TSTP Solution File: GRP226-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP226-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 11:18:14 EDT 2022
% Result : Unsatisfiable 26.07s 26.39s
% Output : Refutation 26.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP226-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 10:59:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 26.07/26.39 ============================== Prover9 ===============================
% 26.07/26.39 Prover9 (32) version 2009-11A, November 2009.
% 26.07/26.39 Process 6676 was started by sandbox2 on n020.cluster.edu,
% 26.07/26.39 Tue Jun 14 10:59:35 2022
% 26.07/26.39 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6523_n020.cluster.edu".
% 26.07/26.39 ============================== end of head ===========================
% 26.07/26.39
% 26.07/26.39 ============================== INPUT =================================
% 26.07/26.39
% 26.07/26.39 % Reading from file /tmp/Prover9_6523_n020.cluster.edu
% 26.07/26.39
% 26.07/26.39 set(prolog_style_variables).
% 26.07/26.39 set(auto2).
% 26.07/26.39 % set(auto2) -> set(auto).
% 26.07/26.39 % set(auto) -> set(auto_inference).
% 26.07/26.39 % set(auto) -> set(auto_setup).
% 26.07/26.39 % set(auto_setup) -> set(predicate_elim).
% 26.07/26.39 % set(auto_setup) -> assign(eq_defs, unfold).
% 26.07/26.39 % set(auto) -> set(auto_limits).
% 26.07/26.39 % set(auto_limits) -> assign(max_weight, "100.000").
% 26.07/26.39 % set(auto_limits) -> assign(sos_limit, 20000).
% 26.07/26.39 % set(auto) -> set(auto_denials).
% 26.07/26.39 % set(auto) -> set(auto_process).
% 26.07/26.39 % set(auto2) -> assign(new_constants, 1).
% 26.07/26.39 % set(auto2) -> assign(fold_denial_max, 3).
% 26.07/26.39 % set(auto2) -> assign(max_weight, "200.000").
% 26.07/26.39 % set(auto2) -> assign(max_hours, 1).
% 26.07/26.39 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 26.07/26.39 % set(auto2) -> assign(max_seconds, 0).
% 26.07/26.39 % set(auto2) -> assign(max_minutes, 5).
% 26.07/26.39 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 26.07/26.39 % set(auto2) -> set(sort_initial_sos).
% 26.07/26.39 % set(auto2) -> assign(sos_limit, -1).
% 26.07/26.39 % set(auto2) -> assign(lrs_ticks, 3000).
% 26.07/26.39 % set(auto2) -> assign(max_megs, 400).
% 26.07/26.39 % set(auto2) -> assign(stats, some).
% 26.07/26.39 % set(auto2) -> clear(echo_input).
% 26.07/26.39 % set(auto2) -> set(quiet).
% 26.07/26.39 % set(auto2) -> clear(print_initial_clauses).
% 26.07/26.39 % set(auto2) -> clear(print_given).
% 26.07/26.39 assign(lrs_ticks,-1).
% 26.07/26.39 assign(sos_limit,10000).
% 26.07/26.39 assign(order,kbo).
% 26.07/26.39 set(lex_order_vars).
% 26.07/26.39 clear(print_given).
% 26.07/26.39
% 26.07/26.39 % formulas(sos). % not echoed (24 formulas)
% 26.07/26.39
% 26.07/26.39 ============================== end of input ==========================
% 26.07/26.39
% 26.07/26.39 % From the command line: assign(max_seconds, 300).
% 26.07/26.39
% 26.07/26.39 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 26.07/26.39
% 26.07/26.39 % Formulas that are not ordinary clauses:
% 26.07/26.39
% 26.07/26.39 ============================== end of process non-clausal formulas ===
% 26.07/26.39
% 26.07/26.39 ============================== PROCESS INITIAL CLAUSES ===============
% 26.07/26.39
% 26.07/26.39 ============================== PREDICATE ELIMINATION =================
% 26.07/26.39
% 26.07/26.39 ============================== end predicate elimination =============
% 26.07/26.39
% 26.07/26.39 Auto_denials: (non-Horn, no changes).
% 26.07/26.39
% 26.07/26.39 Term ordering decisions:
% 26.07/26.39
% 26.07/26.39 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 26.07/26.39 Function symbol KB weights: sk_c7=1. sk_c6=1. sk_c4=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. identity=1. multiply=1. inverse=0.
% 26.07/26.39
% 26.07/26.39 ============================== end of process initial clauses ========
% 26.07/26.39
% 26.07/26.39 ============================== CLAUSES FOR SEARCH ====================
% 26.07/26.39
% 26.07/26.39 ============================== end of clauses for search =============
% 26.07/26.39
% 26.07/26.39 ============================== SEARCH ================================
% 26.07/26.39
% 26.07/26.39 % Starting search at 0.01 seconds.
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=30.000, iters=3352
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=29.000, iters=3358
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=28.000, iters=3451
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=27.000, iters=3460
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=26.000, iters=3440
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=25.000, iters=3361
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=24.000, iters=3343
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=23.000, iters=3344
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=22.000, iters=3439
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=21.000, iters=3418
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=20.000, iters=3337
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=19.000, iters=3342
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=18.000, iters=3337
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=17.000, iters=3333
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=16.000, iters=3337
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=15.000, iters=3350
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=14.000, iters=3335
% 26.07/26.39
% 26.07/26.39 Low Water (keep): wt=13.000, iters=3333
% 26.07/26.39
% 26.07/26.39 ============================== PROOF =================================
% 26.07/26.39 % SZS status Unsatisfiable
% 26.07/26.39 % SZS output start Refutation
% 26.07/26.39
% 26.07/26.39 % Proof 1 at 24.56 (+ 0.85) seconds.
