TSTP Solution File: KLE160+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE160+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 02:22:34 EDT 2022
% Result : Theorem 22.63s 22.92s
% Output : Refutation 22.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE160+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n011.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 07:22:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.76/1.03 ============================== Prover9 ===============================
% 0.76/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.03 Process 20128 was started by sandbox2 on n011.cluster.edu,
% 0.76/1.03 Thu Jun 16 07:22:21 2022
% 0.76/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19974_n011.cluster.edu".
% 0.76/1.03 ============================== end of head ===========================
% 0.76/1.03
% 0.76/1.03 ============================== INPUT =================================
% 0.76/1.03
% 0.76/1.03 % Reading from file /tmp/Prover9_19974_n011.cluster.edu
% 0.76/1.03
% 0.76/1.03 set(prolog_style_variables).
% 0.76/1.03 set(auto2).
% 0.76/1.03 % set(auto2) -> set(auto).
% 0.76/1.03 % set(auto) -> set(auto_inference).
% 0.76/1.03 % set(auto) -> set(auto_setup).
% 0.76/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.03 % set(auto) -> set(auto_limits).
% 0.76/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.03 % set(auto) -> set(auto_denials).
% 0.76/1.03 % set(auto) -> set(auto_process).
% 0.76/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.03 % set(auto2) -> assign(stats, some).
% 0.76/1.03 % set(auto2) -> clear(echo_input).
% 0.76/1.03 % set(auto2) -> set(quiet).
% 0.76/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.03 % set(auto2) -> clear(print_given).
% 0.76/1.03 assign(lrs_ticks,-1).
% 0.76/1.03 assign(sos_limit,10000).
% 0.76/1.03 assign(order,kbo).
% 0.76/1.03 set(lex_order_vars).
% 0.76/1.03 clear(print_given).
% 0.76/1.03
% 0.76/1.03 % formulas(sos). % not echoed (19 formulas)
% 0.76/1.03
% 0.76/1.03 ============================== end of input ==========================
% 0.76/1.03
% 0.76/1.03 % From the command line: assign(max_seconds, 300).
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.03
% 0.76/1.03 % Formulas that are not ordinary clauses:
% 0.76/1.03 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(distributivity1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(distributivity2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 13 (all A all B all C (leq(addition(multiplication(A,C),B),C) -> leq(multiplication(star(A),B),C))) # label(star_induction1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 14 (all A all B all C (leq(addition(multiplication(C,A),B),C) -> leq(multiplication(B,star(A)),C))) # label(star_induction2) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 16 (all A all B all C (leq(C,addition(multiplication(A,C),B)) -> leq(C,multiplication(strong_iteration(A),B)))) # label(infty_coinduction) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 19 -(all X0 all X1 all X2 (leq(multiplication(X0,X1),multiplication(X1,X2)) -> leq(multiplication(star(X0),X1),multiplication(X1,star(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 22.63/22.92
% 22.63/22.92 ============================== end of process non-clausal formulas ===
% 22.63/22.92
% 22.63/22.92 ============================== PROCESS INITIAL CLAUSES ===============
% 22.63/22.92
% 22.63/22.92 ============================== PREDICATE ELIMINATION =================
% 22.63/22.92
% 22.63/22.92 ============================== end predicate elimination =============
% 22.63/22.92
% 22.63/22.92 Auto_denials:
% 22.63/22.92 % copying label goals to answer in negative clause
% 22.63/22.92
% 22.63/22.92 Term ordering decisions:
% 22.63/22.92 Function symbol KB weights: one=1. zero=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 22.63/22.92
% 22.63/22.92 ============================== end of process initial clauses ========
% 22.63/22.92
% 22.63/22.92 ============================== CLAUSES FOR SEARCH ====================
% 22.63/22.92
% 22.63/22.92 ============================== end of clauses for search =============
% 22.63/22.92
% 22.63/22.92 ============================== SEARCH ================================
% 22.63/22.92
% 22.63/22.92 % Starting search at 0.01 seconds.
