TSTP Solution File: KLE043+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE043+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 02:21:57 EDT 2022
% Result : Theorem 131.15s 131.42s
% Output : Refutation 131.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE043+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 15:35:08 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.46/1.03 ============================== Prover9 ===============================
% 0.46/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.03 Process 3080 was started by sandbox2 on n004.cluster.edu,
% 0.46/1.03 Thu Jun 16 15:35:09 2022
% 0.46/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2927_n004.cluster.edu".
% 0.46/1.03 ============================== end of head ===========================
% 0.46/1.03
% 0.46/1.03 ============================== INPUT =================================
% 0.46/1.03
% 0.46/1.03 % Reading from file /tmp/Prover9_2927_n004.cluster.edu
% 0.46/1.03
% 0.46/1.03 set(prolog_style_variables).
% 0.46/1.03 set(auto2).
% 0.46/1.03 % set(auto2) -> set(auto).
% 0.46/1.03 % set(auto) -> set(auto_inference).
% 0.46/1.03 % set(auto) -> set(auto_setup).
% 0.46/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.03 % set(auto) -> set(auto_limits).
% 0.46/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.03 % set(auto) -> set(auto_denials).
% 0.46/1.03 % set(auto) -> set(auto_process).
% 0.46/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.03 % set(auto2) -> assign(stats, some).
% 0.46/1.03 % set(auto2) -> clear(echo_input).
% 0.46/1.03 % set(auto2) -> set(quiet).
% 0.46/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.03 % set(auto2) -> clear(print_given).
% 0.46/1.03 assign(lrs_ticks,-1).
% 0.46/1.03 assign(sos_limit,10000).
% 0.46/1.03 assign(order,kbo).
% 0.46/1.03 set(lex_order_vars).
% 0.46/1.03 clear(print_given).
% 0.46/1.03
% 0.46/1.03 % formulas(sos). % not echoed (17 formulas)
% 0.46/1.03
% 0.46/1.03 ============================== end of input ==========================
% 0.46/1.03
% 0.46/1.03 % From the command line: assign(max_seconds, 300).
% 0.46/1.03
% 0.46/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.03
% 0.46/1.03 % Formulas that are not ordinary clauses:
% 0.46/1.03 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 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].
% 0.46/1.03 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 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].
% 0.46/1.03 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 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].
% 0.46/1.03 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].
% 0.46/1.03 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 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].
% 131.15/131.42 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].
% 131.15/131.42 17 -(all X0 all X1 (leq(multiplication(star(X0),X1),addition(X1,multiplication(multiplication(X0,star(X0)),X1))) & leq(addition(X1,multiplication(multiplication(X0,star(X0)),X1)),multiplication(star(X0),X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 131.15/131.42
% 131.15/131.42 ============================== end of process non-clausal formulas ===
% 131.15/131.42
% 131.15/131.42 ============================== PROCESS INITIAL CLAUSES ===============
% 131.15/131.42
% 131.15/131.42 ============================== PREDICATE ELIMINATION =================
% 131.15/131.42
% 131.15/131.42 ============================== end predicate elimination =============
% 131.15/131.42
% 131.15/131.42 Auto_denials:
% 131.15/131.42 % copying label goals to answer in negative clause
% 131.15/131.42
% 131.15/131.42 Term ordering decisions:
% 131.15/131.42
% 131.15/131.42 % Assigning unary symbol star kb_weight 0 and highest precedence (9).
% 131.15/131.42 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. star=0.
% 131.15/131.42
% 131.15/131.42 ============================== end of process initial clauses ========
% 131.15/131.42
% 131.15/131.42 ============================== CLAUSES FOR SEARCH ====================
% 131.15/131.42
% 131.15/131.42 ============================== end of clauses for search =============
% 131.15/131.42
% 131.15/131.42 ============================== SEARCH ================================
% 131.15/131.42
% 131.15/131.42 % Starting search at 0.01 seconds.
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=38.000, iters=3455
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=35.000, iters=3359
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=33.000, iters=3387
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=32.000, iters=3365
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=31.000, iters=3388
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=30.000, iters=3356
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=29.000, iters=3335
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=27.000, iters=3406
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=25.000, iters=3345
% 131.15/131.42
% 131.15/131.42 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 40 (0.00 of 0.88 sec).
