TSTP Solution File: KLE142+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE142+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 1.57s 1.88s
% Output : Refutation 1.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE142+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 15:36:41 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.49/1.06 ============================== Prover9 ===============================
% 0.49/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.49/1.06 Process 9165 was started by sandbox on n028.cluster.edu,
% 0.49/1.06 Thu Jun 16 15:36:42 2022
% 0.49/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_8997_n028.cluster.edu".
% 0.49/1.06 ============================== end of head ===========================
% 0.49/1.06
% 0.49/1.06 ============================== INPUT =================================
% 0.49/1.06
% 0.49/1.06 % Reading from file /tmp/Prover9_8997_n028.cluster.edu
% 0.49/1.06
% 0.49/1.06 set(prolog_style_variables).
% 0.49/1.06 set(auto2).
% 0.49/1.06 % set(auto2) -> set(auto).
% 0.49/1.06 % set(auto) -> set(auto_inference).
% 0.49/1.06 % set(auto) -> set(auto_setup).
% 0.49/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.49/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.49/1.06 % set(auto) -> set(auto_limits).
% 0.49/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.49/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.49/1.06 % set(auto) -> set(auto_denials).
% 0.49/1.06 % set(auto) -> set(auto_process).
% 0.49/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.49/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.49/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.49/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.49/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.49/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.49/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.49/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.49/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.49/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.49/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.49/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.49/1.06 % set(auto2) -> assign(stats, some).
% 0.49/1.06 % set(auto2) -> clear(echo_input).
% 0.49/1.06 % set(auto2) -> set(quiet).
% 0.49/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.49/1.06 % set(auto2) -> clear(print_given).
% 0.49/1.06 assign(lrs_ticks,-1).
% 0.49/1.06 assign(sos_limit,10000).
% 0.49/1.06 assign(order,kbo).
% 0.49/1.06 set(lex_order_vars).
% 0.49/1.06 clear(print_given).
% 0.49/1.06
% 0.49/1.06 % formulas(sos). % not echoed (19 formulas)
% 0.49/1.06
% 0.49/1.06 ============================== end of input ==========================
% 0.49/1.06
% 0.49/1.06 % From the command line: assign(max_seconds, 300).
% 0.49/1.06
% 0.49/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.49/1.06
% 0.49/1.06 % Formulas that are not ordinary clauses:
% 0.49/1.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 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].
% 0.49/1.06 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 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].
% 1.57/1.88 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 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].
% 1.57/1.88 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 19 -(all X0 strong_iteration(strong_iteration(X0)) = strong_iteration(one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.57/1.88
% 1.57/1.88 ============================== end of process non-clausal formulas ===
% 1.57/1.88
% 1.57/1.88 ============================== PROCESS INITIAL CLAUSES ===============
% 1.57/1.88
% 1.57/1.88 ============================== PREDICATE ELIMINATION =================
% 1.57/1.88
% 1.57/1.88 ============================== end predicate elimination =============
% 1.57/1.88
% 1.57/1.88 Auto_denials:
% 1.57/1.88 % copying label goals to answer in negative clause
% 1.57/1.88
% 1.57/1.88 Term ordering decisions:
% 1.57/1.88 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 1.57/1.88
% 1.57/1.88 ============================== end of process initial clauses ========
% 1.57/1.88
% 1.57/1.88 ============================== CLAUSES FOR SEARCH ====================
% 1.57/1.88
% 1.57/1.88 ============================== end of clauses for search =============
% 1.57/1.88
% 1.57/1.88 ============================== SEARCH ================================
% 1.57/1.88
% 1.57/1.88 % Starting search at 0.01 seconds.
