TSTP Solution File: KLE145-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE145-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 : Sun Jul 17 02:22:27 EDT 2022
% Result : Unsatisfiable 5.44s 5.71s
% Output : Refutation 5.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE145-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n007.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 : Thu Jun 16 10:54:56 EDT 2022
% 0.14/0.36 % CPUTime :
% 5.44/5.71 ============================== Prover9 ===============================
% 5.44/5.71 Prover9 (32) version 2009-11A, November 2009.
% 5.44/5.71 Process 24872 was started by sandbox on n007.cluster.edu,
% 5.44/5.71 Thu Jun 16 10:54:57 2022
% 5.44/5.71 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24718_n007.cluster.edu".
% 5.44/5.71 ============================== end of head ===========================
% 5.44/5.71
% 5.44/5.71 ============================== INPUT =================================
% 5.44/5.71
% 5.44/5.71 % Reading from file /tmp/Prover9_24718_n007.cluster.edu
% 5.44/5.71
% 5.44/5.71 set(prolog_style_variables).
% 5.44/5.71 set(auto2).
% 5.44/5.71 % set(auto2) -> set(auto).
% 5.44/5.71 % set(auto) -> set(auto_inference).
% 5.44/5.71 % set(auto) -> set(auto_setup).
% 5.44/5.71 % set(auto_setup) -> set(predicate_elim).
% 5.44/5.71 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.44/5.71 % set(auto) -> set(auto_limits).
% 5.44/5.71 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.44/5.71 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.44/5.71 % set(auto) -> set(auto_denials).
% 5.44/5.71 % set(auto) -> set(auto_process).
% 5.44/5.71 % set(auto2) -> assign(new_constants, 1).
% 5.44/5.71 % set(auto2) -> assign(fold_denial_max, 3).
% 5.44/5.71 % set(auto2) -> assign(max_weight, "200.000").
% 5.44/5.71 % set(auto2) -> assign(max_hours, 1).
% 5.44/5.71 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.44/5.71 % set(auto2) -> assign(max_seconds, 0).
% 5.44/5.71 % set(auto2) -> assign(max_minutes, 5).
% 5.44/5.71 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.44/5.71 % set(auto2) -> set(sort_initial_sos).
% 5.44/5.71 % set(auto2) -> assign(sos_limit, -1).
% 5.44/5.71 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.44/5.71 % set(auto2) -> assign(max_megs, 400).
% 5.44/5.71 % set(auto2) -> assign(stats, some).
% 5.44/5.71 % set(auto2) -> clear(echo_input).
% 5.44/5.71 % set(auto2) -> set(quiet).
% 5.44/5.71 % set(auto2) -> clear(print_initial_clauses).
% 5.44/5.71 % set(auto2) -> clear(print_given).
% 5.44/5.71 assign(lrs_ticks,-1).
% 5.44/5.71 assign(sos_limit,10000).
% 5.44/5.71 assign(order,kbo).
% 5.44/5.71 set(lex_order_vars).
% 5.44/5.71 clear(print_given).
% 5.44/5.71
% 5.44/5.71 % formulas(sos). % not echoed (23 formulas)
% 5.44/5.71
% 5.44/5.71 ============================== end of input ==========================
% 5.44/5.71
% 5.44/5.71 % From the command line: assign(max_seconds, 300).
% 5.44/5.71
% 5.44/5.71 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.44/5.71
% 5.44/5.71 % Formulas that are not ordinary clauses:
% 5.44/5.71
% 5.44/5.71 ============================== end of process non-clausal formulas ===
% 5.44/5.71
% 5.44/5.71 ============================== PROCESS INITIAL CLAUSES ===============
% 5.44/5.71
% 5.44/5.71 ============================== PREDICATE ELIMINATION =================
% 5.44/5.71
% 5.44/5.71 ============================== end predicate elimination =============
% 5.44/5.71
% 5.44/5.71 Auto_denials:
% 5.44/5.71 % copying label goals to answer in negative clause
% 5.44/5.71
% 5.44/5.71 Term ordering decisions:
% 5.44/5.71 Function symbol KB weights: true=1. one=1. zero=1. sK1_goals_X0=1. multiplication=1. addition=1. leq=1. star=1. strong_iteration=1. ifeq=1. ifeq2=1. ifeq3=1.