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=24.000, iters=3345
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=23.000, iters=3336
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=22.000, iters=3361
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=21.000, iters=3335
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=20.000, iters=3353
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=6116, wt=48.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=6156, wt=47.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=6506, wt=46.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=6514, wt=45.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=6372, wt=44.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=6526, wt=43.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=4127, wt=42.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=6496, wt=41.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=6505, wt=40.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=11489, wt=19.000
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=19.000, iters=3369
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=11765, wt=18.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=12227, wt=17.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=12246, wt=15.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=12282, wt=14.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=12303, wt=13.000
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=12919, wt=12.000
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=18.000, iters=3335
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=17.000, iters=5027
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=15.000, iters=3379
% 131.15/131.42
% 131.15/131.42 Low Water (displace): id=18918, wt=11.000
% 131.15/131.42
% 131.15/131.42 Low Water (keep): wt=14.000, iters=5270
% 131.15/131.42
% 131.15/131.42 ============================== PROOF =================================
% 131.15/131.42 % SZS status Theorem
% 131.15/131.42 % SZS output start Refutation
% 131.15/131.42
% 131.15/131.42 % Proof 1 at 126.92 (+ 3.49) seconds: goals.
% 131.15/131.42 % Length of proof is 196.
% 131.15/131.42 % Level of proof is 35.
% 131.15/131.42 % Maximum clause weight is 29.000.
% 131.15/131.42 % Given clauses 16186.
% 131.15/131.42
% 131.15/131.42 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 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].
% 131.15/131.42 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 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].
% 131.15/131.42 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 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].
% 131.15/131.42 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].
% 131.15/131.42 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 131.15/131.42 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].
% 131.15/131.42 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].
% 131.15/131.42 17 -(all X0 all X1 (leq(multiplication(star(X0),X1),addition(X1,multiplication(multiplication(X0,star(X0)),X1))) & leq(addition(X1,multiplication(multiplication(X0,star(X0)),X1)),multiplication(star(X0),X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 131.15/131.42 18 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 131.15/131.42 19 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 131.15/131.42 20 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 131.15/131.42 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 131.15/131.42 22 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 131.15/131.42 23 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 131.15/131.42 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 131.15/131.42 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(13)].
% 131.15/131.42 26 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 131.15/131.42 27 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 131.15/131.42 28 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(27),rewrite([24(2)]),flip(a)].
% 131.15/131.42 29 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 131.15/131.42 30 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 131.15/131.42 31 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(30),flip(a)].
% 131.15/131.42 32 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 131.15/131.42 33 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(32),flip(a)].
% 131.15/131.42 34 -leq(multiplication(star(c1),c2),addition(c2,multiplication(multiplication(c1,star(c1)),c2))) | -leq(addition(c2,multiplication(multiplication(c1,star(c1)),c2)),multiplication(star(c1),c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 131.15/131.42 35 -leq(multiplication(star(c1),c2),addition(c2,multiplication(c1,multiplication(star(c1),c2)))) | -leq(addition(c2,multiplication(c1,multiplication(star(c1),c2))),multiplication(star(c1),c2)) # answer(goals). [copy(34),rewrite([29(11),29(20)])].
% 131.15/131.43 36 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 131.15/131.43 37 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 131.15/131.43 38 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(15)].
% 131.15/131.43 39 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(38),rewrite([24(2)])].
% 131.15/131.43 40 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(16)].
% 131.15/131.43 41 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(40),rewrite([24(2)])].
% 131.15/131.43 42 leq(addition(one,star(one)),star(one)). [para(21(a,1),25(a,1,2))].
% 131.15/131.43 43 leq(addition(zero,one),star(zero)). [para(23(a,1),25(a,1,2)),rewrite([24(3)])].
% 131.15/131.43 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)])].
% 131.15/131.43 47 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(20(a,1),31(a,1,1)),rewrite([24(4)]),flip(a)].
% 131.15/131.43 48 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(21(a,1),33(a,1,1)),rewrite([24(4)]),flip(a)].
% 131.15/131.43 49 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(29(a,1),33(a,1,1)),rewrite([24(6)])].
% 131.15/131.43 51 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(36,a,26,a),rewrite([24(6)])].
% 131.15/131.43 52 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(36,a,25,a),rewrite([24(6)])].
% 131.15/131.43 53 leq(A,A). [hyper(37,b,19,a)].
