TSTP Solution File: KLE044+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE044+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 02:21:58 EDT 2022
% Result : Theorem 6.33s 6.61s
% Output : Refutation 6.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE044+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 16:07:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 22844 was started by sandbox on n006.cluster.edu,
% 0.43/1.00 Thu Jun 16 16:07:11 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22691_n006.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_22691_n006.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (17 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 6.33/6.61 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].
% 6.33/6.61 17 -(all X0 (leq(star(addition(one,X0)),star(X0)) & leq(star(X0),star(addition(one,X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.33/6.61
% 6.33/6.61 ============================== end of process non-clausal formulas ===
% 6.33/6.61
% 6.33/6.61 ============================== PROCESS INITIAL CLAUSES ===============
% 6.33/6.61
% 6.33/6.61 ============================== PREDICATE ELIMINATION =================
% 6.33/6.61
% 6.33/6.61 ============================== end predicate elimination =============
% 6.33/6.61
% 6.33/6.61 Auto_denials:
% 6.33/6.61 % copying label goals to answer in negative clause
% 6.33/6.61
% 6.33/6.61 Term ordering decisions:
% 6.33/6.61
% 6.33/6.61 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 6.33/6.61 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. star=0.
% 6.33/6.61
% 6.33/6.61 ============================== end of process initial clauses ========
% 6.33/6.61
% 6.33/6.61 ============================== CLAUSES FOR SEARCH ====================
% 6.33/6.61
% 6.33/6.61 ============================== end of clauses for search =============
% 6.33/6.61
% 6.33/6.61 ============================== SEARCH ================================
% 6.33/6.61
% 6.33/6.61 % Starting search at 0.01 seconds.
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=38.000, iters=3455
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=35.000, iters=3359
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=33.000, iters=3387
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=32.000, iters=3365
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=31.000, iters=3388
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=30.000, iters=3356
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=29.000, iters=3335
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=27.000, iters=3406
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=25.000, iters=3345
% 6.33/6.61
% 6.33/6.61 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 40 (0.00 of 0.87 sec).
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=24.000, iters=3345
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=23.000, iters=3336
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=22.000, iters=3361
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=21.000, iters=3335
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=20.000, iters=3353
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=6114, wt=48.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=6154, wt=47.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=6504, wt=46.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=6512, wt=45.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=6370, wt=44.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=6524, wt=43.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=4125, wt=42.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=6494, wt=41.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=6503, wt=40.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=11487, wt=19.000
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=19.000, iters=3369
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=11763, wt=18.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=12225, wt=17.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=12244, wt=15.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=12280, wt=14.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=12301, wt=13.000
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=12917, wt=12.000
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=18.000, iters=3335
% 6.33/6.61
% 6.33/6.61 Low Water (displace): id=16374, wt=11.000
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=17.000, iters=3335
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=16.000, iters=3344
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=15.000, iters=3343
% 6.33/6.61
% 6.33/6.61 Low Water (keep): wt=14.000, iters=3825
% 6.33/6.61
% 6.33/6.61 ============================== PROOF =================================
% 6.33/6.61 % SZS status Theorem
% 6.33/6.61 % SZS output start Refutation
% 6.33/6.61
% 6.33/6.61 % Proof 1 at 5.43 (+ 0.19) seconds: goals.
% 6.33/6.61 % Length of proof is 137.
% 6.33/6.61 % Level of proof is 31.
% 6.33/6.61 % Maximum clause weight is 17.000.
% 6.33/6.61 % Given clauses 2192.
% 6.33/6.61
% 6.33/6.61 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 6.33/6.61 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].
% 6.33/6.61 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 6.33/6.61 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].
% 6.33/6.61 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 6.33/6.61 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 6.33/6.61 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].
% 6.33/6.61 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].
% 6.33/6.61 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 6.33/6.61 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 6.33/6.61 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 6.33/6.61 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].
% 6.33/6.61 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].
% 6.33/6.61 17 -(all X0 (leq(star(addition(one,X0)),star(X0)) & leq(star(X0),star(addition(one,X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.33/6.61 19 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 6.33/6.61 20 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 6.33/6.61 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 6.33/6.61 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 6.33/6.61 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(13)].
% 6.33/6.61 26 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 6.33/6.61 27 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 6.33/6.61 28 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(27),rewrite([24(2)]),flip(a)].
% 6.33/6.61 29 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 6.33/6.61 30 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 6.33/6.61 31 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(30),flip(a)].
% 6.33/6.61 32 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 6.33/6.61 33 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(32),flip(a)].
