TSTP Solution File: KLE039+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE039+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 02:21:55 EDT 2022
% Result : Theorem 1.81s 2.12s
% Output : Refutation 1.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE039+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 : n021.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
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 12:42:15 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.74/0.99 ============================== Prover9 ===============================
% 0.74/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.74/0.99 Process 19912 was started by sandbox2 on n021.cluster.edu,
% 0.74/0.99 Thu Jun 16 12:42:15 2022
% 0.74/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19746_n021.cluster.edu".
% 0.74/0.99 ============================== end of head ===========================
% 0.74/0.99
% 0.74/0.99 ============================== INPUT =================================
% 0.74/0.99
% 0.74/0.99 % Reading from file /tmp/Prover9_19746_n021.cluster.edu
% 0.74/0.99
% 0.74/0.99 set(prolog_style_variables).
% 0.74/0.99 set(auto2).
% 0.74/0.99 % set(auto2) -> set(auto).
% 0.74/0.99 % set(auto) -> set(auto_inference).
% 0.74/0.99 % set(auto) -> set(auto_setup).
% 0.74/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.74/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/0.99 % set(auto) -> set(auto_limits).
% 0.74/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/0.99 % set(auto) -> set(auto_denials).
% 0.74/0.99 % set(auto) -> set(auto_process).
% 0.74/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.74/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.74/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.74/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.74/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.74/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.74/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.74/0.99 % set(auto2) -> assign(stats, some).
% 0.74/0.99 % set(auto2) -> clear(echo_input).
% 0.74/0.99 % set(auto2) -> set(quiet).
% 0.74/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.74/0.99 % set(auto2) -> clear(print_given).
% 0.74/0.99 assign(lrs_ticks,-1).
% 0.74/0.99 assign(sos_limit,10000).
% 0.74/0.99 assign(order,kbo).
% 0.74/0.99 set(lex_order_vars).
% 0.74/0.99 clear(print_given).
% 0.74/0.99
% 0.74/0.99 % formulas(sos). % not echoed (17 formulas)
% 0.74/0.99
% 0.74/0.99 ============================== end of input ==========================
% 0.74/0.99
% 0.74/0.99 % From the command line: assign(max_seconds, 300).
% 0.74/0.99
% 0.74/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/0.99
% 0.74/0.99 % Formulas that are not ordinary clauses:
% 0.74/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 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].
% 0.74/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 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].
% 0.74/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 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].
% 0.74/0.99 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].
% 0.74/0.99 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 15 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 17 -(all X0 star(star(X0)) = star(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.81/2.12
% 1.81/2.12 ============================== end of process non-clausal formulas ===
% 1.81/2.12
% 1.81/2.12 ============================== PROCESS INITIAL CLAUSES ===============
% 1.81/2.12
% 1.81/2.12 ============================== PREDICATE ELIMINATION =================
% 1.81/2.12
% 1.81/2.12 ============================== end predicate elimination =============
% 1.81/2.12
% 1.81/2.12 Auto_denials:
% 1.81/2.12 % copying label goals to answer in negative clause
% 1.81/2.12
% 1.81/2.12 Term ordering decisions:
% 1.81/2.12
% 1.81/2.12 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 1.81/2.12 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. star=0.
% 1.81/2.12
% 1.81/2.12 ============================== end of process initial clauses ========
% 1.81/2.12
% 1.81/2.12 ============================== CLAUSES FOR SEARCH ====================
% 1.81/2.12
% 1.81/2.12 ============================== end of clauses for search =============
% 1.81/2.12
% 1.81/2.12 ============================== SEARCH ================================
% 1.81/2.12
% 1.81/2.12 % Starting search at 0.01 seconds.
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=48.000, iters=3371
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=40.000, iters=3350
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=38.000, iters=3546
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=35.000, iters=3449
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=33.000, iters=3464
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=32.000, iters=3352
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=31.000, iters=3413
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=29.000, iters=3366
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=28.000, iters=3338
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=27.000, iters=3368
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=25.000, iters=3418
% 1.81/2.12
% 1.81/2.12 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 0.85 sec).