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=43.000, iters=3413
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=33.000, iters=3448
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=32.000, iters=3378
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=31.000, iters=3338
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=30.000, iters=3470
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=27.000, iters=3439
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=26.000, iters=3348
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=25.000, iters=3354
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=24.000, iters=3387
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=23.000, iters=3333
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=22.000, iters=3346
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=21.000, iters=3355
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=17.000, iters=3508
% 22.63/22.92
% 22.63/22.92 Low Water (displace): id=5608, wt=43.000
% 22.63/22.92
% 22.63/22.92 Low Water (displace): id=13923, wt=17.000
% 22.63/22.92
% 22.63/22.92 Low Water (displace): id=14099, wt=16.000
% 22.63/22.92
% 22.63/22.92 Low Water (displace): id=14130, wt=14.000
% 22.63/22.92
% 22.63/22.92 Low Water (displace): id=14422, wt=13.000
% 22.63/22.92
% 22.63/22.92 Low Water (displace): id=15080, wt=12.000
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=16.000, iters=3335
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=15.000, iters=3337
% 22.63/22.92
% 22.63/22.92 Low Water (keep): wt=14.000, iters=3335
% 22.63/22.92
% 22.63/22.92 Low Water (displace): id=27607, wt=11.000
% 22.63/22.92
% 22.63/22.92 Low Water (displace): id=29222, wt=10.000
% 22.63/22.92
% 22.63/22.92 ============================== PROOF =================================
% 22.63/22.92 % SZS status Theorem
% 22.63/22.92 % SZS output start Refutation
% 22.63/22.92
% 22.63/22.92 % Proof 1 at 21.23 (+ 0.67) seconds: goals.
% 22.63/22.92 % Length of proof is 89.
% 22.63/22.92 % Level of proof is 15.
% 22.63/22.92 % Maximum clause weight is 24.000.
% 22.63/22.92 % Given clauses 5859.
% 22.63/22.92
% 22.63/22.92 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 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].
% 22.63/22.92 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 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].
% 22.63/22.92 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(distributivity1) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(distributivity2) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 13 (all A all B all C (leq(addition(multiplication(A,C),B),C) -> leq(multiplication(star(A),B),C))) # label(star_induction1) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 14 (all A all B all C (leq(addition(multiplication(C,A),B),C) -> leq(multiplication(B,star(A)),C))) # label(star_induction2) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 22.63/22.92 19 -(all X0 all X1 all X2 (leq(multiplication(X0,X1),multiplication(X1,X2)) -> leq(multiplication(star(X0),X1),multiplication(X1,star(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 22.63/22.92 20 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 22.63/22.92 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 22.63/22.92 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 22.63/22.92 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 22.63/22.92 24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 22.63/22.92 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 22.63/22.92 26 leq(multiplication(c1,c2),multiplication(c2,c3)) # label(goals) # label(negated_conjecture). [clausify(19)].
% 22.63/22.92 27 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 22.63/22.92 28 addition(one,multiplication(A,star(A))) = star(A). [copy(27),flip(a)].
% 22.63/22.92 29 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom). [clausify(12)].
% 22.63/22.92 30 addition(one,multiplication(star(A),A)) = star(A). [copy(29),flip(a)].
% 22.63/22.92 31 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 22.63/22.92 32 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(31),rewrite([25(5)]),flip(a)].
% 22.63/22.92 35 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 22.63/22.92 36 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(35),rewrite([25(2)]),flip(a)].
% 22.63/22.92 37 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 22.63/22.92 38 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 22.63/22.92 39 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(38),flip(a)].
% 22.63/22.92 40 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 22.63/22.92 41 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(40),flip(a)].
% 22.63/22.92 42 -leq(multiplication(star(c1),c2),multiplication(c2,star(c3))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 22.63/22.92 43 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 22.63/22.92 44 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 22.63/22.92 45 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom). [clausify(13)].
% 22.63/22.92 46 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(45),rewrite([25(2)])].
% 22.63/22.92 47 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction2) # label(axiom). [clausify(14)].
% 22.63/22.92 48 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(47),rewrite([25(2)])].
% 22.63/22.92 52 star(zero) = one. [para(24(a,1),28(a,1,2)),rewrite([20(3)]),flip(a)].
% 22.63/22.92 55 addition(A,addition(A,B)) = addition(A,B). [para(36(a,1),21(a,1)),rewrite([25(1),25(2),36(2,R),21(1),25(3)])].
% 22.63/22.92 56 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(37(a,1),28(a,1,2))].
% 22.63/22.92 57 addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)). [para(37(a,1),32(a,1,2))].