% 5.44/5.71
% 5.44/5.71 ============================== end of process initial clauses ========
% 5.44/5.71
% 5.44/5.71 ============================== CLAUSES FOR SEARCH ====================
% 5.44/5.71
% 5.44/5.71 ============================== end of clauses for search =============
% 5.44/5.71
% 5.44/5.71 ============================== SEARCH ================================
% 5.44/5.71
% 5.44/5.71 % Starting search at 0.01 seconds.
% 5.44/5.71
% 5.44/5.71 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 40 (0.00 of 0.55 sec).
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=37.000, iters=3352
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=35.000, iters=3355
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=33.000, iters=3413
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=32.000, iters=3372
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=31.000, iters=3385
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=30.000, iters=3423
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=29.000, iters=3339
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=28.000, iters=3335
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=27.000, iters=3346
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=26.000, iters=3375
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=25.000, iters=3366
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=24.000, iters=3363
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=23.000, iters=3349
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=22.000, iters=3444
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=21.000, iters=3334
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=20.000, iters=3337
% 5.44/5.71
% 5.44/5.71 Low Water (displace): id=6751, wt=61.000
% 5.44/5.71
% 5.44/5.71 Low Water (displace): id=3206, wt=55.000
% 5.44/5.71
% 5.44/5.71 Low Water (displace): id=13075, wt=19.000
% 5.44/5.71
% 5.44/5.71 Low Water (displace): id=13294, wt=13.000
% 5.44/5.71
% 5.44/5.71 Low Water (displace): id=13380, wt=12.000
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=19.000, iters=3336
% 5.44/5.71
% 5.44/5.71 Low Water (displace): id=14635, wt=11.000
% 5.44/5.71
% 5.44/5.71 Low Water (keep): wt=18.000, iters=3334
% 5.44/5.71
% 5.44/5.71 ============================== PROOF =================================
% 5.44/5.71 % SZS status Unsatisfiable
% 5.44/5.71 % SZS output start Refutation
% 5.44/5.71
% 5.44/5.71 % Proof 1 at 4.60 (+ 0.10) seconds: goals.
% 5.44/5.71 % Length of proof is 120.
% 5.44/5.71 % Level of proof is 22.
% 5.44/5.71 % Maximum clause weight is 25.000.
% 5.44/5.71 % Given clauses 1804.
% 5.44/5.71
% 5.44/5.71 1 addition(A,zero) = A # label(additive_identity) # label(axiom). [assumption].
% 5.44/5.71 2 addition(A,A) = A # label(idempotence) # label(axiom). [assumption].
% 5.44/5.71 3 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [assumption].
% 5.44/5.71 4 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [assumption].
% 5.44/5.71 5 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [assumption].
% 5.44/5.71 6 ifeq3(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 5.44/5.71 7 ifeq2(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 5.44/5.71 8 ifeq(A,A,B,C) = B # label(ifeq_axiom_002) # label(axiom). [assumption].
% 5.44/5.71 9 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [assumption].
% 5.44/5.71 10 addition(one,multiplication(A,star(A))) = star(A) # label(star_unfold1) # label(axiom). [assumption].
% 5.44/5.71 11 addition(one,multiplication(star(A),A)) = star(A) # label(star_unfold2) # label(axiom). [assumption].
% 5.44/5.71 12 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [assumption].
% 5.44/5.71 13 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(12),rewrite([9(5)]),flip(a)].
% 5.44/5.71 14 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom). [assumption].
% 5.44/5.71 15 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A). [copy(14),flip(a)].
% 5.44/5.71 16 addition(A,addition(B,C)) = addition(addition(A,B),C) # label(additive_associativity) # label(axiom). [assumption].
% 5.44/5.71 17 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(16),rewrite([9(4)])].
% 5.44/5.71 18 multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) # label(multiplicative_associativity) # label(axiom). [assumption].
% 5.44/5.71 19 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)). [copy(18),flip(a)].
