TSTP Solution File: KLE040+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE040+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 02:21:55 EDT 2022
% Result : Theorem 1.73s 2.08s
% Output : Refutation 1.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE040+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 16 16:32:33 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.41/0.96 ============================== Prover9 ===============================
% 0.41/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.96 Process 11761 was started by sandbox on n024.cluster.edu,
% 0.41/0.96 Thu Jun 16 16:32:33 2022
% 0.41/0.96 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11591_n024.cluster.edu".
% 0.41/0.96 ============================== end of head ===========================
% 0.41/0.96
% 0.41/0.96 ============================== INPUT =================================
% 0.41/0.96
% 0.41/0.96 % Reading from file /tmp/Prover9_11591_n024.cluster.edu
% 0.41/0.96
% 0.41/0.96 set(prolog_style_variables).
% 0.41/0.96 set(auto2).
% 0.41/0.96 % set(auto2) -> set(auto).
% 0.41/0.96 % set(auto) -> set(auto_inference).
% 0.41/0.96 % set(auto) -> set(auto_setup).
% 0.41/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.96 % set(auto) -> set(auto_limits).
% 0.41/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.96 % set(auto) -> set(auto_denials).
% 0.41/0.96 % set(auto) -> set(auto_process).
% 0.41/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.96 % set(auto2) -> assign(stats, some).
% 0.41/0.96 % set(auto2) -> clear(echo_input).
% 0.41/0.96 % set(auto2) -> set(quiet).
% 0.41/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.96 % set(auto2) -> clear(print_given).
% 0.41/0.96 assign(lrs_ticks,-1).
% 0.41/0.96 assign(sos_limit,10000).
% 0.41/0.96 assign(order,kbo).
% 0.41/0.96 set(lex_order_vars).
% 0.41/0.96 clear(print_given).
% 0.41/0.96
% 0.41/0.96 % formulas(sos). % not echoed (17 formulas)
% 0.41/0.96
% 0.41/0.96 ============================== end of input ==========================
% 0.41/0.96
% 0.41/0.96 % From the command line: assign(max_seconds, 300).
% 0.41/0.96
% 0.41/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.96
% 0.41/0.96 % Formulas that are not ordinary clauses:
% 0.41/0.96 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 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].
% 0.41/0.96 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 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].
% 0.41/0.96 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 15 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 17 -(all X0 multiplication(star(X0),star(X0)) = star(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.73/2.08
% 1.73/2.08 ============================== end of process non-clausal formulas ===
% 1.73/2.08
% 1.73/2.08 ============================== PROCESS INITIAL CLAUSES ===============
% 1.73/2.08
% 1.73/2.08 ============================== PREDICATE ELIMINATION =================
% 1.73/2.08
% 1.73/2.08 ============================== end predicate elimination =============
% 1.73/2.08
% 1.73/2.08 Auto_denials:
% 1.73/2.08 % copying label goals to answer in negative clause
% 1.73/2.08
% 1.73/2.08 Term ordering decisions:
% 1.73/2.08
% 1.73/2.08 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 1.73/2.08 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. star=0.
% 1.73/2.08
% 1.73/2.08 ============================== end of process initial clauses ========
% 1.73/2.08
% 1.73/2.08 ============================== CLAUSES FOR SEARCH ====================
% 1.73/2.08
% 1.73/2.08 ============================== end of clauses for search =============
% 1.73/2.08
% 1.73/2.08 ============================== SEARCH ================================
% 1.73/2.08
% 1.73/2.08 % Starting search at 0.01 seconds.
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=48.000, iters=3371
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=40.000, iters=3350
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=38.000, iters=3546
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=35.000, iters=3449
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=33.000, iters=3464
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=32.000, iters=3352
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=31.000, iters=3413
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=29.000, iters=3366
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=28.000, iters=3338
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=27.000, iters=3368
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=25.000, iters=3418
% 1.73/2.08
% 1.73/2.08 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 0.83 sec).
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=24.000, iters=3353
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=23.000, iters=3333
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=22.000, iters=3342
% 1.73/2.08
% 1.73/2.08 Low Water (keep): wt=21.000, iters=3335
% 1.73/2.08
% 1.73/2.08 ============================== PROOF =================================
% 1.73/2.08 % SZS status Theorem
% 1.73/2.08 % SZS output start Refutation
% 1.73/2.08
% 1.73/2.08 % Proof 1 at 1.09 (+ 0.03) seconds: goals.
% 1.73/2.08 % Length of proof is 92.
% 1.73/2.08 % Level of proof is 17.
% 1.73/2.08 % Maximum clause weight is 15.000.
% 1.73/2.08 % Given clauses 722.
% 1.73/2.08
% 1.73/2.08 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 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].
% 1.73/2.08 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 15 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 1.73/2.08 17 -(all X0 multiplication(star(X0),star(X0)) = star(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.73/2.08 18 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 1.73/2.08 19 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 1.73/2.08 20 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 1.73/2.08 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 1.73/2.08 22 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 1.73/2.08 23 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 1.73/2.08 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 1.73/2.08 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(13)].
