TSTP Solution File: KLE140+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE140+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 02:22:25 EDT 2022
% Result : Theorem 36.24s 36.57s
% Output : Refutation 36.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE140+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n005.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 13:27:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 6932 was started by sandbox2 on n005.cluster.edu,
% 0.43/0.99 Thu Jun 16 13:27:39 2022
% 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6778_n005.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_6778_n005.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (19 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 36.24/36.57 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 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].
% 36.24/36.57 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 19 -(all X0 all X1 (leq(X0,X1) -> leq(strong_iteration(X0),strong_iteration(X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 36.24/36.57
% 36.24/36.57 ============================== end of process non-clausal formulas ===
% 36.24/36.57
% 36.24/36.57 ============================== PROCESS INITIAL CLAUSES ===============
% 36.24/36.57
% 36.24/36.57 ============================== PREDICATE ELIMINATION =================
% 36.24/36.57
% 36.24/36.57 ============================== end predicate elimination =============
% 36.24/36.57
% 36.24/36.57 Auto_denials:
% 36.24/36.57 % copying label goals to answer in negative clause
% 36.24/36.57
% 36.24/36.57 Term ordering decisions:
% 36.24/36.57 Function symbol KB weights: one=1. zero=1. c1=1. c2=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 36.24/36.57
% 36.24/36.57 ============================== end of process initial clauses ========
% 36.24/36.57
% 36.24/36.57 ============================== CLAUSES FOR SEARCH ====================
% 36.24/36.57
% 36.24/36.57 ============================== end of clauses for search =============
% 36.24/36.57
% 36.24/36.57 ============================== SEARCH ================================
% 36.24/36.57
% 36.24/36.57 % Starting search at 0.01 seconds.
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=39.000, iters=3382
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=38.000, iters=3358
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=36.000, iters=3336
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=35.000, iters=3390
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=33.000, iters=3372
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=31.000, iters=3350
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=30.000, iters=3480
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=27.000, iters=3479
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=26.000, iters=3361
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=25.000, iters=3341
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=24.000, iters=3341
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=23.000, iters=3341
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=22.000, iters=3379
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=21.000, iters=3349
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=20.000, iters=3343
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=19.000, iters=5761
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=18.000, iters=4753
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=17.000, iters=3795
% 36.24/36.57
% 36.24/36.57 Low Water (displace): id=5450, wt=43.000
% 36.24/36.57
% 36.24/36.57 Low Water (displace): id=13504, wt=17.000
% 36.24/36.57
% 36.24/36.57 Low Water (displace): id=13722, wt=15.000
% 36.24/36.57
% 36.24/36.57 Low Water (displace): id=13772, wt=14.000
% 36.24/36.57
% 36.24/36.57 Low Water (displace): id=14145, wt=13.000
% 36.24/36.57
% 36.24/36.57 Low Water (displace): id=14894, wt=12.000
% 36.24/36.57
% 36.24/36.57 Low Water (displace): id=15575, wt=11.000
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=16.000, iters=3336
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=15.000, iters=3359
% 36.24/36.57
% 36.24/36.57 Low Water (keep): wt=13.000, iters=3382
% 36.24/36.57
% 36.24/36.57 Low Water (displace): id=26888, wt=10.000
% 36.24/36.57
% 36.24/36.57 ============================== PROOF =================================
% 36.24/36.57 % SZS status Theorem
% 36.24/36.57 % SZS output start Refutation
% 36.24/36.57
% 36.24/36.57 % Proof 1 at 34.55 (+ 1.05) seconds: goals.
% 36.24/36.57 % Length of proof is 76.
% 36.24/36.57 % Level of proof is 12.
% 36.24/36.57 % Maximum clause weight is 18.000.
% 36.24/36.57 % Given clauses 9667.
% 36.24/36.57
% 36.24/36.57 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 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].
% 36.24/36.57 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 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].
% 36.24/36.57 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 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].
% 36.24/36.57 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].
% 36.24/36.57 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 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].
