TSTP Solution File: KLE145+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE145+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 02:22:28 EDT 2022
% Result : Theorem 7.82s 8.12s
% Output : Refutation 7.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE145+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 08:12:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/0.98 ============================== Prover9 ===============================
% 0.45/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.45/0.98 Process 15978 was started by sandbox2 on n016.cluster.edu,
% 0.45/0.98 Thu Jun 16 08:12:34 2022
% 0.45/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15825_n016.cluster.edu".
% 0.45/0.98 ============================== end of head ===========================
% 0.45/0.98
% 0.45/0.98 ============================== INPUT =================================
% 0.45/0.98
% 0.45/0.98 % Reading from file /tmp/Prover9_15825_n016.cluster.edu
% 0.45/0.98
% 0.45/0.98 set(prolog_style_variables).
% 0.45/0.98 set(auto2).
% 0.45/0.98 % set(auto2) -> set(auto).
% 0.45/0.98 % set(auto) -> set(auto_inference).
% 0.45/0.98 % set(auto) -> set(auto_setup).
% 0.45/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.45/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/0.98 % set(auto) -> set(auto_limits).
% 0.45/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/0.98 % set(auto) -> set(auto_denials).
% 0.45/0.98 % set(auto) -> set(auto_process).
% 0.45/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.45/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.45/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.45/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.45/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.45/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.45/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.45/0.98 % set(auto2) -> assign(stats, some).
% 0.45/0.98 % set(auto2) -> clear(echo_input).
% 0.45/0.98 % set(auto2) -> set(quiet).
% 0.45/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.45/0.98 % set(auto2) -> clear(print_given).
% 0.45/0.98 assign(lrs_ticks,-1).
% 0.45/0.98 assign(sos_limit,10000).
% 0.45/0.98 assign(order,kbo).
% 0.45/0.98 set(lex_order_vars).
% 0.45/0.98 clear(print_given).
% 0.45/0.98
% 0.45/0.98 % formulas(sos). % not echoed (19 formulas)
% 0.45/0.98
% 0.45/0.98 ============================== end of input ==========================
% 0.45/0.98
% 0.45/0.98 % From the command line: assign(max_seconds, 300).
% 0.45/0.98
% 0.45/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/0.98
% 0.45/0.98 % Formulas that are not ordinary clauses:
% 0.45/0.98 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.98 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].
% 0.45/0.98 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.98 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.98 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].
% 0.45/0.98 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.98 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.98 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].
% 0.45/0.98 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].
% 0.45/0.98 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.98 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.98 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.98 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].
% 0.45/0.98 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].
% 7.82/8.12 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 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].
% 7.82/8.12 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 19 -(all X0 (leq(star(strong_iteration(X0)),strong_iteration(X0)) & leq(strong_iteration(X0),star(strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.82/8.12
% 7.82/8.12 ============================== end of process non-clausal formulas ===
% 7.82/8.12
% 7.82/8.12 ============================== PROCESS INITIAL CLAUSES ===============
% 7.82/8.12
% 7.82/8.12 ============================== PREDICATE ELIMINATION =================
% 7.82/8.12
% 7.82/8.12 ============================== end predicate elimination =============
% 7.82/8.12
% 7.82/8.12 Auto_denials:
% 7.82/8.12 % copying label goals to answer in negative clause
% 7.82/8.12
% 7.82/8.12 Term ordering decisions:
% 7.82/8.12 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 7.82/8.12
% 7.82/8.12 ============================== end of process initial clauses ========
% 7.82/8.12
% 7.82/8.12 ============================== CLAUSES FOR SEARCH ====================
% 7.82/8.12
% 7.82/8.12 ============================== end of clauses for search =============
% 7.82/8.12
% 7.82/8.12 ============================== SEARCH ================================
% 7.82/8.12
% 7.82/8.12 % Starting search at 0.01 seconds.
% 7.82/8.12
% 7.82/8.12 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 0.59 sec).
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=39.000, iters=3401
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=35.000, iters=3341
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=33.000, iters=3368
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=32.000, iters=3471
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=29.000, iters=3361
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=26.000, iters=3338
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=25.000, iters=3418
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=24.000, iters=3389
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=23.000, iters=3363
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=22.000, iters=3348
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=21.000, iters=3356
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=20.000, iters=3349
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=19.000, iters=3350
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=18.000, iters=3348
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=5535, wt=43.000
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=6152, wt=42.000
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=5654, wt=40.000
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=12344, wt=17.000
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=12406, wt=15.000
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=12409, wt=14.000
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=12413, wt=13.000
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=13279, wt=12.000
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=17.000, iters=3333
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=15081, wt=11.000
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=16.000, iters=3341
% 7.82/8.12
% 7.82/8.12 Low Water (displace): id=16956, wt=10.000
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=15.000, iters=3334
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=14.000, iters=3335
% 7.82/8.12
% 7.82/8.12 Low Water (keep): wt=13.000, iters=4498
% 7.82/8.12
% 7.82/8.12 ============================== PROOF =================================
% 7.82/8.12 % SZS status Theorem
% 7.82/8.12 % SZS output start Refutation
% 7.82/8.12
% 7.82/8.12 % Proof 1 at 6.87 (+ 0.28) seconds: goals.