% 6.33/6.61 34 -leq(star(addition(one,c1)),star(c1)) | -leq(star(c1),star(addition(one,c1))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 6.33/6.61 35 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 6.33/6.61 36 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 6.33/6.61 37 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(15)].
% 6.33/6.61 38 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(37),rewrite([24(2)])].
% 6.33/6.61 39 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(16)].
% 6.33/6.61 40 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(39),rewrite([24(2)])].
% 6.33/6.61 41 leq(addition(one,star(one)),star(one)). [para(21(a,1),25(a,1,2))].
% 6.33/6.61 43 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)])].
% 6.33/6.61 46 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(20(a,1),31(a,1,1)),rewrite([24(4)]),flip(a)].
% 6.33/6.61 47 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(21(a,1),33(a,1,1)),rewrite([24(4)]),flip(a)].
% 6.33/6.61 50 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(35,a,26,a),rewrite([24(6)])].
% 6.33/6.61 52 leq(A,A). [hyper(36,b,19,a)].
% 6.33/6.61 55 leq(multiplication(A,B),multiplication(C,B)) | multiplication(addition(A,C),B) != multiplication(C,B). [para(33(a,1),36(b,1))].
% 6.33/6.61 56 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B). [para(19(a,1),38(a,1))].
% 6.33/6.61 57 -leq(addition(A,B),one) | leq(multiplication(star(B),A),one). [para(20(a,1),38(a,1,2))].
% 6.33/6.61 61 -leq(addition(A,multiplication(B,multiplication(C,D))),D) | leq(multiplication(star(multiplication(B,C)),A),D). [para(29(a,1),38(a,1,2))].
% 6.33/6.61 62 -leq(multiplication(A,addition(B,C)),C) | leq(multiplication(star(A),multiplication(A,B)),C). [para(31(a,1),38(a,1))].
% 6.33/6.61 64 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A). [para(19(a,1),40(a,1)),rewrite([29(5)])].
% 6.33/6.61 65 -leq(addition(A,B),B) | leq(multiplication(A,star(one)),B). [para(20(a,1),40(a,1,2))].
% 6.33/6.61 72 addition(one,star(one)) = star(one). [hyper(35,a,41,a),rewrite([24(7),28(7,R),19(6)])].
% 6.33/6.61 77 leq(A,addition(A,B)). [hyper(36,b,43,a)].
% 6.33/6.61 78 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(31(a,1),77(a,2))].
% 6.33/6.61 79 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(33(a,1),77(a,2))].
% 6.33/6.61 97 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(46(a,2),28(a,2,2)),rewrite([24(2)]),flip(a)].
% 6.33/6.61 101 multiplication(A,addition(B,addition(C,one))) = addition(A,multiplication(A,addition(B,C))). [para(46(a,1),31(a,1,2)),rewrite([28(4,R),31(3),24(1)]),flip(a)].
% 6.33/6.61 110 -leq(multiplication(A,addition(B,one)),A) | leq(multiplication(A,star(B)),A). [para(46(a,2),40(a,1))].
% 6.33/6.61 126 addition(A,multiplication(addition(B,one),C)) = addition(C,addition(A,multiplication(B,C))). [para(47(a,2),28(a,2,2)),rewrite([24(2)]),flip(a)].
% 6.33/6.61 190 addition(one,addition(star(A),multiplication(star(A),A))) = star(A). [para(50(a,1),28(a,1)),rewrite([28(7),24(6)]),flip(a)].
% 6.33/6.61 199 -leq(A,one) | leq(multiplication(star(A),A),one). [para(19(a,1),57(a,1))].
% 6.33/6.61 212 leq(star(one),one). [hyper(199,a,52,a),rewrite([20(4)])].
% 6.33/6.61 219 star(one) = one. [hyper(35,a,212,a),rewrite([24(4),72(4)])].
% 6.33/6.61 222 -leq(addition(A,B),B) | leq(A,B). [back_rewrite(65),rewrite([219(4),20(4)])].
% 6.33/6.61 224 -leq(addition(A,addition(B,C)),addition(A,C)) | leq(B,addition(A,C)). [para(28(a,1),222(a,1)),rewrite([24(3),24(5)])].
% 6.33/6.61 340 -leq(multiplication(A,addition(one,multiplication(B,C))),C) | leq(multiplication(star(multiplication(A,B)),A),C). [para(46(a,2),61(a,1)),rewrite([24(3)])].