% 1.57/1.88
% 1.57/1.88 Low Water (keep): wt=43.000, iters=3387
% 1.57/1.88
% 1.57/1.88 Low Water (keep): wt=33.000, iters=3440
% 1.57/1.88
% 1.57/1.88 Low Water (keep): wt=32.000, iters=3369
% 1.57/1.88
% 1.57/1.88 ============================== PROOF =================================
% 1.57/1.88 % SZS status Theorem
% 1.57/1.88 % SZS output start Refutation
% 1.57/1.88
% 1.57/1.88 % Proof 1 at 0.80 (+ 0.02) seconds: goals.
% 1.57/1.88 % Length of proof is 132.
% 1.57/1.88 % Level of proof is 29.
% 1.57/1.88 % Maximum clause weight is 18.000.
% 1.57/1.88 % Given clauses 595.
% 1.57/1.88
% 1.57/1.88 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 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].
% 1.57/1.88 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 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].
% 1.57/1.88 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 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].
% 1.57/1.88 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].
% 1.57/1.88 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 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].
% 1.57/1.88 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 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].
% 1.57/1.88 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.88 19 -(all X0 strong_iteration(strong_iteration(X0)) = strong_iteration(one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.57/1.88 20 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 1.57/1.88 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 1.57/1.88 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 1.57/1.88 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 1.57/1.88 24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 1.57/1.88 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 1.57/1.88 26 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 1.57/1.88 27 addition(one,multiplication(A,star(A))) = star(A). [copy(26),flip(a)].
% 1.57/1.88 28 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom). [clausify(12)].
% 1.57/1.88 29 addition(one,multiplication(star(A),A)) = star(A). [copy(28),flip(a)].
% 1.57/1.88 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 1.57/1.88 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 1.57/1.88 32 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom). [clausify(17)].
% 1.57/1.88 33 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A). [copy(32),flip(a)].
% 1.57/1.88 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 1.57/1.88 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([25(2)]),flip(a)].
% 1.57/1.88 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 1.57/1.88 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 1.57/1.88 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 1.57/1.88 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 1.57/1.88 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 1.57/1.88 41 strong_iteration(strong_iteration(c1)) != strong_iteration(one) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 1.57/1.88 42 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 1.57/1.88 43 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 1.57/1.88 44 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom). [clausify(13)].
% 1.57/1.88 45 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(44),rewrite([25(2)])].
% 1.57/1.88 48 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom). [clausify(16)].
% 1.57/1.88 49 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)). [copy(48),rewrite([25(2)])].
% 1.57/1.88 53 strong_iteration(zero) = one. [para(24(a,1),31(a,1,2)),rewrite([20(3)]),flip(a)].
% 1.57/1.88 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)])].
% 1.57/1.88 55 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(36(a,1),27(a,1,2))].
% 1.57/1.88 56 addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)). [para(36(a,1),31(a,1,2))].
% 1.57/1.88 57 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 1.57/1.88 58 addition(A,multiplication(A,multiplication(B,star(B)))) = multiplication(A,star(B)). [para(27(a,1),38(a,2,2)),rewrite([22(2)])].
% 1.57/1.88 60 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)])].
% 1.57/1.88 61 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(20(a,1),40(a,2,1)),rewrite([24(3),25(3)])].
% 1.57/1.88 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(23(a,1),40(a,1,1)),rewrite([25(4)]),flip(a)].
% 1.57/1.88 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)])].
% 1.57/1.88 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)])].
% 1.57/1.88 69 leq(A,A). [hyper(43,b,21,a)].
% 1.57/1.88 78 -leq(addition(A,B),one) | leq(multiplication(star(B),A),one). [para(22(a,1),45(a,1,2))].
% 1.57/1.88 96 -leq(A,addition(A,B)) | leq(A,multiplication(strong_iteration(one),B)). [para(23(a,1),49(a,2,2)),rewrite([25(1)])].
% 1.57/1.88 98 -leq(A,star(A)) | leq(A,strong_iteration(star(A))). [para(29(a,1),49(a,2)),rewrite([22(6)])].
% 1.57/1.88 109 leq(A,addition(A,B)). [hyper(43,b,54,a)].
