TSTP Solution File: KLE144+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 1.40s 1.71s
% Output : Refutation 1.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.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 16:43:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.00 ============================== Prover9 ===============================
% 0.69/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.69/1.00 Process 6746 was started by sandbox on n025.cluster.edu,
% 0.69/1.00 Thu Jun 16 16:43:27 2022
% 0.69/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6593_n025.cluster.edu".
% 0.69/1.00 ============================== end of head ===========================
% 0.69/1.00
% 0.69/1.00 ============================== INPUT =================================
% 0.69/1.00
% 0.69/1.00 % Reading from file /tmp/Prover9_6593_n025.cluster.edu
% 0.69/1.00
% 0.69/1.00 set(prolog_style_variables).
% 0.69/1.00 set(auto2).
% 0.69/1.00 % set(auto2) -> set(auto).
% 0.69/1.00 % set(auto) -> set(auto_inference).
% 0.69/1.00 % set(auto) -> set(auto_setup).
% 0.69/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.69/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.69/1.00 % set(auto) -> set(auto_limits).
% 0.69/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.69/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.69/1.00 % set(auto) -> set(auto_denials).
% 0.69/1.00 % set(auto) -> set(auto_process).
% 0.69/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.69/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.69/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.69/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.69/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.69/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.69/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.69/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.69/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.69/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.69/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.69/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.69/1.00 % set(auto2) -> assign(stats, some).
% 0.69/1.00 % set(auto2) -> clear(echo_input).
% 0.69/1.00 % set(auto2) -> set(quiet).
% 0.69/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.69/1.00 % set(auto2) -> clear(print_given).
% 0.69/1.00 assign(lrs_ticks,-1).
% 0.69/1.00 assign(sos_limit,10000).
% 0.69/1.00 assign(order,kbo).
% 0.69/1.00 set(lex_order_vars).
% 0.69/1.00 clear(print_given).
% 0.69/1.00
% 0.69/1.00 % formulas(sos). % not echoed (19 formulas)
% 0.69/1.00
% 0.69/1.00 ============================== end of input ==========================
% 0.69/1.00
% 0.69/1.00 % From the command line: assign(max_seconds, 300).
% 0.69/1.00
% 0.69/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.69/1.00
% 0.69/1.00 % Formulas that are not ordinary clauses:
% 0.69/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 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].
% 0.69/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 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].
% 0.69/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 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].
% 0.69/1.00 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].
% 0.69/1.00 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 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].
% 0.69/1.00 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].
% 1.40/1.71 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 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].
% 1.40/1.71 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 19 -(all X0 strong_iteration(star(X0)) = strong_iteration(one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.40/1.71
% 1.40/1.71 ============================== end of process non-clausal formulas ===
% 1.40/1.71
% 1.40/1.71 ============================== PROCESS INITIAL CLAUSES ===============
% 1.40/1.71
% 1.40/1.71 ============================== PREDICATE ELIMINATION =================
% 1.40/1.71
% 1.40/1.71 ============================== end predicate elimination =============
% 1.40/1.71
% 1.40/1.71 Auto_denials:
% 1.40/1.71 % copying label goals to answer in negative clause
% 1.40/1.71
% 1.40/1.71 Term ordering decisions:
% 1.40/1.71 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 1.40/1.71
% 1.40/1.71 ============================== end of process initial clauses ========
% 1.40/1.71
% 1.40/1.71 ============================== CLAUSES FOR SEARCH ====================
% 1.40/1.71
% 1.40/1.71 ============================== end of clauses for search =============
% 1.40/1.71
% 1.40/1.71 ============================== SEARCH ================================
% 1.40/1.71
% 1.40/1.71 % Starting search at 0.01 seconds.
% 1.40/1.71
% 1.40/1.71 Low Water (keep): wt=43.000, iters=3387
% 1.40/1.71
% 1.40/1.71 Low Water (keep): wt=33.000, iters=3440
% 1.40/1.71
% 1.40/1.71 Low Water (keep): wt=32.000, iters=3369
% 1.40/1.71
% 1.40/1.71 ============================== PROOF =================================
% 1.40/1.71 % SZS status Theorem
% 1.40/1.71 % SZS output start Refutation
% 1.40/1.71
% 1.40/1.71 % Proof 1 at 0.69 (+ 0.03) seconds: goals.
% 1.40/1.71 % Length of proof is 95.
% 1.40/1.71 % Level of proof is 23.
% 1.40/1.71 % Maximum clause weight is 17.000.
% 1.40/1.71 % Given clauses 587.
% 1.40/1.71
% 1.40/1.71 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 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].
% 1.40/1.71 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 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].
% 1.40/1.71 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 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].
% 1.40/1.71 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].
% 1.40/1.71 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 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].
% 1.40/1.71 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 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].
