TSTP Solution File: KLE045+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE045+1 : 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 24.14s 24.48s
% Output : Refutation 24.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE045+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 07:33:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 31609 was started by sandbox on n006.cluster.edu,
% 0.44/1.01 Thu Jun 16 07:33:42 2022
% 0.44/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31455_n006.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_31455_n006.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (17 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 24.14/24.48 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].
% 24.14/24.48 17 -(all X0 all X1 all X2 (leq(multiplication(X0,X2),multiplication(X2,X1)) -> leq(multiplication(star(X0),X2),multiplication(X2,star(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 24.14/24.48
% 24.14/24.48 ============================== end of process non-clausal formulas ===
% 24.14/24.48
% 24.14/24.48 ============================== PROCESS INITIAL CLAUSES ===============
% 24.14/24.48
% 24.14/24.48 ============================== PREDICATE ELIMINATION =================
% 24.14/24.48
% 24.14/24.48 ============================== end predicate elimination =============
% 24.14/24.48
% 24.14/24.48 Auto_denials:
% 24.14/24.48 % copying label goals to answer in negative clause
% 24.14/24.48
% 24.14/24.48 Term ordering decisions:
% 24.14/24.48
% 24.14/24.48 % Assigning unary symbol star kb_weight 0 and highest precedence (10).
% 24.14/24.48 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. star=0.
% 24.14/24.48
% 24.14/24.48 ============================== end of process initial clauses ========
% 24.14/24.48
% 24.14/24.48 ============================== CLAUSES FOR SEARCH ====================
% 24.14/24.48
% 24.14/24.48 ============================== end of clauses for search =============
% 24.14/24.48
% 24.14/24.48 ============================== SEARCH ================================
% 24.14/24.48
% 24.14/24.48 % Starting search at 0.01 seconds.
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=38.000, iters=3342
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=35.000, iters=3354
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=34.000, iters=3355
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=33.000, iters=3413
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=32.000, iters=3333
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=29.000, iters=3350
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=27.000, iters=3334
% 24.14/24.48
% 24.14/24.48 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 0.87 sec).
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=25.000, iters=3372
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=24.000, iters=3340
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=23.000, iters=3348
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=22.000, iters=3334
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=21.000, iters=3348
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=20.000, iters=3333
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6007, wt=48.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6061, wt=47.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6380, wt=46.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6386, wt=45.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6257, wt=44.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6398, wt=43.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=4163, wt=42.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6372, wt=41.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6379, wt=40.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6385, wt=39.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6381, wt=38.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6476, wt=37.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=6466, wt=36.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=14345, wt=18.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=14546, wt=17.000
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=19.000, iters=3378
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=14809, wt=16.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=14840, wt=15.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=14844, wt=14.000
% 24.14/24.48
% 24.14/24.48 Low Water (displace): id=15466, wt=12.000
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=18.000, iters=3409
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=17.000, iters=3343
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=16.000, iters=3340
% 24.14/24.48
% 24.14/24.48 Low Water (keep): wt=15.000, iters=3357
% 24.14/24.48
% 24.14/24.48 ============================== PROOF =================================
% 24.14/24.48 % SZS status Theorem
% 24.14/24.48 % SZS output start Refutation
% 24.14/24.48
% 24.14/24.48 % Proof 1 at 22.89 (+ 0.60) seconds: goals.
% 24.14/24.48 % Length of proof is 127.
% 24.14/24.48 % Level of proof is 20.
% 24.14/24.48 % Maximum clause weight is 19.000.
% 24.14/24.48 % Given clauses 5114.
% 24.14/24.48
% 24.14/24.48 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 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].
% 24.14/24.48 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 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].
% 24.14/24.48 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 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].
% 24.14/24.48 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].
% 24.14/24.48 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 24.14/24.48 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].
% 24.14/24.48 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].
