TSTP Solution File: KLE046+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE046+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 30.50s 30.80s
% Output : Refutation 30.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE046+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 16:08:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.98 ============================== Prover9 ===============================
% 0.41/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.98 Process 7040 was started by sandbox2 on n003.cluster.edu,
% 0.41/0.98 Thu Jun 16 16:08:27 2022
% 0.41/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6887_n003.cluster.edu".
% 0.41/0.98 ============================== end of head ===========================
% 0.41/0.98
% 0.41/0.98 ============================== INPUT =================================
% 0.41/0.98
% 0.41/0.98 % Reading from file /tmp/Prover9_6887_n003.cluster.edu
% 0.41/0.98
% 0.41/0.98 set(prolog_style_variables).
% 0.41/0.98 set(auto2).
% 0.41/0.98 % set(auto2) -> set(auto).
% 0.41/0.98 % set(auto) -> set(auto_inference).
% 0.41/0.98 % set(auto) -> set(auto_setup).
% 0.41/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.98 % set(auto) -> set(auto_limits).
% 0.41/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.98 % set(auto) -> set(auto_denials).
% 0.41/0.98 % set(auto) -> set(auto_process).
% 0.41/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.98 % set(auto2) -> assign(stats, some).
% 0.41/0.98 % set(auto2) -> clear(echo_input).
% 0.41/0.98 % set(auto2) -> set(quiet).
% 0.41/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.98 % set(auto2) -> clear(print_given).
% 0.41/0.98 assign(lrs_ticks,-1).
% 0.41/0.98 assign(sos_limit,10000).
% 0.41/0.98 assign(order,kbo).
% 0.41/0.98 set(lex_order_vars).
% 0.41/0.98 clear(print_given).
% 0.41/0.98
% 0.41/0.98 % formulas(sos). % not echoed (17 formulas)
% 0.41/0.98
% 0.41/0.98 ============================== end of input ==========================
% 0.41/0.98
% 0.41/0.98 % From the command line: assign(max_seconds, 300).
% 0.41/0.98
% 0.41/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.98
% 0.41/0.98 % Formulas that are not ordinary clauses:
% 0.41/0.98 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 0.41/0.98 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 0.41/0.98 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 0.41/0.98 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].
% 0.41/0.98 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 30.50/30.80 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].
% 30.50/30.80 17 -(all X0 all X1 (leq(multiplication(star(X1),star(X0)),multiplication(star(X0),star(X1))) -> leq(star(addition(X0,X1)),multiplication(star(X0),star(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 30.50/30.80
% 30.50/30.80 ============================== end of process non-clausal formulas ===
% 30.50/30.80
% 30.50/30.80 ============================== PROCESS INITIAL CLAUSES ===============
% 30.50/30.80
% 30.50/30.80 ============================== PREDICATE ELIMINATION =================
% 30.50/30.80
% 30.50/30.80 ============================== end predicate elimination =============
% 30.50/30.80
% 30.50/30.80 Auto_denials:
% 30.50/30.80 % copying label goals to answer in negative clause
% 30.50/30.80
% 30.50/30.80 Term ordering decisions:
% 30.50/30.80
% 30.50/30.80 % Assigning unary symbol star kb_weight 0 and highest precedence (9).
% 30.50/30.80 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. star=0.
% 30.50/30.80
% 30.50/30.80 ============================== end of process initial clauses ========
% 30.50/30.80
% 30.50/30.80 ============================== CLAUSES FOR SEARCH ====================
% 30.50/30.80
% 30.50/30.80 ============================== end of clauses for search =============
% 30.50/30.80
% 30.50/30.80 ============================== SEARCH ================================
% 30.50/30.80
% 30.50/30.80 % Starting search at 0.01 seconds.
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=48.000, iters=3444
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=40.000, iters=3422
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=37.000, iters=3335
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=35.000, iters=3506
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=34.000, iters=3440
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=31.000, iters=3339
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=29.000, iters=3345
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=28.000, iters=3350
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=27.000, iters=3453
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=25.000, iters=3380
% 30.50/30.80
% 30.50/30.80 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 39 (0.00 of 0.89 sec).
