TSTP Solution File: KLE145+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE145+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 : Theorem 13.94s 14.21s
% Output : Refutation 13.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE145+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.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 : Thu Jun 16 08:28:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/0.98 ============================== Prover9 ===============================
% 0.42/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.98 Process 11607 was started by sandbox on n017.cluster.edu,
% 0.42/0.98 Thu Jun 16 08:28:26 2022
% 0.42/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11438_n017.cluster.edu".
% 0.42/0.98 ============================== end of head ===========================
% 0.42/0.98
% 0.42/0.98 ============================== INPUT =================================
% 0.42/0.98
% 0.42/0.98 % Reading from file /tmp/Prover9_11438_n017.cluster.edu
% 0.42/0.98
% 0.42/0.98 set(prolog_style_variables).
% 0.42/0.98 set(auto2).
% 0.42/0.98 % set(auto2) -> set(auto).
% 0.42/0.98 % set(auto) -> set(auto_inference).
% 0.42/0.98 % set(auto) -> set(auto_setup).
% 0.42/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.98 % set(auto) -> set(auto_limits).
% 0.42/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.98 % set(auto) -> set(auto_denials).
% 0.42/0.98 % set(auto) -> set(auto_process).
% 0.42/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.98 % set(auto2) -> assign(stats, some).
% 0.42/0.98 % set(auto2) -> clear(echo_input).
% 0.42/0.98 % set(auto2) -> set(quiet).
% 0.42/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.98 % set(auto2) -> clear(print_given).
% 0.42/0.98 assign(lrs_ticks,-1).
% 0.42/0.98 assign(sos_limit,10000).
% 0.42/0.98 assign(order,kbo).
% 0.42/0.98 set(lex_order_vars).
% 0.42/0.98 clear(print_given).
% 0.42/0.98
% 0.42/0.98 % formulas(sos). % not echoed (19 formulas)
% 0.42/0.98
% 0.42/0.98 ============================== end of input ==========================
% 0.42/0.98
% 0.42/0.98 % From the command line: assign(max_seconds, 300).
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.98
% 0.42/0.98 % Formulas that are not ordinary clauses:
% 0.42/0.98 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(distributivity1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(distributivity2) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 13 (all A all B all C (leq(addition(multiplication(A,C),B),C) -> leq(multiplication(star(A),B),C))) # label(star_induction1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 14 (all A all B all C (leq(addition(multiplication(C,A),B),C) -> leq(multiplication(B,star(A)),C))) # label(star_induction2) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 16 (all A all B all C (leq(C,addition(multiplication(A,C),B)) -> leq(C,multiplication(strong_iteration(A),B)))) # label(infty_coinduction) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 19 -(all X0 star(strong_iteration(X0)) = strong_iteration(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 13.94/14.21
% 13.94/14.21 ============================== end of process non-clausal formulas ===
% 13.94/14.21
% 13.94/14.21 ============================== PROCESS INITIAL CLAUSES ===============
% 13.94/14.21
% 13.94/14.21 ============================== PREDICATE ELIMINATION =================
% 13.94/14.21
% 13.94/14.21 ============================== end predicate elimination =============
% 13.94/14.21
% 13.94/14.21 Auto_denials:
% 13.94/14.21 % copying label goals to answer in negative clause
% 13.94/14.21
% 13.94/14.21 Term ordering decisions:
% 13.94/14.21 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 13.94/14.21
% 13.94/14.21 ============================== end of process initial clauses ========
% 13.94/14.21
% 13.94/14.21 ============================== CLAUSES FOR SEARCH ====================
% 13.94/14.21
% 13.94/14.21 ============================== end of clauses for search =============
% 13.94/14.21
% 13.94/14.21 ============================== SEARCH ================================
% 13.94/14.21
% 13.94/14.21 % Starting search at 0.01 seconds.
% 13.94/14.21
% 13.94/14.21 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 0.43 sec).