% 131.15/131.43 57 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B). [para(19(a,1),39(a,1))].
% 131.15/131.43 58 -leq(addition(A,B),one) | leq(multiplication(star(B),A),one). [para(20(a,1),39(a,1,2))].
% 131.15/131.43 61 -leq(A,B) | leq(multiplication(star(zero),A),B). [para(23(a,1),39(a,1,2)),rewrite([18(2)])].
% 131.15/131.43 62 -leq(addition(A,multiplication(B,multiplication(C,D))),D) | leq(multiplication(star(multiplication(B,C)),A),D). [para(29(a,1),39(a,1,2))].
% 131.15/131.43 63 -leq(multiplication(A,addition(B,C)),C) | leq(multiplication(star(A),multiplication(A,B)),C). [para(31(a,1),39(a,1))].
% 131.15/131.43 65 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A). [para(19(a,1),41(a,1)),rewrite([29(5)])].
% 131.15/131.43 66 -leq(addition(A,B),B) | leq(multiplication(A,star(one)),B). [para(20(a,1),41(a,1,2))].
% 131.15/131.43 72 -leq(multiplication(addition(A,B),C),B) | leq(multiplication(A,multiplication(C,star(C))),B). [para(33(a,1),41(a,1)),rewrite([29(6)])].
% 131.15/131.43 73 addition(one,star(one)) = star(one). [hyper(36,a,42,a),rewrite([24(7),28(7,R),19(6)])].
% 131.15/131.43 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)])].
% 131.15/131.43 78 leq(A,addition(A,B)). [hyper(37,b,44,a)].
% 131.15/131.43 79 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(31(a,1),78(a,2))].
% 131.15/131.43 80 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(33(a,1),78(a,2))].
% 131.15/131.43 89 leq(multiplication(star(zero),A),A). [hyper(61,a,53,a)].
% 131.15/131.43 96 multiplication(A,addition(zero,one)) = A. [para(22(a,1),47(a,2,2)),rewrite([18(6)])].
% 131.15/131.43 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)].
% 131.15/131.43 102 multiplication(A,addition(B,addition(C,one))) = addition(A,multiplication(A,addition(B,C))). [para(47(a,1),31(a,1,2)),rewrite([28(4,R),31(3),24(1)]),flip(a)].
% 131.15/131.43 111 -leq(multiplication(A,addition(B,one)),A) | leq(multiplication(A,star(B)),A). [para(47(a,2),41(a,1))].
% 131.15/131.43 118 leq(star(zero),one). [para(20(a,1),89(a,1))].
% 131.15/131.43 120 addition(one,star(zero)) = one. [hyper(36,a,118,a),rewrite([24(4)])].
% 131.15/131.43 121 addition(zero,one) = star(zero). [back_rewrite(74),rewrite([120(5)])].
% 131.15/131.43 122 multiplication(A,star(zero)) = A. [back_rewrite(96),rewrite([121(3)])].
% 131.15/131.43 127 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)].
% 131.15/131.43 129 multiplication(addition(one,multiplication(A,B)),C) = addition(C,multiplication(A,multiplication(B,C))). [para(29(a,1),48(a,2,2)),rewrite([24(3)])].
% 131.15/131.43 131 addition(A,addition(multiplication(B,A),multiplication(addition(B,one),C))) = multiplication(addition(B,one),addition(C,A)). [para(48(a,1),31(a,1,2)),rewrite([28(6,R)])].
% 131.15/131.43 145 multiplication(addition(A,one),A) = multiplication(A,addition(A,one)). [para(48(a,2),47(a,2)),flip(a)].
% 131.15/131.43 146 star(zero) = one. [para(122(a,1),21(a,1)),flip(a)].
% 131.15/131.43 153 leq(multiplication(A,multiplication(B,C)),multiplication(D,C)) | multiplication(addition(D,multiplication(A,B)),C) != multiplication(D,C). [para(49(a,1),37(b,1))].
% 131.15/131.43 165 leq(multiplication(A,multiplication(B,C)),multiplication(A,multiplication(addition(B,D),C))). [para(33(a,1),79(a,2,2))].
% 131.15/131.43 191 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)].
% 131.15/131.43 200 -leq(A,one) | leq(multiplication(star(A),A),one). [para(19(a,1),58(a,1))].
% 131.15/131.43 213 leq(star(one),one). [hyper(200,a,53,a),rewrite([20(4)])].
