TSTP Solution File: GRP334-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP334-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 11:18:40 EDT 2022
% Result : Unsatisfiable 7.29s 7.57s
% Output : Refutation 7.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP334-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 18:01:04 EDT 2022
% 0.14/0.34 % CPUTime :
% 7.29/7.57 ============================== Prover9 ===============================
% 7.29/7.57 Prover9 (32) version 2009-11A, November 2009.
% 7.29/7.57 Process 3160 was started by sandbox2 on n011.cluster.edu,
% 7.29/7.57 Mon Jun 13 18:01:04 2022
% 7.29/7.57 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3006_n011.cluster.edu".
% 7.29/7.57 ============================== end of head ===========================
% 7.29/7.57
% 7.29/7.57 ============================== INPUT =================================
% 7.29/7.57
% 7.29/7.57 % Reading from file /tmp/Prover9_3006_n011.cluster.edu
% 7.29/7.57
% 7.29/7.57 set(prolog_style_variables).
% 7.29/7.57 set(auto2).
% 7.29/7.57 % set(auto2) -> set(auto).
% 7.29/7.57 % set(auto) -> set(auto_inference).
% 7.29/7.57 % set(auto) -> set(auto_setup).
% 7.29/7.57 % set(auto_setup) -> set(predicate_elim).
% 7.29/7.57 % set(auto_setup) -> assign(eq_defs, unfold).
% 7.29/7.57 % set(auto) -> set(auto_limits).
% 7.29/7.57 % set(auto_limits) -> assign(max_weight, "100.000").
% 7.29/7.57 % set(auto_limits) -> assign(sos_limit, 20000).
% 7.29/7.57 % set(auto) -> set(auto_denials).
% 7.29/7.57 % set(auto) -> set(auto_process).
% 7.29/7.57 % set(auto2) -> assign(new_constants, 1).
% 7.29/7.57 % set(auto2) -> assign(fold_denial_max, 3).
% 7.29/7.57 % set(auto2) -> assign(max_weight, "200.000").
% 7.29/7.57 % set(auto2) -> assign(max_hours, 1).
% 7.29/7.57 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 7.29/7.57 % set(auto2) -> assign(max_seconds, 0).
% 7.29/7.57 % set(auto2) -> assign(max_minutes, 5).
% 7.29/7.57 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 7.29/7.57 % set(auto2) -> set(sort_initial_sos).
% 7.29/7.57 % set(auto2) -> assign(sos_limit, -1).
% 7.29/7.57 % set(auto2) -> assign(lrs_ticks, 3000).
% 7.29/7.57 % set(auto2) -> assign(max_megs, 400).
% 7.29/7.57 % set(auto2) -> assign(stats, some).
% 7.29/7.57 % set(auto2) -> clear(echo_input).
% 7.29/7.57 % set(auto2) -> set(quiet).
% 7.29/7.57 % set(auto2) -> clear(print_initial_clauses).
% 7.29/7.57 % set(auto2) -> clear(print_given).
% 7.29/7.57 assign(lrs_ticks,-1).
% 7.29/7.57 assign(sos_limit,10000).
% 7.29/7.57 assign(order,kbo).
% 7.29/7.57 set(lex_order_vars).
% 7.29/7.57 clear(print_given).
% 7.29/7.57
% 7.29/7.57 % formulas(sos). % not echoed (25 formulas)
% 7.29/7.57
% 7.29/7.57 ============================== end of input ==========================
% 7.29/7.57
% 7.29/7.57 % From the command line: assign(max_seconds, 300).
% 7.29/7.57
% 7.29/7.57 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 7.29/7.57
% 7.29/7.57 % Formulas that are not ordinary clauses:
% 7.29/7.57
% 7.29/7.57 ============================== end of process non-clausal formulas ===
% 7.29/7.57
% 7.29/7.57 ============================== PROCESS INITIAL CLAUSES ===============
% 7.29/7.57
% 7.29/7.57 ============================== PREDICATE ELIMINATION =================
% 7.29/7.57
% 7.29/7.57 ============================== end predicate elimination =============
% 7.29/7.57
% 7.29/7.57 Auto_denials: (non-Horn, no changes).
