TSTP Solution File: KLE143+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE143+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 02:22:26 EDT 2022
% Result : Theorem 8.04s 8.29s
% Output : Refutation 8.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE143+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 12:37:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.01 ============================== Prover9 ===============================
% 0.43/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01 Process 913 was started by sandbox2 on n026.cluster.edu,
% 0.43/1.01 Thu Jun 16 12:37:24 2022
% 0.43/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_749_n026.cluster.edu".
% 0.43/1.01 ============================== end of head ===========================
% 0.43/1.01
% 0.43/1.01 ============================== INPUT =================================
% 0.43/1.01
% 0.43/1.01 % Reading from file /tmp/Prover9_749_n026.cluster.edu
% 0.43/1.01
% 0.43/1.01 set(prolog_style_variables).
% 0.43/1.01 set(auto2).
% 0.43/1.01 % set(auto2) -> set(auto).
% 0.43/1.01 % set(auto) -> set(auto_inference).
% 0.43/1.01 % set(auto) -> set(auto_setup).
% 0.43/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01 % set(auto) -> set(auto_limits).
% 0.43/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01 % set(auto) -> set(auto_denials).
% 0.43/1.01 % set(auto) -> set(auto_process).
% 0.43/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01 % set(auto2) -> assign(stats, some).
% 0.43/1.01 % set(auto2) -> clear(echo_input).
% 0.43/1.01 % set(auto2) -> set(quiet).
% 0.43/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01 % set(auto2) -> clear(print_given).
% 0.43/1.01 assign(lrs_ticks,-1).
% 0.43/1.01 assign(sos_limit,10000).
% 0.43/1.01 assign(order,kbo).
% 0.43/1.01 set(lex_order_vars).
% 0.43/1.01 clear(print_given).
% 0.43/1.01
% 0.43/1.01 % formulas(sos). % not echoed (19 formulas)
% 0.43/1.01
% 0.43/1.01 ============================== end of input ==========================
% 0.43/1.01
% 0.43/1.01 % From the command line: assign(max_seconds, 300).
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.01
% 0.43/1.01 % Formulas that are not ordinary clauses:
% 0.43/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 8.04/8.29 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 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].
% 8.04/8.29 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 19 -(all X0 multiplication(strong_iteration(X0),strong_iteration(X0)) = strong_iteration(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.04/8.29
% 8.04/8.29 ============================== end of process non-clausal formulas ===
% 8.04/8.29
% 8.04/8.29 ============================== PROCESS INITIAL CLAUSES ===============
% 8.04/8.29
% 8.04/8.29 ============================== PREDICATE ELIMINATION =================
% 8.04/8.29
% 8.04/8.29 ============================== end predicate elimination =============
% 8.04/8.29
% 8.04/8.29 Auto_denials:
% 8.04/8.29 % copying label goals to answer in negative clause
% 8.04/8.29
% 8.04/8.29 Term ordering decisions:
% 8.04/8.29 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 8.04/8.29
% 8.04/8.29 ============================== end of process initial clauses ========
% 8.04/8.29
% 8.04/8.29 ============================== CLAUSES FOR SEARCH ====================
% 8.04/8.29
% 8.04/8.29 ============================== end of clauses for search =============
% 8.04/8.29
% 8.04/8.29 ============================== SEARCH ================================
% 8.04/8.29
% 8.04/8.29 % Starting search at 0.01 seconds.
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=43.000, iters=3387
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=33.000, iters=3440
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=32.000, iters=3369
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=31.000, iters=3337
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=30.000, iters=3456
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=27.000, iters=3431
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=26.000, iters=3333
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=25.000, iters=3353
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=24.000, iters=3355
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=23.000, iters=3360
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=22.000, iters=3351
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=21.000, iters=3343
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=20.000, iters=3343
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=19.000, iters=3335
% 8.04/8.29
% 8.04/8.29 Low Water (displace): id=5533, wt=43.000
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=18.000, iters=3384
% 8.04/8.29
% 8.04/8.29 Low Water (displace): id=13734, wt=17.000
% 8.04/8.29
% 8.04/8.29 Low Water (displace): id=13950, wt=15.000
% 8.04/8.29
% 8.04/8.29 Low Water (displace): id=13974, wt=14.000
% 8.04/8.29
% 8.04/8.29 Low Water (displace): id=14680, wt=13.000
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=17.000, iters=3333
% 8.04/8.29
% 8.04/8.29 Low Water (displace): id=15317, wt=12.000
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=16.000, iters=3334
% 8.04/8.29
% 8.04/8.29 Low Water (keep): wt=15.000, iters=3340
% 8.04/8.29
% 8.04/8.29 ============================== PROOF =================================
% 8.04/8.29 % SZS status Theorem
% 8.04/8.29 % SZS output start Refutation
% 8.04/8.29
% 8.04/8.29 % Proof 1 at 7.04 (+ 0.25) seconds: goals.
