TSTP Solution File: GRP348-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP348-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 11:18:43 EDT 2022
% Result : Unsatisfiable 10.06s 10.33s
% Output : Refutation 10.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP348-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 01:16:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 10.06/10.33 ============================== Prover9 ===============================
% 10.06/10.33 Prover9 (32) version 2009-11A, November 2009.
% 10.06/10.33 Process 26265 was started by sandbox on n012.cluster.edu,
% 10.06/10.33 Tue Jun 14 01:16:56 2022
% 10.06/10.33 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26111_n012.cluster.edu".
% 10.06/10.33 ============================== end of head ===========================
% 10.06/10.33
% 10.06/10.33 ============================== INPUT =================================
% 10.06/10.33
% 10.06/10.33 % Reading from file /tmp/Prover9_26111_n012.cluster.edu
% 10.06/10.33
% 10.06/10.33 set(prolog_style_variables).
% 10.06/10.33 set(auto2).
% 10.06/10.33 % set(auto2) -> set(auto).
% 10.06/10.33 % set(auto) -> set(auto_inference).
% 10.06/10.33 % set(auto) -> set(auto_setup).
% 10.06/10.33 % set(auto_setup) -> set(predicate_elim).
% 10.06/10.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 10.06/10.33 % set(auto) -> set(auto_limits).
% 10.06/10.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 10.06/10.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 10.06/10.33 % set(auto) -> set(auto_denials).
% 10.06/10.33 % set(auto) -> set(auto_process).
% 10.06/10.33 % set(auto2) -> assign(new_constants, 1).
% 10.06/10.33 % set(auto2) -> assign(fold_denial_max, 3).
% 10.06/10.33 % set(auto2) -> assign(max_weight, "200.000").
% 10.06/10.33 % set(auto2) -> assign(max_hours, 1).
% 10.06/10.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 10.06/10.33 % set(auto2) -> assign(max_seconds, 0).
% 10.06/10.33 % set(auto2) -> assign(max_minutes, 5).
% 10.06/10.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 10.06/10.33 % set(auto2) -> set(sort_initial_sos).
% 10.06/10.33 % set(auto2) -> assign(sos_limit, -1).
% 10.06/10.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 10.06/10.33 % set(auto2) -> assign(max_megs, 400).
% 10.06/10.33 % set(auto2) -> assign(stats, some).
% 10.06/10.33 % set(auto2) -> clear(echo_input).
% 10.06/10.33 % set(auto2) -> set(quiet).
% 10.06/10.33 % set(auto2) -> clear(print_initial_clauses).
% 10.06/10.33 % set(auto2) -> clear(print_given).
% 10.06/10.33 assign(lrs_ticks,-1).
% 10.06/10.33 assign(sos_limit,10000).
% 10.06/10.33 assign(order,kbo).
% 10.06/10.33 set(lex_order_vars).
% 10.06/10.33 clear(print_given).
% 10.06/10.33
% 10.06/10.33 % formulas(sos). % not echoed (24 formulas)
% 10.06/10.33
% 10.06/10.33 ============================== end of input ==========================
% 10.06/10.33
% 10.06/10.33 % From the command line: assign(max_seconds, 300).
% 10.06/10.33
% 10.06/10.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 10.06/10.33
% 10.06/10.33 % Formulas that are not ordinary clauses:
% 10.06/10.33
% 10.06/10.33 ============================== end of process non-clausal formulas ===
% 10.06/10.33
% 10.06/10.33 ============================== PROCESS INITIAL CLAUSES ===============
% 10.06/10.33
% 10.06/10.33 ============================== PREDICATE ELIMINATION =================
% 10.06/10.33
% 10.06/10.33 ============================== end predicate elimination =============
% 10.06/10.33
% 10.06/10.33 Auto_denials: (non-Horn, no changes).
% 10.06/10.33
% 10.06/10.33 Term ordering decisions:
% 10.06/10.33
% 10.06/10.33 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 10.06/10.33 Function symbol KB weights: sk_c5=1. sk_c6=1. sk_c4=1. sk_c3=1. sk_c1=1. sk_c2=1. identity=1. multiply=1. inverse=0.
% 10.06/10.33
% 10.06/10.33 ============================== end of process initial clauses ========
% 10.06/10.33
% 10.06/10.33 ============================== CLAUSES FOR SEARCH ====================
% 10.06/10.33
% 10.06/10.33 ============================== end of clauses for search =============
% 10.06/10.33
% 10.06/10.33 ============================== SEARCH ================================
% 10.06/10.33
% 10.06/10.33 % Starting search at 0.01 seconds.