% 7.29/7.57
% 7.29/7.57 Term ordering decisions:
% 7.29/7.57
% 7.29/7.57 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 7.29/7.57 Function symbol KB weights: sk_c6=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c7=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 7.29/7.57
% 7.29/7.57 ============================== end of process initial clauses ========
% 7.29/7.57
% 7.29/7.57 ============================== CLAUSES FOR SEARCH ====================
% 7.29/7.57
% 7.29/7.57 ============================== end of clauses for search =============
% 7.29/7.57
% 7.29/7.57 ============================== SEARCH ================================
% 7.29/7.57
% 7.29/7.57 % Starting search at 0.01 seconds.
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=39.000, iters=3403
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=38.000, iters=3335
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=37.000, iters=3399
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=36.000, iters=3334
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=35.000, iters=3346
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=34.000, iters=3333
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=33.000, iters=3351
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=32.000, iters=3363
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=31.000, iters=3335
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=30.000, iters=3348
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=29.000, iters=3334
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=28.000, iters=3382
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=26.000, iters=3334
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=25.000, iters=3372
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=21.000, iters=3399
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=20.000, iters=3395
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=19.000, iters=3334
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=18.000, iters=3528
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=17.000, iters=3333
% 7.29/7.57
% 7.29/7.57 Low Water (keep): wt=16.000, iters=3357
% 7.29/7.57
% 7.29/7.57 ============================== PROOF =================================
% 7.29/7.57 % SZS status Unsatisfiable
% 7.29/7.57 % SZS output start Refutation
% 7.29/7.57
% 7.29/7.57 % Proof 1 at 6.39 (+ 0.17) seconds.
% 7.29/7.57 % Length of proof is 127.
% 7.29/7.57 % Level of proof is 30.
% 7.29/7.57 % Maximum clause weight is 48.000.
% 7.29/7.57 % Given clauses 1565.
% 7.29/7.57
% 7.29/7.57 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 7.29/7.57 2 multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 7.29/7.57 3 sk_c5 = multiply(sk_c6,sk_c7). [copy(2),flip(a)].
% 7.29/7.57 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 7.29/7.57 5 inverse(sk_c1) = sk_c6 | inverse(sk_c6) = sk_c5 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 7.29/7.57 6 inverse(sk_c1) = sk_c6 | multiply(sk_c6,sk_c7) = inverse(sk_c6). [copy(5),rewrite([3(7)]),flip(b)].
% 7.29/7.57 7 inverse(sk_c1) = sk_c6 | inverse(sk_c7) = sk_c5 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 7.29/7.57 8 inverse(sk_c1) = sk_c6 | multiply(sk_c6,sk_c7) = inverse(sk_c7). [copy(7),rewrite([3(7)]),flip(b)].
% 7.29/7.57 9 inverse(sk_c1) = sk_c6 | inverse(sk_c3) = sk_c6 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 7.29/7.57 10 inverse(sk_c2) = sk_c6 | inverse(sk_c6) = sk_c5 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 7.29/7.57 11 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c7) = inverse(sk_c6). [copy(10),rewrite([3(7)]),flip(b)].
% 7.29/7.57 12 inverse(sk_c2) = sk_c6 | inverse(sk_c7) = sk_c5 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 7.29/7.57 13 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c7) = inverse(sk_c7). [copy(12),rewrite([3(7)]),flip(b)].
% 7.29/7.57 15 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c6) = sk_c5 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 7.29/7.57 16 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c6,sk_c7) = inverse(sk_c6). [copy(15),rewrite([3(8)]),flip(b)].
% 7.29/7.57 17 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c7) = sk_c5 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 7.29/7.57 18 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c6,sk_c7) = inverse(sk_c7). [copy(17),rewrite([3(8)]),flip(b)].
% 7.29/7.57 19 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c3) = sk_c6 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 7.29/7.57 20 inverse(sk_c1) = sk_c6 | multiply(sk_c6,sk_c4) = sk_c5 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 7.29/7.57 21 inverse(sk_c1) = sk_c6 | multiply(sk_c6,sk_c4) = multiply(sk_c6,sk_c7). [copy(20),rewrite([3(8)])].
