000).
% 2.64/2.92 assign(order,kbo).
% 2.64/2.92 set(lex_order_vars).
% 2.64/2.92 clear(print_given).
% 2.64/2.92
% 2.64/2.92 % formulas(sos). % not echoed (25 formulas)
% 2.64/2.92
% 2.64/2.92 ============================== end of input ==========================
% 2.64/2.92
% 2.64/2.92 % From the command line: assign(max_seconds, 300).
% 2.64/2.92
% 2.64/2.92 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.64/2.92
% 2.64/2.92 % Formulas that are not ordinary clauses:
% 2.64/2.92
% 2.64/2.92 ============================== end of process non-clausal formulas ===
% 2.64/2.92
% 2.64/2.92 ============================== PROCESS INITIAL CLAUSES ===============
% 2.64/2.92
% 2.64/2.92 ============================== PREDICATE ELIMINATION =================
% 2.64/2.92
% 2.64/2.92 ============================== end predicate elimination =============
% 2.64/2.92
% 2.64/2.92 Auto_denials: (non-Horn, no changes).
% 2.64/2.92
% 2.64/2.92 Term ordering decisions:
% 2.64/2.92
% 2.64/2.92 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 2.64/2.92 Function symbol KB weights: sk_c6=1. sk_c7=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c1=1. sk_c2=1. identity=1. multiply=1. inverse=0.
% 2.64/2.92
% 2.64/2.92 ============================== end of process initial clauses ========
% 2.64/2.92
% 2.64/2.92 ============================== CLAUSES FOR SEARCH ====================
% 2.64/2.92
% 2.64/2.92 ============================== end of clauses for search =============
% 2.64/2.92
% 2.64/2.92 ============================== SEARCH ================================
% 2.64/2.92
% 2.64/2.92 % Starting search at 0.01 seconds.
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=47.000, iters=3666
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=43.000, iters=3592
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=42.000, iters=3523
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=39.000, iters=3361
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=38.000, iters=3375
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=37.000, iters=3360
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=36.000, iters=3348
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=35.000, iters=3425
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=34.000, iters=3349
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=33.000, iters=3350
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=32.000, iters=3333
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=31.000, iters=3349
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=30.000, iters=3362
% 2.64/2.92
% 2.64/2.92 ============================== PROOF =================================
% 2.64/2.92 % SZS status Unsatisfiable
% 2.64/2.92 % SZS output start Refutation
% 2.64/2.92
% 2.64/2.92 % Proof 1 at 1.90 (+ 0.03) seconds.
% 2.64/2.92 % Length of proof is 130.
% 2.64/2.92 % Level of proof is 23.
% 2.64/2.92 % Maximum clause weight is 45.000.
% 2.64/2.92 % Given clauses 580.
% 2.64/2.92
% 2.64/2.92 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 2.64/2.92 2 multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 2.64/2.92 3 sk_c5 = multiply(sk_c6,sk_c7). [copy(2),flip(a)].
% 2.64/2.92 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 2.64/2.92 5 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 2.64/2.92 6 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 2.64/2.92 7 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 2.64/2.92 8 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 2.64/2.92 11 multiply(sk_c7,sk_c6) = sk_c5 | inverse(sk_c4) = sk_c6 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 2.64/2.92 12 multiply(sk_c7,sk_c6) = multiply(sk_c6,sk_c7) | inverse(sk_c4) = sk_c6. [copy(11),rewrite([3(4)])].
% 2.64/2.92 13 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 2.64/2.92 14 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 2.64/2.92 15 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 2.64/2.92 16 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 2.64/2.92 17 inverse(sk_c1) = sk_c7 | multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6. [copy(16),rewrite([3(6)])].
% 2.64/2.92 18 multiply(sk_c2,sk_c6) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 2.64/2.92 19 multiply(sk_c2,sk_c6) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 2.64/2.92 21 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 2.64/2.92 22 inverse(sk_c2) = sk_c6 | multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6. [copy(21),rewrite([3(6)])].
% 2.64/2.92 27 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 2.64/2.92 28 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 2.64/2.92 29 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6. [copy(28),rewrite([3(7)])].
% 2.64/2.92 31 multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 2.64/2.92 32 multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6. [copy(31),rewrite([3(7)])].