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=37.000, iters=3363
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=36.000, iters=3364
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=35.000, iters=3339
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=34.000, iters=3362
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=33.000, iters=3423
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=32.000, iters=3335
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=31.000, iters=3413
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=30.000, iters=3335
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=29.000, iters=3359
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=28.000, iters=3346
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=27.000, iters=3363
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=24.000, iters=3373
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=21.000, iters=3362
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=20.000, iters=3377
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=19.000, iters=3381
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=18.000, iters=3354
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=17.000, iters=3387
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=16.000, iters=3336
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=15.000, iters=3337
% 10.06/10.33
% 10.06/10.33 Low Water (keep): wt=14.000, iters=3348
% 10.06/10.33
% 10.06/10.33 ============================== PROOF =================================
% 10.06/10.33 % SZS status Unsatisfiable
% 10.06/10.33 % SZS output start Refutation
% 10.06/10.33
% 10.06/10.33 % Proof 1 at 9.10 (+ 0.21) seconds.
% 10.06/10.33 % Length of proof is 163.
% 10.06/10.33 % Level of proof is 31.
% 10.06/10.33 % Maximum clause weight is 41.000.
% 10.06/10.33 % Given clauses 1691.
% 10.06/10.33
% 10.06/10.33 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 10.06/10.33 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 10.06/10.33 3 inverse(sk_c1) = sk_c6 | inverse(sk_c4) = sk_c5 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 10.06/10.33 5 inverse(sk_c2) = sk_c5 | inverse(sk_c4) = sk_c5 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 10.06/10.33 6 inverse(sk_c2) = sk_c5 | inverse(sk_c3) = sk_c6 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 10.06/10.33 7 multiply(sk_c5,sk_c6) = sk_c4 | inverse(sk_c4) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 10.06/10.33 8 multiply(sk_c5,sk_c6) = sk_c4 | inverse(sk_c3) = sk_c6 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 10.06/10.33 9 inverse(sk_c1) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 10.06/10.33 10 inverse(sk_c1) = sk_c6 | multiply(sk_c3,sk_c5) = sk_c6 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 10.06/10.33 11 multiply(sk_c1,sk_c5) = sk_c6 | inverse(sk_c4) = sk_c5 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 10.06/10.33 13 inverse(sk_c2) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 10.06/10.33 15 multiply(sk_c2,sk_c4) = sk_c5 | inverse(sk_c4) = sk_c5 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 10.06/10.33 16 multiply(sk_c2,sk_c4) = sk_c5 | inverse(sk_c3) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 10.06/10.33 17 multiply(sk_c5,sk_c6) = sk_c4 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 10.06/10.33 19 multiply(sk_c1,sk_c5) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 10.06/10.33 20 multiply(sk_c1,sk_c5) = sk_c6 | multiply(sk_c3,sk_c5) = sk_c6 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 10.06/10.33 21 multiply(sk_c2,sk_c4) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 10.06/10.33 23 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 10.06/10.33 24 multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | inverse(B) != sk_c5 | multiply(B,sk_c4) != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 10.06/10.33 25 multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | inverse(B) != sk_c5 | multiply(B,sk_c4) != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6. [factor(24,b,h),merge(h)].
% 10.06/10.33 29 inverse(sk_c4) = sk_c5 | multiply(sk_c6,sk_c1) = identity. [para(3(a,1),2(a,1,1))].
% 10.06/10.33 31 inverse(sk_c4) = sk_c5 | multiply(sk_c5,sk_c2) = identity. [para(5(a,1),2(a,1,1))].
% 10.06/10.33 33 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),23(a,1,1)),rewrite([1(2)]),flip(a)].
% 10.06/10.33 34 inverse(sk_c4) = sk_c5 | multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c4,A). [para(7(a,1),23(a,1,1)),flip(b)].
% 10.06/10.33 35 inverse(sk_c4) = sk_c5 | multiply(A,multiply(sk_c5,sk_c6)) = multiply(A,sk_c4). [para(7(a,1),23(a,2,2)),rewrite([23(8)])].
% 10.06/10.33 37 inverse(sk_c3) = sk_c6 | multiply(A,multiply(sk_c5,sk_c6)) = multiply(A,sk_c4). [para(8(a,1),23(a,2,2)),rewrite([23(8)])].