% 24.14/24.48 17 -(all X0 all X1 all X2 (leq(multiplication(X0,X2),multiplication(X2,X1)) -> leq(multiplication(star(X0),X2),multiplication(X2,star(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 24.14/24.48 18 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 24.14/24.48 19 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 24.14/24.48 20 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 24.14/24.48 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 24.14/24.48 22 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 24.14/24.48 23 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 24.14/24.48 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 24.14/24.48 25 leq(multiplication(c1,c3),multiplication(c3,c2)) # label(goals) # label(negated_conjecture). [clausify(17)].
% 24.14/24.48 26 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(13)].
% 24.14/24.48 27 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 24.14/24.48 28 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 24.14/24.48 29 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(28),rewrite([24(2)]),flip(a)].
% 24.14/24.48 30 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 24.14/24.48 31 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 24.14/24.48 32 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(31),flip(a)].
% 24.14/24.48 33 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 24.14/24.48 34 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(33),flip(a)].
% 24.14/24.48 35 -leq(multiplication(star(c1),c3),multiplication(c3,star(c2))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 24.14/24.48 36 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 24.14/24.48 37 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 24.14/24.48 38 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(15)].
% 24.14/24.48 39 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(38),rewrite([24(2)])].
% 24.14/24.48 40 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(16)].
% 24.14/24.48 41 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(40),rewrite([24(2)])].
% 24.14/24.48 42 leq(addition(one,star(one)),star(one)). [para(21(a,1),26(a,1,2))].
% 24.14/24.48 43 leq(addition(zero,one),star(zero)). [para(23(a,1),26(a,1,2)),rewrite([24(3)])].
% 24.14/24.48 44 addition(A,addition(A,B)) = addition(A,B). [para(29(a,1),19(a,1)),rewrite([24(1),24(2),29(2,R),19(1),24(3)])].
% 24.14/24.48 47 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(20(a,1),32(a,1,1)),rewrite([24(4)]),flip(a)].
% 24.14/24.48 48 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(21(a,1),34(a,1,1)),rewrite([24(4)]),flip(a)].
% 24.14/24.48 49 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(30(a,1),34(a,1,1)),rewrite([24(6)])].
% 24.14/24.48 51 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(36,a,27,a),rewrite([24(6)])].
% 24.14/24.48 52 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(36,a,26,a),rewrite([24(6)])].
% 24.14/24.48 53 addition(multiplication(c1,c3),multiplication(c3,c2)) = multiplication(c3,c2). [hyper(36,a,25,a)].
% 24.14/24.48 54 leq(A,A). [hyper(37,b,19,a)].
% 24.14/24.48 59 -leq(addition(c3,multiplication(c1,multiplication(c3,star(c2)))),multiplication(c3,star(c2))) # answer(goals). [ur(39,b,35,a)].
% 24.14/24.48 61 -leq(addition(A,B),one) | leq(multiplication(star(B),A),one). [para(20(a,1),39(a,1,2))].
% 24.14/24.48 64 -leq(A,B) | leq(multiplication(star(zero),A),B). [para(23(a,1),39(a,1,2)),rewrite([18(2)])].
% 24.14/24.48 69 -leq(addition(A,B),B) | leq(multiplication(A,star(one)),B). [para(20(a,1),41(a,1,2))].
% 24.14/24.48 76 addition(one,star(one)) = star(one). [hyper(36,a,42,a),rewrite([24(7),29(7,R),19(6)])].
% 24.14/24.48 78 addition(zero,addition(one,star(zero))) = star(zero). [hyper(36,a,43,a),rewrite([24(6),29(6),24(5),29(6,R),24(5)])].
% 24.14/24.48 82 leq(A,addition(A,B)). [hyper(37,b,44,a)].
% 24.14/24.48 83 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(32(a,1),82(a,2))].
% 24.14/24.48 84 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(34(a,1),82(a,2))].
% 24.14/24.48 93 leq(multiplication(star(zero),A),A). [hyper(64,a,54,a)].
% 24.14/24.48 101 multiplication(A,addition(zero,one)) = A. [para(22(a,1),47(a,2,2)),rewrite([18(6)])].