% 5.44/5.71 20 ifeq2(leq(A,B),true,addition(A,B),B) = B # label(order_1) # label(axiom). [assumption].
% 5.44/5.71 21 ifeq3(addition(A,B),B,leq(A,B),true) = true # label(order) # label(axiom). [assumption].
% 5.44/5.71 22 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [assumption].
% 5.44/5.71 23 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(22),flip(a)].
% 5.44/5.71 24 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [assumption].
% 5.44/5.71 25 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(24),flip(a)].
% 5.44/5.71 26 ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true # label(star_induction1) # label(axiom). [assumption].
% 5.44/5.71 27 ifeq(leq(addition(A,multiplication(B,C)),C),true,leq(multiplication(star(B),A),C),true) = true. [copy(26),rewrite([9(2)])].
% 5.44/5.71 28 ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true # label(star_induction2) # label(axiom). [assumption].
% 5.44/5.71 29 ifeq(leq(addition(A,multiplication(B,C)),B),true,leq(multiplication(A,star(C)),B),true) = true. [copy(28),rewrite([9(2)])].
% 5.44/5.71 30 ifeq(leq(A,addition(multiplication(B,A),C)),true,leq(A,multiplication(strong_iteration(B),C)),true) = true # label(infty_coinduction) # label(axiom). [assumption].
% 5.44/5.71 31 ifeq(leq(A,addition(B,multiplication(C,A))),true,leq(A,multiplication(strong_iteration(C),B)),true) = true. [copy(30),rewrite([9(2)])].
% 5.44/5.71 32 star(strong_iteration(sK1_goals_X0)) != strong_iteration(sK1_goals_X0) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 5.44/5.71 33 star(strong_iteration(sK1_goals_X0)) = c_0. [new_symbol(32)].
% 5.44/5.71 34 strong_iteration(sK1_goals_X0) != c_0 # answer(goals). [back_rewrite(32),rewrite([33(3)]),flip(a)].
% 5.44/5.71 39 addition(A,addition(A,B)) = addition(A,B). [para(17(a,1),2(a,1)),rewrite([9(1),9(2),17(2,R),2(1),9(3)])].
% 5.44/5.71 40 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(19(a,1),10(a,1,2))].
% 5.44/5.71 44 ifeq2(leq(one,multiplication(A,star(A))),true,star(A),multiplication(A,star(A))) = multiplication(A,star(A)). [para(10(a,1),20(a,1,3))].
% 5.44/5.71 49 leq(A,A) = true. [para(2(a,1),21(a,1,1)),rewrite([6(3)])].
% 5.44/5.71 55 ifeq3(addition(A,addition(B,C)),addition(A,C),leq(B,addition(A,C)),true) = true. [para(17(a,1),21(a,1,1)),rewrite([9(3),9(4)])].
% 5.44/5.71 57 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(3(a,1),23(a,1,1)),rewrite([9(4)]),flip(a)].
% 5.44/5.71 58 addition(A,multiplication(A,multiplication(B,star(B)))) = multiplication(A,star(B)). [para(10(a,1),23(a,2,2)),rewrite([3(2)])].
% 5.44/5.71 63 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(1(a,1),25(a,2,1)),rewrite([5(3),9(3)])].
% 5.44/5.71 64 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(4(a,1),25(a,1,1)),rewrite([9(4)]),flip(a)].
% 5.44/5.71 65 addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A). [para(10(a,1),25(a,2,1)),rewrite([4(2),19(3)])].
% 5.44/5.71 66 addition(A,multiplication(star(B),multiplication(B,A))) = multiplication(star(B),A). [para(11(a,1),25(a,2,1)),rewrite([4(2),19(3)])].
% 5.44/5.71 67 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A). [para(13(a,1),25(a,2,1)),rewrite([4(2),19(3)])].
% 5.44/5.71 73 ifeq(leq(multiplication(A,B),B),true,leq(multiplication(star(A),multiplication(A,B)),B),true) = true. [para(2(a,1),27(a,1,1,1))].
% 5.44/5.71 83 ifeq(leq(multiplication(addition(A,B),C),C),true,leq(multiplication(star(B),multiplication(A,C)),C),true) = true. [para(25(a,1),27(a,1,1,1))].