% 2.64/2.92 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 2.64/2.92 34 multiply(sk_c7,sk_c6) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7 | inverse(D) != sk_c6 | multiply(D,sk_c5) != sk_c6 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 2.64/2.92 35 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7 | inverse(D) != sk_c6 | multiply(D,multiply(sk_c6,sk_c7)) != sk_c6. [copy(34),rewrite([3(4),3(11),3(39)]),xx(b)].
% 2.64/2.92 37 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(B) != sk_c7 | inverse(C) != sk_c6 | multiply(C,multiply(sk_c6,sk_c7)) != sk_c6. [factor(35,d,g)].
% 2.64/2.92 47 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 2.64/2.92 54 inverse(sk_c4) = sk_c6 | multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(14(a,1),33(a,1,1)),flip(b)].
% 2.64/2.92 55 inverse(sk_c4) = sk_c6 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6). [para(14(a,1),33(a,2,2)),rewrite([33(8)])].
% 2.64/2.92 57 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(15(b,1),33(a,2,2)),rewrite([33(8)])].
% 2.64/2.92 61 inverse(sk_c3) = sk_c7 | multiply(A,multiply(sk_c2,sk_c6)) = multiply(A,sk_c7). [para(18(a,1),33(a,2,2)),rewrite([33(8)])].
% 2.64/2.92 63 inverse(sk_c4) = sk_c6 | multiply(A,multiply(sk_c2,sk_c6)) = multiply(A,sk_c7). [para(19(a,1),33(a,2,2)),rewrite([33(8)])].
% 2.64/2.92 73 multiply(sk_c3,sk_c6) = sk_c7 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6). [para(27(a,1),33(a,2,2)),rewrite([33(9)])].
% 2.64/2.92 101 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(C) != sk_c6 | multiply(C,multiply(sk_c6,sk_c7)) != sk_c6. [para(4(a,1),35(b,1))].
% 2.64/2.92 102 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(C) != sk_c6 | multiply(C,multiply(sk_c6,sk_c7)) != sk_c6. [para(4(a,1),35(d,1))].
% 2.64/2.92 161 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(A) != sk_c7 | inverse(B) != sk_c6 | multiply(B,multiply(sk_c6,sk_c7)) != sk_c6. [factor(101,d,g)].
% 2.64/2.92 163 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,multiply(sk_c6,sk_c7)) != sk_c6. [factor(102,c,f)].
% 2.64/2.92 227 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(A) != sk_c7 | multiply(A,multiply(sk_c6,sk_c7)) != sk_c6. [factor(161,e,g)].
% 2.64/2.92 313 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),47(a,1,2))].
% 2.64/2.92 336 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(B) != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | sk_c7 != sk_c6. [para(47(a,1),37(h,1))].
% 2.64/2.92 340 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(47(a,1),47(a,1,2))].
% 2.64/2.92 341 multiply(A,identity) = A. [back_rewrite(313),rewrite([340(4)])].
% 2.64/2.92 344 inverse(identity) = identity. [para(341(a,1),4(a,1))].
% 2.64/2.92 414 multiply(A,inverse(A)) = identity. [para(340(a,1),4(a,1))].
% 2.64/2.92 439 multiply(A,multiply(inverse(A),B)) = B. [para(340(a,1),47(a,1))].
% 2.64/2.92 440 inverse(inverse(A)) = A. [para(340(a,1),341(a,1)),rewrite([341(2)]),flip(a)].
% 2.64/2.92 449 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(B) != sk_c7 | sk_c7 != sk_c6. [back_rewrite(336),rewrite([440(27)]),xx(g)].
% 2.64/2.92 456 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | identity != sk_c6 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(A) != sk_c7 | multiply(A,multiply(sk_c6,sk_c7)) != sk_c6. [back_rewrite(227),rewrite([440(13)]),xx(c)].
% 2.64/2.92 460 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | identity != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,multiply(sk_c6,sk_c7)) != sk_c6. [back_rewrite(163),rewrite([440(20)]),xx(e)].
% 2.64/2.92 473 inverse(sk_c3) = sk_c7 | multiply(sk_c1,sk_c7) = identity. [para(5(a,1),414(a,1,2))].