% 26.07/26.39 % Length of proof is 205.
% 26.07/26.39 % Level of proof is 31.
% 26.07/26.39 % Maximum clause weight is 41.000.
% 26.07/26.39 % Given clauses 3796.
% 26.07/26.39
% 26.07/26.39 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 26.07/26.39 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 26.07/26.39 3 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c7 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 26.07/26.39 4 inverse(sk_c1) = sk_c7 | inverse(sk_c5) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 26.07/26.39 5 inverse(sk_c2) = sk_c7 | inverse(sk_c4) = sk_c7 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 26.07/26.39 6 inverse(sk_c2) = sk_c7 | inverse(sk_c5) = sk_c6 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 26.07/26.39 7 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c6) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 26.07/26.39 8 inverse(sk_c1) = sk_c7 | multiply(sk_c5,sk_c6) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 26.07/26.39 9 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c4) = sk_c7 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 26.07/26.39 10 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c5) = sk_c6 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 26.07/26.40 11 multiply(sk_c7,sk_c3) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 26.07/26.40 12 multiply(sk_c7,sk_c3) = sk_c6 | inverse(sk_c5) = sk_c6 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 26.07/26.40 13 multiply(sk_c2,sk_c7) = sk_c3 | inverse(sk_c4) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 26.07/26.40 14 multiply(sk_c2,sk_c7) = sk_c3 | inverse(sk_c5) = sk_c6 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 26.07/26.40 15 inverse(sk_c2) = sk_c7 | multiply(sk_c4,sk_c6) = sk_c7 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 26.07/26.40 16 inverse(sk_c2) = sk_c7 | multiply(sk_c5,sk_c6) = sk_c7 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 26.07/26.40 17 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c4,sk_c6) = sk_c7 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 26.07/26.40 20 multiply(sk_c7,sk_c3) = sk_c6 | multiply(sk_c5,sk_c6) = sk_c7 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 26.07/26.40 22 multiply(sk_c2,sk_c7) = sk_c3 | multiply(sk_c5,sk_c6) = sk_c7 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 26.07/26.40 23 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 26.07/26.40 24 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,B) != sk_c6 | multiply(C,sk_c7) != B | inverse(C) != sk_c7 | inverse(D) != sk_c7 | multiply(D,sk_c6) != sk_c7 | multiply(E,sk_c6) != sk_c7 | inverse(E) != sk_c6 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 26.07/26.40 26 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,B) != sk_c6 | multiply(C,sk_c7) != B | inverse(C) != sk_c7 | multiply(D,sk_c6) != sk_c7 | inverse(D) != sk_c6. [factor(24,a,f),merge(f)].
% 26.07/26.40 30 inverse(sk_c4) = sk_c7 | multiply(sk_c7,sk_c1) = identity. [para(3(a,1),2(a,1,1))].
% 26.07/26.40 31 inverse(sk_c5) = sk_c6 | multiply(sk_c7,sk_c1) = identity. [para(4(a,1),2(a,1,1))].
% 26.07/26.40 32 inverse(sk_c4) = sk_c7 | multiply(sk_c7,sk_c2) = identity. [para(5(a,1),2(a,1,1))].
% 26.07/26.40 34 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),23(a,1,1)),rewrite([1(2)]),flip(a)].
% 26.07/26.40 35 inverse(sk_c1) = sk_c7 | multiply(sk_c4,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(7(b,1),23(a,1,1)),flip(b)].
% 26.07/26.40 37 inverse(sk_c1) = sk_c7 | multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(8(b,1),23(a,1,1)),flip(b)].
% 26.07/26.40 44 inverse(sk_c4) = sk_c7 | multiply(A,multiply(sk_c7,sk_c3)) = multiply(A,sk_c6). [para(11(a,1),23(a,2,2)),rewrite([23(8)])].
% 26.07/26.40 46 inverse(sk_c5) = sk_c6 | multiply(A,multiply(sk_c7,sk_c3)) = multiply(A,sk_c6). [para(12(a,1),23(a,2,2)),rewrite([23(8)])].
% 26.07/26.40 48 inverse(sk_c4) = sk_c7 | multiply(A,multiply(sk_c2,sk_c7)) = multiply(A,sk_c3). [para(13(a,1),23(a,2,2)),rewrite([23(8)])].
% 26.07/26.40 49 inverse(sk_c5) = sk_c6 | multiply(sk_c2,multiply(sk_c7,A)) = multiply(sk_c3,A). [para(14(a,1),23(a,1,1)),flip(b)].
% 26.07/26.40 50 inverse(sk_c5) = sk_c6 | multiply(A,multiply(sk_c2,sk_c7)) = multiply(A,sk_c3). [para(14(a,1),23(a,2,2)),rewrite([23(8)])].
% 26.07/26.40 61 multiply(sk_c7,sk_c3) = sk_c6 | multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(20(b,1),23(a,1,1)),flip(b)].