% 5.44/5.71 97 ifeq(leq(A,addition(one,multiplication(B,A))),true,leq(A,strong_iteration(B)),true) = true. [para(3(a,1),31(a,1,3,2))].
% 5.44/5.71 104 addition(one,multiplication(strong_iteration(sK1_goals_X0),c_0)) = c_0. [para(33(a,1),10(a,1,2,2)),rewrite([33(9)])].
% 5.44/5.71 126 addition(one,star(A)) = star(A). [para(10(a,1),39(a,1,2)),rewrite([10(7)])].
% 5.44/5.71 127 addition(one,strong_iteration(A)) = strong_iteration(A). [para(13(a,1),39(a,1,2)),rewrite([13(7)])].
% 5.44/5.71 130 addition(one,c_0) = c_0. [para(104(a,1),39(a,1,2)),rewrite([104(9)])].
% 5.44/5.71 134 addition(A,multiplication(A,c_0)) = multiplication(A,c_0). [para(130(a,1),23(a,2,2)),rewrite([3(2)])].
% 5.44/5.71 135 addition(A,multiplication(c_0,A)) = multiplication(c_0,A). [para(130(a,1),25(a,2,1)),rewrite([4(2)])].
% 5.44/5.71 139 addition(A,multiplication(star(B),A)) = multiplication(star(B),A). [para(126(a,1),25(a,2,1)),rewrite([4(2)])].
% 5.44/5.71 140 addition(one,multiplication(A,zero)) = star(multiplication(A,zero)). [para(5(a,1),40(a,1,2,2))].
% 5.44/5.71 144 addition(A,multiplication(A,multiplication(B,multiplication(C,star(multiplication(B,C)))))) = multiplication(A,star(multiplication(B,C))). [para(40(a,1),23(a,2,2)),rewrite([3(2)])].
% 5.44/5.71 148 ifeq(leq(multiplication(A,star(multiplication(B,A))),star(multiplication(B,A))),true,leq(multiplication(A,star(multiplication(B,A))),strong_iteration(B)),true) = true. [para(40(a,1),31(a,1,1,2)),rewrite([3(13)])].
% 5.44/5.71 152 addition(A,multiplication(strong_iteration(B),A)) = multiplication(strong_iteration(B),A). [para(127(a,1),25(a,2,1)),rewrite([4(2)])].
% 5.44/5.71 208 addition(A,multiplication(A,multiplication(B,zero))) = multiplication(A,star(multiplication(B,zero))). [para(140(a,1),23(a,2,2)),rewrite([3(2)])].
% 5.44/5.71 209 multiplication(star(multiplication(A,zero)),B) = addition(B,multiplication(A,zero)). [para(140(a,1),25(a,2,1)),rewrite([4(2),19(3),5(2)]),flip(a)].
% 5.44/5.71 295 ifeq(leq(multiplication(A,addition(B,one)),A),true,leq(multiplication(A,star(B)),A),true) = true. [para(57(a,2),29(a,1,1,1))].
% 5.44/5.71 334 multiplication(addition(A,one),zero) = multiplication(A,zero). [para(64(a,2),63(a,1))].
% 5.44/5.71 342 multiplication(addition(one,multiplication(A,B)),zero) = multiplication(A,multiplication(B,zero)). [para(19(a,1),334(a,2)),rewrite([9(3)])].
% 5.44/5.71 344 multiplication(addition(A,addition(B,one)),zero) = multiplication(addition(A,B),zero). [para(334(a,1),25(a,1,1)),rewrite([25(5),9(6),17(6,R),9(5)]),flip(a)].
% 5.44/5.71 363 leq(A,addition(B,A)) = true. [para(2(a,1),55(a,1,1,2)),rewrite([6(6)])].
% 5.44/5.71 373 leq(A,addition(B,addition(A,C))) = true. [para(39(a,1),55(a,1,1,2)),rewrite([6(9)])].
% 5.44/5.71 392 leq(multiplication(A,star(A)),star(A)) = true. [para(10(a,1),363(a,1,2))].