% 2.64/2.92 474 inverse(sk_c4) = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(6(a,1),414(a,1,2))].
% 2.64/2.92 475 inverse(sk_c3) = sk_c7 | multiply(sk_c2,sk_c6) = identity. [para(7(a,1),414(a,1,2))].
% 2.64/2.92 476 inverse(sk_c4) = sk_c6 | multiply(sk_c2,sk_c6) = identity. [para(8(a,1),414(a,1,2))].
% 2.64/2.92 477 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(414(a,1),33(a,1)),flip(a)].
% 2.64/2.92 543 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | identity != sk_c6 | multiply(sk_c4,sk_c6) != sk_c7 | inverse(sk_c4) != sk_c6 | inverse(sk_c4) != sk_c7 | multiply(sk_c1,sk_c7) = sk_c6. [resolve(456,f,29,b)].
% 2.64/2.92 601 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(A,multiply(B,sk_c7)) != sk_c6 | inverse(multiply(A,B)) != sk_c7 | multiply(C,sk_c6) != sk_c7 | inverse(C) != sk_c6 | inverse(C) != sk_c7 | sk_c7 != sk_c6. [para(33(a,1),449(b,1))].
% 2.64/2.92 779 inverse(sk_c3) = sk_c7 | identity = sk_c7. [para(475(b,1),18(a,1)),merge(c)].
% 2.64/2.92 784 identity = sk_c7 | multiply(sk_c7,sk_c3) = identity. [para(779(a,1),4(a,1,1))].
% 2.64/2.92 785 identity = sk_c7 | multiply(sk_c7,multiply(sk_c3,A)) = A. [para(779(a,1),47(a,1,1))].
% 2.64/2.92 787 identity = sk_c7 | multiply(sk_c3,sk_c7) = identity. [para(779(a,1),414(a,1,2))].
% 2.64/2.92 796 inverse(sk_c4) = sk_c6 | multiply(A,sk_c6) = A. [para(474(b,1),55(b,1,2)),rewrite([341(10)]),flip(c),merge(b)].
% 2.64/2.92 852 identity = sk_c7 | multiply(A,multiply(sk_c7,sk_c3)) = A. [para(784(b,1),33(a,2,2)),rewrite([33(7),341(9)])].
% 2.64/2.92 855 identity = sk_c7 | multiply(A,multiply(sk_c3,sk_c7)) = A. [para(787(b,1),33(a,2,2)),rewrite([33(7),341(9)])].
% 2.64/2.92 857 inverse(sk_c4) = sk_c6 | identity = sk_c7. [para(476(b,1),19(a,1)),merge(c)].
% 2.64/2.92 926 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | identity != sk_c6 | identity != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(A,multiply(sk_c6,sk_c7)) != sk_c6. [para(4(a,1),460(b,1)),rewrite([440(13)]),xx(c)].
% 2.64/2.92 938 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | identity != sk_c6 | identity != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c6. [para(1(a,1),926(f,1)),rewrite([344(21)]),merge(e)].
% 2.64/2.92 943 identity = sk_c7 | multiply(sk_c6,sk_c4) = identity. [para(857(a,1),4(a,1,1))].
% 2.64/2.92 944 identity = sk_c7 | multiply(sk_c6,multiply(sk_c4,A)) = A. [para(857(a,1),47(a,1,1))].
% 2.64/2.92 947 identity = sk_c7 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(857(a,1),439(a,1,2,1))].
% 2.64/2.92 953 identity = sk_c7 | multiply(A,multiply(sk_c6,sk_c4)) = A. [para(943(b,1),33(a,2,2)),rewrite([33(7),341(9)])].
% 2.64/2.92 959 inverse(sk_c1) = sk_c7 | multiply(inverse(multiply(sk_c3,sk_c6)),sk_c7) = identity. [para(57(b,1),4(a,1))].
% 2.64/2.92 1421 inverse(sk_c3) = sk_c7 | multiply(A,sk_c7) = A. [para(475(b,1),61(b,1,2)),rewrite([341(10)]),flip(c),merge(b)].
% 2.64/2.92 1668 inverse(sk_c4) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c7. [para(796(b,1),12(a,1)),flip(b),merge(c)].