% 10.06/10.33 39 inverse(sk_c1) = sk_c6 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c6). [para(9(b,1),23(a,2,2)),rewrite([23(8)])].
% 10.06/10.33 42 inverse(sk_c4) = sk_c5 | multiply(sk_c1,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(11(a,1),23(a,1,1)),flip(b)].
% 10.06/10.33 43 inverse(sk_c4) = sk_c5 | multiply(A,multiply(sk_c1,sk_c5)) = multiply(A,sk_c6). [para(11(a,1),23(a,2,2)),rewrite([23(8)])].
% 10.06/10.33 51 inverse(sk_c4) = sk_c5 | multiply(A,multiply(sk_c2,sk_c4)) = multiply(A,sk_c5). [para(15(a,1),23(a,2,2)),rewrite([23(8)])].
% 10.06/10.33 63 multiply(sk_c4,sk_c5) = sk_c6 | multiply(A,multiply(sk_c2,sk_c4)) = multiply(A,sk_c5). [para(21(a,1),23(a,2,2)),rewrite([23(9)])].
% 10.06/10.33 75 multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | inverse(identity) != sk_c5 | sk_c4 != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6. [para(1(a,1),25(e,1))].
% 10.06/10.33 98 inverse(sk_c4) = sk_c5 | multiply(sk_c6,multiply(sk_c1,A)) = A. [para(29(b,1),23(a,1,1)),rewrite([1(6)]),flip(b)].
% 10.06/10.33 105 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),33(a,1,2))].
% 10.06/10.33 111 inverse(sk_c1) = sk_c6 | multiply(inverse(sk_c4),sk_c6) = sk_c5. [para(9(b,1),33(a,1,2))].
% 10.06/10.33 112 inverse(sk_c1) = sk_c6 | multiply(inverse(sk_c3),sk_c6) = sk_c5. [para(10(b,1),33(a,1,2))].
% 10.06/10.33 117 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c2),sk_c5) = sk_c4. [para(15(a,1),33(a,1,2))].
% 10.06/10.33 118 inverse(sk_c3) = sk_c6 | multiply(inverse(sk_c2),sk_c5) = sk_c4. [para(16(a,1),33(a,1,2))].
% 10.06/10.33 126 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c6),identity) = sk_c1. [para(29(b,1),33(a,1,2))].
% 10.06/10.33 127 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(33(a,1),33(a,1,2))].
% 10.06/10.33 128 multiply(A,identity) = A. [back_rewrite(105),rewrite([127(4)])].
% 10.06/10.33 129 inverse(sk_c4) = sk_c5 | inverse(sk_c6) = sk_c1. [back_rewrite(126),rewrite([128(8)])].
% 10.06/10.33 131 inverse(identity) = identity. [para(128(a,1),2(a,1))].
% 10.06/10.33 136 multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | identity != sk_c5 | sk_c4 != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6. [back_rewrite(75),rewrite([131(14)])].
% 10.06/10.33 150 multiply(sk_c5,sk_c6) != sk_c4 | inverse(multiply(A,B)) != sk_c6 | multiply(A,multiply(B,sk_c5)) != sk_c6 | identity != sk_c5 | sk_c4 != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6. [para(23(a,1),136(c,1))].
% 10.06/10.33 156 inverse(sk_c4) = sk_c5 | inverse(sk_c5) = sk_c2. [para(31(b,1),33(a,1,2)),rewrite([128(8)])].
% 10.06/10.33 162 inverse(sk_c4) = sk_c5 | multiply(sk_c4,sk_c1) = sk_c5. [para(29(b,1),34(b,1,2)),rewrite([128(11)]),flip(c),merge(b)].
% 10.06/10.33 186 multiply(A,inverse(A)) = identity. [para(127(a,1),2(a,1))].
% 10.06/10.33 189 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c5),A) = multiply(sk_c2,A). [para(5(a,1),127(a,1,1,1))].
% 10.06/10.33 195 multiply(A,multiply(inverse(A),B)) = B. [para(127(a,1),33(a,1))].
% 10.06/10.33 196 inverse(inverse(A)) = A. [para(127(a,1),128(a,1)),rewrite([128(2)]),flip(a)].
% 10.06/10.33 205 inverse(sk_c4) = sk_c5 | multiply(sk_c1,sk_c6) = identity. [para(3(a,1),186(a,1,2))].
% 10.06/10.33 209 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(186(a,1),23(a,1)),flip(a)].