% 7.29/7.57 22 inverse(sk_c1) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c4 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 7.29/7.57 28 multiply(sk_c2,sk_c5) = sk_c6 | inverse(sk_c7) = sk_c5 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 7.29/7.57 29 multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 | multiply(sk_c6,sk_c7) = inverse(sk_c7). [copy(28),rewrite([3(2),3(10)]),flip(b)].
% 7.29/7.57 32 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c6,sk_c4) = sk_c5 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 7.29/7.57 33 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c6,sk_c4) = multiply(sk_c6,sk_c7). [copy(32),rewrite([3(9)])].
% 7.29/7.57 34 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c4 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 7.29/7.57 39 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 7.29/7.57 40 multiply(sk_c6,sk_c7) != sk_c5 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6 | inverse(sk_c6) != sk_c5 | inverse(sk_c7) != sk_c5 | multiply(sk_c6,C) != sk_c5 | multiply(D,sk_c6) != C | inverse(D) != sk_c6 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 7.29/7.57 41 multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(B) != sk_c6 | multiply(B,multiply(sk_c6,sk_c7)) != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7) | multiply(sk_c6,sk_c7) != multiply(sk_c6,C) | multiply(D,sk_c6) != C | inverse(D) != sk_c6. [copy(40),rewrite([3(4),3(18),3(26),3(32),3(38)]),flip(f),flip(g),flip(h),xx(a)].
% 7.29/7.57 42 multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(B) != sk_c6 | multiply(B,multiply(sk_c6,sk_c7)) != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [factor(41,a,h),xx(g),merge(g)].
% 7.29/7.57 44 inverse(sk_c1) = sk_c6 | inverse(sk_c7) = inverse(sk_c6). [para(8(b,1),6(b,1)),merge(b)].
% 7.29/7.57 45 inverse(sk_c1) = sk_c6 | multiply(sk_c6,sk_c3) = identity. [para(9(b,1),4(a,1,1))].
% 7.29/7.57 46 inverse(sk_c2) = sk_c6 | inverse(sk_c7) = inverse(sk_c6). [para(13(b,1),11(b,1)),merge(b)].
% 7.29/7.57 52 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),39(a,1,1)),rewrite([1(2)]),flip(a)].
% 7.29/7.57 63 multiply(sk_c6,sk_c7) = inverse(sk_c7) | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(18(a,1),39(a,1,1)),flip(b)].
% 7.29/7.57 70 inverse(sk_c1) = sk_c6 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c4). [para(22(b,1),39(a,2,2)),rewrite([39(8)])].
% 7.29/7.57 81 multiply(sk_c6,sk_c4) = multiply(sk_c6,sk_c7) | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(33(a,1),39(a,1,1)),flip(b)].
% 7.29/7.57 84 multiply(sk_c1,sk_c6) = sk_c7 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c4). [para(34(b,1),39(a,2,2)),rewrite([39(9)])].
% 7.29/7.57 146 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),52(a,1,2))].
% 7.29/7.57 154 multiply(sk_c6,sk_c7) = inverse(sk_c7) | multiply(inverse(sk_c1),sk_c7) = sk_c6. [para(18(a,1),52(a,1,2))].
% 7.29/7.57 167 multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C. [para(39(a,1),52(a,1,2))].
% 7.29/7.57 168 multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(inverse(sk_c6)) != sk_c6 | sk_c7 != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [para(52(a,1),42(d,1))].
% 7.29/7.57 171 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(52(a,1),52(a,1,2))].
% 7.29/7.57 172 multiply(A,identity) = A. [back_rewrite(146),rewrite([171(4)])].
% 7.29/7.57 173 inverse(identity) = identity. [para(172(a,1),4(a,1))].
% 7.29/7.57 200 inverse(sk_c1) = sk_c6 | inverse(sk_c6) = sk_c3. [para(45(b,1),52(a,1,2)),rewrite([172(8)])].