% 24.14/24.48 103 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(47(a,2),29(a,2,2)),rewrite([24(2)]),flip(a)].
% 24.14/24.48 104 multiplication(addition(A,multiplication(A,B)),C) = multiplication(A,multiplication(addition(B,one),C)). [para(47(a,1),30(a,1,1))].
% 24.14/24.48 110 multiplication(addition(A,multiplication(A,B)),B) = multiplication(A,multiplication(B,addition(B,one))). [para(47(a,2),34(a,1)),rewrite([30(4)]),flip(a)].
% 24.14/24.48 116 -leq(multiplication(A,addition(B,one)),A) | leq(multiplication(A,star(B)),A). [para(47(a,2),41(a,1))].
% 24.14/24.48 123 leq(star(zero),one). [para(20(a,1),93(a,1))].
% 24.14/24.48 125 addition(one,star(zero)) = one. [hyper(36,a,123,a),rewrite([24(4)])].
% 24.14/24.48 126 addition(zero,one) = star(zero). [back_rewrite(78),rewrite([125(5)])].
% 24.14/24.48 127 multiplication(A,star(zero)) = A. [back_rewrite(101),rewrite([126(3)])].
% 24.14/24.48 132 addition(A,multiplication(addition(B,one),C)) = addition(C,addition(A,multiplication(B,C))). [para(48(a,2),29(a,2,2)),rewrite([24(2)]),flip(a)].
% 24.14/24.48 151 star(zero) = one. [para(127(a,1),21(a,1)),flip(a)].
% 24.14/24.48 196 addition(one,addition(star(A),multiplication(star(A),A))) = star(A). [para(51(a,1),29(a,1)),rewrite([29(7),24(6)]),flip(a)].
% 24.14/24.48 209 -leq(A,one) | leq(multiplication(star(A),A),one). [para(19(a,1),61(a,1))].
% 24.14/24.48 223 addition(one,addition(star(A),multiplication(A,star(A)))) = star(A). [para(52(a,1),29(a,1)),rewrite([29(7),24(6)]),flip(a)].
% 24.14/24.48 227 leq(star(one),one). [hyper(209,a,54,a),rewrite([20(4)])].
% 24.14/24.48 229 star(one) = one. [hyper(36,a,227,a),rewrite([24(4),76(4)])].
% 24.14/24.48 232 -leq(addition(A,B),B) | leq(A,B). [back_rewrite(69),rewrite([229(4),20(4)])].
% 24.14/24.48 233 -leq(addition(c3,multiplication(addition(one,c1),multiplication(c3,star(c2)))),multiplication(c3,star(c2))) # answer(goals). [ur(232,b,59,a),rewrite([24(13),29(13,R),24(12),48(12,R),24(4)])].
% 24.14/24.48 367 addition(one,star(A)) = star(A). [para(196(a,1),44(a,1,2)),rewrite([196(9)])].
% 24.14/24.48 369 addition(one,multiplication(star(A),addition(A,one))) = star(A). [para(47(a,2),196(a,1,2))].
% 24.14/24.48 370 leq(A,multiplication(A,star(B))). [para(196(a,1),83(a,2,2)),rewrite([20(2)])].
% 24.14/24.48 395 leq(addition(A,one),addition(star(B),multiplication(A,star(B)))). [para(48(a,1),370(a,2))].
% 24.14/24.48 398 addition(star(A),one) = star(A). [para(367(a,1),24(a,1)),flip(a)].
% 24.14/24.48 437 -leq(star(A),star(A)) | leq(star(addition(A,one)),star(A)). [para(369(a,1),41(a,1)),rewrite([21(8)])].
% 24.14/24.48 477 addition(star(A),multiplication(A,star(A))) = star(A). [para(223(a,1),29(a,1)),rewrite([367(6),24(5)]),flip(a)].
% 24.14/24.48 485 multiplication(addition(A,one),star(A)) = star(A). [para(477(a,1),48(a,2))].