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=38.000, iters=3360
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=33.000, iters=3478
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=32.000, iters=3406
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=31.000, iters=3425
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=29.000, iters=3334
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=28.000, iters=3339
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=27.000, iters=3336
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=25.000, iters=3346
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=24.000, iters=3338
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=23.000, iters=3342
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=22.000, iters=3474
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=21.000, iters=3356
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=20.000, iters=3350
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=19.000, iters=3338
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=18.000, iters=3355
% 13.94/14.21
% 13.94/14.21 Low Water (displace): id=5137, wt=43.000
% 13.94/14.21
% 13.94/14.21 Low Water (displace): id=12631, wt=17.000
% 13.94/14.21
% 13.94/14.21 Low Water (displace): id=12834, wt=13.000
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=17.000, iters=3333
% 13.94/14.21
% 13.94/14.21 Low Water (displace): id=14100, wt=12.000
% 13.94/14.21
% 13.94/14.21 Low Water (displace): id=14413, wt=11.000
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=16.000, iters=3337
% 13.94/14.21
% 13.94/14.21 Low Water (displace): id=16460, wt=10.000
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=15.000, iters=3335
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=14.000, iters=3333
% 13.94/14.21
% 13.94/14.21 Low Water (keep): wt=13.000, iters=3347
% 13.94/14.21
% 13.94/14.21 ============================== PROOF =================================
% 13.94/14.21 % SZS status Theorem
% 13.94/14.21 % SZS output start Refutation
% 13.94/14.21
% 13.94/14.21 % Proof 1 at 12.78 (+ 0.46) seconds: goals.
% 13.94/14.21 % Length of proof is 130.
% 13.94/14.21 % Level of proof is 25.
% 13.94/14.21 % Maximum clause weight is 20.000.
% 13.94/14.21 % Given clauses 6081.
% 13.94/14.21
% 13.94/14.21 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(distributivity1) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(distributivity2) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 13 (all A all B all C (leq(addition(multiplication(A,C),B),C) -> leq(multiplication(star(A),B),C))) # label(star_induction1) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 14 (all A all B all C (leq(addition(multiplication(C,A),B),C) -> leq(multiplication(B,star(A)),C))) # label(star_induction2) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 16 (all A all B all C (leq(C,addition(multiplication(A,C),B)) -> leq(C,multiplication(strong_iteration(A),B)))) # label(infty_coinduction) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 13.94/14.21 19 -(all X0 star(strong_iteration(X0)) = strong_iteration(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 13.94/14.21 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 13.94/14.21 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 13.94/14.21 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 13.94/14.21 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 13.94/14.21 26 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 13.94/14.21 27 addition(one,multiplication(A,star(A))) = star(A). [copy(26),flip(a)].
% 13.94/14.21 28 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom). [clausify(12)].
% 13.94/14.21 29 addition(one,multiplication(star(A),A)) = star(A). [copy(28),flip(a)].
% 13.94/14.21 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 13.94/14.21 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 13.94/14.21 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 13.94/14.21 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([25(2)]),flip(a)].
% 13.94/14.21 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 13.94/14.21 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 13.94/14.21 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 13.94/14.21 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 13.94/14.21 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 13.94/14.21 41 strong_iteration(c1) != star(strong_iteration(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 13.94/14.21 42 star(strong_iteration(c1)) != strong_iteration(c1) # answer(goals). [copy(41),flip(a)].
% 13.94/14.21 43 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 13.94/14.21 44 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 13.94/14.21 45 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom). [clausify(13)].
% 13.94/14.21 46 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(45),rewrite([25(2)])].
% 13.94/14.21 47 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction2) # label(axiom). [clausify(14)].
% 13.94/14.21 48 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(47),rewrite([25(2)])].
% 13.94/14.21 49 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom). [clausify(16)].
% 13.94/14.21 50 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)). [copy(49),rewrite([25(2)])].
% 13.94/14.21 51 star(strong_iteration(c1)) = c_0. [new_symbol(42)].
% 13.94/14.21 52 strong_iteration(c1) != c_0 # answer(goals). [back_rewrite(42),rewrite([51(3)]),flip(a)].