% 1.73/2.08 26 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 1.73/2.08 27 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 1.73/2.08 28 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(27),rewrite([24(2)]),flip(a)].
% 1.73/2.08 30 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 1.73/2.08 31 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(30),flip(a)].
% 1.73/2.08 32 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 1.73/2.08 33 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(32),flip(a)].
% 1.73/2.08 34 star(c1) != multiplication(star(c1),star(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 1.73/2.08 35 multiplication(star(c1),star(c1)) != star(c1) # answer(goals). [copy(34),flip(a)].
% 1.73/2.08 36 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 1.73/2.08 37 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 1.73/2.08 38 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(15)].
% 1.73/2.08 39 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(38),rewrite([24(2)])].
% 1.73/2.08 40 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(16)].
% 1.73/2.08 41 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(40),rewrite([24(2)])].
% 1.73/2.08 43 leq(addition(zero,one),star(zero)). [para(23(a,1),25(a,1,2)),rewrite([24(3)])].
% 1.73/2.08 44 addition(A,addition(A,B)) = addition(A,B). [para(28(a,1),19(a,1)),rewrite([24(1),24(2),28(2,R),19(1),24(3)])].
% 1.73/2.08 47 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(20(a,1),31(a,1,1)),rewrite([24(4)]),flip(a)].
% 1.73/2.08 48 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(21(a,1),33(a,1,1)),rewrite([24(4)]),flip(a)].
% 1.73/2.08 51 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(36,a,26,a),rewrite([24(6)])].
% 1.73/2.08 52 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(36,a,25,a),rewrite([24(6)])].
% 1.73/2.08 53 leq(A,A). [hyper(37,b,19,a)].
% 1.73/2.08 61 -leq(A,B) | leq(multiplication(star(zero),A),B). [para(23(a,1),39(a,1,2)),rewrite([18(2)])].
% 1.73/2.08 74 addition(zero,addition(one,star(zero))) = star(zero). [hyper(36,a,43,a),rewrite([24(6),28(6),24(5),28(6,R),24(5)])].
% 1.73/2.08 78 leq(A,addition(A,B)). [hyper(37,b,44,a)].
% 1.73/2.08 79 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(31(a,1),78(a,2))].
% 1.73/2.08 89 leq(multiplication(star(zero),A),A). [hyper(61,a,53,a)].
% 1.73/2.08 96 multiplication(A,addition(zero,one)) = A. [para(22(a,1),47(a,2,2)),rewrite([18(6)])].
% 1.73/2.08 98 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(47(a,2),28(a,2,2)),rewrite([24(2)]),flip(a)].
% 1.73/2.08 111 -leq(multiplication(A,addition(B,one)),A) | leq(multiplication(A,star(B)),A). [para(47(a,2),41(a,1))].
% 1.73/2.08 118 leq(star(zero),one). [para(20(a,1),89(a,1))].
% 1.73/2.08 120 addition(one,star(zero)) = one. [hyper(36,a,118,a),rewrite([24(4)])].
% 1.73/2.08 121 addition(zero,one) = star(zero). [back_rewrite(74),rewrite([120(5)])].
% 1.73/2.08 122 multiplication(A,star(zero)) = A. [back_rewrite(96),rewrite([121(3)])].
% 1.73/2.08 127 addition(A,multiplication(addition(B,one),C)) = addition(C,addition(A,multiplication(B,C))). [para(48(a,2),28(a,2,2)),rewrite([24(2)]),flip(a)].
% 1.73/2.08 146 star(zero) = one. [para(122(a,1),21(a,1)),flip(a)].
% 1.73/2.08 191 addition(one,addition(star(A),multiplication(star(A),A))) = star(A). [para(51(a,1),28(a,1)),rewrite([28(7),24(6)]),flip(a)].
% 1.73/2.08 214 addition(one,addition(star(A),multiplication(A,star(A)))) = star(A). [para(52(a,1),28(a,1)),rewrite([28(7),24(6)]),flip(a)].
% 1.73/2.08 349 addition(one,star(A)) = star(A). [para(191(a,1),44(a,1,2)),rewrite([191(9)])].
% 1.73/2.08 351 addition(one,multiplication(star(A),addition(A,one))) = star(A). [para(47(a,2),191(a,1,2))].
% 1.73/2.08 352 leq(A,multiplication(A,star(B))). [para(191(a,1),79(a,2,2)),rewrite([20(2)])].
% 1.73/2.08 361 leq(addition(A,one),addition(star(B),multiplication(A,star(B)))). [para(48(a,1),352(a,2))].
% 1.73/2.08 379 addition(star(A),one) = star(A). [para(349(a,1),24(a,1)),flip(a)].