% 10.06/10.33 210 inverse(sk_c6) = sk_c1 | multiply(sk_c4,sk_c5) = identity. [para(129(a,1),186(a,1,2))].
% 10.06/10.33 212 inverse(sk_c5) = sk_c2 | multiply(sk_c4,sk_c5) = identity. [para(156(a,1),186(a,1,2))].
% 10.06/10.33 214 inverse(sk_c4) = sk_c5 | multiply(sk_c5,multiply(sk_c6,inverse(sk_c4))) = identity. [para(186(a,1),34(b,2))].
% 10.06/10.33 244 inverse(sk_c4) = sk_c5 | multiply(sk_c1,multiply(sk_c6,A)) = A. [para(3(a,1),195(a,1,2,1))].
% 10.06/10.33 246 inverse(sk_c4) = sk_c5 | multiply(sk_c2,multiply(sk_c5,A)) = A. [para(5(a,1),195(a,1,2,1))].
% 10.06/10.33 304 multiply(sk_c5,sk_c6) != sk_c4 | inverse(multiply(A,inverse(sk_c5))) != sk_c6 | sk_c6 != A | identity != sk_c5 | sk_c4 != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6. [para(2(a,1),150(c,1,2)),rewrite([128(13)]),flip(c)].
% 10.06/10.33 344 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c4),sk_c5) = sk_c1. [para(162(b,1),33(a,1,2))].
% 10.06/10.33 381 inverse(sk_c1) = sk_c6 | multiply(inverse(sk_c6),multiply(sk_c4,sk_c5)) = identity. [para(2(a,1),39(b,2))].
% 10.06/10.33 452 inverse(sk_c6) = sk_c1 | inverse(sk_c1) = sk_c6 | identity = sk_c6. [para(210(b,1),9(b,1))].
% 10.06/10.33 478 inverse(sk_c5) = sk_c2 | inverse(sk_c2) = sk_c5 | identity = sk_c6. [para(212(b,1),13(b,1))].
% 10.06/10.33 705 inverse(sk_c4) = sk_c5 | multiply(sk_c1,multiply(sk_c5,sk_c1)) = identity. [para(29(b,1),42(b,2)),merge(b)].
% 10.06/10.33 801 inverse(sk_c4) = sk_c5 | multiply(sk_c5,multiply(sk_c1,sk_c5)) = sk_c4. [para(7(a,1),43(b,2)),merge(b)].
% 10.06/10.33 805 inverse(sk_c4) = sk_c5 | multiply(sk_c1,multiply(sk_c1,sk_c5)) = identity. [para(205(b,1),43(b,2)),merge(b)].
% 10.06/10.33 1186 inverse(sk_c4) = sk_c5 | multiply(sk_c5,sk_c5) = sk_c4. [para(5(a,1),117(b,1,1)),merge(b)].
% 10.06/10.33 1191 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c5),sk_c4) = sk_c5. [para(1186(b,1),33(a,1,2))].
% 10.06/10.33 1193 inverse(sk_c3) = sk_c6 | multiply(sk_c5,sk_c5) = sk_c4. [para(6(a,1),118(b,1,1)),merge(b)].
% 10.06/10.33 1224 inverse(sk_c3) = sk_c6 | multiply(inverse(sk_c5),sk_c4) = sk_c5. [para(1193(b,1),33(a,1,2))].
% 10.06/10.33 1391 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(209(a,1),33(a,1,2)),rewrite([128(3)]),flip(a)].
% 10.06/10.33 1406 inverse(sk_c1) = sk_c6 | multiply(inverse(sk_c4),multiply(sk_c6,inverse(sk_c5))) = identity. [para(111(b,1),209(a,1,2,2,1))].
% 10.06/10.33 1436 multiply(sk_c4,sk_c5) = sk_c6 | multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c1). [para(19(a,1),1391(a,1,2,1))].
% 10.06/10.33 1443 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(1391(a,1),33(a,1,2)),flip(a)].
% 10.06/10.33 1451 inverse(sk_c4) = sk_c5 | multiply(sk_c5,inverse(sk_c4)) = sk_c2. [para(117(b,1),1391(a,1,2,1)),rewrite([196(11)])].
% 10.06/10.33 2042 multiply(sk_c5,sk_c6) != sk_c4 | multiply(sk_c5,inverse(A)) != sk_c6 | sk_c6 != A | identity != sk_c5 | sk_c4 != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6. [back_rewrite(304),rewrite([1443(9),196(8)])].