% 24.14/24.48 496 leq(addition(A,one),star(A)). [para(477(a,1),395(a,2))].
% 24.14/24.48 522 addition(A,star(A)) = star(A). [hyper(36,a,496,a),rewrite([24(4),29(4,R),367(3)])].
% 24.14/24.48 654 addition(A,addition(B,multiplication(C,addition(D,one)))) = addition(C,addition(A,addition(B,multiplication(C,D)))). [para(103(a,2),29(a,2,2)),rewrite([24(3),29(3,R),24(2),29(9,R),24(8)]),flip(a)].
% 24.14/24.48 662 leq(A,addition(B,multiplication(A,addition(C,one)))). [para(103(a,2),82(a,2))].
% 24.14/24.48 700 leq(A,multiplication(addition(A,B),addition(C,one))). [para(34(a,1),662(a,2)),rewrite([24(1)])].
% 24.14/24.48 701 leq(A,addition(B,multiplication(A,star(C)))). [para(398(a,1),662(a,2,2,2))].
% 24.14/24.48 819 multiplication(addition(A,multiplication(A,B)),star(B)) = multiplication(A,star(B)). [para(485(a,1),104(a,2,2))].
% 24.14/24.48 830 leq(A,multiplication(addition(A,B),star(C))). [para(34(a,1),701(a,2)),rewrite([24(1)])].
% 24.14/24.48 838 addition(A,multiplication(addition(A,B),star(C))) = multiplication(addition(A,B),star(C)). [hyper(36,a,830,a)].
% 24.14/24.48 988 leq(one,multiplication(star(A),addition(B,one))). [para(196(a,1),700(a,2,1))].
% 24.14/24.48 994 addition(one,multiplication(star(A),addition(B,one))) = multiplication(star(A),addition(B,one)). [hyper(36,a,988,a)].
% 24.14/24.48 996 multiplication(star(A),addition(A,one)) = star(A). [back_rewrite(369),rewrite([994(6)])].
% 24.14/24.48 1147 leq(multiplication(star(A),A),star(A)). [para(996(a,1),83(a,2))].
% 24.14/24.48 1610 leq(multiplication(star(addition(A,one)),star(A)),star(addition(A,one))). [hyper(116,a,1147,a)].
% 24.14/24.48 1808 leq(A,addition(B,multiplication(addition(C,one),A))). [para(132(a,2),82(a,2))].
% 24.14/24.48 1846 leq(A,addition(B,multiplication(star(C),A))). [para(398(a,1),1808(a,2,2,1))].
% 24.14/24.48 1852 leq(A,multiplication(star(B),addition(A,C))). [para(32(a,1),1846(a,2)),rewrite([24(2)])].
% 24.14/24.48 1867 leq(multiplication(A,B),multiplication(star(C),multiplication(addition(A,D),B))). [para(34(a,1),1852(a,2,2))].
% 24.14/24.48 9889 leq(star(addition(A,one)),star(A)). [hyper(437,a,54,a)].
% 24.14/24.48 9890 addition(star(A),star(addition(A,one))) = star(A). [hyper(36,a,9889,a),rewrite([24(5)])].
% 24.14/24.48 10523 multiplication(star(addition(A,one)),star(A)) = star(addition(A,one)). [hyper(36,a,1610,a),rewrite([24(9),47(9,R),398(6)])].
% 24.14/24.48 10909 leq(multiplication(A,B),multiplication(star(C),multiplication(star(A),B))). [para(522(a,1),1867(a,2,2,1))].
% 24.14/24.48 10951 leq(star(A),multiplication(star(B),star(addition(A,one)))). [para(485(a,1),10909(a,1)),rewrite([10523(7)])].
% 24.14/24.48 11034 leq(star(A),star(addition(A,one))). [para(151(a,1),10951(a,2,1)),rewrite([21(6)])].
% 24.14/24.48 11036 star(addition(A,one)) = star(A). [hyper(36,a,11034,a),rewrite([9890(5)]),flip(a)].