% 5.44/5.71 393 leq(multiplication(star(A),A),star(A)) = true. [para(11(a,1),363(a,1,2))].
% 5.44/5.71 396 leq(addition(A,B),addition(A,addition(B,C))) = true. [para(17(a,1),363(a,1,2)),rewrite([9(2),17(3,R),9(2)])].
% 5.44/5.71 397 leq(multiplication(strong_iteration(sK1_goals_X0),c_0),c_0) = true. [para(104(a,1),363(a,1,2))].
% 5.44/5.71 427 multiplication(strong_iteration(sK1_goals_X0),c_0) = c_0. [para(397(a,1),20(a,1,1)),rewrite([9(8),152(8),7(8)])].
% 5.44/5.71 428 multiplication(strong_iteration(sK1_goals_X0),multiplication(c_0,A)) = multiplication(c_0,A). [para(427(a,1),19(a,1,1)),flip(a)].
% 5.44/5.71 429 addition(c_0,multiplication(strong_iteration(sK1_goals_X0),A)) = multiplication(strong_iteration(sK1_goals_X0),addition(A,c_0)). [para(427(a,1),23(a,1,1)),rewrite([9(9)])].
% 5.44/5.71 437 addition(c_0,strong_iteration(sK1_goals_X0)) = c_0. [para(427(a,1),134(a,1,2)),rewrite([9(4),427(8)])].
% 5.44/5.71 521 leq(A,addition(B,multiplication(A,star(C)))) = true. [para(58(a,1),373(a,1,2,2))].
% 5.44/5.71 617 multiplication(addition(A,one),star(A)) = star(A). [para(392(a,1),20(a,1,1)),rewrite([9(6),64(6,R),7(8)])].
% 5.44/5.71 619 multiplication(star(A),addition(A,one)) = star(A). [para(393(a,1),20(a,1,1)),rewrite([9(6),57(6,R),7(8)])].
% 5.44/5.71 623 multiplication(star(A),multiplication(A,B)) = multiplication(A,multiplication(star(A),B)). [para(65(a,1),23(a,1)),rewrite([66(7)])].
% 5.44/5.71 638 ifeq(leq(multiplication(A,B),B),true,leq(multiplication(A,multiplication(star(A),B)),B),true) = true. [back_rewrite(73),rewrite([623(6)])].
% 5.44/5.71 657 multiplication(A,addition(B,multiplication(strong_iteration(A),multiplication(A,B)))) = multiplication(strong_iteration(A),multiplication(A,B)). [para(67(a,1),23(a,1)),flip(a)].
% 5.44/5.71 662 multiplication(A,addition(one,multiplication(strong_iteration(A),A))) = multiplication(strong_iteration(A),A). [para(67(a,1),57(a,2)),rewrite([9(4)])].
% 5.44/5.71 666 multiplication(addition(one,sK1_goals_X0),c_0) = c_0. [para(427(a,1),67(a,1,2,2)),rewrite([64(5,R),9(3),427(9)])].
% 5.44/5.71 1102 addition(A,star(A)) = star(A). [para(617(a,1),57(a,2,2)),rewrite([9(5),126(5),617(4),9(5),17(5),9(4),17(5,R),9(4),126(4)]),flip(a)].
% 5.44/5.71 1116 leq(A,star(A)) = true. [para(1102(a,1),21(a,1,1)),rewrite([6(6)])].
% 5.44/5.71 1229 leq(multiplication(star(sK1_goals_X0),c_0),c_0) = true. [para(666(a,1),83(a,1,1,1)),rewrite([49(3),4(7),8(10)])].
% 5.44/5.71 1235 multiplication(star(sK1_goals_X0),c_0) = c_0. [para(1229(a,1),20(a,1,1)),rewrite([9(8),139(8),7(8)])].
% 5.44/5.71 1236 multiplication(star(sK1_goals_X0),multiplication(c_0,A)) = multiplication(c_0,A). [para(1235(a,1),19(a,1,1)),flip(a)].
% 5.44/5.71 2461 leq(A,multiplication(addition(A,B),star(C))) = true. [para(25(a,1),521(a,1,2)),rewrite([9(1)])].