% 1.57/1.88 110 addition(one,star(A)) = star(A). [para(27(a,1),54(a,1,2)),rewrite([27(7)])].
% 1.57/1.88 113 leq(A,multiplication(strong_iteration(B),A)). [hyper(49,a,109,a)].
% 1.57/1.88 117 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(38(a,1),109(a,2))].
% 1.57/1.88 118 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(40(a,1),109(a,2))].
% 1.57/1.88 119 addition(one,multiplication(A,zero)) = star(multiplication(A,zero)). [para(24(a,1),55(a,1,2,2))].
% 1.57/1.88 142 -leq(A,multiplication(B,A)) | leq(A,multiplication(strong_iteration(B),zero)). [para(61(a,1),49(a,2))].
% 1.57/1.88 144 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(57(a,2),35(a,2,2)),rewrite([25(2)]),flip(a)].
% 1.57/1.88 170 addition(A,addition(B,multiplication(A,multiplication(C,star(C))))) = addition(B,multiplication(A,star(C))). [para(58(a,1),35(a,2,2)),rewrite([25(4)])].
% 1.57/1.88 192 leq(multiplication(A,zero),multiplication(A,multiplication(B,C))). [para(61(a,1),117(a,2,2))].
% 1.57/1.88 194 leq(multiplication(A,B),addition(A,multiplication(A,B))). [para(57(a,1),117(a,2))].
% 1.57/1.88 200 -leq(multiplication(A,strong_iteration(A)),multiplication(B,strong_iteration(A))) | leq(multiplication(A,strong_iteration(A)),multiplication(strong_iteration(B),B)). [para(60(a,1),49(a,2))].
% 1.57/1.88 204 leq(multiplication(star(A),B),multiplication(strong_iteration(A),B)). [para(33(a,1),118(a,2,1))].
% 1.57/1.88 230 multiplication(addition(A,one),zero) = multiplication(A,zero). [para(62(a,2),61(a,1))].
% 1.57/1.88 242 leq(multiplication(A,zero),multiplication(A,B)). [para(22(a,1),192(a,2,2))].
% 1.57/1.88 245 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)])].
% 1.57/1.88 250 multiplication(star(A),A) = multiplication(A,star(A)). [para(63(a,1),57(a,2)),rewrite([25(4),29(4)]),flip(a)].
% 1.57/1.88 265 leq(multiplication(A,star(A)),star(A)). [para(55(a,1),194(a,2)),rewrite([23(3),23(4),23(4)])].
% 1.57/1.88 278 multiplication(addition(A,one),star(A)) = star(A). [hyper(42,a,265,a),rewrite([25(4),62(4,R)])].
% 1.57/1.88 386 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)].
% 1.57/1.88 389 leq(multiplication(A,zero),star(A)). [para(278(a,1),242(a,2)),rewrite([230(4)])].
% 1.57/1.88 392 addition(star(A),multiplication(A,zero)) = star(A). [hyper(42,a,389,a),rewrite([25(4)])].
% 1.57/1.88 395 leq(A,star(A)). [hyper(43,b,386,a)].
% 1.57/1.88 399 leq(A,strong_iteration(star(A))). [hyper(98,a,395,a)].
% 1.57/1.88 400 addition(A,strong_iteration(star(A))) = strong_iteration(star(A)). [hyper(42,a,399,a)].
% 1.57/1.88 519 -leq(A,one) | leq(multiplication(A,star(A)),one). [para(21(a,1),78(a,1)),rewrite([250(4)])].
% 1.57/1.88 596 leq(star(one),one). [hyper(519,a,69,a),rewrite([23(4)])].
% 1.57/1.88 600 star(one) = one. [hyper(42,a,596,a),rewrite([25(4),386(4)])].
% 1.57/1.88 620 star(multiplication(strong_iteration(one),zero)) = strong_iteration(one). [para(600(a,1),33(a,1,1)),rewrite([119(6)])].
% 1.57/1.88 657 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)])].