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=24.000, iters=3353
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=23.000, iters=3333
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=22.000, iters=3342
% 1.81/2.12
% 1.81/2.12 Low Water (keep): wt=21.000, iters=3335
% 1.81/2.12
% 1.81/2.12 ============================== PROOF =================================
% 1.81/2.12 % SZS status Theorem
% 1.81/2.12 % SZS output start Refutation
% 1.81/2.12
% 1.81/2.12 % Proof 1 at 1.12 (+ 0.02) seconds: goals.
% 1.81/2.12 % Length of proof is 100.
% 1.81/2.12 % Level of proof is 18.
% 1.81/2.12 % Maximum clause weight is 15.000.
% 1.81/2.12 % Given clauses 723.
% 1.81/2.12
% 1.81/2.12 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 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].
% 1.81/2.12 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 15 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 1.81/2.12 17 -(all X0 star(star(X0)) = star(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.81/2.12 18 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 1.81/2.12 19 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 1.81/2.12 20 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 1.81/2.12 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 1.81/2.12 22 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 1.81/2.12 23 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 1.81/2.12 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 1.81/2.12 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(13)].
% 1.81/2.12 26 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 1.81/2.12 27 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 1.81/2.12 28 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(27),rewrite([24(2)]),flip(a)].
% 1.81/2.12 29 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 1.81/2.12 30 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 1.81/2.12 31 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(30),flip(a)].
% 1.81/2.12 32 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 1.81/2.12 33 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(32),flip(a)].
% 1.81/2.12 34 star(star(c1)) != star(c1) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 1.81/2.12 35 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 1.81/2.12 36 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 1.81/2.12 37 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(15)].
% 1.81/2.12 38 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(37),rewrite([24(2)])].
% 1.81/2.12 39 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(16)].
% 1.81/2.12 40 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(39),rewrite([24(2)])].
% 1.81/2.12 42 leq(addition(zero,one),star(zero)). [para(23(a,1),25(a,1,2)),rewrite([24(3)])].
% 1.81/2.12 43 addition(A,addition(A,B)) = addition(A,B). [para(28(a,1),19(a,1)),rewrite([24(1),24(2),28(2,R),19(1),24(3)])].
% 1.81/2.12 46 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(20(a,1),31(a,1,1)),rewrite([24(4)]),flip(a)].
% 1.81/2.12 47 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(21(a,1),33(a,1,1)),rewrite([24(4)]),flip(a)].
% 1.81/2.12 50 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(35,a,26,a),rewrite([24(6)])].
% 1.81/2.12 51 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(35,a,25,a),rewrite([24(6)])].
% 1.81/2.12 52 leq(A,A). [hyper(36,b,19,a)].
% 1.81/2.12 60 -leq(A,B) | leq(multiplication(star(zero),A),B). [para(23(a,1),38(a,1,2)),rewrite([18(2)])].
% 1.81/2.12 64 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A). [para(19(a,1),40(a,1)),rewrite([29(5)])].
% 1.81/2.12 73 addition(zero,addition(one,star(zero))) = star(zero). [hyper(35,a,42,a),rewrite([24(6),28(6),24(5),28(6,R),24(5)])].
% 1.81/2.12 77 leq(A,addition(A,B)). [hyper(36,b,43,a)].
% 1.81/2.12 78 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(31(a,1),77(a,2))].
% 1.81/2.12 79 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(33(a,1),77(a,2))].
% 1.81/2.12 88 leq(multiplication(star(zero),A),A). [hyper(60,a,52,a)].
% 1.81/2.12 95 multiplication(A,addition(zero,one)) = A. [para(22(a,1),46(a,2,2)),rewrite([18(6)])].
% 1.81/2.12 97 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(46(a,2),28(a,2,2)),rewrite([24(2)]),flip(a)].