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=23.000, iters=3341
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=22.000, iters=3388
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=21.000, iters=3335
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=20.000, iters=3338
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=19.000, iters=5172
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=5983, wt=46.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=6124, wt=45.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=4123, wt=44.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=5080, wt=43.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=4302, wt=42.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=5094, wt=41.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=5995, wt=40.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=6134, wt=39.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=14063, wt=18.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=14655, wt=16.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=14754, wt=14.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=15338, wt=13.000
% 30.50/30.80
% 30.50/30.80 Low Water (displace): id=17447, wt=12.000
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=18.000, iters=3338
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=17.000, iters=5610
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=15.000, iters=3397
% 30.50/30.80
% 30.50/30.80 Low Water (keep): wt=14.000, iters=4088
% 30.50/30.80
% 30.50/30.80 ============================== PROOF =================================
% 30.50/30.80 % SZS status Theorem
% 30.50/30.80 % SZS output start Refutation
% 30.50/30.80
% 30.50/30.80 % Proof 1 at 29.05 (+ 0.79) seconds: goals.
% 30.50/30.80 % Length of proof is 182.
% 30.50/30.80 % Level of proof is 28.
% 30.50/30.80 % Maximum clause weight is 21.000.
% 30.50/30.80 % Given clauses 5824.
% 30.50/30.80
% 30.50/30.80 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 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].
% 30.50/30.80 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 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].
% 30.50/30.80 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 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].
% 30.50/30.80 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].
% 30.50/30.80 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 30.50/30.80 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].
% 30.50/30.80 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].
% 30.50/30.80 17 -(all X0 all X1 (leq(multiplication(star(X1),star(X0)),multiplication(star(X0),star(X1))) -> leq(star(addition(X0,X1)),multiplication(star(X0),star(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 30.50/30.80 18 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 30.50/30.80 19 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 30.50/30.80 20 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 30.50/30.80 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 30.50/30.80 22 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 30.50/30.80 23 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 30.50/30.80 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 30.50/30.80 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(13)].
% 30.50/30.80 26 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 30.50/30.80 27 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 30.50/30.80 28 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(27),rewrite([24(2)]),flip(a)].
% 30.50/30.80 29 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 30.50/30.80 30 leq(multiplication(star(c2),star(c1)),multiplication(star(c1),star(c2))) # label(goals) # label(negated_conjecture). [clausify(17)].
% 30.50/30.80 31 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 30.50/30.80 32 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(31),flip(a)].
% 30.50/30.80 33 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 30.50/30.80 34 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(33),flip(a)].
% 30.50/30.80 35 -leq(star(addition(c1,c2)),multiplication(star(c1),star(c2))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 30.50/30.80 36 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 30.50/30.80 37 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 30.50/30.80 38 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(15)].
% 30.50/30.80 39 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(38),rewrite([24(2)])].
% 30.50/30.80 40 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(16)].
% 30.50/30.80 41 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(40),rewrite([24(2)])].
% 30.50/30.80 43 leq(addition(zero,one),star(zero)). [para(23(a,1),25(a,1,2)),rewrite([24(3)])].
% 30.50/30.80 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)])].
% 30.50/30.80 47 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(20(a,1),32(a,1,1)),rewrite([24(4)]),flip(a)].
% 30.50/30.80 48 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(21(a,1),34(a,1,1)),rewrite([24(4)]),flip(a)].
% 30.50/30.80 49 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(29(a,1),34(a,1,1)),rewrite([24(6)])].
% 30.50/30.80 50 addition(multiplication(A,B),multiplication(C,multiplication(D,B))) = multiplication(addition(A,multiplication(C,D)),B). [para(29(a,1),34(a,1,2))].
% 30.50/30.80 51 addition(multiplication(star(c1),star(c2)),multiplication(star(c2),star(c1))) = multiplication(star(c1),star(c2)). [hyper(36,a,30,a),rewrite([24(11)])].
% 30.50/30.80 52 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(36,a,26,a),rewrite([24(6)])].
% 30.50/30.80 53 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(36,a,25,a),rewrite([24(6)])].
% 30.50/30.80 54 leq(A,A). [hyper(37,b,19,a)].
% 30.50/30.80 59 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B). [para(19(a,1),39(a,1))].
% 30.50/30.80 63 -leq(A,B) | leq(multiplication(star(zero),A),B). [para(23(a,1),39(a,1,2)),rewrite([18(2)])].
% 30.50/30.80 64 -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))].
% 30.50/30.80 65 -leq(multiplication(A,addition(B,C)),C) | leq(multiplication(star(A),multiplication(A,B)),C). [para(32(a,1),39(a,1))].
% 30.50/30.80 67 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A). [para(19(a,1),41(a,1)),rewrite([29(5)])].