% 36.24/36.57 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 36.24/36.57 19 -(all X0 all X1 (leq(X0,X1) -> leq(strong_iteration(X0),strong_iteration(X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 36.24/36.57 20 leq(c1,c2) # label(goals) # label(negated_conjecture). [clausify(19)].
% 36.24/36.57 21 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 36.24/36.57 22 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 36.24/36.57 23 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 36.24/36.57 24 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 36.24/36.57 25 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 36.24/36.57 26 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 36.24/36.57 27 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 36.24/36.57 28 addition(one,multiplication(A,star(A))) = star(A). [copy(27),flip(a)].
% 36.24/36.57 29 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom). [clausify(12)].
% 36.24/36.57 30 addition(one,multiplication(star(A),A)) = star(A). [copy(29),flip(a)].
% 36.24/36.57 31 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 36.24/36.57 32 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(31),rewrite([26(5)]),flip(a)].
% 36.24/36.57 33 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom). [clausify(17)].
% 36.24/36.57 34 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A). [copy(33),flip(a)].
% 36.24/36.57 35 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 36.24/36.57 36 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(35),rewrite([26(2)]),flip(a)].
% 36.24/36.57 37 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 36.24/36.57 38 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 36.24/36.57 39 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(38),flip(a)].
% 36.24/36.57 40 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 36.24/36.57 41 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(40),flip(a)].
% 36.24/36.57 42 -leq(strong_iteration(c1),strong_iteration(c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 36.24/36.57 43 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 36.24/36.57 44 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 36.24/36.57 49 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom). [clausify(16)].
% 36.24/36.57 50 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)). [copy(49),rewrite([26(2)])].
% 36.24/36.57 55 addition(A,addition(A,B)) = addition(A,B). [para(36(a,1),22(a,1)),rewrite([26(1),26(2),36(2,R),22(1),26(3)])].
% 36.24/36.57 58 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(23(a,1),39(a,1,1)),rewrite([26(4)]),flip(a)].
% 36.24/36.57 61 addition(A,multiplication(A,multiplication(B,strong_iteration(B)))) = multiplication(A,strong_iteration(B)). [para(32(a,1),39(a,2,2)),rewrite([23(2)])].
% 36.24/36.57 62 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(21(a,1),41(a,2,1)),rewrite([25(3),26(3)])].
% 36.24/36.57 64 addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A). [para(28(a,1),41(a,2,1)),rewrite([24(2),37(3)])].
% 36.24/36.57 66 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A). [para(32(a,1),41(a,2,1)),rewrite([24(2),37(3)])].
% 36.24/36.57 67 addition(multiplication(star(A),B),multiplication(strong_iteration(A),zero)) = multiplication(strong_iteration(A),B). [para(34(a,1),41(a,2,1)),rewrite([37(6),25(5)])].
% 36.24/36.57 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([26(6)])].
% 36.24/36.57 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))].
% 36.24/36.57 70 addition(c1,c2) = c2. [hyper(43,a,20,a)].
% 36.24/36.57 112 leq(A,addition(A,B)). [hyper(44,b,55,a)].
% 36.24/36.57 128 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(39(a,1),112(a,2))].
% 36.24/36.57 129 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(41(a,1),112(a,2))].
% 36.24/36.57 147 multiplication(A,addition(B,addition(C,one))) = addition(A,multiplication(A,addition(B,C))). [para(58(a,1),39(a,1,2)),rewrite([36(4,R),39(3),26(1)]),flip(a)].
% 36.24/36.57 196 -leq(multiplication(A,strong_iteration(A)),multiplication(B,strong_iteration(A))) | leq(multiplication(A,strong_iteration(A)),multiplication(strong_iteration(B),B)). [para(61(a,1),50(a,2))].
% 36.24/36.57 203 leq(addition(A,multiplication(A,B)),multiplication(A,addition(B,addition(C,one)))). [para(58(a,1),128(a,1)),rewrite([26(5),36(5,R),26(4)])].
% 36.24/36.57 211 leq(multiplication(c1,A),multiplication(c2,A)). [para(70(a,1),129(a,2,1))].
% 36.24/36.57 251 multiplication(star(A),A) = multiplication(A,star(A)). [para(64(a,1),58(a,2)),rewrite([26(4),30(4)]),flip(a)].