% 1.81/2.12 110 -leq(multiplication(A,addition(B,one)),A) | leq(multiplication(A,star(B)),A). [para(46(a,2),40(a,1))].
% 1.81/2.12 117 leq(star(zero),one). [para(20(a,1),88(a,1))].
% 1.81/2.12 119 addition(one,star(zero)) = one. [hyper(35,a,117,a),rewrite([24(4)])].
% 1.81/2.12 120 addition(zero,one) = star(zero). [back_rewrite(73),rewrite([119(5)])].
% 1.81/2.12 121 multiplication(A,star(zero)) = A. [back_rewrite(95),rewrite([120(3)])].
% 1.81/2.12 126 addition(A,multiplication(addition(B,one),C)) = addition(C,addition(A,multiplication(B,C))). [para(47(a,2),28(a,2,2)),rewrite([24(2)]),flip(a)].
% 1.81/2.12 145 star(zero) = one. [para(121(a,1),21(a,1)),flip(a)].
% 1.81/2.12 190 addition(one,addition(star(A),multiplication(star(A),A))) = star(A). [para(50(a,1),28(a,1)),rewrite([28(7),24(6)]),flip(a)].
% 1.81/2.12 213 addition(one,addition(star(A),multiplication(A,star(A)))) = star(A). [para(51(a,1),28(a,1)),rewrite([28(7),24(6)]),flip(a)].
% 1.81/2.12 348 addition(one,star(A)) = star(A). [para(190(a,1),43(a,1,2)),rewrite([190(9)])].
% 1.81/2.12 350 addition(one,multiplication(star(A),addition(A,one))) = star(A). [para(46(a,2),190(a,1,2))].
% 1.81/2.12 351 leq(A,multiplication(A,star(B))). [para(190(a,1),78(a,2,2)),rewrite([20(2)])].
% 1.81/2.12 352 leq(A,multiplication(star(B),A)). [para(190(a,1),79(a,2,1)),rewrite([21(2)])].
% 1.81/2.12 360 leq(addition(A,one),addition(star(B),multiplication(A,star(B)))). [para(47(a,1),351(a,2))].
% 1.81/2.12 361 addition(A,multiplication(star(B),A)) = multiplication(star(B),A). [hyper(35,a,352,a)].
% 1.81/2.12 378 addition(star(A),one) = star(A). [para(348(a,1),24(a,1)),flip(a)].
% 1.81/2.12 412 -leq(star(A),star(A)) | leq(star(addition(A,one)),star(A)). [para(350(a,1),40(a,1)),rewrite([21(8)])].
% 1.81/2.12 443 addition(star(A),multiplication(A,star(A))) = star(A). [para(213(a,1),28(a,1)),rewrite([348(6),24(5)]),flip(a)].
% 1.81/2.12 464 multiplication(addition(A,one),star(A)) = star(A). [para(443(a,1),47(a,2))].
% 1.81/2.12 475 leq(addition(A,one),star(A)). [para(443(a,1),360(a,2))].
% 1.81/2.12 476 multiplication(star(A),star(star(A))) = star(star(A)). [para(443(a,1),361(a,1)),flip(a)].
% 1.81/2.12 481 addition(A,star(A)) = star(A). [hyper(35,a,475,a),rewrite([24(4),28(4,R),348(3)])].
% 1.81/2.12 651 leq(A,addition(B,multiplication(A,addition(C,one)))). [para(97(a,2),77(a,2))].
% 1.81/2.12 685 leq(A,multiplication(addition(A,B),addition(C,one))). [para(33(a,1),651(a,2)),rewrite([24(1)])].
% 1.81/2.12 970 leq(one,multiplication(star(A),addition(B,one))). [para(190(a,1),685(a,2,1))].
% 1.81/2.12 976 addition(one,multiplication(star(A),addition(B,one))) = multiplication(star(A),addition(B,one)). [hyper(35,a,970,a)].