% 13.94/14.21 57 addition(A,addition(A,B)) = addition(A,B). [para(35(a,1),21(a,1)),rewrite([25(1),25(2),35(2,R),21(1),25(3)])].
% 13.94/14.21 58 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(36(a,1),27(a,1,2))].
% 13.94/14.21 60 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 13.94/14.21 61 addition(A,multiplication(A,multiplication(B,star(B)))) = multiplication(A,star(B)). [para(27(a,1),38(a,2,2)),rewrite([22(2)])].
% 13.94/14.21 63 addition(A,multiplication(A,multiplication(B,strong_iteration(B)))) = multiplication(A,strong_iteration(B)). [para(31(a,1),38(a,2,2)),rewrite([22(2)])].
% 13.94/14.21 65 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(23(a,1),40(a,1,1)),rewrite([25(4)]),flip(a)].
% 13.94/14.21 66 addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A). [para(27(a,1),40(a,2,1)),rewrite([23(2),36(3)])].
% 13.94/14.21 68 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A). [para(31(a,1),40(a,2,1)),rewrite([23(2),36(3)])].
% 13.94/14.21 70 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(36(a,1),40(a,1,1)),rewrite([25(6)])].
% 13.94/14.21 72 leq(A,A). [hyper(44,b,21,a)].
% 13.94/14.21 86 -leq(addition(A,multiplication(B,multiplication(C,D))),D) | leq(multiplication(star(multiplication(B,C)),A),D). [para(36(a,1),46(a,1,2))].
% 13.94/14.21 89 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A). [para(21(a,1),48(a,1)),rewrite([36(5)])].
% 13.94/14.21 96 -leq(multiplication(addition(A,B),C),B) | leq(multiplication(A,multiplication(C,star(C))),B). [para(40(a,1),48(a,1)),rewrite([36(6)])].
% 13.94/14.21 106 addition(one,multiplication(strong_iteration(c1),c_0)) = c_0. [para(51(a,1),27(a,1,2,2)),rewrite([51(9)])].
% 13.94/14.21 124 leq(A,addition(A,B)). [hyper(44,b,57,a)].
% 13.94/14.21 125 addition(one,star(A)) = star(A). [para(27(a,1),57(a,1,2)),rewrite([27(7)])].
% 13.94/14.21 128 addition(one,c_0) = c_0. [para(106(a,1),57(a,1,2)),rewrite([106(9)])].
% 13.94/14.21 129 leq(A,multiplication(strong_iteration(B),A)). [hyper(50,a,124,a)].
% 13.94/14.21 133 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(38(a,1),124(a,2))].
% 13.94/14.21 134 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(40(a,1),124(a,2))].
% 13.94/14.21 138 addition(A,multiplication(A,multiplication(B,multiplication(C,star(multiplication(B,C)))))) = multiplication(A,star(multiplication(B,C))). [para(58(a,1),38(a,2,2)),rewrite([22(2)])].
% 13.94/14.21 141 -leq(star(multiplication(A,B)),multiplication(B,star(multiplication(A,B)))) | leq(star(A),multiplication(B,star(multiplication(A,B)))). [para(58(a,1),46(a,1)),rewrite([22(9)])].
% 13.94/14.21 143 -leq(multiplication(A,star(multiplication(B,A))),star(multiplication(B,A))) | leq(multiplication(A,star(multiplication(B,A))),strong_iteration(B)). [para(58(a,1),50(a,2)),rewrite([22(12)])].
% 13.94/14.21 148 addition(A,multiplication(strong_iteration(B),A)) = multiplication(strong_iteration(B),A). [hyper(43,a,129,a)].
% 13.94/14.21 191 addition(A,addition(B,multiplication(A,multiplication(C,star(C))))) = addition(B,multiplication(A,star(C))). [para(61(a,1),35(a,2,2)),rewrite([25(4)])].
% 13.94/14.21 197 leq(A,multiplication(A,star(B))). [para(61(a,1),124(a,2))].