% 36.24/36.57 275 multiplication(A,multiplication(strong_iteration(A),zero)) = multiplication(strong_iteration(A),zero). [para(66(a,1),62(a,1)),flip(a)].
% 36.24/36.57 307 addition(multiplication(A,zero),multiplication(B,C)) = multiplication(addition(B,multiplication(A,zero)),C). [para(25(a,1),68(a,1,1,2))].
% 36.24/36.57 343 addition(multiplication(A,star(A)),multiplication(strong_iteration(A),zero)) = multiplication(strong_iteration(A),A). [para(251(a,1),67(a,1,1))].
% 36.24/36.57 367 addition(multiplication(A,B),multiplication(C,zero)) = multiplication(addition(A,multiplication(C,zero)),B). [para(25(a,1),69(a,1,2,2))].
% 36.24/36.57 385 multiplication(addition(A,multiplication(strong_iteration(A),zero)),star(A)) = multiplication(strong_iteration(A),A). [back_rewrite(343),rewrite([367(6)])].
% 36.24/36.57 3987 leq(multiplication(c1,strong_iteration(c1)),multiplication(strong_iteration(c2),c2)). [hyper(196,a,211,a)].
% 36.24/36.57 4157 leq(addition(A,multiplication(A,B)),addition(A,multiplication(A,addition(B,C)))). [para(147(a,1),203(a,2))].
% 36.24/36.57 4273 addition(multiplication(c1,strong_iteration(c1)),multiplication(strong_iteration(c2),c2)) = multiplication(strong_iteration(c2),c2). [hyper(43,a,3987,a)].
% 36.24/36.57 8006 multiplication(addition(A,multiplication(strong_iteration(A),zero)),B) = multiplication(A,addition(B,multiplication(strong_iteration(A),zero))). [para(275(a,1),39(a,1,1)),rewrite([307(5),26(9)])].
% 36.24/36.57 8070 multiplication(strong_iteration(A),A) = multiplication(A,strong_iteration(A)). [back_rewrite(385),rewrite([8006(6),34(5)]),flip(a)].
% 36.24/36.57 8105 addition(multiplication(c1,strong_iteration(c1)),multiplication(c2,strong_iteration(c2))) = multiplication(c2,strong_iteration(c2)). [back_rewrite(4273),rewrite([8070(8),8070(13)])].
% 36.24/36.57 34784 leq(multiplication(A,strong_iteration(c1)),multiplication(A,strong_iteration(c2))). [para(8105(a,1),4157(a,2,2,2)),rewrite([61(6),61(9)])].
% 36.24/36.57 34991 leq(strong_iteration(c1),strong_iteration(c2)). [para(24(a,1),34784(a,1)),rewrite([24(6)])].
% 36.24/36.57 34992 $F # answer(goals). [resolve(34991,a,42,a)].
% 36.24/36.57
% 36.24/36.57 % SZS output end Refutation
% 36.24/36.57 ============================== end of proof ==========================
% 36.24/36.57
% 36.24/36.57 ============================== STATISTICS ============================
% 36.24/36.57
% 36.24/36.57 Given=9667. Generated=1881211. Kept=34962. proofs=1.
% 36.24/36.57 Usable=7276. Sos=9252. Demods=1187. Limbo=1, Disabled=18453. Hints=0.
% 36.24/36.57 Megabytes=21.16.
% 36.24/36.57 User_CPU=34.55, System_CPU=1.05, Wall_clock=36.
% 36.24/36.57
% 36.24/36.57 ============================== end of statistics =====================
% 36.24/36.57
% 36.24/36.57 ============================== end of search =========================
% 36.24/36.57
% 36.24/36.57 THEOREM PROVED
% 36.24/36.57 % SZS status Theorem
% 36.24/36.57
% 36.24/36.57 Exiting with 1 proof.
% 36.24/36.57
% 36.24/36.57 Process 6932 exit (max_proofs) Thu Jun 16 13:28:15 2022
% 36.24/36.57 Prover9 interrupted
%------------------------------------------------------------------------------