% 26.07/26.40 84 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,identity) != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6. [resolve(26,d,2,a)].
% 26.07/26.40 102 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,B) != sk_c6 | multiply(C,sk_c7) != B | inverse(C) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6. [para(2(a,1),26(f,1))].
% 26.07/26.40 134 inverse(inverse(sk_c7)) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(sk_c7,identity) != sk_c6 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6. [factor(84,a,d)].
% 26.07/26.40 175 inverse(inverse(sk_c7)) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | multiply(sk_c7,identity) != sk_c6 | inverse(inverse(sk_c7)) != sk_c6. [factor(134,b,d)].
% 26.07/26.40 231 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),34(a,1,2))].
% 26.07/26.40 235 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c4),sk_c7) = sk_c6. [para(7(b,1),34(a,1,2))].
% 26.07/26.40 237 inverse(sk_c4) = sk_c7 | multiply(inverse(sk_c1),sk_c7) = sk_c6. [para(9(a,1),34(a,1,2))].
% 26.07/26.40 238 inverse(sk_c5) = sk_c6 | multiply(inverse(sk_c1),sk_c7) = sk_c6. [para(10(a,1),34(a,1,2))].
% 26.07/26.40 243 inverse(sk_c2) = sk_c7 | multiply(inverse(sk_c4),sk_c7) = sk_c6. [para(15(b,1),34(a,1,2))].
% 26.07/26.40 252 inverse(sk_c4) = sk_c7 | multiply(inverse(sk_c7),identity) = sk_c1. [para(30(b,1),34(a,1,2))].
% 26.07/26.40 253 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(34(a,1),34(a,1,2))].
% 26.07/26.40 254 multiply(A,identity) = A. [back_rewrite(231),rewrite([253(4)])].
% 26.07/26.40 255 inverse(sk_c4) = sk_c7 | inverse(sk_c7) = sk_c1. [back_rewrite(252),rewrite([254(8)])].
% 26.07/26.40 257 inverse(inverse(sk_c7)) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7 | inverse(inverse(sk_c7)) != sk_c6. [back_rewrite(175),rewrite([254(14)]),flip(c)].
% 26.07/26.40 261 inverse(identity) = identity. [para(254(a,1),2(a,1))].
% 26.07/26.40 303 inverse(sk_c4) = sk_c7 | inverse(sk_c7) = sk_c2. [para(32(b,1),34(a,1,2)),rewrite([254(8)])].
% 26.07/26.40 317 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c4),multiply(sk_c7,A)) = multiply(sk_c6,A). [para(35(b,1),34(a,1,2))].
% 26.07/26.40 360 multiply(A,inverse(A)) = identity. [para(253(a,1),2(a,1))].
% 26.07/26.40 361 inverse(sk_c4) = sk_c7 | multiply(inverse(sk_c7),A) = multiply(sk_c1,A). [para(3(a,1),253(a,1,1,1))].
% 26.07/26.40 362 inverse(sk_c5) = sk_c6 | multiply(inverse(sk_c7),A) = multiply(sk_c1,A). [para(4(a,1),253(a,1,1,1))].
% 26.07/26.40 373 multiply(A,multiply(inverse(A),B)) = B. [para(253(a,1),34(a,1))].
% 26.07/26.40 374 inverse(inverse(A)) = A. [para(253(a,1),254(a,1)),rewrite([254(2)]),flip(a)].
% 26.07/26.40 396 multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7. [back_rewrite(257),rewrite([374(3),374(15)]),flip(d),xx(a),merge(c)].
% 26.07/26.40 400 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,B) != sk_c6 | multiply(C,sk_c7) != B | inverse(C) != sk_c7 | identity != sk_c7. [back_rewrite(102),rewrite([374(23)]),xx(g)].
% 26.07/26.40 402 inverse(sk_c7) = sk_c1 | inverse(sk_c7) = sk_c4. [para(255(a,1),374(a,1,1))].
% 26.07/26.40 404 inverse(sk_c7) = sk_c2 | inverse(sk_c7) = sk_c4. [para(303(a,1),374(a,1,1))].
% 26.07/26.40 408 inverse(sk_c4) = sk_c7 | multiply(sk_c2,sk_c7) = identity. [para(5(a,1),360(a,1,2))].
% 26.07/26.40 409 inverse(sk_c5) = sk_c6 | multiply(sk_c2,sk_c7) = identity. [para(6(a,1),360(a,1,2))].
% 26.07/26.40 410 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(360(a,1),23(a,1)),flip(a)].
% 26.07/26.40 418 inverse(sk_c1) = sk_c7 | multiply(sk_c7,inverse(sk_c6)) = sk_c4. [para(360(a,1),35(b,1,2)),rewrite([254(7)]),flip(b)].
% 26.07/26.40 488 inverse(sk_c7) = sk_c4 | sk_c2 = sk_c1. [para(404(a,1),402(a,1)),merge(c)].
% 26.07/26.40 495 inverse(sk_c1) = sk_c7 | multiply(sk_c7,inverse(sk_c6)) = sk_c5. [para(360(a,1),37(b,1,2)),rewrite([254(7)]),flip(b)].
% 26.07/26.40 532 sk_c2 = sk_c1 | multiply(sk_c4,sk_c7) = identity. [para(488(a,1),2(a,1,1))].