% 13.94/14.21 199 leq(A,multiplication(A,c_0)). [para(51(a,1),197(a,2,2))].
% 13.94/14.21 200 leq(multiplication(A,B),multiplication(A,multiplication(B,c_0))). [para(36(a,1),199(a,2))].
% 13.94/14.21 224 leq(multiplication(A,B),addition(A,multiplication(A,B))). [para(60(a,1),133(a,2))].
% 13.94/14.21 236 -leq(multiplication(addition(A,one),B),B) | leq(multiplication(star(A),B),B). [para(65(a,2),46(a,1))].
% 13.94/14.21 254 leq(A,multiplication(star(B),A)). [para(27(a,1),134(a,2,1)),rewrite([23(2)])].
% 13.94/14.21 268 multiplication(star(A),A) = multiplication(A,star(A)). [para(66(a,1),60(a,2)),rewrite([25(4),29(4)]),flip(a)].
% 13.94/14.21 286 addition(A,addition(B,multiplication(C,multiplication(strong_iteration(C),A)))) = addition(B,multiplication(strong_iteration(C),A)). [para(68(a,1),35(a,2,2)),rewrite([25(4)])].
% 13.94/14.21 287 multiplication(A,addition(B,multiplication(strong_iteration(A),multiplication(A,B)))) = multiplication(strong_iteration(A),multiplication(A,B)). [para(68(a,1),38(a,1)),flip(a)].
% 13.94/14.21 294 leq(addition(A,multiplication(A,B)),multiplication(A,multiplication(addition(B,one),c_0))). [para(60(a,1),200(a,1))].
% 13.94/14.21 315 leq(multiplication(A,star(A)),star(A)). [para(58(a,1),224(a,2)),rewrite([23(3),23(4),23(4)])].
% 13.94/14.21 321 multiplication(addition(A,one),star(A)) = star(A). [hyper(43,a,315,a),rewrite([25(4),65(4,R)])].
% 13.94/14.21 323 leq(multiplication(strong_iteration(c1),c_0),c_0). [para(51(a,1),315(a,1,2)),rewrite([51(7)])].
% 13.94/14.21 341 multiplication(strong_iteration(c1),c_0) = c_0. [hyper(43,a,323,a),rewrite([25(6),148(6)])].
% 13.94/14.21 343 addition(c_0,multiplication(strong_iteration(c1),A)) = multiplication(strong_iteration(c1),addition(A,c_0)). [para(341(a,1),38(a,1,1)),rewrite([25(9)])].
% 13.94/14.21 349 addition(c_0,strong_iteration(c1)) = c_0. [para(341(a,1),60(a,2,2)),rewrite([25(5),128(5),341(4),25(5)]),flip(a)].
% 13.94/14.21 352 multiplication(addition(one,c1),c_0) = c_0. [para(341(a,1),68(a,1,2,2)),rewrite([65(5,R),25(3),341(9)])].
% 13.94/14.21 567 -leq(addition(A,multiplication(B,c_0)),c_0) | leq(multiplication(star(multiplication(B,strong_iteration(c1))),A),c_0). [para(341(a,1),86(a,1,2,2))].
% 13.94/14.21 616 multiplication(c_0,strong_iteration(c1)) = c_0. [para(51(a,1),268(a,1,1)),rewrite([51(9),341(8)])].
% 13.94/14.21 617 multiplication(star(A),addition(A,one)) = star(A). [para(268(a,1),60(a,2,2)),rewrite([65(8,R),321(8)])].
% 13.94/14.21 619 multiplication(star(multiplication(A,strong_iteration(A))),strong_iteration(A)) = multiplication(strong_iteration(A),star(multiplication(A,strong_iteration(A)))). [para(268(a,1),63(a,1,2)),rewrite([36(9),68(10)]),flip(a)].
% 13.94/14.21 664 -leq(c_0,c_0) | leq(multiplication(c_0,c_0),c_0). [para(616(a,1),89(a,1)),rewrite([51(9),341(8)])].
% 13.94/14.21 756 leq(multiplication(c_0,c_0),c_0). [hyper(664,a,72,a)].