% 30.50/30.80 76 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)])].
% 30.50/30.80 80 leq(A,addition(A,B)). [hyper(37,b,44,a)].
% 30.50/30.80 81 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(32(a,1),80(a,2))].
% 30.50/30.80 82 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(34(a,1),80(a,2))].
% 30.50/30.80 91 leq(multiplication(star(zero),A),A). [hyper(63,a,54,a)].
% 30.50/30.80 99 multiplication(A,addition(zero,one)) = A. [para(22(a,1),47(a,2,2)),rewrite([18(6)])].
% 30.50/30.80 101 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)].
% 30.50/30.80 105 multiplication(A,addition(B,addition(C,one))) = addition(A,multiplication(A,addition(B,C))). [para(47(a,1),32(a,1,2)),rewrite([28(4,R),32(3),24(1)]),flip(a)].
% 30.50/30.80 108 multiplication(addition(A,multiplication(A,B)),B) = multiplication(A,multiplication(B,addition(B,one))). [para(47(a,2),34(a,1)),rewrite([29(4)]),flip(a)].
% 30.50/30.80 114 -leq(multiplication(A,addition(B,one)),A) | leq(multiplication(A,star(B)),A). [para(47(a,2),41(a,1))].
% 30.50/30.80 121 leq(star(zero),one). [para(20(a,1),91(a,1))].
% 30.50/30.80 123 addition(one,star(zero)) = one. [hyper(36,a,121,a),rewrite([24(4)])].
% 30.50/30.80 124 addition(zero,one) = star(zero). [back_rewrite(76),rewrite([123(5)])].
% 30.50/30.80 125 multiplication(A,star(zero)) = A. [back_rewrite(99),rewrite([124(3)])].
% 30.50/30.80 130 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)].
% 30.50/30.80 133 addition(addition(A,multiplication(B,A)),multiplication(addition(B,one),C)) = multiplication(addition(B,one),addition(A,C)). [para(48(a,1),32(a,1,1))].
% 30.50/30.80 136 addition(addition(A,multiplication(B,A)),multiplication(C,A)) = multiplication(addition(B,addition(C,one)),A). [para(48(a,1),34(a,1,1)),rewrite([24(7),28(7,R),24(6)])].
% 30.50/30.80 137 multiplication(addition(A,addition(B,one)),C) = addition(C,multiplication(addition(A,B),C)). [para(48(a,1),34(a,1,2)),rewrite([28(4,R),34(3),24(1)]),flip(a)].
% 30.50/30.80 149 star(zero) = one. [para(125(a,1),21(a,1)),flip(a)].
% 30.50/30.80 156 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))].
% 30.50/30.80 183 addition(addition(A,multiplication(B,A)),multiplication(C,multiplication(D,A))) = multiplication(addition(addition(B,one),multiplication(C,D)),A). [para(48(a,1),50(a,1,1))].
% 30.50/30.80 190 leq(multiplication(A,B),addition(B,multiplication(A,B))). [para(48(a,1),82(a,2))].
% 30.50/30.80 217 addition(one,addition(star(A),multiplication(star(A),A))) = star(A). [para(52(a,1),28(a,1)),rewrite([28(7),24(6)]),flip(a)].
% 30.50/30.80 242 addition(one,addition(star(A),multiplication(A,star(A)))) = star(A). [para(53(a,1),28(a,1)),rewrite([28(7),24(6)]),flip(a)].
% 30.50/30.80 352 addition(one,star(A)) = star(A). [para(217(a,1),44(a,1,2)),rewrite([217(9)])].
% 30.50/30.80 354 addition(one,multiplication(star(A),addition(A,one))) = star(A). [para(47(a,2),217(a,1,2))].
% 30.50/30.80 355 leq(A,multiplication(A,star(B))). [para(217(a,1),81(a,2,2)),rewrite([20(2)])].
% 30.50/30.80 356 leq(A,multiplication(star(B),A)). [para(217(a,1),82(a,2,1)),rewrite([21(2)])].
% 30.50/30.80 362 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)). [hyper(36,a,355,a)].
% 30.50/30.80 364 leq(addition(A,one),addition(star(B),multiplication(A,star(B)))). [para(48(a,1),355(a,2))].
% 30.50/30.80 365 addition(A,multiplication(star(B),A)) = multiplication(star(B),A). [hyper(36,a,356,a)].