% 5.44/5.71 2581 multiplication(addition(one,multiplication(A,B)),star(multiplication(A,B))) = star(multiplication(A,B)). [para(617(a,1),144(a,2)),rewrite([9(3),9(6),57(12,R),9(9),40(9)])].
% 5.44/5.71 3284 leq(one,multiplication(star(A),star(B))) = true. [para(10(a,1),2461(a,1,2,1))].
% 5.44/5.71 3318 multiplication(star(A),star(star(A))) = star(star(A)). [para(3284(a,1),44(a,1,1)),rewrite([7(9)]),flip(a)].
% 5.44/5.71 4473 multiplication(star(sK1_goals_X0),star(multiplication(c_0,zero))) = addition(star(sK1_goals_X0),multiplication(c_0,zero)). [para(1236(a,1),208(a,1,2)),flip(a)].
% 5.44/5.71 5252 leq(addition(A,B),addition(A,star(B))) = true. [para(1102(a,1),396(a,1,2,2))].
% 5.44/5.71 5384 leq(strong_iteration(A),star(multiplication(A,strong_iteration(A)))) = true. [para(13(a,1),5252(a,1,1)),rewrite([126(6)])].
% 5.44/5.71 5476 addition(strong_iteration(A),star(multiplication(A,strong_iteration(A)))) = star(multiplication(A,strong_iteration(A))). [para(5384(a,1),20(a,1,1)),rewrite([7(11)])].
% 5.44/5.71 8090 leq(multiplication(star(A),star(A)),star(A)) = true. [para(619(a,1),295(a,1,1,1)),rewrite([49(3),8(9)])].
% 5.44/5.71 8092 leq(star(star(A)),star(A)) = true. [para(3318(a,1),295(a,1,3,1)),rewrite([9(4),126(4),8090(5),8(8)])].
% 5.44/5.71 8096 star(star(A)) = star(A). [para(8092(a,1),20(a,1,1)),rewrite([9(6),1102(6),7(6)])].
% 5.44/5.71 11122 multiplication(addition(A,star(multiplication(B,zero))),zero) = multiplication(addition(A,B),zero). [para(209(a,1),342(a,1,1,2)),rewrite([17(5,R),9(4),140(4),209(12),25(11)])].
% 5.44/5.71 16992 multiplication(strong_iteration(sK1_goals_X0),multiplication(sK1_goals_X0,c_0)) = multiplication(sK1_goals_X0,c_0). [para(429(a,1),657(a,1,2)),rewrite([9(8),64(8,R),9(6),666(8),427(5)]),flip(a)].
% 5.44/5.71 17030 leq(multiplication(c_0,multiplication(sK1_goals_X0,c_0)),multiplication(sK1_goals_X0,c_0)) = true. [para(16992(a,1),638(a,1,1,1)),rewrite([49(7),33(7),428(10),8(13)])].
% 5.44/5.71 17072 leq(star(multiplication(strong_iteration(A),A)),strong_iteration(A)) = true. [para(662(a,1),148(a,1,1,1,2,1)),rewrite([2581(8),662(8),49(7),662(11),2581(10),8(9)])].
% 5.44/5.71 17098 multiplication(c_0,multiplication(sK1_goals_X0,c_0)) = multiplication(sK1_goals_X0,c_0). [para(17030(a,1),20(a,1,1)),rewrite([9(11),135(11),7(11)])].
% 5.44/5.71 17099 multiplication(c_0,multiplication(sK1_goals_X0,multiplication(c_0,A))) = multiplication(sK1_goals_X0,multiplication(c_0,A)). [para(17098(a,1),19(a,1,1)),rewrite([19(4),19(9)]),flip(a)].
% 5.44/5.71 17103 multiplication(c_0,addition(one,multiplication(sK1_goals_X0,c_0))) = c_0. [para(17098(a,1),57(a,2,2)),rewrite([9(6),64(12,R),9(10),666(12)])].
% 5.44/5.71 17148 multiplication(sK1_goals_X0,multiplication(c_0,zero)) = multiplication(c_0,zero). [para(17103(a,1),342(a,1,1,2)),rewrite([130(3),342(11),17099(10)]),flip(a)].