% 26.07/26.40 620 sk_c2 = sk_c1 | multiply(A,multiply(sk_c4,sk_c7)) = A. [para(532(b,1),23(a,2,2)),rewrite([23(7),254(9)])].
% 26.07/26.40 787 inverse(sk_c4) = sk_c7 | identity = sk_c3. [para(408(b,1),13(a,1)),merge(c)].
% 26.07/26.40 794 identity = sk_c3 | inverse(sk_c7) = sk_c4. [para(787(a,1),374(a,1,1))].
% 26.07/26.40 1447 inverse(sk_c4) = sk_c7 | multiply(sk_c7,sk_c7) = sk_c6. [para(3(a,1),237(b,1,1)),merge(b)].
% 26.07/26.40 1476 inverse(sk_c4) = sk_c7 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(1447(b,1),34(a,1,2))].
% 26.07/26.40 1488 inverse(sk_c5) = sk_c6 | multiply(sk_c7,sk_c7) = sk_c6. [para(4(a,1),238(b,1,1)),merge(b)].
% 26.07/26.40 1648 inverse(sk_c5) = sk_c6 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(1488(b,1),34(a,1,2))].
% 26.07/26.40 1905 inverse(sk_c4) = sk_c7 | multiply(A,sk_c3) = A. [para(408(b,1),48(b,1,2)),rewrite([254(10)]),flip(c),merge(b)].
% 26.07/26.40 2057 inverse(sk_c5) = sk_c6 | multiply(sk_c3,sk_c1) = sk_c2. [para(31(b,1),49(b,1,2)),rewrite([254(11)]),flip(c),merge(b)].
% 26.07/26.40 2260 inverse(sk_c5) = sk_c6 | multiply(A,sk_c3) = A. [para(409(b,1),50(b,1,2)),rewrite([254(10)]),flip(c),merge(b)].
% 26.07/26.40 2349 inverse(sk_c5) = sk_c6 | inverse(sk_c3) = identity. [para(2260(b,1),2(a,1))].
% 26.07/26.40 2377 inverse(sk_c5) = sk_c6 | multiply(sk_c3,A) = A. [para(2349(b,1),34(a,1,1)),rewrite([1(8)])].
% 26.07/26.40 2721 inverse(sk_c5) = sk_c6 | sk_c2 = sk_c1. [para(2377(b,1),2057(b,1)),flip(c),merge(b)].
% 26.07/26.40 2744 sk_c2 = sk_c1 | multiply(sk_c5,sk_c6) = identity. [para(2721(a,1),360(a,1,2))].
% 26.07/26.40 2869 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,B) != sk_c6 | sk_c7 != B | identity != sk_c7. [para(1(a,1),400(d,1)),rewrite([261(15)]),merge(f)].
% 26.07/26.40 2935 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | identity != sk_c7. [resolve(2869,c,373,a),flip(c)].
% 26.07/26.40 2952 multiply(inverse(sk_c7),sk_c6) != sk_c7 | identity != sk_c7. [factor(2935,b,c),rewrite([374(3)]),xx(a)].
% 26.07/26.40 2975 sk_c2 = sk_c1 | inverse(sk_c1) = sk_c7 | identity = sk_c7. [para(2744(b,1),8(b,1))].
% 26.07/26.40 2976 sk_c2 = sk_c1 | inverse(sk_c2) = sk_c7 | identity = sk_c7. [para(2744(b,1),16(b,1))].
% 26.07/26.40 3173 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(410(a,1),34(a,1,2)),rewrite([254(3)]),flip(a)].
% 26.07/26.40 3234 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(3173(a,1),34(a,1,2)),flip(a)].
% 26.07/26.40 4177 inverse(sk_c1) = sk_c7 | sk_c5 = sk_c4. [para(418(b,1),37(b,2)),rewrite([360(13),254(11)]),merge(b)].
% 26.07/26.40 4187 sk_c5 = sk_c4 | inverse(sk_c7) = sk_c1. [para(4177(a,1),374(a,1,1))].
% 26.07/26.40 4189 sk_c5 = sk_c4 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(4177(a,1),373(a,1,2,1))].
% 26.07/26.40 4196 sk_c5 = sk_c4 | identity = sk_c3 | sk_c1 = sk_c4. [para(4187(b,1),794(b,1))].
% 26.07/26.40 4536 sk_c2 = sk_c1 | multiply(inverse(sk_c7),inverse(sk_c4)) = identity. [para(620(b,1),2(a,1)),rewrite([3234(7)])].
% 26.07/26.40 5495 inverse(sk_c4) = sk_c7 | identity != sk_c7. [resolve(1476,b,2952,a)].
% 26.07/26.40 5503 inverse(sk_c4) = sk_c7 | sk_c3 = sk_c7. [para(1476(b,1),44(b,2)),rewrite([34(14)]),merge(b)].
% 26.07/26.40 5667 sk_c3 = sk_c7 | inverse(sk_c7) = sk_c4. [para(5503(a,1),374(a,1,1))].
% 26.07/26.40 5704 sk_c3 = sk_c7 | sk_c5 = sk_c4 | sk_c1 = sk_c4. [para(5667(b,1),4187(b,1)),flip(c)].