% 7.29/7.57 210 multiply(A,multiply(B,sk_c6)) != sk_c7 | inverse(multiply(A,B)) != sk_c6 | inverse(inverse(sk_c6)) != sk_c6 | sk_c7 != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [para(39(a,1),168(a,1))].
% 7.29/7.57 304 multiply(A,inverse(A)) = identity. [para(171(a,1),4(a,1))].
% 7.29/7.57 312 inverse(inverse(A)) = A. [para(171(a,1),172(a,1)),rewrite([172(2)]),flip(a)].
% 7.29/7.57 353 multiply(A,multiply(B,sk_c6)) != sk_c7 | inverse(multiply(A,B)) != sk_c6 | sk_c7 != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [back_rewrite(210),rewrite([312(12)]),xx(c)].
% 7.29/7.57 368 inverse(sk_c1) = sk_c6 | sk_c7 = sk_c6. [para(44(b,1),312(a,1,1)),rewrite([312(7)]),flip(b)].
% 7.29/7.57 369 inverse(sk_c6) = sk_c3 | inverse(sk_c6) = sk_c1. [para(200(a,1),312(a,1,1))].
% 7.29/7.57 370 inverse(sk_c2) = sk_c6 | sk_c7 = sk_c6. [para(46(b,1),312(a,1,1)),rewrite([312(7)]),flip(b)].
% 7.29/7.57 375 inverse(sk_c1) = sk_c6 | multiply(sk_c3,sk_c6) = identity. [para(9(b,1),304(a,1,2))].
% 7.29/7.57 388 sk_c7 = sk_c6 | inverse(sk_c6) = sk_c2. [para(370(a,1),312(a,1,1))].
% 7.29/7.57 394 sk_c7 != A | inverse(multiply(A,inverse(sk_c6))) != sk_c6 | sk_c7 != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [para(4(a,1),353(a,1,2)),rewrite([172(2)]),flip(a)].
% 7.29/7.57 408 sk_c7 = sk_c6 | multiply(sk_c2,multiply(sk_c6,A)) = A. [para(388(b,1),52(a,1,1))].
% 7.29/7.57 2001 multiply(sk_c6,sk_c7) = inverse(sk_c7) | multiply(sk_c1,multiply(sk_c6,inverse(sk_c7))) = identity. [para(304(a,1),63(b,2))].
% 7.29/7.57 3729 inverse(sk_c1) = sk_c6 | multiply(A,sk_c4) = A. [para(375(b,1),70(b,1,2)),rewrite([172(10)]),flip(c),merge(b)].
% 7.29/7.57 4115 inverse(sk_c1) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c6. [para(3729(b,1),21(b,1)),flip(c),merge(b)].
% 7.29/7.57 4869 inverse(sk_c1) = sk_c6 | identity = sk_c7. [para(4115(b,1),52(a,1,2)),rewrite([4(8)])].
% 7.29/7.57 4889 identity = sk_c7 | inverse(sk_c6) = sk_c1. [para(4869(a,1),312(a,1,1))].
% 7.29/7.57 4890 identity = sk_c7 | multiply(sk_c1,sk_c6) = identity. [para(4869(a,1),304(a,1,2))].
% 7.29/7.57 5040 identity = sk_c7 | multiply(sk_c6,sk_c7) = inverse(sk_c6). [para(4890(b,1),16(a,1)),merge(b)].
% 7.29/7.57 5041 identity = sk_c7 | multiply(sk_c6,sk_c7) = inverse(sk_c7). [para(4890(b,1),18(a,1)),merge(b)].
% 7.29/7.57 5042 identity = sk_c7 | inverse(sk_c3) = sk_c6. [para(4890(b,1),19(a,1)),merge(b)].
% 7.29/7.57 5055 identity = sk_c7 | inverse(sk_c6) = sk_c3. [para(5042(b,1),312(a,1,1))].
% 7.29/7.57 5097 identity = sk_c7 | sk_c3 = sk_c1. [para(5055(b,1),4889(b,1)),merge(b)].
% 7.29/7.57 5102 sk_c3 = sk_c1 | multiply(sk_c7,A) = A. [para(5097(a,1),1(a,1,1))].