% 2.64/2.92 1741 inverse(sk_c4) = sk_c6 | multiply(A,sk_c7) = A. [para(476(b,1),63(b,1,2)),rewrite([341(10)]),flip(c),merge(b)].
% 2.64/2.92 2469 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | sk_c6 != A | inverse(multiply(A,inverse(sk_c7))) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(B) != sk_c7 | sk_c7 != sk_c6. [para(4(a,1),601(b,1,2)),rewrite([341(9)]),flip(b)].
% 2.64/2.92 2510 inverse(sk_c3) = sk_c7 | sk_c1 = sk_c6. [para(1421(b,1),13(a,1)),merge(c)].
% 2.64/2.92 2535 inverse(sk_c3) = sk_c7 | identity = sk_c1. [para(1421(b,1),473(b,1)),flip(c),merge(b)].
% 2.64/2.92 2571 sk_c1 = sk_c6 | multiply(sk_c3,sk_c7) = identity. [para(2510(a,1),414(a,1,2))].
% 2.64/2.92 2576 identity = sk_c1 | multiply(sk_c3,sk_c7) = identity. [para(2535(a,1),414(a,1,2))].
% 2.64/2.92 3282 inverse(sk_c4) = sk_c6 | inverse(sk_c7) = identity. [para(1741(b,1),4(a,1))].
% 2.64/2.92 3349 inverse(sk_c4) = sk_c6 | sk_c7 = sk_c6. [para(1741(b,1),1668(b,1)),flip(c),merge(b)].
% 2.64/2.92 3476 sk_c7 = sk_c6 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(3349(a,1),439(a,1,2,1))].
% 2.64/2.92 3719 inverse(sk_c7) = identity | multiply(sk_c4,sk_c6) = identity. [para(3282(a,1),414(a,1,2))].
% 2.64/2.92 3737 multiply(sk_c3,sk_c6) = sk_c7 | multiply(inverse(multiply(sk_c1,sk_c7)),sk_c6) = identity. [para(73(b,1),4(a,1))].
% 2.64/2.92 5726 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(477(a,1),47(a,1,2)),rewrite([341(3)]),flip(a)].
% 2.64/2.92 5735 inverse(sk_c4) = sk_c6 | multiply(sk_c6,inverse(multiply(sk_c1,sk_c7))) = identity. [para(477(a,1),54(b,1)),flip(b)].
% 2.64/2.92 5932 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(5726(a,1),47(a,1,2)),flip(a)].
% 2.64/2.92 6100 inverse(sk_c4) = sk_c6 | multiply(sk_c6,multiply(inverse(sk_c7),inverse(sk_c1))) = identity. [back_rewrite(5735),rewrite([5932(9)])].
% 2.64/2.92 6511 multiply(sk_c3,sk_c6) = sk_c7 | multiply(inverse(sk_c7),multiply(inverse(sk_c1),sk_c6)) = identity. [back_rewrite(3737),rewrite([5932(9),33(12)])].
% 2.64/2.92 6833 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | sk_c6 != A | multiply(sk_c7,inverse(A)) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(B) != sk_c7 | sk_c7 != sk_c6. [back_rewrite(2469),rewrite([5932(13),440(12)])].
% 2.64/2.92 7071 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c6),multiply(inverse(sk_c3),sk_c7)) = identity. [back_rewrite(959),rewrite([5932(8),33(11)])].
% 2.64/2.92 7946 identity = sk_c7 | multiply(inverse(sk_c7),A) = multiply(sk_c3,A). [para(785(b,1),47(a,1,2))].
% 2.64/2.92 7947 identity = sk_c7 | multiply(inverse(sk_c3),A) = multiply(sk_c7,A). [para(439(a,1),785(b,1,2)),flip(b)].
% 2.64/2.92 8196 identity = sk_c7 | multiply(inverse(sk_c6),A) = multiply(sk_c4,A). [para(944(b,1),47(a,1,2))].
% 2.64/2.92 8256 identity = sk_c7 | multiply(sk_c4,sk_c6) = multiply(sk_c7,sk_c3). [para(852(b,1),947(b,1,2)),merge(b)].