% 1.57/1.88 659 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)])].
% 1.57/1.88 661 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)])].
% 1.57/1.88 921 leq(A,multiplication(strong_iteration(one),B)). [hyper(96,a,109,a)].
% 1.57/1.88 922 addition(A,multiplication(strong_iteration(one),B)) = multiplication(strong_iteration(one),B). [hyper(42,a,921,a)].
% 1.57/1.88 924 multiplication(strong_iteration(one),zero) = multiplication(strong_iteration(one),A). [back_rewrite(657),rewrite([922(5)])].
% 1.57/1.88 925 multiplication(strong_iteration(one),zero) = strong_iteration(strong_iteration(one)). [back_rewrite(661),rewrite([924(6,R)])].
% 1.57/1.88 926 strong_iteration(strong_iteration(one)) = strong_iteration(one). [back_rewrite(659),rewrite([924(5,R),925(4)])].
% 1.57/1.88 927 multiplication(strong_iteration(one),A) = strong_iteration(one). [back_rewrite(924),rewrite([925(4),926(3)]),flip(a)].
% 1.57/1.88 929 addition(A,strong_iteration(one)) = strong_iteration(one). [back_rewrite(922),rewrite([927(3),927(6)])].
% 1.57/1.88 951 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)])].
% 1.57/1.88 1010 multiplication(star(A),strong_iteration(one)) = strong_iteration(one). [para(951(a,1),63(a,1)),flip(a)].
% 1.57/1.88 1011 multiplication(strong_iteration(A),strong_iteration(one)) = strong_iteration(one). [para(951(a,1),65(a,1)),flip(a)].
% 1.57/1.88 1012 addition(strong_iteration(one),star(A)) = strong_iteration(one). [para(278(a,1),951(a,1,2))].
% 1.57/1.88 1428 leq(A,multiplication(strong_iteration(strong_iteration(B)),zero)). [hyper(142,a,113,a)].
% 1.57/1.88 1436 addition(A,multiplication(strong_iteration(strong_iteration(B)),zero)) = multiplication(strong_iteration(strong_iteration(B)),zero). [hyper(42,a,1428,a)].
% 1.57/1.88 1696 leq(A,addition(B,multiplication(A,addition(C,one)))). [para(144(a,2),109(a,2))].
% 1.57/1.88 1742 leq(A,multiplication(addition(A,B),addition(C,one))). [para(40(a,1),1696(a,2)),rewrite([25(1)])].
% 1.57/1.88 2084 leq(A,multiplication(star(B),multiplication(A,addition(C,one)))). [para(63(a,1),1742(a,2,1)),rewrite([36(5)])].
% 1.57/1.88 2591 leq(A,multiplication(star(B),addition(A,multiplication(A,C)))). [para(57(a,1),2084(a,2,2))].
% 1.57/1.88 3075 leq(one,multiplication(star(A),strong_iteration(B))). [para(56(a,1),2591(a,2,2)),rewrite([23(4)])].
% 1.57/1.88 3112 leq(one,multiplication(strong_iteration(A),star(strong_iteration(A)))). [para(250(a,1),3075(a,2))].
% 1.57/1.88 3115 multiplication(strong_iteration(A),star(strong_iteration(A))) = star(strong_iteration(A)). [hyper(42,a,3112,a),rewrite([27(6)]),flip(a)].
% 1.57/1.88 3543 multiplication(addition(A,one),star(strong_iteration(A))) = star(strong_iteration(A)). [para(3115(a,1),65(a,1,2,2)),rewrite([62(6,R),3115(9)])].
% 1.57/1.88 3726 addition(A,star(strong_iteration(A))) = star(strong_iteration(A)). [para(65(a,1),170(a,1,2)),rewrite([3115(4),62(9,R),3543(8)])].
% 1.57/1.88 3920 leq(multiplication(A,B),multiplication(A,star(strong_iteration(B)))). [para(3726(a,1),117(a,2,2))].