% 7.29/7.57 5104 sk_c3 = sk_c1 | inverse(sk_c7) = identity. [para(5097(a,1),173(a,1,1))].
% 7.29/7.57 5247 sk_c3 = sk_c1 | inverse(sk_c7) = sk_c7. [para(5097(a,1),5104(b,2)),merge(b)].
% 7.29/7.57 5248 sk_c3 = sk_c1 | multiply(sk_c7,sk_c7) = identity. [para(5247(b,1),4(a,1,1))].
% 7.29/7.57 5457 sk_c3 = sk_c1 | sk_c7 != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [para(5102(b,1),394(b,1,1)),rewrite([312(9)]),xx(b),xx(c)].
% 7.29/7.57 5945 multiply(sk_c6,sk_c4) = multiply(sk_c6,sk_c7) | multiply(sk_c1,multiply(sk_c6,inverse(sk_c7))) = identity. [para(304(a,1),81(b,2))].
% 7.29/7.57 6433 multiply(sk_c1,sk_c6) = sk_c7 | multiply(inverse(multiply(sk_c3,sk_c6)),sk_c4) = identity. [para(84(b,1),4(a,1))].
% 7.29/7.57 7000 identity = sk_c7 | multiply(sk_c6,sk_c7) = sk_c1. [para(4889(b,1),5040(b,2)),merge(b)].
% 7.29/7.57 7109 identity = sk_c7 | inverse(sk_c7) = sk_c1. [para(5041(b,1),7000(b,1)),merge(b)].
% 7.29/7.57 7114 identity = sk_c7 | inverse(sk_c1) = sk_c7. [para(7109(b,1),312(a,1,1))].
% 7.29/7.57 7160 identity = sk_c7 | sk_c7 = sk_c6. [para(7114(b,1),368(a,1)),merge(c)].
% 7.29/7.57 7162 sk_c7 = sk_c6 | multiply(A,sk_c7) = A. [para(7160(a,1),172(a,1,2))].
% 7.29/7.57 7163 sk_c7 = sk_c6 | inverse(sk_c7) = identity. [para(7160(a,1),173(a,1,1))].
% 7.29/7.57 7183 sk_c7 = sk_c6 | inverse(sk_c7) = sk_c7. [para(7160(a,1),7163(b,2)),merge(b)].
% 7.29/7.57 9459 multiply(inverse(multiply(A,B)),A) = inverse(B). [para(304(a,1),167(a,1,2,2)),rewrite([172(4)])].
% 7.29/7.57 9590 multiply(sk_c6,sk_c7) = inverse(sk_c7) | multiply(inverse(sk_c6),multiply(inverse(sk_c1),multiply(sk_c7,A))) = A. [para(154(b,1),167(a,1,1,1))].
% 7.29/7.57 10138 multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(sk_c6,multiply(sk_c7,B)) != sk_c6 | inverse(B) != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [para(9459(a,1),42(d,1)),rewrite([39(11),312(13)])].
% 7.29/7.57 10140 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(52(a,1),9459(a,1,1,1)),flip(a)].
% 7.29/7.57 10147 multiply(inverse(A),sk_c6) != sk_c7 | sk_c6 != A | sk_c7 != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [para(9459(a,1),394(b,1,1)),rewrite([10140(5),312(5),312(7)]),flip(a),flip(b)].
% 7.29/7.57 10464 multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(sk_c6,multiply(sk_c7,A)) != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [factor(10138,b,d)].
% 7.29/7.57 10567 multiply(sk_c1,sk_c6) = sk_c7 | multiply(inverse(sk_c6),multiply(inverse(sk_c3),sk_c4)) = identity. [back_rewrite(6433),rewrite([10140(9),39(12)])].
% 7.29/7.57 10792 multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c7 != sk_c6 | multiply(sk_c6,sk_c7) != inverse(sk_c6) | multiply(sk_c6,sk_c7) != inverse(sk_c7). [para(304(a,1),10464(c,1,2)),rewrite([312(9),172(12)]),xx(c)].
% 7.29/7.57 11944 sk_c7 = sk_c6 | multiply(sk_c6,sk_c7) = inverse(sk_c7). [para(408(b,1),29(a,1)),merge(b)].