% 2.64/2.92 8257 identity = sk_c7 | multiply(sk_c4,sk_c6) = multiply(sk_c3,sk_c7). [para(855(b,1),947(b,1,2)),merge(b)].
% 2.64/2.92 8283 identity = sk_c7 | multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c4). [para(953(b,1),947(b,1,2)),merge(b)].
% 2.64/2.92 8361 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | inverse(A) != sk_c6 | multiply(sk_c7,A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(B) != sk_c7 | sk_c7 != sk_c6. [para(440(a,1),6833(c,1,2)),flip(b)].
% 2.64/2.92 8843 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(inverse(A),sk_c7) != sk_c6 | sk_c7 != A | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(B) != sk_c7 | sk_c7 != sk_c6. [para(439(a,1),8361(c,1)),rewrite([5932(11),440(11)]),flip(c)].
% 2.64/2.92 8850 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(inverse(sk_c6),sk_c7) != sk_c6 | sk_c7 != sk_c6 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(A) != sk_c7. [factor(8843,c,g)].
% 2.64/2.92 8860 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(inverse(sk_c6),sk_c7) != sk_c6 | sk_c7 != sk_c6 | multiply(A,multiply(B,sk_c6)) != sk_c7 | multiply(inverse(B),inverse(A)) != sk_c6 | multiply(inverse(B),inverse(A)) != sk_c7. [para(33(a,1),8850(d,1)),rewrite([5932(23),5932(28)])].
% 2.64/2.92 9646 sk_c7 = sk_c6 | inverse(sk_c1) = sk_c7. [para(3476(b,1),17(b,1)),merge(c)].
% 2.64/2.92 9647 sk_c7 = sk_c6 | inverse(sk_c2) = sk_c6. [para(3476(b,1),22(b,1)),merge(c)].
% 2.64/2.92 9649 sk_c7 = sk_c6 | multiply(sk_c1,sk_c7) = sk_c6. [para(3476(b,1),29(b,1)),merge(c)].
% 2.64/2.92 9650 sk_c7 = sk_c6 | multiply(sk_c2,sk_c6) = sk_c7. [para(3476(b,1),32(b,1)),merge(c)].
% 2.64/2.92 9659 sk_c7 = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(9646(b,1),414(a,1,2))].
% 2.64/2.92 9666 sk_c7 = sk_c6 | multiply(sk_c2,sk_c6) = identity. [para(9647(b,1),414(a,1,2))].
% 2.64/2.92 9730 sk_c7 = sk_c6 | identity = sk_c6. [para(9659(b,1),9649(b,1)),merge(b)].
% 2.64/2.92 9756 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(inverse(sk_c6),sk_c7) != sk_c6 | sk_c7 != sk_c6 | sk_c7 != A | multiply(sk_c6,inverse(A)) != sk_c6 | multiply(sk_c6,inverse(A)) != sk_c7. [para(4(a,1),8860(d,1,2)),rewrite([341(18),440(21),440(26)]),flip(d)].
% 2.64/2.92 9820 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(inverse(sk_c6),sk_c7) != sk_c6 | sk_c7 != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,A) != sk_c7. [para(440(a,1),9756(f,1,2)),rewrite([440(22)]),flip(d)].
% 2.64/2.92 9833 multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7) | multiply(inverse(sk_c6),sk_c7) != sk_c6 | sk_c7 != sk_c6 | multiply(inverse(sk_c7),sk_c6) != sk_c7. [resolve(9820,f,439,a),rewrite([5932(21),440(21),439(28)]),merge(e)].
% 2.64/2.92 9913 sk_c7 = sk_c6 | identity = sk_c7. [para(9666(b,1),9650(b,1)),merge(b)].
% 2.64/2.92 9932 sk_c7 = sk_c6. [para(9913(b,1),9730(b,1)),merge(b),merge(c)].
% 2.64/2.92 9967 identity != sk_c6. [back_rewrite(9833),rewrite([9932(1),9932(5),9932(10),4(11),9932(11),9932(14),4(17),9932(15)]),xx(a),xx(c),merge(b)].
% 2.64/2.92 10468 multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c4). [back_rewrite(8283),rewrite([9932(2)]),unit_del(a,9967)].