% 10.06/10.33 2234 multiply(sk_c5,sk_c6) != sk_c4 | multiply(sk_c5,A) != sk_c6 | inverse(A) != sk_c6 | identity != sk_c5 | sk_c4 != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6. [para(196(a,1),2042(b,1,2)),flip(c)].
% 10.06/10.33 2285 multiply(sk_c5,sk_c6) != sk_c4 | multiply(inverse(sk_c6),sk_c5) != sk_c6 | identity != sk_c5 | sk_c4 != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6. [resolve(2234,b,195,a),rewrite([1443(10),196(10)])].
% 10.06/10.33 2331 inverse(sk_c4) = sk_c5 | sk_c6 = sk_c5. [para(1191(b,1),35(b,2)),rewrite([33(14)]),merge(b)].
% 10.06/10.33 2335 sk_c6 = sk_c5 | multiply(sk_c4,sk_c5) = identity. [para(2331(a,1),186(a,1,2))].
% 10.06/10.33 2433 sk_c6 = sk_c5 | inverse(sk_c1) = sk_c6 | identity = sk_c6. [para(2335(b,1),9(b,1))].
% 10.06/10.33 2457 inverse(sk_c3) = sk_c6 | sk_c6 = sk_c5. [para(1224(b,1),37(b,2)),rewrite([33(14)]),merge(b)].
% 10.06/10.33 2554 sk_c6 = sk_c5 | multiply(sk_c6,sk_c3) = identity. [para(2457(a,1),2(a,1,1))].
% 10.06/10.33 2555 sk_c6 = sk_c5 | multiply(sk_c6,multiply(sk_c3,A)) = A. [para(2457(a,1),33(a,1,1))].
% 10.06/10.33 2556 sk_c6 = sk_c5 | inverse(sk_c6) = sk_c3. [para(2457(a,1),196(a,1,1))].
% 10.06/10.33 2969 sk_c6 = sk_c5 | multiply(inverse(sk_c3),inverse(sk_c6)) = identity. [para(2554(b,1),1443(a,1,1)),rewrite([131(5)]),flip(b)].
% 10.06/10.33 3450 sk_c6 = sk_c5 | identity = sk_c6 | inverse(sk_c6) = sk_c1. [para(2433(b,1),196(a,1,1))].
% 10.06/10.33 4387 sk_c6 = sk_c5 | identity = sk_c6 | sk_c1 = sk_c3. [para(3450(c,1),2556(b,1)),merge(c)].
% 10.06/10.33 4638 sk_c6 = sk_c5 | sk_c1 = sk_c3 | inverse(sk_c6) = identity. [para(4387(b,1),131(a,1,1))].
% 10.06/10.33 5168 sk_c6 = sk_c5 | sk_c1 = sk_c3 | inverse(sk_c3) = identity. [para(4638(c,1),2969(b,1,2)),rewrite([128(13)]),merge(c)].
% 10.06/10.33 5252 sk_c6 = sk_c5 | sk_c1 = sk_c3 | inverse(sk_c1) = sk_c6. [para(5168(c,1),112(b,1,1)),rewrite([1(13)]),merge(d)].
% 10.06/10.33 5401 sk_c6 = sk_c5 | sk_c1 = sk_c3 | inverse(sk_c6) = sk_c1. [para(5252(c,1),196(a,1,1))].
% 10.06/10.33 5723 sk_c6 = sk_c5 | sk_c1 = sk_c3. [para(5401(c,1),2556(b,1)),merge(c),merge(d)].
% 10.06/10.33 5725 sk_c6 = sk_c5 | multiply(sk_c3,sk_c5) = sk_c6. [para(5723(b,1),20(a,1,1)),merge(c)].
% 10.06/10.33 5745 sk_c6 = sk_c5 | multiply(sk_c6,sk_c6) = sk_c5. [para(5725(b,1),2555(b,1,2)),merge(b)].
% 10.06/10.33 5824 sk_c6 = sk_c5 | multiply(inverse(sk_c6),sk_c5) = sk_c6. [para(5745(b,1),33(a,1,2))].
% 10.06/10.33 6778 inverse(sk_c4) = sk_c5 | multiply(sk_c2,sk_c4) = sk_c6. [para(7(a,1),246(b,1,2)),merge(b)].
% 10.06/10.33 6784 inverse(sk_c4) = sk_c5 | multiply(sk_c2,sk_c2) = inverse(sk_c4). [para(1451(b,1),246(b,1,2)),merge(b)].
% 10.06/10.33 6788 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c2),sk_c6) = sk_c4. [para(6778(b,1),33(a,1,2))].