% 131.15/131.43 220 star(one) = one. [hyper(36,a,213,a),rewrite([24(4),73(4)])].
% 131.15/131.43 223 -leq(addition(A,B),B) | leq(A,B). [back_rewrite(66),rewrite([220(4),20(4)])].
% 131.15/131.43 224 -leq(addition(A,B),A) | leq(B,A). [para(24(a,1),223(a,1))].
% 131.15/131.43 225 -leq(addition(A,addition(B,C)),addition(A,C)) | leq(B,addition(A,C)). [para(28(a,1),223(a,1)),rewrite([24(3),24(5)])].
% 131.15/131.43 234 -leq(addition(A,addition(B,C)),C) | leq(addition(A,B),C). [para(28(a,2),224(a,1))].
% 131.15/131.43 267 multiplication(addition(A,one),multiplication(A,B)) = multiplication(A,multiplication(addition(A,one),B)). [para(145(a,1),29(a,1,1)),rewrite([29(4)]),flip(a)].
% 131.15/131.43 341 -leq(multiplication(A,addition(one,multiplication(B,C))),C) | leq(multiplication(star(multiplication(A,B)),A),C). [para(47(a,2),62(a,1)),rewrite([24(3)])].
% 131.15/131.43 350 addition(one,star(A)) = star(A). [para(191(a,1),44(a,1,2)),rewrite([191(9)])].
% 131.15/131.43 352 addition(one,multiplication(star(A),addition(A,one))) = star(A). [para(47(a,2),191(a,1,2))].
% 131.15/131.43 353 leq(A,multiplication(A,star(B))). [para(191(a,1),79(a,2,2)),rewrite([20(2)])].
% 131.15/131.43 354 leq(A,multiplication(star(B),A)). [para(191(a,1),80(a,2,1)),rewrite([21(2)])].
% 131.15/131.43 356 leq(one,addition(star(A),multiplication(star(A),A))). [para(191(a,1),223(a,1)),unit_del(a,78)].
% 131.15/131.43 360 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)). [hyper(36,a,353,a)].
% 131.15/131.43 361 leq(multiplication(A,B),multiplication(A,multiplication(B,star(C)))). [para(29(a,1),353(a,2))].
% 131.15/131.43 363 addition(A,multiplication(star(B),A)) = multiplication(star(B),A). [hyper(36,a,354,a)].
% 131.15/131.43 373 -leq(multiplication(A,multiplication(addition(B,one),C)),multiplication(B,C)) | leq(multiplication(star(A),multiplication(A,C)),multiplication(B,C)). [para(48(a,2),63(a,1,2))].
% 131.15/131.43 380 addition(star(A),one) = star(A). [para(350(a,1),24(a,1)),flip(a)].
% 131.15/131.43 382 -leq(multiplication(A,star(B)),star(B)) | leq(multiplication(star(A),A),star(B)). [para(350(a,1),63(a,1,2)),rewrite([20(7)])].
% 131.15/131.43 388 addition(star(A),multiplication(star(A),A)) = star(A). [hyper(36,a,356,a),rewrite([191(6)]),flip(a)].
% 131.15/131.43 390 leq(one,multiplication(star(A),addition(A,one))). [para(47(a,2),356(a,2))].
% 131.15/131.43 401 multiplication(star(A),addition(A,one)) = star(A). [hyper(36,a,390,a),rewrite([352(6)]),flip(a)].
% 131.15/131.43 404 multiplication(star(A),multiplication(addition(A,one),B)) = multiplication(star(A),B). [para(401(a,1),29(a,1,1)),flip(a)].
% 131.15/131.43 410 addition(A,star(A)) = star(A). [para(401(a,1),48(a,2,2)),rewrite([380(3),401(4),24(5),28(5,R),350(4)]),flip(a)].
% 131.15/131.43 413 leq(multiplication(star(A),A),star(A)). [para(401(a,1),79(a,2))].
% 131.15/131.43 423 multiplication(star(star(A)),star(A)) = star(star(A)). [para(380(a,1),401(a,1,2))].
% 131.15/131.43 429 leq(multiplication(star(A),star(addition(A,one))),star(A)). [para(401(a,1),65(a,1)),rewrite([404(11)]),unit_del(a,53)].