% 26.07/26.40 5989 sk_c5 = sk_c4 | sk_c1 = sk_c4 | identity = sk_c7. [para(5704(a,1),4196(b,2)),merge(c),merge(e)].
% 26.07/26.40 5992 sk_c5 = sk_c4 | sk_c1 = sk_c4 | inverse(sk_c4) = sk_c7. [resolve(5989,c,5495,b)].
% 26.07/26.40 6141 inverse(sk_c5) = sk_c6 | identity != sk_c7. [resolve(1648,b,2952,a)].
% 26.07/26.40 7472 sk_c2 = sk_c1 | identity = sk_c7 | inverse(sk_c7) = sk_c1. [para(2975(b,1),374(a,1,1))].
% 26.07/26.40 7483 sk_c2 = sk_c1 | identity = sk_c7 | inverse(sk_c7) = sk_c2. [para(2976(b,1),374(a,1,1))].
% 26.07/26.40 8370 sk_c5 = sk_c4 | sk_c1 = sk_c4 | inverse(sk_c7) = sk_c4. [para(5992(c,1),374(a,1,1))].
% 26.07/26.40 9188 sk_c2 = sk_c1 | identity = sk_c7. [para(7483(c,1),7472(c,1)),merge(c),merge(d),merge(e)].
% 26.07/26.40 9203 sk_c2 = sk_c1 | inverse(sk_c7) = identity. [para(9188(b,1),261(a,1,1))].
% 26.07/26.40 9239 sk_c2 = sk_c1 | inverse(sk_c7) = sk_c7. [para(9188(b,1),9203(b,2)),merge(b)].
% 26.07/26.40 9297 sk_c2 = sk_c1 | multiply(sk_c7,sk_c7) = identity. [para(9239(b,1),2(a,1,1))].
% 26.07/26.40 9309 sk_c2 = sk_c1 | multiply(sk_c7,inverse(sk_c4)) = identity. [para(9239(b,1),4536(b,1,1)),merge(b)].
% 26.07/26.40 9479 sk_c2 = sk_c1 | multiply(inverse(sk_c7),inverse(sk_c7)) = identity. [para(9297(b,1),3234(a,1,1)),rewrite([261(5)]),flip(b)].
% 26.07/26.40 9530 sk_c2 = sk_c1 | inverse(sk_c4) = inverse(sk_c7). [para(9309(b,1),34(a,1,2)),rewrite([254(7)]),flip(b)].
% 26.07/26.40 9545 sk_c2 = sk_c1 | inverse(sk_c1) = sk_c7 | identity = sk_c6. [para(9530(b,1),235(b,1,1)),rewrite([2(11)])].
% 26.07/26.40 9546 sk_c2 = sk_c1 | inverse(sk_c2) = sk_c7 | identity = sk_c6. [para(9530(b,1),243(b,1,1)),rewrite([2(11)])].
% 26.07/26.40 10081 sk_c5 = sk_c4 | sk_c1 = sk_c4. [para(8370(c,1),4187(b,1)),flip(d),merge(c),merge(d)].
% 26.07/26.40 10084 sk_c5 = sk_c4 | multiply(sk_c4,sk_c6) = sk_c7. [para(10081(b,1),17(a,1,1)),merge(c)].
% 26.07/26.40 10101 sk_c5 = sk_c4 | multiply(sk_c4,multiply(sk_c7,A)) = A. [para(10081(b,1),4189(b,1,1)),merge(b)].
% 26.07/26.40 10199 sk_c5 = sk_c4 | multiply(inverse(sk_c4),sk_c7) = sk_c6. [para(10084(b,1),34(a,1,2))].
% 26.07/26.40 10305 sk_c5 = sk_c4 | multiply(inverse(sk_c7),sk_c4) = inverse(sk_c6). [para(10199(b,1),3234(a,1,1)),rewrite([374(10)]),flip(b)].
% 26.07/26.40 10946 sk_c2 = sk_c1 | identity = sk_c6 | inverse(sk_c7) = sk_c1. [para(9545(b,1),374(a,1,1))].
% 26.07/26.40 10953 sk_c2 = sk_c1 | identity = sk_c6 | inverse(sk_c7) = sk_c2. [para(9546(b,1),374(a,1,1))].
% 26.07/26.40 11273 sk_c5 = sk_c4 | multiply(sk_c7,inverse(sk_c6)) = sk_c4. [para(10305(b,1),34(a,1,2)),rewrite([374(6)])].
% 26.07/26.40 11278 sk_c5 = sk_c4 | multiply(sk_c1,sk_c4) = inverse(sk_c6). [para(4187(b,1),10305(b,1,1)),merge(b)].
% 26.07/26.40 11288 sk_c5 = sk_c4 | multiply(sk_c7,sk_c3) = sk_c6. [para(11273(b,1),61(b,2)),rewrite([360(13),254(11)]),merge(c)].
% 26.07/26.40 11314 sk_c5 = sk_c4 | multiply(sk_c4,sk_c6) = sk_c3. [para(11288(b,1),10101(b,1,2)),merge(b)].
% 26.07/26.40 11367 sk_c5 = sk_c4 | multiply(inverse(sk_c4),inverse(sk_c1)) = sk_c6. [para(11278(b,1),3234(a,1,1)),rewrite([374(6)]),flip(b)].