% 10.06/10.33 7276 inverse(sk_c6) = sk_c1 | identity = sk_c6. [para(452(b,1),196(a,1,1)),merge(c)].
% 10.06/10.33 7536 inverse(sk_c5) = sk_c2 | identity = sk_c6. [para(478(b,1),196(a,1,1)),merge(c)].
% 10.06/10.33 7538 identity = sk_c6 | multiply(sk_c2,multiply(sk_c5,A)) = A. [para(7536(a,1),33(a,1,1))].
% 10.06/10.33 8091 inverse(sk_c4) = sk_c5 | multiply(sk_c5,sk_c1) = inverse(sk_c1). [para(705(b,1),33(a,1,2)),rewrite([128(8)]),flip(b)].
% 10.06/10.33 8094 inverse(sk_c4) = sk_c5 | multiply(sk_c5,sk_c1) = sk_c6. [para(705(b,1),98(b,1,2)),rewrite([128(11)]),flip(c),merge(b)].
% 10.06/10.33 8245 inverse(sk_c4) = sk_c5 | multiply(sk_c6,inverse(sk_c4)) = sk_c2. [para(214(b,1),246(b,1,2)),rewrite([128(11)]),flip(c),merge(b)].
% 10.06/10.33 8263 inverse(sk_c4) = sk_c5 | multiply(sk_c1,sk_c2) = inverse(sk_c4). [para(8245(b,1),244(b,1,2)),merge(b)].
% 10.06/10.33 8278 inverse(sk_c4) = sk_c5 | multiply(sk_c1,sk_c5) = inverse(sk_c1). [para(805(b,1),33(a,1,2)),rewrite([128(8)]),flip(b)].
% 10.06/10.33 8295 inverse(sk_c4) = sk_c5 | multiply(sk_c5,inverse(sk_c1)) = sk_c4. [para(8278(b,1),801(b,1,2)),merge(b)].
% 10.06/10.33 8308 inverse(sk_c4) = sk_c5 | multiply(sk_c2,sk_c4) = inverse(sk_c1). [para(8295(b,1),246(b,1,2)),merge(b)].
% 10.06/10.33 8309 inverse(sk_c4) = sk_c5 | inverse(sk_c1) = sk_c5. [para(8308(b,1),15(a,1)),merge(c)].
% 10.06/10.33 8366 inverse(sk_c4) = sk_c5 | multiply(sk_c5,sk_c1) = identity. [para(8309(b,1),2(a,1,1))].
% 10.06/10.33 8369 inverse(sk_c4) = sk_c5 | multiply(sk_c1,sk_c5) = identity. [para(8309(b,1),186(a,1,2))].
% 10.06/10.33 8567 inverse(sk_c4) = sk_c5 | identity = sk_c6. [para(8366(b,1),8094(b,1)),merge(b)].
% 10.06/10.33 8568 inverse(sk_c4) = sk_c5 | inverse(sk_c1) = identity. [para(8366(b,1),8091(b,1)),flip(c),merge(b)].
% 10.06/10.33 8594 identity = sk_c6 | multiply(sk_c5,multiply(sk_c4,A)) = A. [para(8567(a,1),33(a,1,1))].
% 10.06/10.33 8596 identity = sk_c6 | multiply(sk_c4,sk_c5) = identity. [para(8567(a,1),186(a,1,2))].
% 10.06/10.33 8801 inverse(sk_c4) = sk_c5 | multiply(sk_c2,sk_c4) = identity. [para(8568(b,1),8308(b,2)),merge(b)].
% 10.06/10.33 9016 identity = sk_c6 | multiply(sk_c5,sk_c6) = sk_c4. [para(8596(b,1),17(b,1)),merge(c)].
% 10.06/10.33 9308 identity = sk_c6 | multiply(inverse(sk_c5),sk_c4) = sk_c6. [para(9016(b,1),33(a,1,2))].
% 10.06/10.33 9327 inverse(sk_c4) = sk_c5 | multiply(A,sk_c6) = A. [para(8369(b,1),43(b,1,2)),rewrite([128(10)]),flip(c),merge(b)].
% 10.06/10.33 9662 inverse(sk_c4) = sk_c5 | multiply(A,sk_c5) = A. [para(8801(b,1),51(b,1,2)),rewrite([128(10)]),flip(c),merge(b)].