% 131.15/131.43 432 addition(A,addition(B,star(A))) = addition(B,star(A)). [para(410(a,1),28(a,2,2)),rewrite([24(2)])].
% 131.15/131.43 497 -leq(multiplication(A,multiplication(addition(B,one),C)),multiplication(A,B)) | leq(multiplication(A,multiplication(C,star(C))),multiplication(A,B)). [para(47(a,2),72(a,1,1)),rewrite([29(4)])].
% 131.15/131.43 522 leq(multiplication(star(A),star(A)),star(A)). [para(388(a,1),41(a,1)),unit_del(a,53)].
% 131.15/131.43 545 leq(multiplication(star(star(A)),multiplication(star(A),star(A))),star(A)). [hyper(57,a,522,a)].
% 131.15/131.43 546 multiplication(star(A),star(A)) = star(A). [hyper(36,a,522,a),rewrite([24(5),360(5)])].
% 131.15/131.43 547 leq(star(star(A)),star(A)). [back_rewrite(545),rewrite([546(5),423(4)])].
% 131.15/131.43 548 star(star(A)) = star(A). [hyper(36,a,547,a),rewrite([24(4),410(4)])].
% 131.15/131.43 560 multiplication(star(A),multiplication(star(A),B)) = multiplication(star(A),B). [para(546(a,1),29(a,1,1)),flip(a)].
% 131.15/131.43 561 addition(star(A),multiplication(star(A),B)) = multiplication(star(A),addition(B,star(A))). [para(546(a,1),31(a,1,1)),rewrite([24(7)])].
% 131.15/131.43 592 multiplication(star(A),star(addition(A,one))) = star(A). [hyper(36,a,429,a),rewrite([24(7),360(7)])].
% 131.15/131.43 639 leq(A,addition(B,multiplication(A,addition(C,one)))). [para(98(a,2),78(a,2))].
% 131.15/131.43 673 leq(A,addition(B,multiplication(A,star(C)))). [para(380(a,1),639(a,2,2,2))].
% 131.15/131.43 798 leq(A,multiplication(addition(A,B),star(C))). [para(33(a,1),673(a,2)),rewrite([24(1)])].
% 131.15/131.43 807 leq(A,multiplication(A,multiplication(addition(B,one),star(C)))). [para(47(a,2),798(a,2,1)),rewrite([29(5)])].
% 131.15/131.43 957 addition(star(A),star(addition(A,one))) = star(A). [para(592(a,1),48(a,2,2)),rewrite([380(3),592(5),24(6)]),flip(a)].
% 131.15/131.43 1058 leq(one,multiplication(addition(A,one),star(B))). [para(21(a,1),807(a,2))].
% 131.15/131.43 1096 addition(one,multiplication(addition(A,one),star(B))) = multiplication(addition(A,one),star(B)). [hyper(36,a,1058,a)].
% 131.15/131.43 1427 leq(multiplication(A,B),multiplication(addition(C,star(A)),B)). [para(432(a,1),80(a,2,1))].
% 131.15/131.43 1472 leq(multiplication(star(A),B),multiplication(addition(C,star(A)),B)). [para(548(a,1),1427(a,2,1,2))].
% 131.15/131.43 1478 leq(multiplication(addition(A,one),B),multiplication(star(A),B)). [para(957(a,1),1427(a,2,1))].
% 131.15/131.43 1588 leq(multiplication(star(addition(A,one)),star(A)),star(addition(A,one))). [hyper(111,a,413,a)].
% 131.15/131.43 1702 leq(multiplication(star(addition(A,one)),B),multiplication(star(A),B)). [para(957(a,1),1472(a,2,1))].
% 131.15/131.43 1757 leq(multiplication(star(addition(A,one)),star(A)),star(A)). [para(546(a,1),1702(a,2))].
% 131.15/131.43 1765 multiplication(star(addition(A,one)),star(A)) = star(A). [hyper(36,a,1757,a),rewrite([24(7),363(7)])].
% 131.15/131.43 1766 leq(star(A),star(addition(A,one))). [back_rewrite(1588),rewrite([1765(5)])].
% 131.15/131.43 1774 leq(A,addition(B,multiplication(addition(C,one),A))). [para(127(a,2),78(a,2))].
% 131.15/131.43 1780 multiplication(addition(A,one),star(A)) = star(A). [para(127(a,2),52(a,1)),rewrite([1096(6)])].