% 26.07/26.40 12358 sk_c2 = sk_c1 | identity = sk_c6. [para(10953(c,1),10946(c,1)),merge(c),merge(d),merge(e)].
% 26.07/26.40 12377 sk_c2 = sk_c1 | inverse(sk_c7) = sk_c6. [para(12358(b,1),9203(b,2)),merge(b)].
% 26.07/26.40 12503 sk_c2 = sk_c1 | multiply(inverse(sk_c7),sk_c6) = identity. [para(12377(b,1),9479(b,1,2)),merge(b)].
% 26.07/26.40 13384 sk_c2 = sk_c1 | identity != sk_c7. [para(12503(b,1),2952(a,1)),merge(c)].
% 26.07/26.40 13387 sk_c2 = sk_c1. [resolve(13384,b,9188,b),merge(b)].
% 26.07/26.40 13661 multiply(sk_c1,sk_c7) = sk_c3 | multiply(sk_c5,sk_c6) = sk_c7. [back_rewrite(22),rewrite([13387(1)])].
% 26.07/26.40 13756 sk_c5 = sk_c4 | multiply(sk_c4,sk_c6) = inverse(sk_c1). [para(11367(b,1),34(a,1,2)),rewrite([374(6)])].
% 26.07/26.40 13764 sk_c5 = sk_c4 | inverse(sk_c1) = sk_c3. [para(13756(b,1),11314(b,1)),merge(b)].
% 26.07/26.40 13778 sk_c5 = sk_c4 | inverse(sk_c4) = sk_c3. [para(10081(b,1),13764(b,1,1)),merge(b)].
% 26.07/26.40 13812 sk_c5 = sk_c4 | multiply(sk_c3,inverse(sk_c1)) = sk_c6. [para(13778(b,1),11367(b,1,1)),merge(b)].
% 26.07/26.40 13969 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c4),sk_c5) = identity. [para(495(b,1),317(b,1,2)),rewrite([360(16)]),merge(b)].
% 26.07/26.40 14065 inverse(sk_c4) = sk_c7 | multiply(sk_c1,sk_c6) = sk_c3. [para(361(b,1),44(b,2)),rewrite([34(14)]),flip(c),merge(b)].
% 26.07/26.40 14127 inverse(sk_c5) = sk_c6 | multiply(sk_c1,sk_c6) = sk_c3. [para(362(b,1),46(b,2)),rewrite([34(14)]),flip(c),merge(b)].
% 26.07/26.40 14171 sk_c5 = sk_c4 | multiply(sk_c3,inverse(sk_c4)) = sk_c6. [para(10081(b,1),13812(b,1,2,1)),merge(b)].
% 26.07/26.40 14331 inverse(sk_c4) = sk_c7 | multiply(inverse(sk_c1),sk_c3) = sk_c6. [para(14065(b,1),34(a,1,2))].
% 26.07/26.40 14362 inverse(sk_c5) = sk_c6 | multiply(inverse(sk_c1),sk_c3) = sk_c6. [para(14127(b,1),34(a,1,2))].
% 26.07/26.40 14368 sk_c5 = sk_c4 | multiply(sk_c4,inverse(sk_c3)) = inverse(sk_c6). [para(14171(b,1),3234(a,1,1)),rewrite([374(8)]),flip(b)].
% 26.07/26.40 15173 inverse(sk_c4) = sk_c7 | inverse(sk_c1) = sk_c6. [para(14331(b,1),1905(b,1)),flip(c),merge(b)].
% 26.07/26.40 15178 inverse(sk_c4) = sk_c7 | multiply(sk_c1,sk_c6) = identity. [para(15173(b,1),360(a,1,2))].
% 26.07/26.40 15235 inverse(sk_c4) = sk_c7 | identity = sk_c7. [para(15178(b,1),9(a,1)),merge(c)].
% 26.07/26.40 15253 identity = sk_c7 | inverse(sk_c7) = sk_c4. [para(15235(a,1),374(a,1,1))].
% 26.07/26.40 15254 identity = sk_c7 | multiply(sk_c4,sk_c7) = identity. [para(15235(a,1),360(a,1,2))].
% 26.07/26.40 15255 identity = sk_c7 | multiply(sk_c4,multiply(sk_c7,A)) = A. [para(15235(a,1),373(a,1,2,1))].
% 26.07/26.40 15295 identity = sk_c7 | multiply(A,multiply(sk_c4,sk_c7)) = A. [para(15254(b,1),23(a,2,2)),rewrite([23(7),254(9)])].
% 26.07/26.40 16537 inverse(sk_c5) = sk_c6 | inverse(sk_c1) = sk_c6. [para(14362(b,1),2260(b,1)),flip(c),merge(b)].
% 26.07/26.40 16541 inverse(sk_c5) = sk_c6 | inverse(sk_c6) = sk_c1. [para(16537(b,1),374(a,1,1))].
% 26.07/26.40 16542 inverse(sk_c5) = sk_c6 | multiply(sk_c1,sk_c6) = identity. [para(16537(b,1),360(a,1,2))].
% 26.07/26.40 16561 inverse(sk_c6) = sk_c1 | inverse(sk_c6) = sk_c5. [para(16541(a,1),374(a,1,1))].