% 8.04/8.29 % Length of proof is 78.
% 8.04/8.29 % Level of proof is 13.
% 8.04/8.29 % Maximum clause weight is 23.000.
% 8.04/8.29 % Given clauses 3231.
% 8.04/8.29
% 8.04/8.29 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 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].
% 8.04/8.29 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 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].
% 8.04/8.29 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 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].
% 8.04/8.29 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].
% 8.04/8.29 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 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].
% 8.04/8.29 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 8.04/8.29 19 -(all X0 multiplication(strong_iteration(X0),strong_iteration(X0)) = strong_iteration(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.04/8.29 20 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 8.04/8.29 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 8.04/8.29 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 8.04/8.29 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 8.04/8.29 24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 8.04/8.29 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 8.04/8.29 26 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 8.04/8.29 27 addition(one,multiplication(A,star(A))) = star(A). [copy(26),flip(a)].
% 8.04/8.29 28 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom). [clausify(12)].
% 8.04/8.29 29 addition(one,multiplication(star(A),A)) = star(A). [copy(28),flip(a)].
% 8.04/8.29 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 8.04/8.29 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 8.04/8.29 32 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom). [clausify(17)].
% 8.04/8.29 33 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A). [copy(32),flip(a)].
% 8.04/8.29 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 8.04/8.29 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([25(2)]),flip(a)].
% 8.04/8.29 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 8.04/8.29 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 8.04/8.29 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 8.04/8.29 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 8.04/8.29 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 8.04/8.29 41 strong_iteration(c1) != multiplication(strong_iteration(c1),strong_iteration(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 8.04/8.29 42 multiplication(strong_iteration(c1),strong_iteration(c1)) != strong_iteration(c1) # answer(goals). [copy(41),flip(a)].
% 8.04/8.29 43 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 8.04/8.29 44 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 8.04/8.29 45 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom). [clausify(13)].
% 8.04/8.29 46 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(45),rewrite([25(2)])].
% 8.04/8.29 55 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)])].
% 8.04/8.29 56 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(36(a,1),27(a,1,2))].
% 8.04/8.29 57 addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)). [para(36(a,1),31(a,1,2))].
% 8.04/8.29 58 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 8.04/8.29 61 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)])].
% 8.04/8.29 63 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(23(a,1),40(a,1,1)),rewrite([25(4)]),flip(a)].
% 8.04/8.29 64 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)])].
% 8.04/8.29 65 addition(A,multiplication(star(B),multiplication(B,A))) = multiplication(star(B),A). [para(29(a,1),40(a,2,1)),rewrite([23(2),36(3)])].
% 8.04/8.29 66 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)])].
% 8.04/8.29 68 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)])].
% 8.04/8.29 69 addition(multiplication(A,B),multiplication(C,multiplication(D,B))) = multiplication(addition(A,multiplication(C,D)),B). [para(36(a,1),40(a,1,2))].
% 8.04/8.29 78 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B). [para(21(a,1),46(a,1))].
% 8.04/8.29 110 leq(A,addition(A,B)). [hyper(44,b,55,a)].
% 8.04/8.29 112 addition(one,strong_iteration(A)) = strong_iteration(A). [para(31(a,1),55(a,1,2)),rewrite([31(7)])].
% 8.04/8.29 118 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(38(a,1),110(a,2))].
% 8.04/8.29 120 addition(one,multiplication(A,zero)) = star(multiplication(A,zero)). [para(24(a,1),56(a,1,2,2))].
% 8.04/8.29 129 strong_iteration(multiplication(A,zero)) = star(multiplication(A,zero)). [para(24(a,1),57(a,1,2,2)),rewrite([120(4)]),flip(a)].
% 8.04/8.29 195 leq(multiplication(A,B),addition(A,multiplication(A,B))). [para(58(a,1),118(a,2))].
% 8.04/8.29 233 multiplication(addition(A,one),A) = multiplication(A,addition(A,one)). [para(63(a,2),58(a,2)),flip(a)].