% 131.15/131.43 1811 star(addition(A,one)) = star(A). [hyper(36,a,1766,a),rewrite([957(5)]),flip(a)].
% 131.15/131.43 1849 leq(A,addition(B,multiplication(star(C),A))). [para(380(a,1),1774(a,2,2,1))].
% 131.15/131.43 2012 leq(A,multiplication(star(B),addition(A,C))). [para(31(a,1),1849(a,2)),rewrite([24(2)])].
% 131.15/131.43 2033 leq(A,multiplication(star(B),addition(addition(A,C),star(B)))). [para(102(a,1),2012(a,2)),rewrite([561(5)])].
% 131.15/131.43 2057 -leq(multiplication(star(c1),c2),addition(c2,multiplication(c1,multiplication(star(c1),c2)))) | -leq(multiplication(addition(one,multiplication(c1,star(c1))),c2),multiplication(star(c1),c2)) # answer(goals). [para(129(a,2),35(b,1))].
% 131.15/131.43 2070 multiplication(addition(one,multiplication(A,B)),A) = multiplication(A,addition(one,multiplication(B,A))). [para(129(a,2),47(a,2)),rewrite([24(3)]),flip(a)].
% 131.15/131.43 2312 addition(star(A),addition(one,multiplication(B,star(A)))) = multiplication(addition(B,one),star(A)). [para(350(a,1),131(a,2,2)),rewrite([20(7),28(6),24(5),360(5)])].
% 131.15/131.43 2640 leq(A,star(addition(A,B))). [para(410(a,1),2033(a,2,2)),rewrite([546(5)])].
% 131.15/131.43 2656 addition(A,star(addition(A,B))) = star(addition(A,B)). [hyper(36,a,2640,a)].
% 131.15/131.43 3420 leq(multiplication(A,B),C) | addition(C,multiplication(A,B)) != C. [para(20(a,1),153(b,1)),rewrite([20(2),20(3),20(6)])].
% 131.15/131.43 4516 leq(multiplication(A,B),multiplication(star(addition(A,C)),B)). [para(2656(a,1),80(a,2,1))].
% 131.15/131.43 5064 leq(multiplication(A,star(addition(A,B))),star(addition(A,B))). [para(546(a,1),4516(a,2))].
% 131.15/131.43 5292 leq(multiplication(A,multiplication(B,C)),multiplication(A,multiplication(star(B),C))). [para(410(a,1),165(a,2,2,1))].
% 131.15/131.43 5320 leq(multiplication(A,multiplication(B,star(B))),multiplication(A,star(B))). [para(1780(a,1),165(a,2,2))].
% 131.15/131.43 8578 leq(A,addition(B,addition(A,C))). [para(44(a,1),225(a,1,2)),unit_del(a,53)].
% 131.15/131.43 8598 leq(A,addition(B,addition(C,multiplication(A,addition(D,one))))). [para(98(a,2),8578(a,2,2))].
% 131.15/131.43 10233 leq(A,addition(B,addition(C,multiplication(A,star(D))))). [para(380(a,1),8598(a,2,2,2,2))].
% 131.15/131.43 10240 leq(A,addition(B,multiplication(addition(A,C),star(D)))). [para(33(a,1),10233(a,2,2)),rewrite([24(1)])].
% 131.15/131.43 10262 leq(A,multiplication(addition(addition(A,B),multiplication(C,D)),star(E))). [para(49(a,1),10240(a,2))].
% 131.15/131.43 12548 -leq(addition(A,multiplication(star(B),C)),C) | leq(multiplication(star(B),A),C). [para(560(a,1),62(a,1,2)),rewrite([546(7),548(6)])].
% 131.15/131.43 13157 -leq(addition(one,multiplication(A,B)),B) | leq(star(A),B). [para(21(a,1),341(a,1)),rewrite([21(6),20(7)])].
% 131.15/131.43 13169 -leq(addition(one,multiplication(A,multiplication(B,C))),C) | leq(star(multiplication(A,B)),C). [para(29(a,1),13157(a,1,2))].
% 131.15/131.43 13282 leq(multiplication(star(A),multiplication(A,B)),multiplication(star(A),B)). [para(267(a,1),5292(a,2)),rewrite([380(3),380(7),560(7)])].