% 24.14/24.48 11051 multiplication(star(A),star(A)) = star(A). [back_rewrite(10523),rewrite([11036(3),11036(6)])].
% 24.14/24.48 20529 leq(A,addition(B,addition(C,multiplication(A,addition(D,one))))). [para(654(a,2),82(a,2))].
% 24.14/24.48 20570 leq(A,addition(B,addition(C,multiplication(A,star(D))))). [para(398(a,1),20529(a,2,2,2,2))].
% 24.14/24.48 20579 leq(A,addition(B,multiplication(addition(A,C),star(D)))). [para(34(a,1),20570(a,2,2)),rewrite([24(1)])].
% 24.14/24.48 20597 leq(A,multiplication(addition(addition(A,B),multiplication(C,D)),star(E))). [para(49(a,1),20579(a,2))].
% 24.14/24.48 23231 leq(A,addition(addition(A,B),multiplication(C,D))). [para(151(a,1),20597(a,2,2)),rewrite([20(5)])].
% 24.14/24.48 23250 leq(multiplication(c1,c3),addition(multiplication(c3,c2),multiplication(A,B))). [para(53(a,1),23231(a,2,1))].
% 24.14/24.48 23927 leq(multiplication(c1,c3),multiplication(addition(A,multiplication(c3,c2)),star(B))). [para(838(a,1),23250(a,2)),rewrite([24(7)])].
% 24.14/24.48 26546 leq(multiplication(c1,c3),multiplication(c3,star(c2))). [para(819(a,1),23927(a,2))].
% 24.14/24.48 26547 addition(multiplication(c1,c3),multiplication(c3,star(c2))) = multiplication(c3,star(c2)). [hyper(36,a,26546,a)].
% 24.14/24.48 30201 leq(multiplication(c1,multiplication(c3,A)),multiplication(c3,multiplication(star(c2),A))). [para(26547(a,1),84(a,2,1)),rewrite([30(4),30(9)])].
% 24.14/24.48 30253 leq(multiplication(c1,multiplication(c3,star(c2))),multiplication(c3,star(c2))). [para(110(a,2),30201(a,2)),rewrite([24(6),367(6),47(12,R),24(11),367(11),30(13),11051(12)])].
% 24.14/24.48 30258 multiplication(addition(one,c1),multiplication(c3,star(c2))) = multiplication(c3,star(c2)). [hyper(36,a,30253,a),rewrite([24(11),48(11,R),24(3)])].
% 24.14/24.48 30259 -leq(multiplication(c3,star(c2)),multiplication(c3,star(c2))) # answer(goals). [back_rewrite(233),rewrite([30258(9),47(6,R),24(5),367(5)])].
% 24.14/24.48 30260 $F # answer(goals). [resolve(30259,a,54,a)].
% 24.14/24.48
% 24.14/24.48 % SZS output end Refutation
% 24.14/24.48 ============================== end of proof ==========================
% 24.14/24.48
% 24.14/24.48 ============================== STATISTICS ============================
% 24.14/24.48
% 24.14/24.48 Given=5114. Generated=1142780. Kept=30237. proofs=1.
% 24.14/24.48 Usable=4240. Sos=8642. Demods=384. Limbo=1, Disabled=17372. Hints=0.
% 24.14/24.48 Megabytes=18.41.
% 24.14/24.48 User_CPU=22.90, System_CPU=0.60, Wall_clock=23.
% 24.14/24.48
% 24.14/24.48 ============================== end of statistics =====================
% 24.14/24.48
% 24.14/24.48 ============================== end of search =========================
% 24.14/24.48
% 24.14/24.48 THEOREM PROVED
% 24.14/24.48 % SZS status Theorem
% 24.14/24.48
% 24.14/24.48 Exiting with 1 proof.
% 24.14/24.48
% 24.14/24.48 Process 31609 exit (max_proofs) Thu Jun 16 07:34:05 2022
% 24.14/24.48 Prover9 interrupted
%------------------------------------------------------------------------------