% 22.63/22.92 58 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),39(a,1,1)),rewrite([25(4)]),flip(a)].
% 22.63/22.92 59 addition(A,multiplication(A,multiplication(B,star(B)))) = multiplication(A,star(B)). [para(28(a,1),39(a,2,2)),rewrite([22(2)])].
% 22.63/22.92 63 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(23(a,1),41(a,1,1)),rewrite([25(4)]),flip(a)].
% 22.63/22.92 64 addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A). [para(28(a,1),41(a,2,1)),rewrite([23(2),37(3)])].
% 22.63/22.92 66 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A). [para(32(a,1),41(a,2,1)),rewrite([23(2),37(3)])].
% 22.63/22.92 68 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(37(a,1),41(a,1,1)),rewrite([25(6)])].
% 22.63/22.92 69 addition(multiplication(A,B),multiplication(C,multiplication(D,B))) = multiplication(addition(A,multiplication(C,D)),B). [para(37(a,1),41(a,1,2))].
% 22.63/22.92 70 addition(multiplication(c1,c2),multiplication(c2,c3)) = multiplication(c2,c3). [hyper(43,a,26,a)].
% 22.63/22.92 71 leq(A,A). [hyper(44,b,21,a)].
% 22.63/22.92 80 -leq(addition(c2,multiplication(c1,multiplication(c2,star(c3)))),multiplication(c2,star(c3))) # answer(goals). [ur(46,b,42,a)].
% 22.63/22.92 82 -leq(addition(A,B),one) | leq(multiplication(star(B),A),one). [para(22(a,1),46(a,1,2))].
% 22.63/22.92 91 -leq(addition(A,B),B) | leq(multiplication(A,star(one)),B). [para(22(a,1),48(a,1,2))].
% 22.63/22.92 114 leq(A,addition(A,B)). [hyper(44,b,55,a)].
% 22.63/22.92 115 addition(one,star(A)) = star(A). [para(28(a,1),55(a,1,2)),rewrite([28(7)])].
% 22.63/22.92 122 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(39(a,1),114(a,2))].
% 22.63/22.92 124 addition(one,multiplication(A,zero)) = star(multiplication(A,zero)). [para(24(a,1),56(a,1,2,2))].
% 22.63/22.92 133 strong_iteration(multiplication(A,zero)) = star(multiplication(A,zero)). [para(24(a,1),57(a,1,2,2)),rewrite([124(4)]),flip(a)].
% 22.63/22.92 174 addition(A,multiplication(A,zero)) = A. [para(24(a,1),59(a,1,2,2)),rewrite([52(5),22(5)])].
% 22.63/22.92 175 addition(A,addition(B,multiplication(A,multiplication(C,star(C))))) = addition(B,multiplication(A,star(C))). [para(59(a,1),36(a,2,2)),rewrite([25(4)])].
% 22.63/22.92 183 addition(A,addition(B,multiplication(A,zero))) = addition(A,B). [para(174(a,1),36(a,2,2)),rewrite([25(3),25(5)])].
% 22.63/22.92 199 leq(multiplication(A,B),addition(A,multiplication(A,B))). [para(58(a,1),122(a,2))].
% 22.63/22.92 255 multiplication(star(A),A) = multiplication(A,star(A)). [para(64(a,1),58(a,2)),rewrite([25(4),30(4)]),flip(a)].
% 22.63/22.92 270 leq(multiplication(A,star(A)),star(A)). [para(56(a,1),199(a,2)),rewrite([23(3),23(4),23(4)])].
% 22.63/22.92 281 multiplication(star(multiplication(A,zero)),B) = addition(B,multiplication(A,zero)). [para(133(a,1),66(a,1,2,2,1)),rewrite([37(7),24(6),133(6)]),flip(a)].
% 22.63/22.92 283 multiplication(addition(A,one),star(A)) = star(A). [hyper(43,a,270,a),rewrite([25(4),63(4,R)])].
% 22.63/22.92 332 leq(multiplication(A,multiplication(B,C)),multiplication(D,C)) | multiplication(addition(D,multiplication(A,B)),C) != multiplication(D,C). [para(68(a,1),44(b,1))].
% 22.63/22.92 366 -leq(multiplication(addition(A,multiplication(B,C)),D),B) | leq(multiplication(A,multiplication(D,star(multiplication(C,D)))),B). [para(69(a,1),48(a,1)),rewrite([37(8)])].