% 1.57/1.88 4206 leq(multiplication(star(A),strong_iteration(star(A))),multiplication(strong_iteration(strong_iteration(A)),strong_iteration(A))). [hyper(200,a,204,a)].
% 1.57/1.88 6981 leq(A,addition(B,multiplication(star(C),A))). [para(245(a,1),109(a,2))].
% 1.57/1.88 7037 leq(A,multiplication(strong_iteration(star(B)),C)). [hyper(49,a,6981,a)].
% 1.57/1.88 7062 leq(A,strong_iteration(star(B))). [para(22(a,1),7037(a,2))].
% 1.57/1.88 7066 addition(A,strong_iteration(star(B))) = strong_iteration(star(B)). [hyper(42,a,7062,a)].
% 1.57/1.88 7226 leq(multiplication(A,B),multiplication(A,strong_iteration(star(C)))). [para(7066(a,1),117(a,2,2))].
% 1.57/1.88 7332 leq(strong_iteration(one),multiplication(strong_iteration(A),strong_iteration(star(B)))). [para(1011(a,1),7226(a,1))].
% 1.57/1.88 7346 multiplication(strong_iteration(A),strong_iteration(star(B))) = strong_iteration(one). [hyper(42,a,7332,a),rewrite([951(7)]),flip(a)].
% 1.57/1.88 7379 strong_iteration(star(A)) = strong_iteration(one). [para(53(a,1),7346(a,1,1)),rewrite([23(4)])].
% 1.57/1.88 7381 leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(A)),strong_iteration(A))). [back_rewrite(4206),rewrite([7379(3),1010(4)])].
% 1.57/1.88 7382 multiplication(strong_iteration(strong_iteration(A)),strong_iteration(A)) = strong_iteration(one). [hyper(42,a,7381,a),rewrite([951(7)]),flip(a)].
% 1.57/1.88 7409 leq(strong_iteration(one),star(strong_iteration(strong_iteration(A)))). [para(7382(a,1),3920(a,1)),rewrite([3115(8)])].
% 1.57/1.88 7430 star(strong_iteration(strong_iteration(A))) = strong_iteration(one). [hyper(42,a,7409,a),rewrite([1012(6)]),flip(a)].
% 1.57/1.88 7437 multiplication(strong_iteration(strong_iteration(A)),zero) = strong_iteration(one). [para(7430(a,1),392(a,1,1)),rewrite([1436(7),7430(7)])].
% 1.57/1.88 7438 strong_iteration(strong_iteration(A)) = strong_iteration(one). [para(7437(a,1),33(a,1,2)),rewrite([25(5),1012(5)]),flip(a)].
% 1.57/1.88 7439 $F # answer(goals). [resolve(7438,a,41,a)].
% 1.57/1.88
% 1.57/1.88 % SZS output end Refutation
% 1.57/1.88 ============================== end of proof ==========================
% 1.57/1.88
% 1.57/1.88 ============================== STATISTICS ============================
% 1.57/1.88
% 1.57/1.88 Given=595. Generated=28297. Kept=7409. proofs=1.
% 1.57/1.88 Usable=469. Sos=5715. Demods=1074. Limbo=0, Disabled=1244. Hints=0.
% 1.57/1.88 Megabytes=7.16.
% 1.57/1.88 User_CPU=0.81, System_CPU=0.02, Wall_clock=1.
% 1.57/1.88
% 1.57/1.88 ============================== end of statistics =====================
% 1.57/1.88
% 1.57/1.88 ============================== end of search =========================
% 1.57/1.88
% 1.57/1.88 THEOREM PROVED
% 1.57/1.88 % SZS status Theorem
% 1.57/1.88
% 1.57/1.88 Exiting with 1 proof.
% 1.57/1.88
% 1.57/1.88 Process 9165 exit (max_proofs) Thu Jun 16 15:36:43 2022
% 1.57/1.88 Prover9 interrupted
%------------------------------------------------------------------------------