% 6.33/6.61 349 addition(one,star(A)) = star(A). [para(190(a,1),43(a,1,2)),rewrite([190(9)])].
% 6.33/6.61 351 addition(one,multiplication(star(A),addition(A,one))) = star(A). [para(46(a,2),190(a,1,2))].
% 6.33/6.61 352 leq(A,multiplication(A,star(B))). [para(190(a,1),78(a,2,2)),rewrite([20(2)])].
% 6.33/6.61 353 leq(A,multiplication(star(B),A)). [para(190(a,1),79(a,2,1)),rewrite([21(2)])].
% 6.33/6.61 355 leq(one,addition(star(A),multiplication(star(A),A))). [para(190(a,1),222(a,1)),unit_del(a,77)].
% 6.33/6.61 359 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)). [hyper(35,a,352,a)].
% 6.33/6.61 362 addition(A,multiplication(star(B),A)) = multiplication(star(B),A). [hyper(35,a,353,a)].
% 6.33/6.61 379 addition(star(A),one) = star(A). [para(349(a,1),24(a,1)),flip(a)].
% 6.33/6.61 381 -leq(multiplication(A,star(B)),star(B)) | leq(multiplication(star(A),A),star(B)). [para(349(a,1),62(a,1,2)),rewrite([20(7)])].
% 6.33/6.61 387 addition(star(A),multiplication(star(A),A)) = star(A). [hyper(35,a,355,a),rewrite([190(6)]),flip(a)].
% 6.33/6.61 389 leq(one,multiplication(star(A),addition(A,one))). [para(46(a,2),355(a,2))].
% 6.33/6.61 400 multiplication(star(A),addition(A,one)) = star(A). [hyper(35,a,389,a),rewrite([351(6)]),flip(a)].
% 6.33/6.61 403 multiplication(star(A),multiplication(addition(A,one),B)) = multiplication(star(A),B). [para(400(a,1),29(a,1,1)),flip(a)].
% 6.33/6.61 409 addition(A,star(A)) = star(A). [para(400(a,1),47(a,2,2)),rewrite([379(3),400(4),24(5),28(5,R),349(4)]),flip(a)].
% 6.33/6.61 412 leq(multiplication(star(A),A),star(A)). [para(400(a,1),78(a,2))].
% 6.33/6.61 422 multiplication(star(star(A)),star(A)) = star(star(A)). [para(379(a,1),400(a,1,2))].
% 6.33/6.61 428 leq(multiplication(star(A),star(addition(A,one))),star(A)). [para(400(a,1),64(a,1)),rewrite([403(11)]),unit_del(a,52)].
% 6.33/6.61 431 addition(A,addition(B,star(A))) = addition(B,star(A)). [para(409(a,1),28(a,2,2)),rewrite([24(2)])].
% 6.33/6.61 521 leq(multiplication(star(A),star(A)),star(A)). [para(387(a,1),40(a,1)),unit_del(a,52)].
% 6.33/6.61 544 leq(multiplication(star(star(A)),multiplication(star(A),star(A))),star(A)). [hyper(56,a,521,a)].
% 6.33/6.61 545 multiplication(star(A),star(A)) = star(A). [hyper(35,a,521,a),rewrite([24(5),359(5)])].
% 6.33/6.61 546 leq(star(star(A)),star(A)). [back_rewrite(544),rewrite([545(5),422(4)])].
% 6.33/6.61 547 star(star(A)) = star(A). [hyper(35,a,546,a),rewrite([24(4),409(4)])].
% 6.33/6.61 560 addition(star(A),multiplication(star(A),B)) = multiplication(star(A),addition(B,star(A))). [para(545(a,1),31(a,1,1)),rewrite([24(7)])].
% 6.33/6.61 569 leq(multiplication(A,star(B)),star(B)) | multiplication(addition(A,star(B)),star(B)) != star(B). [para(545(a,1),55(b,2)),rewrite([545(5)])].
% 6.33/6.61 591 multiplication(star(A),star(addition(A,one))) = star(A). [hyper(35,a,428,a),rewrite([24(7),359(7)])].
% 6.33/6.61 638 leq(A,addition(B,multiplication(A,addition(C,one)))). [para(97(a,2),77(a,2))].
% 6.33/6.61 672 leq(A,addition(B,multiplication(A,star(C)))). [para(379(a,1),638(a,2,2,2))].
% 6.33/6.61 797 leq(A,multiplication(addition(A,B),star(C))). [para(33(a,1),672(a,2)),rewrite([24(1)])].