% 22.63/22.92 391 addition(A,star(A)) = star(A). [para(283(a,1),58(a,2,2)),rewrite([25(5),115(5),283(4),25(5),36(5),25(4),36(5,R),25(4),115(4)]),flip(a)].
% 22.63/22.92 539 -leq(A,one) | leq(multiplication(A,star(A)),one). [para(21(a,1),82(a,1)),rewrite([255(4)])].
% 22.63/22.92 624 leq(star(one),one). [hyper(539,a,71,a),rewrite([23(4)])].
% 22.63/22.92 627 star(one) = one. [hyper(43,a,624,a),rewrite([25(4),391(4)])].
% 22.63/22.92 646 -leq(addition(A,B),B) | leq(A,B). [back_rewrite(91),rewrite([627(4),22(4)])].
% 22.63/22.92 1505 addition(A,star(multiplication(A,zero))) = addition(A,one). [para(124(a,1),183(a,1,2))].
% 22.63/22.92 3785 addition(A,multiplication(addition(B,multiplication(A,C)),star(C))) = multiplication(addition(A,B),star(C)). [para(41(a,1),175(a,2)),rewrite([69(6),25(6)])].
% 22.63/22.92 11445 -leq(addition(A,multiplication(B,zero)),B) | leq(A,B). [para(124(a,1),366(a,1,1)),rewrite([281(4),24(7),52(7),22(7),23(6)])].
% 22.63/22.92 11510 -leq(addition(multiplication(c1,multiplication(c2,star(c3))),multiplication(c2,star(multiplication(star(c3),zero)))),multiplication(c2,star(c3))) # answer(goals). [ur(11445,b,80,a),rewrite([37(14),25(15),36(15),25(14),58(14,R),25(13),124(13)])].
% 22.63/22.92 11544 -leq(addition(multiplication(c2,star(c3)),addition(multiplication(c1,multiplication(c2,star(c3))),multiplication(c2,star(multiplication(star(c3),zero))))),multiplication(c2,star(c3))) # answer(goals). [ur(646,b,11510,a),rewrite([25(19)])].
% 22.63/22.92 11578 -leq(multiplication(addition(one,c1),multiplication(c2,star(c3))),multiplication(c2,star(c3))) # answer(goals). [para(36(a,2),11544(a,1)),rewrite([25(18),39(18),1505(15),25(11),115(11),25(11),63(11,R),25(3)])].
% 22.63/22.92 11580 multiplication(addition(one,c1),multiplication(c2,star(c3))) != multiplication(c2,star(c3)) # answer(goals). [ur(332,a,11578,a),rewrite([63(7,R),25(5),55(5),37(8)])].
% 22.63/22.92 31447 multiplication(addition(one,c1),multiplication(c2,star(c3))) = multiplication(c2,star(c3)). [para(70(a,1),3785(a,1,2,1)),rewrite([37(7),58(8,R),25(7),28(7),63(9,R),25(7),37(12)]),flip(a)].
% 22.63/22.92 31448 $F # answer(goals). [resolve(31447,a,11580,a)].
% 22.63/22.92
% 22.63/22.92 % SZS output end Refutation
% 22.63/22.92 ============================== end of proof ==========================
% 22.63/22.92
% 22.63/22.92 ============================== STATISTICS ============================
% 22.63/22.92
% 22.63/22.92 Given=5859. Generated=1302040. Kept=31418. proofs=1.
% 22.63/22.92 Usable=4466. Sos=9869. Demods=773. Limbo=0, Disabled=17103. Hints=0.
% 22.63/22.92 Megabytes=18.89.
% 22.63/22.92 User_CPU=21.23, System_CPU=0.67, Wall_clock=22.
% 22.63/22.92
% 22.63/22.92 ============================== end of statistics =====================
% 22.63/22.92
% 22.63/22.92 ============================== end of search =========================
% 22.63/22.92
% 22.63/22.92 THEOREM PROVED
% 22.63/22.92 % SZS status Theorem
% 22.63/22.92
% 22.63/22.92 Exiting with 1 proof.
% 22.63/22.92
% 22.63/22.92 Process 20128 exit (max_proofs) Thu Jun 16 07:22:43 2022
% 22.63/22.92 Prover9 interrupted
%------------------------------------------------------------------------------