% 1.40/1.71 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 1.40/1.71 19 -(all X0 strong_iteration(star(X0)) = strong_iteration(one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.40/1.71 20 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 1.40/1.71 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 1.40/1.71 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 1.40/1.71 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 1.40/1.71 24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 1.40/1.71 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 1.40/1.71 26 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 1.40/1.71 27 addition(one,multiplication(A,star(A))) = star(A). [copy(26),flip(a)].
% 1.40/1.71 28 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom). [clausify(12)].
% 1.40/1.71 29 addition(one,multiplication(star(A),A)) = star(A). [copy(28),flip(a)].
% 1.40/1.71 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 1.40/1.71 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 1.40/1.71 32 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom). [clausify(17)].
% 1.40/1.71 33 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A). [copy(32),flip(a)].
% 1.40/1.71 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 1.40/1.71 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([25(2)]),flip(a)].
% 1.40/1.71 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 1.40/1.71 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 1.40/1.71 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 1.40/1.71 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 1.40/1.71 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 1.40/1.71 41 strong_iteration(star(c1)) != strong_iteration(one) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 1.40/1.71 42 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 1.40/1.71 43 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 1.40/1.71 44 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom). [clausify(13)].
% 1.40/1.71 45 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(44),rewrite([25(2)])].
% 1.40/1.71 48 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom). [clausify(16)].
% 1.40/1.71 49 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)). [copy(48),rewrite([25(2)])].
% 1.40/1.71 53 strong_iteration(zero) = one. [para(24(a,1),31(a,1,2)),rewrite([20(3)]),flip(a)].
% 1.40/1.71 54 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)])].
% 1.40/1.71 55 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(36(a,1),27(a,1,2))].
% 1.40/1.71 57 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 1.40/1.71 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(23(a,1),40(a,1,1)),rewrite([25(4)]),flip(a)].
% 1.40/1.71 63 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)])].
% 1.40/1.71 65 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)])].
% 1.40/1.71 69 leq(A,A). [hyper(43,b,21,a)].
% 1.40/1.71 78 -leq(addition(A,B),one) | leq(multiplication(star(B),A),one). [para(22(a,1),45(a,1,2))].
% 1.40/1.71 96 -leq(A,addition(A,B)) | leq(A,multiplication(strong_iteration(one),B)). [para(23(a,1),49(a,2,2)),rewrite([25(1)])].
% 1.40/1.71 98 -leq(A,star(A)) | leq(A,strong_iteration(star(A))). [para(29(a,1),49(a,2)),rewrite([22(6)])].
% 1.40/1.71 109 leq(A,addition(A,B)). [hyper(43,b,54,a)].
% 1.40/1.71 110 addition(one,star(A)) = star(A). [para(27(a,1),54(a,1,2)),rewrite([27(7)])].
% 1.40/1.71 117 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(38(a,1),109(a,2))].
% 1.40/1.71 119 addition(one,multiplication(A,zero)) = star(multiplication(A,zero)). [para(24(a,1),55(a,1,2,2))].
% 1.40/1.71 194 leq(multiplication(A,B),addition(A,multiplication(A,B))). [para(57(a,1),117(a,2))].
% 1.40/1.71 245 addition(A,addition(B,multiplication(C,multiplication(star(C),A)))) = addition(B,multiplication(star(C),A)). [para(63(a,1),35(a,2,2)),rewrite([25(4)])].
% 1.40/1.71 250 multiplication(star(A),A) = multiplication(A,star(A)). [para(63(a,1),57(a,2)),rewrite([25(4),29(4)]),flip(a)].
% 1.40/1.71 265 leq(multiplication(A,star(A)),star(A)). [para(55(a,1),194(a,2)),rewrite([23(3),23(4),23(4)])].
% 1.40/1.71 278 multiplication(addition(A,one),star(A)) = star(A). [hyper(42,a,265,a),rewrite([25(4),62(4,R)])].
% 1.40/1.71 386 addition(A,star(A)) = star(A). [para(278(a,1),57(a,2,2)),rewrite([25(5),110(5),278(4),25(5),35(5),25(4),35(5,R),25(4),110(4)]),flip(a)].
% 1.40/1.71 395 leq(A,star(A)). [hyper(43,b,386,a)].
% 1.40/1.71 399 leq(A,strong_iteration(star(A))). [hyper(98,a,395,a)].
% 1.40/1.71 400 addition(A,strong_iteration(star(A))) = strong_iteration(star(A)). [hyper(42,a,399,a)].
% 1.40/1.71 519 -leq(A,one) | leq(multiplication(A,star(A)),one). [para(21(a,1),78(a,1)),rewrite([250(4)])].
% 1.40/1.71 596 leq(star(one),one). [hyper(519,a,69,a),rewrite([23(4)])].
% 1.40/1.71 600 star(one) = one. [hyper(42,a,596,a),rewrite([25(4),386(4)])].