% 7.82/8.12 % Length of proof is 72.
% 7.82/8.12 % Level of proof is 13.
% 7.82/8.12 % Maximum clause weight is 17.000.
% 7.82/8.12 % Given clauses 3367.
% 7.82/8.12
% 7.82/8.12 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 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].
% 7.82/8.12 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 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].
% 7.82/8.12 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 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].
% 7.82/8.12 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].
% 7.82/8.12 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 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].
% 7.82/8.12 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 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].
% 7.82/8.12 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 7.82/8.12 19 -(all X0 (leq(star(strong_iteration(X0)),strong_iteration(X0)) & leq(strong_iteration(X0),star(strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.82/8.12 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 7.82/8.12 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 7.82/8.12 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 7.82/8.12 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 7.82/8.12 26 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 7.82/8.12 27 addition(one,multiplication(A,star(A))) = star(A). [copy(26),flip(a)].
% 7.82/8.12 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 7.82/8.12 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 7.82/8.12 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 7.82/8.12 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([25(2)]),flip(a)].
% 7.82/8.12 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 7.82/8.12 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 7.82/8.12 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 7.82/8.12 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 7.82/8.12 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 7.82/8.12 41 -leq(star(strong_iteration(c1)),strong_iteration(c1)) | -leq(strong_iteration(c1),star(strong_iteration(c1))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 7.82/8.12 42 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 7.82/8.12 43 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 7.82/8.12 44 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom). [clausify(13)].
% 7.82/8.12 45 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(44),rewrite([25(2)])].
% 7.82/8.12 48 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom). [clausify(16)].
% 7.82/8.12 49 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)). [copy(48),rewrite([25(2)])].
% 7.82/8.12 54 addition(A,addition(A,B)) = addition(A,B). [para(35(a,1),21(a,1)),rewrite([25(1),25(2),35(2,R),21(1),25(3)])].
% 7.82/8.12 55 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(36(a,1),27(a,1,2))].
% 7.82/8.12 56 addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)). [para(36(a,1),31(a,1,2))].
% 7.82/8.12 57 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 7.82/8.12 60 addition(A,multiplication(A,multiplication(B,strong_iteration(B)))) = multiplication(A,strong_iteration(B)). [para(31(a,1),38(a,2,2)),rewrite([22(2)])].
% 7.82/8.12 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(23(a,1),40(a,1,1)),rewrite([25(4)]),flip(a)].
% 7.82/8.12 65 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A). [para(31(a,1),40(a,2,1)),rewrite([23(2),36(3)])].
% 7.82/8.12 69 leq(A,A). [hyper(43,b,21,a)].
% 7.82/8.12 83 -leq(addition(A,multiplication(B,multiplication(C,D))),D) | leq(multiplication(star(multiplication(B,C)),A),D). [para(36(a,1),45(a,1,2))].
% 7.82/8.12 99 -leq(A,addition(B,multiplication(C,multiplication(D,A)))) | leq(A,multiplication(strong_iteration(multiplication(C,D)),B)). [para(36(a,1),49(a,2,2))].
% 7.82/8.12 109 leq(A,addition(A,B)). [hyper(43,b,54,a)].
% 7.82/8.12 110 addition(one,star(A)) = star(A). [para(27(a,1),54(a,1,2)),rewrite([27(7)])].
% 7.82/8.12 111 addition(one,strong_iteration(A)) = strong_iteration(A). [para(31(a,1),54(a,1,2)),rewrite([31(7)])].
% 7.82/8.12 116 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(38(a,1),109(a,2))].
% 7.82/8.12 147 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(57(a,2),35(a,2,2)),rewrite([25(2)]),flip(a)].
% 7.82/8.12 197 leq(multiplication(A,B),addition(A,multiplication(A,B))). [para(57(a,1),116(a,2))].
% 7.82/8.12 201 addition(A,addition(B,multiplication(A,multiplication(C,strong_iteration(C))))) = addition(B,multiplication(A,strong_iteration(C))). [para(60(a,1),35(a,2,2)),rewrite([25(4)])].
% 7.82/8.12 238 addition(A,addition(B,addition(one,multiplication(A,B)))) = multiplication(addition(A,one),addition(B,one)). [para(62(a,1),57(a,2,2)),rewrite([35(10,R),35(9),25(8),35(9,R),25(8),35(10,R),25(9)]),flip(a)].