% 1.73/2.08 413 -leq(star(A),star(A)) | leq(star(addition(A,one)),star(A)). [para(351(a,1),41(a,1)),rewrite([21(8)])].
% 1.73/2.08 444 addition(star(A),multiplication(A,star(A))) = star(A). [para(214(a,1),28(a,1)),rewrite([349(6),24(5)]),flip(a)].
% 1.73/2.08 465 multiplication(addition(A,one),star(A)) = star(A). [para(444(a,1),48(a,2))].
% 1.73/2.08 476 leq(addition(A,one),star(A)). [para(444(a,1),361(a,2))].
% 1.73/2.08 482 addition(A,star(A)) = star(A). [hyper(36,a,476,a),rewrite([24(4),28(4,R),349(3)])].
% 1.73/2.08 652 leq(A,addition(B,multiplication(A,addition(C,one)))). [para(98(a,2),78(a,2))].
% 1.73/2.08 686 leq(A,multiplication(addition(A,B),addition(C,one))). [para(33(a,1),652(a,2)),rewrite([24(1)])].
% 1.73/2.08 971 leq(one,multiplication(star(A),addition(B,one))). [para(191(a,1),686(a,2,1))].
% 1.73/2.08 977 addition(one,multiplication(star(A),addition(B,one))) = multiplication(star(A),addition(B,one)). [hyper(36,a,971,a)].
% 1.73/2.08 979 multiplication(star(A),addition(A,one)) = star(A). [back_rewrite(351),rewrite([977(6)])].
% 1.73/2.08 1129 leq(multiplication(star(A),A),star(A)). [para(979(a,1),79(a,2))].
% 1.73/2.08 1588 leq(multiplication(star(addition(A,one)),star(A)),star(addition(A,one))). [hyper(111,a,1129,a)].
% 1.73/2.08 1790 leq(A,addition(B,multiplication(addition(C,one),A))). [para(127(a,2),78(a,2))].
% 1.73/2.08 1827 leq(A,addition(B,multiplication(star(C),A))). [para(379(a,1),1790(a,2,2,1))].
% 1.73/2.08 1833 leq(A,multiplication(star(B),addition(A,C))). [para(31(a,1),1827(a,2)),rewrite([24(2)])].
% 1.73/2.08 1848 leq(multiplication(A,B),multiplication(star(C),multiplication(addition(A,D),B))). [para(33(a,1),1833(a,2,2))].
% 1.73/2.08 9594 leq(star(addition(A,one)),star(A)). [hyper(413,a,53,a)].
% 1.73/2.08 9595 addition(star(A),star(addition(A,one))) = star(A). [hyper(36,a,9594,a),rewrite([24(5)])].
% 1.73/2.08 10242 multiplication(star(addition(A,one)),star(A)) = star(addition(A,one)). [hyper(36,a,1588,a),rewrite([24(9),47(9,R),379(6)])].
% 1.73/2.08 10678 leq(multiplication(A,B),multiplication(star(C),multiplication(star(A),B))). [para(482(a,1),1848(a,2,2,1))].
% 1.73/2.08 10731 leq(star(A),multiplication(star(B),star(addition(A,one)))). [para(465(a,1),10678(a,1)),rewrite([10242(7)])].
% 1.73/2.08 10755 leq(star(A),star(addition(A,one))). [para(146(a,1),10731(a,2,1)),rewrite([21(6)])].
% 1.73/2.08 10757 star(addition(A,one)) = star(A). [hyper(36,a,10755,a),rewrite([9595(5)]),flip(a)].
% 1.73/2.08 10772 multiplication(star(A),star(A)) = star(A). [back_rewrite(10242),rewrite([10757(3),10757(6)])].
% 1.73/2.08 10773 $F # answer(goals). [resolve(10772,a,35,a)].
% 1.73/2.08
% 1.73/2.08 % SZS output end Refutation
% 1.73/2.08 ============================== end of proof ==========================
% 1.73/2.08
% 1.73/2.08 ============================== STATISTICS ============================
% 1.73/2.08
% 1.73/2.08 Given=722. Generated=42864. Kept=10749. proofs=1.
% 1.73/2.08 Usable=673. Sos=9605. Demods=836. Limbo=15, Disabled=473. Hints=0.
% 1.73/2.08 Megabytes=10.21.
% 1.73/2.08 User_CPU=1.09, System_CPU=0.03, Wall_clock=1.
% 1.73/2.08
% 1.73/2.08 ============================== end of statistics =====================
% 1.73/2.08
% 1.73/2.08 ============================== end of search =========================
% 1.73/2.08
% 1.73/2.08 THEOREM PROVED
% 1.73/2.08 % SZS status Theorem
% 1.73/2.08
% 1.73/2.08 Exiting with 1 proof.
% 1.73/2.08
% 1.73/2.08 Process 11761 exit (max_proofs) Thu Jun 16 16:32:34 2022
% 1.73/2.08 Prover9 interrupted
%------------------------------------------------------------------------------