% 30.50/30.80 371 -leq(multiplication(A,addition(one,multiplication(B,C))),C) | leq(multiplication(star(multiplication(A,B)),A),C). [para(47(a,2),64(a,1)),rewrite([24(3)])].
% 30.50/30.80 377 addition(star(A),one) = star(A). [para(352(a,1),24(a,1)),flip(a)].
% 30.50/30.80 399 -leq(multiplication(A,star(B)),star(B)) | leq(multiplication(star(A),A),star(B)). [para(352(a,1),65(a,1,2)),rewrite([20(7)])].
% 30.50/30.80 416 -leq(star(A),star(A)) | leq(star(addition(A,one)),star(A)). [para(354(a,1),41(a,1)),rewrite([21(8)])].
% 30.50/30.80 486 addition(star(A),multiplication(A,star(A))) = star(A). [para(242(a,1),28(a,1)),rewrite([352(6),24(5)]),flip(a)].
% 30.50/30.80 507 multiplication(addition(A,one),star(A)) = star(A). [para(486(a,1),48(a,2))].
% 30.50/30.80 509 leq(multiplication(A,star(A)),star(A)). [para(486(a,1),190(a,2))].
% 30.50/30.80 518 leq(addition(A,one),star(A)). [para(486(a,1),364(a,2))].
% 30.50/30.80 519 multiplication(star(A),star(star(A))) = star(star(A)). [para(486(a,1),365(a,1)),flip(a)].
% 30.50/30.80 525 addition(A,star(A)) = star(A). [hyper(36,a,518,a),rewrite([24(4),28(4,R),352(3)])].
% 30.50/30.80 529 leq(multiplication(star(A),multiplication(A,star(A))),star(A)). [hyper(59,a,509,a)].
% 30.50/30.80 552 addition(A,addition(B,star(A))) = addition(B,star(A)). [para(525(a,1),28(a,2,2)),rewrite([24(2)])].
% 30.50/30.80 691 leq(multiplication(star(star(A)),star(star(A))),star(star(A))). [para(519(a,1),529(a,1,2))].
% 30.50/30.80 704 leq(A,addition(B,multiplication(A,addition(C,one)))). [para(101(a,2),80(a,2))].
% 30.50/30.80 741 leq(A,multiplication(addition(A,B),addition(C,one))). [para(34(a,1),704(a,2)),rewrite([24(1)])].
% 30.50/30.80 742 leq(A,addition(B,multiplication(A,star(C)))). [para(377(a,1),704(a,2,2,2))].
% 30.50/30.80 748 leq(addition(A,one),addition(B,star(A))). [para(507(a,1),742(a,2,2))].
% 30.50/30.80 987 addition(addition(A,one),star(B)) = addition(A,star(B)). [hyper(36,a,748,a),rewrite([28(5),24(4),28(4,R),24(3),28(5,R),552(5)])].
% 30.50/30.80 1031 leq(one,multiplication(star(A),addition(B,one))). [para(217(a,1),741(a,2,1))].
% 30.50/30.80 1037 addition(one,multiplication(star(A),addition(B,one))) = multiplication(star(A),addition(B,one)). [hyper(36,a,1031,a)].
% 30.50/30.80 1038 leq(one,addition(star(A),multiplication(star(A),B))). [para(47(a,1),1031(a,2))].
% 30.50/30.80 1039 multiplication(star(A),addition(A,one)) = star(A). [back_rewrite(354),rewrite([1037(6)])].
% 30.50/30.80 1071 leq(multiplication(A,B),addition(A,multiplication(A,addition(B,C)))). [para(105(a,1),81(a,2))].
% 30.50/30.80 1183 addition(one,addition(star(A),multiplication(star(A),B))) = addition(star(A),multiplication(star(A),B)). [hyper(36,a,1038,a)].
% 30.50/30.80 1186 addition(star(A),multiplication(star(A),A)) = star(A). [back_rewrite(217),rewrite([1183(6)])].
% 30.50/30.80 1194 leq(multiplication(star(A),A),star(A)). [para(1039(a,1),81(a,2))].
% 30.50/30.80 1663 leq(multiplication(star(addition(A,one)),star(A)),star(addition(A,one))). [hyper(114,a,1194,a)].
% 30.50/30.80 1851 multiplication(star(star(A)),star(star(A))) = star(star(A)). [hyper(36,a,691,a),rewrite([24(8),362(8)])].