% 5.44/5.71 17169 multiplication(sK1_goals_X0,star(multiplication(c_0,zero))) = addition(sK1_goals_X0,multiplication(c_0,zero)). [para(17148(a,1),57(a,2,2)),rewrite([9(6),140(6)])].
% 5.44/5.71 17172 leq(multiplication(c_0,zero),strong_iteration(sK1_goals_X0)) = true. [para(17148(a,1),97(a,1,1,2,2)),rewrite([140(8),1116(8),8(10)])].
% 5.44/5.71 17209 addition(strong_iteration(sK1_goals_X0),multiplication(c_0,zero)) = strong_iteration(sK1_goals_X0). [para(17172(a,1),20(a,1,1)),rewrite([9(8),7(11)])].
% 5.44/5.71 17217 multiplication(strong_iteration(sK1_goals_X0),zero) = multiplication(c_0,zero). [para(17209(a,1),344(a,2,1)),rewrite([9(7),140(7),11122(9),9(4),437(4)]),flip(a)].
% 5.44/5.71 17259 addition(star(sK1_goals_X0),multiplication(c_0,zero)) = strong_iteration(sK1_goals_X0). [para(17217(a,1),15(a,1,2))].
% 5.44/5.71 17290 multiplication(star(sK1_goals_X0),star(multiplication(c_0,zero))) = strong_iteration(sK1_goals_X0). [back_rewrite(4473),rewrite([17259(13)])].
% 5.44/5.71 17418 multiplication(star(sK1_goals_X0),addition(A,multiplication(c_0,zero))) = multiplication(strong_iteration(sK1_goals_X0),A). [para(17290(a,1),19(a,1,1)),rewrite([209(10)]),flip(a)].
% 5.44/5.71 17425 multiplication(strong_iteration(sK1_goals_X0),sK1_goals_X0) = multiplication(sK1_goals_X0,strong_iteration(sK1_goals_X0)). [para(17290(a,1),623(a,2,2)),rewrite([17169(8),17418(8)])].
% 5.44/5.71 17473 leq(star(multiplication(sK1_goals_X0,strong_iteration(sK1_goals_X0))),strong_iteration(sK1_goals_X0)) = true. [para(17425(a,1),17072(a,1,1,1))].
% 5.44/5.71 17581 star(multiplication(sK1_goals_X0,strong_iteration(sK1_goals_X0))) = strong_iteration(sK1_goals_X0). [para(17473(a,1),20(a,1,1)),rewrite([9(10),5476(10),7(10)])].
% 5.44/5.71 17601 strong_iteration(sK1_goals_X0) = c_0. [para(17581(a,1),8096(a,1,1)),rewrite([33(3),17581(6)]),flip(a)].
% 5.44/5.71 17602 $F # answer(goals). [resolve(17601,a,34,a)].
% 5.44/5.71
% 5.44/5.71 % SZS output end Refutation
% 5.44/5.71 ============================== end of proof ==========================
% 5.44/5.71
% 5.44/5.71 ============================== STATISTICS ============================
% 5.44/5.71
% 5.44/5.71 Given=1804. Generated=197679. Kept=17592. proofs=1.
% 5.44/5.71 Usable=1503. Sos=9950. Demods=11125. Limbo=18, Disabled=6143. Hints=0.
% 5.44/5.71 Megabytes=17.46.
% 5.44/5.71 User_CPU=4.60, System_CPU=0.10, Wall_clock=4.
% 5.44/5.71
% 5.44/5.71 ============================== end of statistics =====================
% 5.44/5.71
% 5.44/5.71 ============================== end of search =========================
% 5.44/5.71
% 5.44/5.71 THEOREM PROVED
% 5.44/5.71 % SZS status Unsatisfiable
% 5.44/5.71
% 5.44/5.71 Exiting with 1 proof.
% 5.44/5.71
% 5.44/5.71 Process 24872 exit (max_proofs) Thu Jun 16 10:55:01 2022
% 5.44/5.71 Prover9 interrupted
%------------------------------------------------------------------------------