% 7.29/7.57 12379 sk_c7 = sk_c6 | inverse(sk_c7) = sk_c6. [para(11944(b,1),7162(b,1)),merge(b)].
% 7.29/7.57 12397 sk_c7 = sk_c6. [para(12379(b,1),7183(b,1)),flip(c),merge(b),merge(c)].
% 7.29/7.57 12891 identity != sk_c6 | multiply(sk_c6,sk_c6) != inverse(sk_c6). [back_rewrite(10792),rewrite([12397(1),4(4),12397(2),12397(4),12397(8),12397(14),12397(16)]),xx(b),merge(c)].
% 7.29/7.57 12984 multiply(sk_c1,sk_c6) = sk_c6 | multiply(inverse(sk_c6),multiply(inverse(sk_c3),sk_c4)) = identity. [back_rewrite(10567),rewrite([12397(4)])].
% 7.29/7.57 13150 multiply(inverse(A),sk_c6) != sk_c6 | sk_c6 != A | multiply(sk_c6,sk_c6) != inverse(sk_c6). [back_rewrite(10147),rewrite([12397(4),12397(8),12397(12),12397(18),12397(20)]),xx(c),merge(d)].
% 7.29/7.57 13297 multiply(sk_c6,sk_c6) = inverse(sk_c6) | multiply(inverse(sk_c6),multiply(inverse(sk_c1),multiply(sk_c6,A))) = A. [back_rewrite(9590),rewrite([12397(2),12397(4),12397(11)])].
% 7.29/7.57 14060 multiply(sk_c6,sk_c4) = multiply(sk_c6,sk_c6) | identity = sk_c1. [back_rewrite(5945),rewrite([12397(5),12397(10),304(12),172(10)]),flip(b)].
% 7.29/7.57 14115 sk_c3 = sk_c1 | multiply(sk_c6,sk_c6) != inverse(sk_c6). [back_rewrite(5457),rewrite([12397(4),12397(8),12397(14),12397(16)]),xx(b),merge(c)].
% 7.29/7.57 14155 sk_c3 = sk_c1 | multiply(sk_c6,sk_c6) = identity. [back_rewrite(5248),rewrite([12397(4),12397(5)])].
% 7.29/7.57 14195 sk_c3 = sk_c1 | inverse(sk_c6) = identity. [back_rewrite(5104),rewrite([12397(4)])].
% 7.29/7.57 14345 multiply(sk_c6,sk_c6) = inverse(sk_c6) | identity = sk_c1. [back_rewrite(2001),rewrite([12397(2),12397(4),12397(9),304(11),172(9)]),flip(b)].
% 7.29/7.57 18997 sk_c3 = sk_c1 | inverse(sk_c6) != identity. [para(14155(b,1),14115(b,1)),flip(c),merge(b)].
% 7.29/7.57 19000 sk_c3 = sk_c1. [resolve(18997,b,14195,b),merge(b)].
% 7.29/7.57 19600 multiply(sk_c1,sk_c6) = sk_c6 | multiply(inverse(sk_c6),multiply(inverse(sk_c1),sk_c4)) = identity. [back_rewrite(12984),rewrite([19000(8)])].
% 7.29/7.57 19754 inverse(sk_c6) = sk_c1. [back_rewrite(369),rewrite([19000(3)]),merge(b)].
% 7.29/7.57 19762 inverse(sk_c1) = sk_c6. [back_rewrite(9),rewrite([19000(5)]),merge(b)].
% 7.29/7.57 19765 multiply(sk_c1,sk_c6) = sk_c6 | multiply(sk_c1,multiply(sk_c6,sk_c4)) = identity. [back_rewrite(19600),rewrite([19754(7),19762(8)])].
% 7.29/7.57 21235 multiply(sk_c6,sk_c6) = sk_c1 | identity = sk_c1. [back_rewrite(14345),rewrite([19754(5)])].
% 7.29/7.57 21253 multiply(sk_c6,sk_c6) = sk_c1 | multiply(sk_c1,multiply(sk_c6,multiply(sk_c6,A))) = A. [back_rewrite(13297),rewrite([19754(5),19754(7),19762(8)])].