% 30.50/30.80 1875 leq(A,addition(B,multiplication(addition(C,one),A))). [para(130(a,2),80(a,2))].
% 30.50/30.80 1914 leq(A,multiplication(addition(addition(B,one),multiplication(C,D)),A)). [para(49(a,1),1875(a,2))].
% 30.50/30.80 1915 leq(A,addition(B,multiplication(star(C),A))). [para(377(a,1),1875(a,2,2,1))].
% 30.50/30.80 1921 leq(A,multiplication(star(B),addition(A,C))). [para(32(a,1),1915(a,2)),rewrite([24(2)])].
% 30.50/30.80 1936 leq(multiplication(A,B),multiplication(star(C),multiplication(addition(A,D),B))). [para(34(a,1),1921(a,2,2))].
% 30.50/30.80 1943 leq(A,addition(star(B),multiplication(star(B),addition(A,C)))). [para(105(a,1),1921(a,2))].
% 30.50/30.80 2285 addition(A,addition(B,addition(one,multiplication(B,A)))) = multiplication(addition(B,one),addition(A,one)). [para(20(a,1),133(a,1,2)),rewrite([24(5),28(5,R),28(4),24(3),28(4,R),24(3)])].
% 30.50/30.80 2418 multiplication(addition(addition(A,one),multiplication(B,C)),D) = multiplication(addition(A,addition(one,multiplication(B,C))),D). [para(29(a,1),136(a,1,2)),rewrite([183(5),24(8)])].
% 30.50/30.80 2456 leq(A,multiplication(addition(B,addition(one,multiplication(C,D))),A)). [back_rewrite(1914),rewrite([2418(5)])].
% 30.50/30.80 2509 leq(multiplication(A,B),addition(B,multiplication(addition(A,C),B))). [para(137(a,1),82(a,2))].
% 30.50/30.80 2639 leq(addition(A,one),addition(A,star(B))). [para(987(a,1),80(a,2))].
% 30.50/30.80 2702 leq(multiplication(star(addition(A,B)),A),star(addition(A,B))). [para(1186(a,1),1071(a,2))].
% 30.50/30.80 2763 multiplication(star(star(A)),multiplication(star(star(A)),B)) = multiplication(star(star(A)),B). [para(1851(a,1),29(a,1,1)),flip(a)].
% 30.50/30.80 2782 leq(A,star(addition(A,B))). [para(1186(a,1),1943(a,2))].
% 30.50/30.80 2790 addition(A,star(addition(A,B))) = star(addition(A,B)). [hyper(36,a,2782,a)].
% 30.50/30.80 3527 leq(multiplication(star(c2),multiplication(star(c1),A)),multiplication(star(c1),multiplication(star(c2),A))). [para(51(a,1),156(b,1,1)),rewrite([29(12),29(19),29(25)]),xx(b)].
% 30.50/30.80 4782 leq(one,addition(A,addition(one,multiplication(B,C)))). [para(20(a,1),2456(a,2))].
% 30.50/30.80 4793 leq(one,addition(A,addition(B,addition(one,multiplication(B,C))))). [para(47(a,1),4782(a,2,2,2)),rewrite([28(5,R),24(4)])].
% 30.50/30.80 5111 leq(multiplication(A,star(addition(A,B))),star(addition(A,B))). [para(486(a,1),2509(a,2))].
% 30.50/30.80 5367 leq(addition(A,one),star(addition(A,B))). [para(2790(a,1),2639(a,2))].
% 30.50/30.80 5408 leq(addition(one,multiplication(A,B)),star(multiplication(A,addition(B,C)))). [para(32(a,1),5367(a,2,1)),rewrite([24(3)])].
% 30.50/30.80 7412 leq(one,addition(A,multiplication(addition(B,one),addition(C,one)))). [para(48(a,1),4793(a,2,2,2,2)),rewrite([28(7,R),24(6),28(8,R),24(7),28(7,R),28(6),24(5),28(6,R),24(5),28(7,R),24(6),44(6),2285(6)])].
% 30.50/30.80 9111 leq(one,addition(A,multiplication(star(B),addition(C,one)))). [para(377(a,1),7412(a,2,2,1))].
% 30.50/30.80 9118 leq(one,addition(A,multiplication(star(B),star(C)))). [para(377(a,1),9111(a,2,2,2))].
% 30.50/30.80 9119 leq(one,multiplication(addition(star(A),multiplication(B,C)),star(D))). [para(49(a,1),9118(a,2))].