% 1.81/2.12 978 multiplication(star(A),addition(A,one)) = star(A). [back_rewrite(350),rewrite([976(6)])].
% 1.81/2.12 1128 leq(multiplication(star(A),A),star(A)). [para(978(a,1),78(a,2))].
% 1.81/2.12 1587 leq(multiplication(star(addition(A,one)),star(A)),star(addition(A,one))). [hyper(110,a,1128,a)].
% 1.81/2.12 1789 leq(A,addition(B,multiplication(addition(C,one),A))). [para(126(a,2),77(a,2))].
% 1.81/2.12 1826 leq(A,addition(B,multiplication(star(C),A))). [para(378(a,1),1789(a,2,2,1))].
% 1.81/2.12 1832 leq(A,multiplication(star(B),addition(A,C))). [para(31(a,1),1826(a,2)),rewrite([24(2)])].
% 1.81/2.12 1847 leq(multiplication(A,B),multiplication(star(C),multiplication(addition(A,D),B))). [para(33(a,1),1832(a,2,2))].
% 1.81/2.12 9593 leq(star(addition(A,one)),star(A)). [hyper(412,a,52,a)].
% 1.81/2.12 9594 addition(star(A),star(addition(A,one))) = star(A). [hyper(35,a,9593,a),rewrite([24(5)])].
% 1.81/2.12 10240 leq(multiplication(star(addition(A,one)),star(star(A))),star(addition(A,one))). [hyper(64,a,1587,a),rewrite([476(7)])].
% 1.81/2.12 10241 multiplication(star(addition(A,one)),star(A)) = star(addition(A,one)). [hyper(35,a,1587,a),rewrite([24(9),46(9,R),378(6)])].
% 1.81/2.12 10677 leq(multiplication(A,B),multiplication(star(C),multiplication(star(A),B))). [para(481(a,1),1847(a,2,2,1))].
% 1.81/2.12 10730 leq(star(A),multiplication(star(B),star(addition(A,one)))). [para(464(a,1),10677(a,1)),rewrite([10241(7)])].
% 1.81/2.12 10754 leq(star(A),star(addition(A,one))). [para(145(a,1),10730(a,2,1)),rewrite([21(6)])].
% 1.81/2.12 10756 star(addition(A,one)) = star(A). [hyper(35,a,10754,a),rewrite([9594(5)]),flip(a)].
% 1.81/2.12 10772 leq(star(star(A)),star(A)). [back_rewrite(10240),rewrite([10756(3),476(4),10756(5)])].
% 1.81/2.12 10835 star(star(A)) = star(A). [hyper(35,a,10772,a),rewrite([24(4),481(4)])].
% 1.81/2.12 10836 $F # answer(goals). [resolve(10835,a,34,a)].
% 1.81/2.12
% 1.81/2.12 % SZS output end Refutation
% 1.81/2.12 ============================== end of proof ==========================
% 1.81/2.12
% 1.81/2.12 ============================== STATISTICS ============================
% 1.81/2.12
% 1.81/2.12 Given=723. Generated=43057. Kept=10813. proofs=1.
% 1.81/2.12 Usable=656. Sos=9510. Demods=828. Limbo=0, Disabled=664. Hints=0.
% 1.81/2.12 Megabytes=10.23.
% 1.81/2.12 User_CPU=1.12, System_CPU=0.02, Wall_clock=1.
% 1.81/2.12
% 1.81/2.12 ============================== end of statistics =====================
% 1.81/2.12
% 1.81/2.12 ============================== end of search =========================
% 1.81/2.12
% 1.81/2.12 THEOREM PROVED
% 1.81/2.12 % SZS status Theorem
% 1.81/2.12
% 1.81/2.12 Exiting with 1 proof.
% 1.81/2.12
% 1.81/2.12 Process 19912 exit (max_proofs) Thu Jun 16 12:42:16 2022
% 1.88/2.12 Prover9 interrupted
%------------------------------------------------------------------------------