% 26.07/26.40 16570 inverse(sk_c6) = sk_c5 | multiply(sk_c1,sk_c6) = identity. [para(16561(a,1),2(a,1,1))].
% 26.07/26.40 16660 inverse(sk_c5) = sk_c6 | identity = sk_c7. [para(16542(b,1),10(a,1)),merge(c)].
% 26.07/26.40 16669 identity = sk_c7 | inverse(sk_c6) = sk_c5. [para(16660(a,1),374(a,1,1))].
% 26.07/26.40 16670 identity = sk_c7 | multiply(sk_c5,sk_c6) = identity. [para(16660(a,1),360(a,1,2))].
% 26.07/26.40 16671 identity = sk_c7 | multiply(sk_c5,multiply(sk_c6,A)) = A. [para(16660(a,1),373(a,1,2,1))].
% 26.07/26.40 16762 identity = sk_c7 | inverse(sk_c1) = sk_c7. [para(16670(b,1),8(b,1)),merge(c)].
% 26.07/26.40 16763 identity = sk_c7 | multiply(sk_c7,sk_c3) = sk_c6. [para(16670(b,1),20(b,1)),merge(c)].
% 26.07/26.40 16766 identity = sk_c7 | multiply(inverse(sk_c6),inverse(sk_c5)) = identity. [para(16670(b,1),3234(a,1,1)),rewrite([261(5)]),flip(b)].
% 26.07/26.40 16769 identity = sk_c7 | multiply(sk_c7,multiply(sk_c1,A)) = A. [para(16762(b,1),34(a,1,1))].
% 26.07/26.40 16770 identity = sk_c7 | inverse(sk_c7) = sk_c1. [para(16762(b,1),374(a,1,1))].
% 26.07/26.40 16822 identity = sk_c7 | sk_c1 = sk_c4. [para(16770(b,1),15253(b,1)),merge(b)].
% 26.07/26.40 16823 sk_c1 = sk_c4 | inverse(sk_c5) = sk_c6. [resolve(16822,a,6141,b)].
% 26.07/26.40 16824 sk_c1 = sk_c4 | inverse(sk_c4) = sk_c7. [resolve(16822,a,5495,b)].
% 26.07/26.40 16828 sk_c1 = sk_c4 | inverse(sk_c7) = identity. [para(16822(a,1),261(a,1,1))].
% 26.07/26.40 16874 sk_c1 = sk_c4 | multiply(sk_c6,sk_c5) = identity. [para(16823(b,1),2(a,1,1))].
% 26.07/26.40 16898 sk_c1 = sk_c4 | inverse(sk_c7) = sk_c4. [para(16824(b,1),374(a,1,1))].
% 26.07/26.40 16940 sk_c1 = sk_c4 | identity = sk_c4. [para(16898(b,1),16828(b,1)),flip(c),merge(b)].
% 26.07/26.40 16958 sk_c1 = sk_c4 | inverse(sk_c4) = identity. [para(16940(b,1),261(a,1,1))].
% 26.07/26.40 17019 sk_c1 = sk_c4 | inverse(sk_c1) = sk_c7 | identity = sk_c5. [para(16958(b,1),13969(b,1,1)),rewrite([1(10)]),flip(c)].
% 26.07/26.40 17074 identity = sk_c7 | multiply(inverse(sk_c7),sk_c6) = sk_c3. [para(16763(b,1),34(a,1,2))].
% 26.07/26.40 17187 sk_c1 = sk_c4 | multiply(sk_c6,sk_c5) = sk_c7. [para(16822(a,1),16874(b,2)),merge(b)].
% 26.07/26.40 17326 sk_c1 = sk_c4 | multiply(inverse(sk_c6),sk_c7) = sk_c5. [para(17187(b,1),34(a,1,2))].
% 26.07/26.40 18070 identity = sk_c7 | multiply(sk_c4,sk_c6) = sk_c3. [para(15253(b,1),17074(b,1,1)),merge(b)].
% 26.07/26.40 18148 sk_c1 = sk_c4 | multiply(inverse(sk_c7),sk_c6) = inverse(sk_c5). [para(17326(b,1),3234(a,1,1)),rewrite([374(10)]),flip(b)].
% 26.07/26.40 19010 identity = sk_c7 | sk_c5 = sk_c4 | multiply(sk_c4,inverse(sk_c3)) = sk_c5. [para(16669(b,1),14368(b,2))].
% 26.07/26.40 20437 identity = sk_c7 | multiply(sk_c5,sk_c6) = multiply(sk_c4,sk_c7). [para(15295(b,1),16671(b,1,2)),merge(b)].
% 26.07/26.40 20458 identity = sk_c7 | multiply(A,multiply(inverse(sk_c6),inverse(sk_c5))) = A. [para(16766(b,1),23(a,2,2)),rewrite([23(9),254(11)])].
% 26.07/26.40 20476 multiply(sk_c5,sk_c6) = sk_c7 | identity = sk_c7 | multiply(sk_c7,sk_c3) = sk_c7. [para(13661(a,1),16769(b,1,2))].
% 26.07/26.40 20478 identity = sk_c7 | multiply(sk_c1,A) = multiply(sk_c4,A). [para(16769(b,1),15255(b,1,2)),flip(c),merge(b)].
% 26.07/26.40 20571 sk_c1 = sk_c4 | identity = sk_c5 | inverse(sk_c7) = sk_c1. [para(17019(b,1),374(a,1,1))].