% 13.94/14.21 758 multiplication(c_0,c_0) = c_0. [hyper(43,a,756,a),rewrite([25(5),60(5,R),25(4),128(4)])].
% 13.94/14.21 765 multiplication(addition(A,multiplication(B,c_0)),c_0) = multiplication(addition(B,A),c_0). [para(758(a,1),70(a,1,1,2)),rewrite([40(5)]),flip(a)].
% 13.94/14.21 889 -leq(multiplication(star(A),B),star(A)) | leq(multiplication(B,star(B)),star(A)). [para(125(a,1),96(a,1,1)),rewrite([23(8)])].
% 13.94/14.21 1249 addition(A,star(A)) = star(A). [para(321(a,1),60(a,2,2)),rewrite([25(5),125(5),321(4),25(5),35(5),25(4),35(5,R),25(4),125(4)]),flip(a)].
% 13.94/14.21 1264 multiplication(addition(one,multiplication(A,B)),star(multiplication(A,B))) = star(multiplication(A,B)). [para(321(a,1),138(a,2)),rewrite([25(3),25(6),60(12,R),25(9),58(9)])].
% 13.94/14.21 1290 leq(star(A),multiplication(star(B),star(multiplication(A,star(B))))). [hyper(141,a,254,a)].
% 13.94/14.21 1643 multiplication(star(A),multiplication(addition(A,one),B)) = multiplication(star(A),B). [para(617(a,1),36(a,1,1)),flip(a)].
% 13.94/14.21 1657 -leq(star(A),star(A)) | leq(multiplication(star(A),star(addition(A,one))),star(A)). [para(617(a,1),89(a,1)),rewrite([1643(11)])].
% 13.94/14.21 3581 leq(A,addition(B,multiplication(A,star(C)))). [para(191(a,1),124(a,2))].
% 13.94/14.21 3618 leq(A,multiplication(addition(A,B),star(C))). [para(40(a,1),3581(a,2)),rewrite([25(1)])].
% 13.94/14.21 3801 leq(one,multiplication(strong_iteration(A),star(B))). [para(31(a,1),3618(a,2,1))].
% 13.94/14.21 3840 addition(one,multiplication(strong_iteration(A),star(B))) = multiplication(strong_iteration(A),star(B)). [hyper(43,a,3801,a)].
% 13.94/14.21 5284 leq(multiplication(star(A),star(addition(A,one))),star(addition(A,one))). [hyper(236,a,315,a)].
% 13.94/14.21 7371 multiplication(strong_iteration(A),star(multiplication(A,strong_iteration(A)))) = star(multiplication(A,strong_iteration(A))). [para(58(a,1),286(a,1,2)),rewrite([21(7),3840(10)]),flip(a)].
% 13.94/14.21 7426 multiplication(star(multiplication(A,strong_iteration(A))),strong_iteration(A)) = star(multiplication(A,strong_iteration(A))). [back_rewrite(619),rewrite([7371(10)])].
% 13.94/14.21 9855 multiplication(strong_iteration(c1),multiplication(c1,c_0)) = multiplication(c1,c_0). [para(343(a,1),287(a,1,2)),rewrite([25(8),65(8,R),25(6),352(8),341(5)]),flip(a)].
% 13.94/14.21 12520 leq(addition(strong_iteration(c1),multiplication(c1,c_0)),c_0). [para(9855(a,1),294(a,1,2)),rewrite([25(13),765(15),25(11),352(13),341(10)])].
% 13.94/14.21 13502 leq(star(multiplication(c1,strong_iteration(c1))),c_0). [hyper(567,a,12520,a),rewrite([7426(8)])].
% 13.94/14.21 13511 addition(c_0,star(multiplication(c1,strong_iteration(c1)))) = c_0. [hyper(43,a,13502,a),rewrite([25(7)])].
% 13.94/14.21 20262 multiplication(star(A),star(star(A))) = star(star(A)). [para(321(a,1),1264(a,1,1,2)),rewrite([125(3),321(5),321(8)])].