% 6.33/6.61 803 addition(A,multiplication(addition(A,B),star(C))) = multiplication(addition(A,B),star(C)). [hyper(35,a,797,a)].
% 6.33/6.61 956 addition(star(A),star(addition(A,one))) = star(A). [para(591(a,1),47(a,2,2)),rewrite([379(3),591(5),24(6)]),flip(a)].
% 6.33/6.61 1423 leq(A,addition(B,star(A))). [hyper(36,b,431,a)].
% 6.33/6.61 1426 leq(multiplication(A,B),multiplication(addition(C,star(A)),B)). [para(431(a,1),79(a,2,1))].
% 6.33/6.61 1471 leq(multiplication(star(A),B),multiplication(addition(C,star(A)),B)). [para(547(a,1),1426(a,2,1,2))].
% 6.33/6.61 1587 leq(multiplication(star(addition(A,one)),star(A)),star(addition(A,one))). [hyper(110,a,412,a)].
% 6.33/6.61 1701 leq(multiplication(star(addition(A,one)),B),multiplication(star(A),B)). [para(956(a,1),1471(a,2,1))].
% 6.33/6.61 1756 leq(multiplication(star(addition(A,one)),star(A)),star(A)). [para(545(a,1),1701(a,2))].
% 6.33/6.61 1764 multiplication(star(addition(A,one)),star(A)) = star(A). [hyper(35,a,1756,a),rewrite([24(7),362(7)])].
% 6.33/6.61 1765 leq(star(A),star(addition(A,one))). [back_rewrite(1587),rewrite([1764(5)])].
% 6.33/6.61 1773 leq(A,addition(B,multiplication(addition(C,one),A))). [para(126(a,2),77(a,2))].
% 6.33/6.61 1810 star(addition(A,one)) = star(A). [hyper(35,a,1765,a),rewrite([956(5)]),flip(a)].
% 6.33/6.61 1839 addition(addition(A,one),star(B)) = addition(A,star(B)). [para(1810(a,1),431(a,1,2,2)),rewrite([28(5),24(4),28(4,R),24(3),28(5,R),431(5),1810(7)])].
% 6.33/6.61 1840 leq(addition(A,one),addition(B,star(A))). [para(1810(a,1),1423(a,2,2))].
% 6.33/6.61 1848 leq(A,addition(B,multiplication(star(C),A))). [para(379(a,1),1773(a,2,2,1))].
% 6.33/6.61 2011 leq(A,multiplication(star(B),addition(A,C))). [para(31(a,1),1848(a,2)),rewrite([24(2)])].
% 6.33/6.61 2032 leq(A,multiplication(star(B),addition(addition(A,C),star(B)))). [para(101(a,1),2011(a,2)),rewrite([560(5)])].
% 6.33/6.61 2638 leq(A,star(addition(A,B))). [para(409(a,1),2032(a,2,2)),rewrite([545(5)])].
% 6.33/6.61 2654 addition(A,star(addition(A,B))) = star(addition(A,B)). [hyper(35,a,2638,a)].
% 6.33/6.61 4511 addition(A,addition(B,star(addition(A,C)))) = addition(B,star(addition(A,C))). [para(2654(a,1),28(a,2,2)),rewrite([24(3)])].
% 6.33/6.61 4514 leq(multiplication(A,B),multiplication(star(addition(A,C)),B)). [para(2654(a,1),79(a,2,1))].
% 6.33/6.61 4532 leq(addition(A,addition(B,one)),star(addition(A,B))). [para(2654(a,1),1840(a,2)),rewrite([24(3),28(3),24(2),28(3,R),24(2)])].
% 6.33/6.61 5062 leq(multiplication(A,star(addition(A,B))),star(addition(A,B))). [para(545(a,1),4514(a,2))].
% 6.33/6.61 5126 addition(A,star(addition(B,A))) = star(addition(B,A)). [hyper(35,a,4532,a),rewrite([24(6),28(6,R),1839(5),4511(4)])].
% 6.33/6.61 7644 leq(A,star(addition(B,A))). [para(5126(a,1),222(a,1)),unit_del(a,52)].
% 6.33/6.61 7671 leq(addition(A,B),star(addition(A,addition(B,C)))). [para(28(a,1),7644(a,2,1)),rewrite([24(2),28(3,R),24(2)])].
% 6.33/6.61 7688 leq(addition(A,B),star(addition(A,star(B)))). [para(409(a,1),7671(a,2,1,2))].
% 6.33/6.61 8571 leq(A,addition(B,A)). [para(19(a,1),224(a,1,2)),unit_del(a,52)].