% 26.07/26.40 22734 identity = sk_c7 | multiply(sk_c4,sk_c6) = sk_c7. [para(20478(b,1),17(a,1)),merge(c)].
% 26.07/26.40 22748 identity = sk_c7 | multiply(inverse(sk_c4),sk_c7) = sk_c6. [para(22734(b,1),34(a,1,2))].
% 26.07/26.40 23122 sk_c1 = sk_c4 | identity = sk_c5. [para(20571(c,1),16898(b,1)),merge(c),merge(d)].
% 26.07/26.40 23125 sk_c1 = sk_c4 | inverse(sk_c5) = identity. [para(23122(b,1),261(a,1,1))].
% 26.07/26.40 23251 sk_c1 = sk_c4 | multiply(inverse(sk_c7),sk_c6) = identity. [para(23125(b,1),18148(b,2)),merge(b)].
% 26.07/26.40 24017 sk_c1 = sk_c4 | identity != sk_c7. [para(23251(b,1),2952(a,1)),merge(c)].
% 26.07/26.40 24019 sk_c1 = sk_c4. [resolve(24017,b,16822,a),merge(b)].
% 26.07/26.40 24828 inverse(sk_c6) = sk_c5 | multiply(sk_c4,sk_c6) = identity. [back_rewrite(16570),rewrite([24019(5)])].
% 26.07/26.40 24838 inverse(sk_c5) = sk_c6 | multiply(sk_c4,sk_c6) = identity. [back_rewrite(16542),rewrite([24019(5)])].
% 26.07/26.40 25919 inverse(sk_c7) = sk_c4. [back_rewrite(402),rewrite([24019(3)]),merge(b)].
% 26.07/26.40 25957 multiply(sk_c4,sk_c6) = sk_c7. [back_rewrite(17),rewrite([24019(1)]),merge(b)].
% 26.07/26.40 25960 inverse(sk_c4) = sk_c7. [back_rewrite(3),rewrite([24019(1)]),merge(b)].
% 26.07/26.40 28373 identity != sk_c7. [back_rewrite(2952),rewrite([25919(2),25957(3)]),xx(a)].
% 26.07/26.40 28413 sk_c6 != sk_c7. [back_rewrite(396),rewrite([25919(2),25957(3)]),xx(a)].
% 26.07/26.40 28421 inverse(sk_c5) = sk_c6. [back_rewrite(24838),rewrite([25957(7)]),flip(b),unit_del(b,28373)].
% 26.07/26.40 28422 inverse(sk_c6) = sk_c5. [back_rewrite(24828),rewrite([25957(7)]),flip(b),unit_del(b,28373)].
% 26.07/26.40 28424 sk_c3 = sk_c7. [back_rewrite(18070),rewrite([25957(6)]),flip(b),unit_del(a,28373)].
% 26.07/26.40 28450 multiply(sk_c7,sk_c7) = sk_c6. [back_rewrite(22748),rewrite([25960(5)]),unit_del(a,28373)].
% 26.07/26.40 28528 multiply(sk_c5,sk_c6) = sk_c7. [back_unit_del(20476),rewrite([28424(10),28450(11)]),unit_del(b,28373),unit_del(c,28413)].
% 26.07/26.40 28529 multiply(A,sk_c7) = A. [back_unit_del(20458),rewrite([28422(5),28421(6),28528(6)]),unit_del(a,28373)].
% 26.07/26.40 28534 sk_c4 = sk_c7. [back_unit_del(20437),rewrite([28528(6),28529(7)]),flip(b),unit_del(a,28373)].
% 26.07/26.40 28535 sk_c5 = sk_c7. [back_unit_del(19010),rewrite([28534(5),28534(7),28424(8),25919(9),28534(8),28529(9)]),flip(c),merge(c),unit_del(a,28373)].
% 26.07/26.40 28539 $F. [back_unit_del(16766),rewrite([28422(5),28535(4),28535(5),25919(6),28534(5),28529(6)]),flip(b),merge(b),unit_del(a,28373)].
% 26.07/26.40
% 26.07/26.40 % SZS output end Refutation
% 26.07/26.40 ============================== end of proof ==========================
% 26.07/26.40
% 26.07/26.40 ============================== STATISTICS ============================
% 26.07/26.40
% 26.07/26.40 Given=3796. Generated=1625806. Kept=28538. proofs=1.
% 26.07/26.40 Usable=589. Sos=2200. Demods=45. Limbo=166, Disabled=25607. Hints=0.
% 26.07/26.40 Megabytes=21.09.
% 26.07/26.40 User_CPU=24.56, System_CPU=0.85, Wall_clock=26.
% 26.07/26.40
% 26.07/26.40 ============================== end of statistics =====================
% 26.07/26.40
% 26.07/26.40 ============================== end of search =========================
% 26.07/26.40
% 26.07/26.40 THEOREM PROVED
% 26.07/26.40 % SZS status Unsatisfiable
% 26.07/26.40
% 26.07/26.40 Exiting with 1 proof.
% 26.07/26.40
% 26.07/26.40 Process 6676 exit (max_proofs) Tue Jun 14 11:00:01 2022
% 26.07/26.40 Prover9 interrupted
%------------------------------------------------------------------------------