% 13.94/14.21 20269 leq(star(addition(one,multiplication(A,B))),star(star(multiplication(A,B)))). [para(1264(a,1),1290(a,2,2,1)),rewrite([20262(10)])].
% 13.94/14.21 22342 leq(multiplication(star(A),star(addition(A,one))),star(A)). [hyper(1657,a,72,a)].
% 13.94/14.21 22345 leq(star(star(addition(A,one))),star(A)). [hyper(889,a,22342,a),rewrite([20262(8)])].
% 13.94/14.21 22346 multiplication(star(A),star(addition(A,one))) = star(A). [hyper(43,a,22342,a),rewrite([25(7),60(7,R),25(6),125(6)])].
% 13.94/14.21 22349 leq(star(A),star(addition(A,one))). [back_rewrite(5284),rewrite([22346(5)])].
% 13.94/14.21 22350 addition(star(A),star(addition(A,one))) = star(addition(A,one)). [hyper(43,a,22349,a)].
% 13.94/14.21 22351 addition(star(A),star(star(addition(A,one)))) = star(A). [hyper(43,a,22345,a),rewrite([25(6)])].
% 13.94/14.21 22355 star(addition(A,one)) = star(A). [para(22346(a,1),65(a,2,2)),rewrite([25(3),125(3),22346(5),25(6),22350(6)]),flip(a)].
% 13.94/14.21 22359 star(star(A)) = star(A). [back_rewrite(22351),rewrite([22355(4),1249(4)])].
% 13.94/14.21 22412 leq(star(addition(one,multiplication(A,B))),star(multiplication(A,B))). [back_rewrite(20269),rewrite([22359(7)])].
% 13.94/14.21 27834 leq(star(strong_iteration(A)),star(multiplication(A,strong_iteration(A)))). [para(31(a,1),22412(a,1,1))].
% 13.94/14.21 27863 leq(c_0,star(multiplication(c1,strong_iteration(c1)))). [para(51(a,1),27834(a,1))].
% 13.94/14.21 27866 star(multiplication(c1,strong_iteration(c1))) = c_0. [hyper(43,a,27863,a),rewrite([13511(7)]),flip(a)].
% 13.94/14.21 27876 -leq(c_0,c_0) | leq(c_0,strong_iteration(c1)). [para(27866(a,1),143(a,1,2)),rewrite([341(4),27866(6),27866(10),341(7)])].
% 13.94/14.21 28085 leq(c_0,strong_iteration(c1)). [hyper(27876,a,72,a)].
% 13.94/14.21 28089 strong_iteration(c1) = c_0. [hyper(43,a,28085,a),rewrite([349(4)]),flip(a)].
% 13.94/14.21 28090 $F # answer(goals). [resolve(28089,a,52,a)].
% 13.94/14.21
% 13.94/14.21 % SZS output end Refutation
% 13.94/14.21 ============================== end of proof ==========================
% 13.94/14.21
% 13.94/14.21 ============================== STATISTICS ============================
% 13.94/14.21
% 13.94/14.21 Given=6081. Generated=826209. Kept=28059. proofs=1.
% 13.94/14.21 Usable=5164. Sos=9868. Demods=1033. Limbo=3, Disabled=13043. Hints=0.
% 13.94/14.21 Megabytes=17.33.
% 13.94/14.21 User_CPU=12.78, System_CPU=0.46, Wall_clock=13.
% 13.94/14.21
% 13.94/14.21 ============================== end of statistics =====================
% 13.94/14.21
% 13.94/14.21 ============================== end of search =========================
% 13.94/14.21
% 13.94/14.21 THEOREM PROVED
% 13.94/14.21 % SZS status Theorem
% 13.94/14.21
% 13.94/14.21 Exiting with 1 proof.
% 13.94/14.21
% 13.94/14.21 Process 11607 exit (max_proofs) Thu Jun 16 08:28:39 2022
% 13.94/14.21 Prover9 interrupted
%------------------------------------------------------------------------------