% 6.33/6.61 8586 leq(addition(A,B),addition(A,addition(B,C))). [para(28(a,1),8571(a,2)),rewrite([24(2),28(3,R),24(2)])].
% 6.33/6.61 8716 leq(addition(A,B),addition(A,addition(C,star(B)))). [para(431(a,1),8586(a,2,2))].
% 6.33/6.61 8965 leq(addition(A,B),addition(B,addition(C,star(A)))). [para(24(a,1),8716(a,1))].
% 6.33/6.61 9151 leq(addition(A,B),addition(addition(B,C),star(A))). [para(43(a,1),8965(a,1)),rewrite([28(5),24(4),28(4),24(3),28(4,R),24(3),28(5,R),431(5)])].
% 6.33/6.61 9278 leq(addition(A,B),addition(addition(A,C),star(B))). [para(24(a,1),9151(a,1))].
% 6.33/6.61 9368 addition(addition(A,B),star(C)) = addition(A,addition(B,star(C))). [hyper(35,a,9278,a),rewrite([28(5),28(4),24(3),43(3),28(3),24(2),28(3,R),24(2),28(4,R),24(3),28(3),24(2),409(2)]),flip(a)].
% 6.33/6.61 13155 -leq(addition(one,multiplication(A,B)),B) | leq(star(A),B). [para(21(a,1),340(a,1)),rewrite([21(6),20(7)])].
% 6.33/6.61 13505 leq(multiplication(star(A),A),star(addition(A,B))). [hyper(381,a,5062,a)].
% 6.33/6.61 13510 leq(star(A),star(addition(A,addition(B,one)))). [para(46(a,1),13505(a,1)),rewrite([1810(3),1810(4),560(4),409(3),545(3),24(4),28(4,R),24(3)])].
% 6.33/6.61 13525 leq(star(A),star(addition(A,star(B)))). [para(379(a,1),13510(a,2,1,2))].
% 6.33/6.61 13527 leq(star(A),star(addition(A,B))). [para(2654(a,1),13525(a,2,1)),rewrite([547(4)])].
% 6.33/6.61 13528 addition(star(A),star(addition(A,B))) = star(addition(A,B)). [hyper(35,a,13527,a)].
% 6.33/6.61 19743 leq(addition(A,star(B)),star(addition(B,A))). [para(13528(a,1),7688(a,2,1)),rewrite([28(3),24(2),409(2),547(5)])].
% 6.33/6.61 19840 addition(star(A),star(addition(B,A))) = star(addition(B,A)). [hyper(35,a,19743,a),rewrite([24(3),9368(5),4511(5),24(5)])].
% 6.33/6.61 23379 leq(star(A),star(addition(B,A))). [para(19840(a,1),222(a,1)),unit_del(a,52)].
% 6.33/6.61 23418 -leq(star(addition(one,c1)),star(c1)) # answer(goals). [back_unit_del(34),unit_del(b,23379)].
% 6.33/6.61 23419 -leq(multiplication(addition(one,c1),star(c1)),star(c1)) # answer(goals). [ur(13155,b,23418,a),rewrite([803(8)])].
% 6.33/6.61 23422 $F # answer(goals). [ur(569,a,23419,a),rewrite([24(6),28(6),24(5),349(5),409(4),545(5)]),xx(a)].
% 6.33/6.61
% 6.33/6.61 % SZS output end Refutation
% 6.33/6.61 ============================== end of proof ==========================
% 6.33/6.61
% 6.33/6.61 ============================== STATISTICS ============================
% 6.33/6.61
% 6.33/6.61 Given=2192. Generated=288273. Kept=23399. proofs=1.
% 6.33/6.61 Usable=1967. Sos=9996. Demods=449. Limbo=1, Disabled=11453. Hints=0.
% 6.33/6.61 Megabytes=15.15.
% 6.33/6.61 User_CPU=5.44, System_CPU=0.19, Wall_clock=6.
% 6.33/6.61
% 6.33/6.61 ============================== end of statistics =====================
% 6.33/6.61
% 6.33/6.61 ============================== end of search =========================
% 6.33/6.61
% 6.33/6.61 THEOREM PROVED
% 6.33/6.61 % SZS status Theorem
% 6.33/6.61
% 6.33/6.61 Exiting with 1 proof.
% 6.33/6.61
% 6.33/6.61 Process 22844 exit (max_proofs) Thu Jun 16 16:07:17 2022
% 6.33/6.61 Prover9 interrupted
%------------------------------------------------------------------------------