% 30.50/30.80 9599 leq(one,multiplication(star(A),multiplication(star(B),star(C)))). [para(362(a,1),9119(a,2,1)),rewrite([29(6)])].
% 30.50/30.80 9608 addition(one,multiplication(star(A),multiplication(star(B),star(C)))) = multiplication(star(A),multiplication(star(B),star(C))). [hyper(36,a,9599,a)].
% 30.50/30.80 9682 leq(star(addition(A,one)),star(A)). [hyper(416,a,54,a)].
% 30.50/30.80 9683 addition(star(A),star(addition(A,one))) = star(A). [hyper(36,a,9682,a),rewrite([24(5)])].
% 30.50/30.80 10520 leq(multiplication(star(addition(A,one)),star(star(A))),star(addition(A,one))). [hyper(67,a,1663,a),rewrite([519(7)])].
% 30.50/30.80 10521 multiplication(star(addition(A,one)),star(A)) = star(addition(A,one)). [hyper(36,a,1663,a),rewrite([24(9),47(9,R),377(6)])].
% 30.50/30.80 10780 leq(multiplication(A,B),multiplication(star(C),multiplication(star(A),B))). [para(525(a,1),1936(a,2,2,1))].
% 30.50/30.80 10781 leq(multiplication(A,star(A)),multiplication(star(B),star(A))). [para(507(a,1),1936(a,2,2))].
% 30.50/30.80 10817 multiplication(addition(A,star(B)),star(A)) = multiplication(star(B),star(A)). [hyper(36,a,10781,a),rewrite([34(6)])].
% 30.50/30.80 10824 leq(star(A),multiplication(star(B),star(addition(A,one)))). [para(507(a,1),10780(a,1)),rewrite([10521(7)])].
% 30.50/30.80 10848 leq(star(A),star(addition(A,one))). [para(149(a,1),10824(a,2,1)),rewrite([21(6)])].
% 30.50/30.80 10850 star(addition(A,one)) = star(A). [hyper(36,a,10848,a),rewrite([9683(5)]),flip(a)].
% 30.50/30.80 10857 multiplication(star(A),star(A)) = star(A). [back_rewrite(10521),rewrite([10850(3),10850(6)])].
% 30.50/30.80 10858 leq(star(star(A)),star(A)). [back_rewrite(10520),rewrite([10850(3),519(4),10850(5)])].
% 30.50/30.80 10936 star(star(A)) = star(A). [hyper(36,a,10858,a),rewrite([24(4),525(4)])].
% 30.50/30.80 11025 multiplication(star(A),multiplication(star(A),B)) = multiplication(star(A),B). [back_rewrite(2763),rewrite([10936(2),10936(3),10936(6)])].
% 30.50/30.80 12707 leq(addition(A,addition(B,one)),star(addition(A,addition(B,C)))). [para(105(a,2),5408(a,1)),rewrite([21(5),24(6),28(6),24(5),28(6,R),24(5),21(7)])].
% 30.50/30.80 13514 -leq(addition(one,multiplication(A,B)),B) | leq(star(A),B). [para(21(a,1),371(a,1)),rewrite([21(6),20(7)])].
% 30.50/30.80 13812 leq(multiplication(star(A),A),star(addition(A,B))). [hyper(399,a,5111,a)].
% 30.50/30.80 13831 leq(star(A),star(addition(A,star(B)))). [para(987(a,1),13812(a,2,1)),rewrite([10850(3),1039(4)])].
% 30.50/30.80 13833 leq(star(A),star(addition(A,B))). [para(2790(a,1),13831(a,2,1)),rewrite([10936(4)])].
% 30.50/30.80 13834 addition(star(A),star(addition(A,B))) = star(addition(A,B)). [hyper(36,a,13833,a)].
% 30.50/30.80 13836 leq(star(multiplication(A,B)),star(multiplication(addition(A,C),B))). [para(34(a,1),13833(a,2,1))].
% 30.50/30.80 13840 leq(star(A),star(multiplication(A,star(B)))). [para(362(a,1),13833(a,2,1))].
% 30.50/30.80 13860 addition(star(A),star(multiplication(A,star(B)))) = star(multiplication(A,star(B))). [hyper(36,a,13840,a)].
% 30.50/30.80 15021 leq(star(multiplication(A,B)),star(multiplication(star(A),B))). [para(525(a,1),13836(a,2,1,1))].