% 10.06/10.33 9778 identity = sk_c6 | multiply(inverse(sk_c4),sk_c5) = inverse(sk_c6). [para(9308(b,1),1443(a,1,1)),rewrite([196(10)]),flip(b)].
% 10.06/10.33 9804 inverse(sk_c4) = sk_c5 | inverse(sk_c6) = identity. [para(9327(b,1),2(a,1))].
% 10.06/10.33 9821 inverse(sk_c4) = sk_c5 | multiply(sk_c2,sk_c6) = inverse(sk_c5). [para(9327(b,1),189(b,1)),flip(c),merge(b)].
% 10.06/10.33 9872 inverse(sk_c6) = identity | multiply(sk_c4,sk_c5) = identity. [para(9804(a,1),186(a,1,2))].
% 10.06/10.33 10305 inverse(sk_c4) = sk_c5 | inverse(sk_c4) = sk_c1. [para(9662(b,1),344(b,1)),merge(b)].
% 10.06/10.33 10433 inverse(sk_c4) = sk_c5 | multiply(sk_c5,sk_c1) = sk_c2. [para(10305(b,1),1451(b,1,2)),merge(b)].
% 10.06/10.33 10903 inverse(sk_c6) = identity | inverse(sk_c1) = sk_c6. [para(9872(b,1),381(b,1,2)),rewrite([128(12)]),merge(c)].
% 10.06/10.33 10916 inverse(sk_c6) = identity | inverse(sk_c6) = sk_c1. [para(10903(b,1),196(a,1,1))].
% 10.06/10.33 10929 inverse(sk_c6) = sk_c1 | sk_c6 = sk_c5. [para(10916(a,1),5824(b,1,1)),rewrite([1(10)]),flip(c),merge(c)].
% 10.06/10.33 10933 sk_c6 = sk_c5 | inverse(sk_c1) = sk_c6. [para(10929(a,1),196(a,1,1))].
% 10.06/10.33 11273 inverse(sk_c4) = sk_c5 | multiply(sk_c1,sk_c2) = identity. [para(10433(b,1),705(b,1,2)),merge(b)].
% 10.06/10.33 12163 inverse(sk_c4) = sk_c5 | inverse(sk_c4) = identity. [para(11273(b,1),8263(b,1)),flip(c),merge(b)].
% 10.06/10.33 12191 inverse(sk_c4) = sk_c5 | multiply(sk_c2,sk_c2) = identity. [para(12163(b,1),6784(b,2)),merge(b)].
% 10.06/10.33 12577 inverse(sk_c4) = sk_c5 | inverse(sk_c2) = sk_c2. [para(12191(b,1),33(a,1,2)),rewrite([128(8)])].
% 10.06/10.33 12582 inverse(sk_c4) = sk_c5 | multiply(sk_c2,sk_c6) = sk_c4. [para(12577(b,1),6788(b,1,1)),merge(b)].
% 10.06/10.33 13309 identity = sk_c6 | multiply(sk_c4,inverse(sk_c6)) = sk_c5. [para(9778(b,1),33(a,1,2)),rewrite([196(6)])].
% 10.06/10.33 13325 identity = sk_c6 | multiply(sk_c4,sk_c1) = sk_c5. [para(7276(a,1),13309(b,1,2)),merge(b)].
% 10.06/10.33 13339 identity = sk_c6 | multiply(sk_c5,sk_c5) = sk_c1. [para(13325(b,1),8594(b,1,2)),merge(b)].
% 10.06/10.33 13348 identity = sk_c6 | multiply(sk_c2,sk_c1) = sk_c5. [para(13339(b,1),7538(b,1,2)),merge(b)].
% 10.06/10.33 13351 identity = sk_c6 | multiply(inverse(sk_c2),sk_c5) = sk_c1. [para(13348(b,1),33(a,1,2))].
% 10.06/10.33 13380 identity = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 | sk_c1 = sk_c4. [para(13351(b,1),63(b,2)),rewrite([33(14)]),flip(c)].
% 10.06/10.33 13481 inverse(sk_c4) = sk_c5 | inverse(sk_c5) = sk_c4. [para(9821(b,1),12582(b,1)),merge(b)].
% 10.06/10.33 13484 inverse(sk_c5) = sk_c4. [para(13481(a,1),196(a,1,1)),merge(b)].
% 10.06/10.33 13909 inverse(sk_c1) = sk_c6 | multiply(inverse(sk_c4),multiply(sk_c6,sk_c4)) = identity. [back_rewrite(1406),rewrite([13484(9)])].