% 7.29/7.57 21261 multiply(inverse(A),sk_c6) != sk_c6 | sk_c6 != A | multiply(sk_c6,sk_c6) != sk_c1. [back_rewrite(13150),rewrite([19754(12)])].
% 7.29/7.57 21289 identity != sk_c6 | multiply(sk_c6,sk_c6) != sk_c1. [back_rewrite(12891),rewrite([19754(8)])].
% 7.29/7.57 21323 multiply(sk_c1,sk_c6) = identity. [para(19754(a,1),4(a,1,1))].
% 7.29/7.57 21324 multiply(sk_c1,multiply(sk_c6,A)) = A. [para(19754(a,1),52(a,1,1))].
% 7.29/7.57 21343 identity = sk_c6 | identity = sk_c4. [back_rewrite(19765),rewrite([21323(3),21324(8)]),flip(b)].
% 7.29/7.57 21355 multiply(sk_c6,sk_c6) = sk_c1 | multiply(sk_c6,A) = A. [back_rewrite(21253),rewrite([21324(11)])].
% 7.29/7.57 21358 multiply(sk_c6,sk_c6) != sk_c6 | sk_c1 != sk_c6 | multiply(sk_c6,sk_c6) != sk_c1. [para(19762(a,1),21261(a,1,1)),flip(b)].
% 7.29/7.57 21379 identity = sk_c1 | identity != sk_c6. [resolve(21235,a,21289,b)].
% 7.29/7.57 21440 identity = sk_c1 | sk_c4 = sk_c6. [para(14060(a,1),52(a,1,2)),rewrite([19754(5),21324(8)]),flip(b)].
% 7.29/7.57 21449 sk_c4 = sk_c6 | identity = sk_c6. [para(21440(a,1),173(a,1,1)),rewrite([19762(5)]),flip(b)].
% 7.29/7.57 21471 sk_c4 = sk_c6 | sk_c1 = sk_c6. [para(21449(b,1),21440(a,1)),flip(b),merge(c)].
% 7.29/7.57 21473 sk_c1 = sk_c6 | identity = sk_c6. [para(21471(a,1),21343(b,2)),merge(c)].
% 7.29/7.57 21474 sk_c1 = sk_c6 | identity = sk_c1. [resolve(21473,b,21379,b)].
% 7.29/7.57 21479 sk_c1 = sk_c6. [para(21474(b,1),21473(b,1)),merge(b),merge(c)].
% 7.29/7.57 21529 multiply(sk_c6,sk_c6) != sk_c6. [back_rewrite(21358),rewrite([21479(6),21479(12)]),xx(b),merge(b)].
% 7.29/7.57 21531 multiply(sk_c6,A) = A. [back_rewrite(21355),rewrite([21479(4)]),unit_del(a,21529)].
% 7.29/7.57 21532 $F. [resolve(21531,a,21529,a)].
% 7.29/7.57
% 7.29/7.57 % SZS output end Refutation
% 7.29/7.57 ============================== end of proof ==========================
% 7.29/7.57
% 7.29/7.57 ============================== STATISTICS ============================
% 7.29/7.57
% 7.29/7.57 Given=1565. Generated=266404. Kept=21515. proofs=1.
% 7.29/7.57 Usable=48. Sos=820. Demods=22. Limbo=52, Disabled=20619. Hints=0.
% 7.29/7.57 Megabytes=17.79.
% 7.29/7.57 User_CPU=6.39, System_CPU=0.17, Wall_clock=7.
% 7.29/7.57
% 7.29/7.57 ============================== end of statistics =====================
% 7.29/7.57
% 7.29/7.57 ============================== end of search =========================
% 7.29/7.57
% 7.29/7.57 THEOREM PROVED
% 7.29/7.57 % SZS status Unsatisfiable
% 7.29/7.57
% 7.29/7.57 Exiting with 1 proof.
% 7.29/7.57
% 7.29/7.57 Process 3160 exit (max_proofs) Mon Jun 13 18:01:11 2022
% 7.29/7.57 Prover9 interrupted
%------------------------------------------------------------------------------