% 30.50/30.80 16992 leq(addition(A,addition(B,one)),star(addition(A,star(B)))). [para(525(a,1),12707(a,2,1,2))].
% 30.50/30.80 17400 leq(multiplication(star(addition(A,B)),star(A)),star(addition(A,B))). [para(13834(a,1),2702(a,1,1,1)),rewrite([10936(3),13834(8),10936(7)])].
% 30.50/30.80 17431 leq(addition(A,star(B)),star(addition(B,A))). [para(13834(a,1),16992(a,2,1)),rewrite([24(4),28(4),24(3),28(4,R),24(3),28(5,R),987(4),552(3),10936(5)])].
% 30.50/30.80 17490 leq(star(addition(A,B)),star(addition(B,star(A)))). [para(13834(a,1),17431(a,1)),rewrite([24(5),28(5),24(4),525(4)])].
% 30.50/30.80 17572 leq(star(addition(A,B)),star(addition(A,star(B)))). [para(24(a,1),17490(a,1,1))].
% 30.50/30.80 17595 leq(star(addition(A,star(B))),star(addition(B,A))). [para(13834(a,1),17490(a,2,1)),rewrite([24(3),28(3),24(2),525(2),10936(6)])].
% 30.50/30.80 17596 addition(star(addition(A,B)),star(addition(A,star(B)))) = star(addition(A,star(B))). [hyper(36,a,17572,a)].
% 30.50/30.80 17609 star(addition(A,star(B))) = star(addition(A,B)). [hyper(36,a,17595,a),rewrite([24(4),24(6),17596(6),24(4)])].
% 30.50/30.80 20106 multiplication(star(addition(A,B)),star(A)) = star(addition(A,B)). [hyper(36,a,17400,a),rewrite([24(7),47(7,R),377(5)])].
% 30.50/30.80 21108 leq(star(multiplication(addition(A,B),star(A))),star(addition(A,B))). [para(20106(a,1),15021(a,2,1)),rewrite([10936(7)])].
% 30.50/30.80 22964 star(multiplication(addition(A,B),star(A))) = star(addition(A,B)). [hyper(36,a,21108,a),rewrite([24(7),13860(7)])].
% 30.50/30.80 25006 star(addition(A,B)) = star(multiplication(star(B),star(A))). [para(987(a,1),22964(a,1,1,1)),rewrite([10850(5),10817(4),987(8),17609(7)]),flip(a)].
% 30.50/30.80 25473 -leq(star(multiplication(star(c2),star(c1))),multiplication(star(c1),star(c2))) # answer(goals). [back_rewrite(35),rewrite([25006(4)])].
% 30.50/30.80 25475 -leq(multiplication(star(c2),multiplication(star(c1),star(c2))),multiplication(star(c1),star(c2))) # answer(goals). [ur(13514,b,25473,a),rewrite([29(12),11025(11),9608(10)])].
% 30.50/30.80 30938 leq(multiplication(star(c2),multiplication(star(c1),star(c2))),multiplication(star(c1),star(c2))). [para(108(a,2),3527(a,2)),rewrite([24(8),352(8),47(16,R),24(14),352(14),29(16),10857(15)])].
% 30.50/30.80 30939 $F # answer(goals). [resolve(30938,a,25475,a)].
% 30.50/30.80
% 30.50/30.80 % SZS output end Refutation
% 30.50/30.80 ============================== end of proof ==========================
% 30.50/30.80
% 30.50/30.80 ============================== STATISTICS ============================
% 30.50/30.80
% 30.50/30.80 Given=5824. Generated=1375834. Kept=30916. proofs=1.
% 30.50/30.80 Usable=5028. Sos=9641. Demods=426. Limbo=0, Disabled=16265. Hints=0.
% 30.50/30.80 Megabytes=18.86.
% 30.50/30.80 User_CPU=29.05, System_CPU=0.79, Wall_clock=30.
% 30.50/30.80
% 30.50/30.80 ============================== end of statistics =====================
% 30.50/30.80
% 30.50/30.80 ============================== end of search =========================
% 30.50/30.80
% 30.50/30.80 THEOREM PROVED
% 30.50/30.80 % SZS status Theorem
% 30.50/30.80
% 30.50/30.80 Exiting with 1 proof.
% 30.50/30.80
% 30.50/30.80 Process 7040 exit (max_proofs) Thu Jun 16 16:08:57 2022
% 30.50/30.80 Prover9 interrupted
%------------------------------------------------------------------------------