% 10.06/10.33 13937 multiply(sk_c4,sk_c5) = identity. [para(13484(a,1),2(a,1,1))].
% 10.06/10.33 13939 inverse(sk_c4) = sk_c5. [para(13484(a,1),196(a,1,1))].
% 10.06/10.33 13940 multiply(sk_c5,sk_c4) = identity. [para(13484(a,1),186(a,1,2))].
% 10.06/10.33 14792 identity = sk_c6 | sk_c1 = sk_c4. [back_rewrite(13380),rewrite([13937(6)]),merge(b)].
% 10.06/10.33 16522 multiply(sk_c5,sk_c6) != sk_c4 | multiply(inverse(sk_c6),sk_c5) != sk_c6 | identity != sk_c5 | sk_c4 != sk_c5 | identity != sk_c6. [back_rewrite(2285),rewrite([13939(19),13937(23)]),xx(e)].
% 10.06/10.33 16679 identity = sk_c6 | multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c1). [back_rewrite(1436),rewrite([13937(3)])].
% 10.06/10.33 16755 inverse(sk_c1) = sk_c6 | multiply(sk_c5,multiply(sk_c6,sk_c4)) = identity. [back_rewrite(13909),rewrite([13939(6)])].
% 10.06/10.33 17001 sk_c1 = sk_c4 | inverse(sk_c6) = identity. [para(14792(a,1),131(a,1,1))].
% 10.06/10.33 17143 sk_c1 = sk_c4 | sk_c6 = sk_c5. [para(17001(b,1),5824(b,1,1)),rewrite([1(9)]),flip(c),merge(c)].
% 10.06/10.33 17189 sk_c6 = sk_c5. [para(17143(a,1),10933(b,1,1)),rewrite([13939(8)]),flip(c),merge(b),merge(c)].
% 10.06/10.33 17423 inverse(sk_c1) = sk_c5 | identity = sk_c5. [back_rewrite(16755),rewrite([17189(3),17189(6),13940(8),128(7)]),flip(b)].
% 10.06/10.33 17473 identity = sk_c5 | inverse(sk_c1) = identity. [back_rewrite(16679),rewrite([17189(2),17189(5),13484(6),13940(6)]),flip(b)].
% 10.06/10.33 17549 multiply(sk_c5,sk_c5) != sk_c4 | identity != sk_c5 | sk_c4 != sk_c5. [back_rewrite(16522),rewrite([17189(2),17189(6),13484(7),13937(8),17189(7),17189(16)]),merge(c),merge(e)].
% 10.06/10.33 19265 identity = sk_c5. [para(17473(b,1),17423(a,1)),merge(b),merge(c)].
% 10.06/10.33 19673 multiply(sk_c5,sk_c5) != sk_c4 | sk_c4 != sk_c5. [back_rewrite(17549),rewrite([19265(6)]),xx(b)].
% 10.06/10.33 19761 sk_c4 = sk_c5. [back_rewrite(131),rewrite([19265(1),13484(2),19265(2)])].
% 10.06/10.33 19762 multiply(A,sk_c5) = A. [back_rewrite(128),rewrite([19265(1)])].
% 10.06/10.33 19777 $F. [back_rewrite(19673),rewrite([19762(3),19761(2),19761(4)]),xx(a),xx(b)].
% 10.06/10.33
% 10.06/10.33 % SZS output end Refutation
% 10.06/10.33 ============================== end of proof ==========================
% 10.06/10.33
% 10.06/10.33 ============================== STATISTICS ============================
% 10.06/10.33
% 10.06/10.33 Given=1691. Generated=395593. Kept=19776. proofs=1.
% 10.06/10.33 Usable=33. Sos=1107. Demods=20. Limbo=16, Disabled=18644. Hints=0.
% 10.06/10.33 Megabytes=17.12.
% 10.06/10.33 User_CPU=9.10, System_CPU=0.21, Wall_clock=9.
% 10.06/10.33
% 10.06/10.33 ============================== end of statistics =====================
% 10.06/10.33
% 10.06/10.33 ============================== end of search =========================
% 10.06/10.33
% 10.06/10.33 THEOREM PROVED
% 10.06/10.33 % SZS status Unsatisfiable
% 10.06/10.33
% 10.06/10.33 Exiting with 1 proof.
% 10.06/10.33
% 10.06/10.33 Process 26265 exit (max_proofs) Tue Jun 14 01:17:05 2022
% 10.06/10.33 Prover9 interrupted
%------------------------------------------------------------------------------