% 131.15/131.43 13390 leq(multiplication(star(A),multiplication(A,star(A))),multiplication(A,star(A))). [hyper(373,a,5320,a),rewrite([1811(4),1811(7)])].
% 131.15/131.43 13507 leq(multiplication(star(A),A),star(addition(A,B))). [hyper(382,a,5064,a)].
% 131.15/131.43 13512 leq(star(A),star(addition(A,addition(B,one)))). [para(47(a,1),13507(a,1)),rewrite([1811(3),1811(4),561(4),410(3),546(3),24(4),28(4,R),24(3)])].
% 131.15/131.43 13527 leq(star(A),star(addition(A,star(B)))). [para(380(a,1),13512(a,2,1,2))].
% 131.15/131.43 13529 leq(star(A),star(addition(A,B))). [para(2656(a,1),13527(a,2,1)),rewrite([548(4)])].
% 131.15/131.43 13531 leq(star(multiplication(A,B)),star(multiplication(A,addition(B,C)))). [para(31(a,1),13529(a,2,1))].
% 131.15/131.43 13532 leq(star(multiplication(A,B)),star(multiplication(addition(A,C),B))). [para(33(a,1),13529(a,2,1))].
% 131.15/131.43 13541 leq(star(A),star(multiplication(A,star(B)))). [para(360(a,1),13529(a,2,1))].
% 131.15/131.43 13542 leq(star(A),star(multiplication(star(B),A))). [para(363(a,1),13529(a,2,1))].
% 131.15/131.43 13553 addition(star(A),star(multiplication(A,star(B)))) = star(multiplication(A,star(B))). [hyper(36,a,13541,a)].
% 131.15/131.43 13562 addition(star(A),star(multiplication(star(B),A))) = star(multiplication(star(B),A)). [hyper(36,a,13542,a)].
% 131.15/131.43 13607 leq(star(multiplication(star(A),A)),star(A)). [para(401(a,1),13531(a,2,1)),rewrite([548(5)])].
% 131.15/131.43 13620 star(multiplication(star(A),A)) = star(A). [hyper(36,a,13607,a),rewrite([24(5),13562(5)])].
% 131.15/131.43 13641 multiplication(star(A),addition(one,multiplication(A,star(A)))) = star(A). [para(13620(a,1),1780(a,1,2)),rewrite([24(4),2070(6),13620(9)])].
% 131.15/131.43 14773 leq(star(multiplication(A,star(A))),star(A)). [para(1780(a,1),13532(a,2,1)),rewrite([548(5)])].
% 131.15/131.43 14784 star(multiplication(A,star(A))) = star(A). [hyper(36,a,14773,a),rewrite([24(5),13553(5)])].
% 131.15/131.43 14797 leq(multiplication(addition(one,multiplication(A,star(A))),B),multiplication(star(A),B)). [para(14784(a,1),1478(a,2,1)),rewrite([24(4)])].
% 131.15/131.43 15044 -leq(multiplication(star(c1),c2),addition(c2,multiplication(c1,multiplication(star(c1),c2)))) # answer(goals). [back_unit_del(2057),unit_del(b,14797)].
% 131.15/131.43 15064 -leq(multiplication(star(c1),c2),multiplication(addition(one,multiplication(c1,star(c1))),c2)) # answer(goals). [para(129(a,2),15044(a,2))].
% 131.15/131.43 16108 leq(multiplication(star(A),multiplication(A,star(A))),multiplication(star(A),A)). [hyper(497,a,13282,a),rewrite([1811(3),1811(7)])].
% 131.15/131.43 16557 leq(A,addition(addition(A,B),multiplication(C,D))). [para(146(a,1),10262(a,2,2)),rewrite([20(5)])].
% 131.15/131.43 16571 addition(A,addition(addition(A,B),multiplication(C,D))) = addition(addition(A,B),multiplication(C,D)). [hyper(36,a,16557,a)].
% 131.15/131.43 18555 multiplication(star(A),multiplication(A,star(A))) = multiplication(A,star(A)). [hyper(36,a,13390,a),rewrite([24(7),363(7)])].
% 131.15/131.43 18569 leq(multiplication(A,star(A)),multiplication(star(A),A)). [back_rewrite(16108),rewrite([18555(4)])].
% 131.15/131.43 18602 addition(multiplication(A,star(A)),multiplication(star(A),A)) = multiplication(star(A),A). [hyper(36,a,18569,a)].