% 2.64/2.92 10487 multiply(sk_c3,sk_c6) = multiply(sk_c6,sk_c4). [back_rewrite(8257),rewrite([9932(2),10468(6),9932(8)]),flip(b),unit_del(a,9967)].
% 2.64/2.92 10488 multiply(sk_c6,sk_c4) = multiply(sk_c6,sk_c3). [back_rewrite(8256),rewrite([9932(2),10468(6),9932(7)]),unit_del(a,9967)].
% 2.64/2.92 10511 multiply(inverse(sk_c6),A) = multiply(sk_c4,A). [back_rewrite(8196),rewrite([9932(2)]),unit_del(a,9967)].
% 2.64/2.92 10550 multiply(inverse(sk_c3),A) = multiply(sk_c6,A). [back_rewrite(7947),rewrite([9932(2),9932(7)]),unit_del(a,9967)].
% 2.64/2.92 10551 multiply(sk_c4,A) = multiply(sk_c3,A). [back_rewrite(7946),rewrite([9932(2),9932(4),10511(6)]),unit_del(a,9967)].
% 2.64/2.92 10637 inverse(sk_c1) = sk_c6. [back_rewrite(7071),rewrite([9932(3),9932(9),10550(10),47(10)]),flip(b),unit_del(b,9967)].
% 2.64/2.93 10653 multiply(sk_c6,sk_c3) = sk_c6. [back_rewrite(6511),rewrite([10487(3),10488(3),9932(4),9932(6),10637(9),47(11)]),flip(b),unit_del(b,9967)].
% 2.64/2.93 10658 inverse(sk_c4) = sk_c6. [back_rewrite(6100),rewrite([9932(6),10637(9),4(9),341(7)]),flip(b),unit_del(b,9967)].
% 2.64/2.93 10703 inverse(sk_c6) = identity. [back_rewrite(3719),rewrite([9932(1),10551(7),10487(7),10488(7),10653(7)]),flip(b),unit_del(b,9967)].
% 2.64/2.93 10708 identity = sk_c1. [back_rewrite(2576),rewrite([9932(5),10487(6),10488(6),10653(6)]),flip(b),unit_del(b,9967)].
% 2.64/2.93 10710 sk_c1 = sk_c6. [back_rewrite(2571),rewrite([9932(5),10487(6),10488(6),10653(6),10708(5)]),flip(b),merge(b)].
% 2.64/2.93 10729 multiply(sk_c6,sk_c6) != sk_c6. [back_rewrite(938),rewrite([9932(1),9932(5),10708(8),10710(8),10708(11),10710(11),9932(12),9932(14),10703(15),10708(14),10710(14),9932(17),9932(20)]),xx(a),xx(b),xx(c),merge(b)].
% 2.64/2.93 10731 $F. [back_rewrite(543),rewrite([9932(1),9932(5),10708(8),10710(8),10551(13),10487(13),10488(13),10653(13),9932(12),10658(15),10658(18),9932(18),10710(20),9932(21)]),xx(a),xx(b),xx(c),xx(d),xx(e),unit_del(a,10729)].
% 2.64/2.93
% 2.64/2.93 % SZS output end Refutation
% 2.64/2.93 ============================== end of proof ==========================
% 2.64/2.93
% 2.64/2.93 ============================== STATISTICS ============================
% 2.64/2.93
% 2.64/2.93 Given=580. Generated=48523. Kept=10720. proofs=1.
% 2.64/2.93 Usable=192. Sos=274. Demods=41. Limbo=799, Disabled=9480. Hints=0.
% 2.64/2.93 Megabytes=11.96.
% 2.64/2.93 User_CPU=1.91, System_CPU=0.03, Wall_clock=2.
% 2.64/2.93
% 2.64/2.93 ============================== end of statistics =====================
% 2.64/2.93
% 2.64/2.93 ============================== end of search =========================
% 2.64/2.93
% 2.64/2.93 THEOREM PROVED
% 2.64/2.93 % SZS status Unsatisfiable
% 2.64/2.93
% 2.64/2.93 Exiting with 1 proof.
% 2.64/2.93
% 2.64/2.93 Process 12656 exit (max_proofs) Mon Jun 13 20:41:16 2022
% 2.64/2.93 Prover9 interrupted
%------------------------------------------------------------------------------