% 8.04/8.29 241 addition(A,multiplication(A,multiplication(B,zero))) = multiplication(A,star(multiplication(B,zero))). [para(129(a,1),61(a,1,2,2,2)),rewrite([36(6),24(5),129(7)])].
% 8.04/8.29 247 multiplication(star(A),multiplication(A,B)) = multiplication(A,multiplication(star(A),B)). [para(64(a,1),38(a,1)),rewrite([65(7)])].
% 8.04/8.29 253 -leq(multiplication(A,B),B) | leq(multiplication(A,multiplication(star(A),B)),B). [back_rewrite(78),rewrite([247(5)])].
% 8.04/8.29 267 leq(multiplication(A,strong_iteration(A)),strong_iteration(A)). [para(57(a,1),195(a,2)),rewrite([23(3),23(4),23(4)])].
% 8.04/8.29 277 multiplication(star(multiplication(A,zero)),B) = addition(B,multiplication(A,zero)). [para(129(a,1),66(a,1,2,2,1)),rewrite([36(7),24(6),129(6)]),flip(a)].
% 8.04/8.29 334 addition(A,addition(multiplication(A,B),multiplication(C,multiplication(D,addition(B,one))))) = multiplication(addition(A,multiplication(C,D)),addition(B,one)). [para(58(a,1),68(a,1,2)),rewrite([35(7,R)])].
% 8.04/8.29 358 addition(multiplication(A,B),multiplication(C,zero)) = multiplication(addition(A,multiplication(C,zero)),B). [para(24(a,1),69(a,1,2,2))].
% 8.04/8.29 1505 multiplication(addition(one,multiplication(A,B)),multiplication(A,B)) = multiplication(A,multiplication(B,addition(one,multiplication(A,B)))). [para(233(a,1),36(a,2)),rewrite([25(3),36(5),25(9),36(10)])].
% 8.04/8.29 7352 leq(multiplication(A,multiplication(star(A),strong_iteration(A))),strong_iteration(A)). [hyper(253,a,267,a)].
% 8.04/8.29 8503 multiplication(star(A),strong_iteration(A)) = strong_iteration(A). [hyper(43,a,7352,a),rewrite([25(6),64(6)])].
% 8.04/8.29 8530 multiplication(star(A),multiplication(strong_iteration(A),B)) = multiplication(strong_iteration(A),B). [para(8503(a,1),36(a,1,1)),flip(a)].
% 8.04/8.29 10375 addition(star(A),multiplication(strong_iteration(A),B)) = multiplication(strong_iteration(A),addition(B,one)). [para(33(a,1),334(a,2,1)),rewrite([24(8),358(7),33(6)])].
% 8.04/8.29 21985 multiplication(star(A),star(multiplication(strong_iteration(A),zero))) = strong_iteration(A). [para(8530(a,1),241(a,1,2)),rewrite([10375(5),25(4),20(4),22(3)]),flip(a)].
% 8.04/8.29 23106 multiplication(strong_iteration(A),strong_iteration(A)) = strong_iteration(A). [para(21985(a,1),1505(a,1,1,2)),rewrite([112(3),21985(7),21985(15),112(11),277(10),58(9,R),25(8),20(8),22(7),8503(6)])].
% 8.04/8.29 23107 $F # answer(goals). [resolve(23106,a,42,a)].
% 8.04/8.29
% 8.04/8.29 % SZS output end Refutation
% 8.04/8.29 ============================== end of proof ==========================
% 8.04/8.29
% 8.04/8.29 ============================== STATISTICS ============================
% 8.04/8.29
% 8.04/8.29 Given=3231. Generated=462099. Kept=23076. proofs=1.
% 8.04/8.29 Usable=2554. Sos=9996. Demods=1006. Limbo=1, Disabled=10544. Hints=0.
% 8.04/8.29 Megabytes=15.24.
% 8.04/8.29 User_CPU=7.05, System_CPU=0.25, Wall_clock=7.
% 8.04/8.29
% 8.04/8.29 ============================== end of statistics =====================
% 8.04/8.29
% 8.04/8.29 ============================== end of search =========================
% 8.04/8.29
% 8.04/8.29 THEOREM PROVED
% 8.04/8.29 % SZS status Theorem
% 8.04/8.29
% 8.04/8.29 Exiting with 1 proof.
% 8.04/8.29
% 8.04/8.29 Process 913 exit (max_proofs) Thu Jun 16 12:37:31 2022
% 8.04/8.29 Prover9 interrupted
%------------------------------------------------------------------------------