% 131.15/131.43 21959 leq(multiplication(star(A),A),multiplication(A,star(A))). [para(18555(a,1),361(a,2))].
% 131.15/131.43 21979 multiplication(star(A),A) = multiplication(A,star(A)). [hyper(36,a,21959,a),rewrite([24(5),18602(5)])].
% 131.15/131.43 22037 multiplication(star(A),multiplication(A,B)) = multiplication(A,multiplication(star(A),B)). [para(21979(a,1),29(a,1,1)),rewrite([29(3)]),flip(a)].
% 131.15/131.43 29290 -leq(addition(c2,multiplication(star(c1),multiplication(addition(one,multiplication(c1,star(c1))),c2))),multiplication(addition(one,multiplication(c1,star(c1))),c2)) # answer(goals). [ur(12548,b,15064,a)].
% 131.15/131.43 29292 -leq(addition(c2,multiplication(star(c1),multiplication(addition(one,multiplication(c1,star(c1))),c2))),addition(c2,multiplication(c1,multiplication(star(c1),c2)))) # answer(goals). [para(129(a,1),29290(a,2))].
% 131.15/131.43 29294 -leq(addition(addition(c2,multiplication(c1,multiplication(star(c1),c2))),multiplication(star(c1),multiplication(addition(one,multiplication(c1,star(c1))),c2))),addition(c2,multiplication(c1,multiplication(star(c1),c2)))) # answer(goals). [ur(234,b,29292,a),rewrite([24(21),16571(22)])].
% 131.15/131.43 29297 -leq(multiplication(star(c1),multiplication(addition(one,multiplication(c1,star(c1))),c2)),addition(c2,multiplication(c1,multiplication(star(c1),c2)))) # answer(goals). [para(129(a,2),29294(a,1,1)),rewrite([363(20)])].
% 131.15/131.43 29300 -leq(multiplication(star(c1),multiplication(addition(one,multiplication(c1,star(c1))),c2)),multiplication(addition(one,multiplication(c1,star(c1))),c2)) # answer(goals). [para(129(a,2),29297(a,2))].
% 131.15/131.43 29301 multiplication(star(c1),multiplication(addition(one,multiplication(c1,star(c1))),c2)) != multiplication(addition(one,multiplication(c1,star(c1))),c2) # answer(goals). [ur(3420,a,29300,a),rewrite([363(20)])].
% 131.15/131.43 36344 -leq(addition(one,multiplication(A,multiplication(star(A),B))),B) | leq(star(A),B). [para(22037(a,1),13169(a,1,2)),rewrite([21979(8),14784(9)])].
% 131.15/131.43 36345 leq(star(A),addition(one,multiplication(A,star(A)))). [para(13641(a,1),36344(a,1,2,2)),unit_del(a,53)].
% 131.15/131.43 36347 addition(one,multiplication(A,star(A))) = star(A). [hyper(36,a,36345,a),rewrite([2312(6),1780(4)]),flip(a)].
% 131.15/131.43 36362 $F # answer(goals). [back_rewrite(29301),rewrite([36347(8),560(7),36347(10)]),xx(a)].
% 131.15/131.43
% 131.15/131.43 % SZS output end Refutation
% 131.15/131.43 ============================== end of proof ==========================
% 131.15/131.43
% 131.15/131.43 ============================== STATISTICS ============================
% 131.15/131.43
% 131.15/131.43 Given=16186. Generated=6381220. Kept=36338. proofs=1.
% 131.15/131.43 Usable=15167. Sos=6144. Demods=424. Limbo=15, Disabled=15030. Hints=0.
% 131.15/131.43 Megabytes=22.70.
% 131.15/131.43 User_CPU=126.93, System_CPU=3.49, Wall_clock=131.
% 131.15/131.43
% 131.15/131.43 ============================== end of statistics =====================
% 131.15/131.43
% 131.15/131.43 ============================== end of search =========================
% 131.15/131.43
% 131.15/131.43 THEOREM PROVED
% 131.15/131.43 % SZS status Theorem
% 131.15/131.43
% 131.15/131.43 Exiting with 1 proof.
% 131.15/131.43
% 131.15/131.43 Process 3080 exit (max_proofs) Thu Jun 16 15:37:20 2022
% 131.15/131.43 Prover9 interrupted
%------------------------------------------------------------------------------