% 7.82/8.12 281 leq(multiplication(A,star(A)),star(A)). [para(55(a,1),197(a,2)),rewrite([23(3),23(4),23(4)])].
% 7.82/8.12 287 multiplication(addition(A,one),star(A)) = star(A). [hyper(42,a,281,a),rewrite([25(4),62(4,R)])].
% 7.82/8.12 394 addition(A,star(A)) = star(A). [para(287(a,1),57(a,2,2)),rewrite([25(5),110(5),287(4),25(5),35(5),25(4),35(5,R),25(4),110(4)]),flip(a)].
% 7.82/8.12 404 leq(A,star(A)). [hyper(43,b,394,a)].
% 7.82/8.12 409 -leq(star(strong_iteration(c1)),strong_iteration(c1)) # answer(goals). [back_unit_del(41),unit_del(b,404)].
% 7.82/8.12 649 -leq(multiplication(A,addition(one,multiplication(B,C))),C) | leq(multiplication(star(multiplication(A,B)),A),C). [para(57(a,2),83(a,1)),rewrite([25(3)])].
% 7.82/8.12 915 -leq(A,multiplication(B,addition(one,multiplication(C,A)))) | leq(A,multiplication(strong_iteration(multiplication(B,C)),B)). [para(57(a,2),99(a,2)),rewrite([25(3)])].
% 7.82/8.12 1787 leq(A,addition(B,multiplication(A,addition(C,one)))). [para(147(a,2),109(a,2))].
% 7.82/8.12 1830 leq(A,multiplication(addition(A,B),addition(C,one))). [para(40(a,1),1787(a,2)),rewrite([25(1)])].
% 7.82/8.12 2149 leq(A,multiplication(strong_iteration(B),multiplication(A,addition(C,one)))). [para(65(a,1),1830(a,2,1)),rewrite([36(5)])].
% 7.82/8.12 2616 leq(A,multiplication(strong_iteration(B),addition(A,multiplication(A,C)))). [para(57(a,1),2149(a,2,2))].
% 7.82/8.12 3213 leq(one,multiplication(strong_iteration(A),strong_iteration(B))). [para(56(a,1),2616(a,2,2)),rewrite([23(4)])].
% 7.82/8.12 3235 addition(one,multiplication(strong_iteration(A),strong_iteration(B))) = multiplication(strong_iteration(A),strong_iteration(B)). [hyper(42,a,3213,a)].
% 7.82/8.12 6437 addition(one,multiplication(A,multiplication(strong_iteration(A),strong_iteration(A)))) = multiplication(strong_iteration(A),strong_iteration(A)). [para(201(a,1),238(a,1,2)),rewrite([36(7),35(9,R),25(8),38(8),57(6,R),25(5),111(5),25(10),31(10),25(11),31(11)])].
% 7.82/8.12 14853 -leq(addition(one,multiplication(A,B)),B) | leq(star(A),B). [para(23(a,1),649(a,1)),rewrite([23(6),22(7)])].
% 7.82/8.12 17734 -leq(A,addition(one,multiplication(B,A))) | leq(A,strong_iteration(B)). [para(23(a,1),915(a,2)),rewrite([23(6),22(7)])].
% 7.82/8.12 19889 -leq(multiplication(strong_iteration(c1),strong_iteration(c1)),strong_iteration(c1)) # answer(goals). [ur(14853,b,409,a),rewrite([3235(7)])].
% 7.82/8.12 21836 $F # answer(goals). [ur(17734,b,19889,a),rewrite([6437(14)]),unit_del(a,69)].
% 7.82/8.12
% 7.82/8.12 % SZS output end Refutation
% 7.82/8.12 ============================== end of proof ==========================
% 7.82/8.12
% 7.82/8.12 ============================== STATISTICS ============================
% 7.82/8.12
% 7.82/8.12 Given=3367. Generated=477344. Kept=21806. proofs=1.
% 7.82/8.12 Usable=3183. Sos=9985. Demods=729. Limbo=0, Disabled=8658. Hints=0.
% 7.82/8.12 Megabytes=14.04.
% 7.82/8.12 User_CPU=6.87, System_CPU=0.28, Wall_clock=7.
% 7.82/8.12
% 7.82/8.12 ============================== end of statistics =====================
% 7.82/8.12
% 7.82/8.12 ============================== end of search =========================
% 7.82/8.12
% 7.82/8.12 THEOREM PROVED
% 7.82/8.12 % SZS status Theorem
% 7.82/8.12
% 7.82/8.12 Exiting with 1 proof.
% 7.82/8.12
% 7.82/8.12 Process 15978 exit (max_proofs) Thu Jun 16 08:12:41 2022
% 7.82/8.12 Prover9 interrupted
%------------------------------------------------------------------------------