% 1.40/1.71 620 star(multiplication(strong_iteration(one),zero)) = strong_iteration(one). [para(600(a,1),33(a,1,1)),rewrite([119(6)])].
% 1.40/1.71 657 addition(A,multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),A). [para(620(a,1),63(a,1,2,2,1)),rewrite([36(8),24(7),620(10)])].
% 1.40/1.71 659 multiplication(strong_iteration(one),strong_iteration(one)) = strong_iteration(one). [para(620(a,1),278(a,1,2)),rewrite([25(6),657(6),22(4),620(10)])].
% 1.40/1.71 661 multiplication(strong_iteration(one),strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)). [para(620(a,1),400(a,1,2,1)),rewrite([25(8),657(8),620(11)])].
% 1.40/1.71 921 leq(A,multiplication(strong_iteration(one),B)). [hyper(96,a,109,a)].
% 1.40/1.71 922 addition(A,multiplication(strong_iteration(one),B)) = multiplication(strong_iteration(one),B). [hyper(42,a,921,a)].
% 1.40/1.71 924 multiplication(strong_iteration(one),zero) = multiplication(strong_iteration(one),A). [back_rewrite(657),rewrite([922(5)])].
% 1.40/1.71 925 multiplication(strong_iteration(one),zero) = strong_iteration(strong_iteration(one)). [back_rewrite(661),rewrite([924(6,R)])].
% 1.40/1.71 926 strong_iteration(strong_iteration(one)) = strong_iteration(one). [back_rewrite(659),rewrite([924(5,R),925(4)])].
% 1.40/1.71 927 multiplication(strong_iteration(one),A) = strong_iteration(one). [back_rewrite(924),rewrite([925(4),926(3)]),flip(a)].
% 1.40/1.71 929 addition(A,strong_iteration(one)) = strong_iteration(one). [back_rewrite(922),rewrite([927(3),927(6)])].
% 1.40/1.71 951 addition(strong_iteration(one),multiplication(A,B)) = strong_iteration(one). [para(927(a,1),40(a,1,1)),rewrite([25(7),929(7),927(7)])].
% 1.40/1.71 1011 multiplication(strong_iteration(A),strong_iteration(one)) = strong_iteration(one). [para(951(a,1),65(a,1)),flip(a)].
% 1.40/1.71 6981 leq(A,addition(B,multiplication(star(C),A))). [para(245(a,1),109(a,2))].
% 1.40/1.71 7037 leq(A,multiplication(strong_iteration(star(B)),C)). [hyper(49,a,6981,a)].
% 1.40/1.71 7062 leq(A,strong_iteration(star(B))). [para(22(a,1),7037(a,2))].
% 1.40/1.71 7066 addition(A,strong_iteration(star(B))) = strong_iteration(star(B)). [hyper(42,a,7062,a)].
% 1.40/1.71 7226 leq(multiplication(A,B),multiplication(A,strong_iteration(star(C)))). [para(7066(a,1),117(a,2,2))].
% 1.40/1.71 7332 leq(strong_iteration(one),multiplication(strong_iteration(A),strong_iteration(star(B)))). [para(1011(a,1),7226(a,1))].
% 1.40/1.71 7346 multiplication(strong_iteration(A),strong_iteration(star(B))) = strong_iteration(one). [hyper(42,a,7332,a),rewrite([951(7)]),flip(a)].
% 1.40/1.71 7379 strong_iteration(star(A)) = strong_iteration(one). [para(53(a,1),7346(a,1,1)),rewrite([23(4)])].
% 1.40/1.71 7380 $F # answer(goals). [resolve(7379,a,41,a)].
% 1.40/1.71
% 1.40/1.71 % SZS output end Refutation
% 1.40/1.71 ============================== end of proof ==========================
% 1.40/1.71
% 1.40/1.71 ============================== STATISTICS ============================
% 1.40/1.71
% 1.40/1.71 Given=587. Generated=26750. Kept=7350. proofs=1.
% 1.40/1.71 Usable=483. Sos=5831. Demods=1086. Limbo=4, Disabled=1051. Hints=0.
% 1.40/1.71 Megabytes=7.14.
% 1.40/1.71 User_CPU=0.69, System_CPU=0.03, Wall_clock=1.
% 1.40/1.71
% 1.40/1.71 ============================== end of statistics =====================
% 1.40/1.71
% 1.40/1.71 ============================== end of search =========================
% 1.40/1.71
% 1.40/1.71 THEOREM PROVED
% 1.40/1.71 % SZS status Theorem
% 1.40/1.71
% 1.40/1.71 Exiting with 1 proof.
% 1.40/1.71
% 1.40/1.71 Process 6746 exit (max_proofs) Thu Jun 16 16:43:28 2022
% 1.40/1.71 Prover9 interrupted
%------------------------------------------------------------------------------