TSTP Solution File: KLE087+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE087+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 02:22:10 EDT 2022
% Result : Theorem 72.09s 72.37s
% Output : Refutation 72.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE087+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 14:34:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.43/0.97 ============================== Prover9 ===============================
% 0.43/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.97 Process 27081 was started by sandbox on n018.cluster.edu,
% 0.43/0.97 Thu Jun 16 14:34:46 2022
% 0.43/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26928_n018.cluster.edu".
% 0.43/0.97 ============================== end of head ===========================
% 0.43/0.97
% 0.43/0.97 ============================== INPUT =================================
% 0.43/0.97
% 0.43/0.97 % Reading from file /tmp/Prover9_26928_n018.cluster.edu
% 0.43/0.97
% 0.43/0.97 set(prolog_style_variables).
% 0.43/0.97 set(auto2).
% 0.43/0.97 % set(auto2) -> set(auto).
% 0.43/0.97 % set(auto) -> set(auto_inference).
% 0.43/0.97 % set(auto) -> set(auto_setup).
% 0.43/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.97 % set(auto) -> set(auto_limits).
% 0.43/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.97 % set(auto) -> set(auto_denials).
% 0.43/0.97 % set(auto) -> set(auto_process).
% 0.43/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.97 % set(auto2) -> assign(stats, some).
% 0.43/0.97 % set(auto2) -> clear(echo_input).
% 0.43/0.97 % set(auto2) -> set(quiet).
% 0.43/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.97 % set(auto2) -> clear(print_given).
% 0.43/0.97 assign(lrs_ticks,-1).
% 0.43/0.97 assign(sos_limit,10000).
% 0.43/0.97 assign(order,kbo).
% 0.43/0.97 set(lex_order_vars).
% 0.43/0.97 clear(print_given).
% 0.43/0.97
% 0.43/0.97 % formulas(sos). % not echoed (21 formulas)
% 0.43/0.97
% 0.43/0.97 ============================== end of input ==========================
% 0.43/0.97
% 0.43/0.97 % From the command line: assign(max_seconds, 300).
% 0.43/0.97
% 0.43/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.97
% 0.43/0.97 % Formulas that are not ordinary clauses:
% 0.43/0.97 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.97 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].
% 0.43/0.97 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.97 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.97 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].
% 0.43/0.97 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.97 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.97 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].
% 0.43/0.97 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].
% 0.43/0.97 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.97 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.97 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.97 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.97 14 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 18 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 21 -(all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 72.09/72.37
% 72.09/72.37 ============================== end of process non-clausal formulas ===
% 72.09/72.37
% 72.09/72.37 ============================== PROCESS INITIAL CLAUSES ===============
% 72.09/72.37
% 72.09/72.37 ============================== PREDICATE ELIMINATION =================
% 72.09/72.37 22 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 72.09/72.37 23 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 72.09/72.37
% 72.09/72.37 ============================== end predicate elimination =============
% 72.09/72.37
% 72.09/72.37 Auto_denials:
% 72.09/72.37 % copying label goals to answer in negative clause
% 72.09/72.37
% 72.09/72.37 Term ordering decisions:
% 72.09/72.37 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. antidomain=1. coantidomain=1. codomain=1. domain=1.
% 72.09/72.37
% 72.09/72.37 ============================== end of process initial clauses ========
% 72.09/72.37
% 72.09/72.37 ============================== CLAUSES FOR SEARCH ====================
% 72.09/72.37
% 72.09/72.37 ============================== end of clauses for search =============
% 72.09/72.37
% 72.09/72.37 ============================== SEARCH ================================
% 72.09/72.37
% 72.09/72.37 % Starting search at 0.01 seconds.
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=39.000, iters=3344
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=37.000, iters=3454
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=33.000, iters=3341
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=32.000, iters=3364
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=30.000, iters=3338
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=29.000, iters=3397
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=28.000, iters=3333
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=27.000, iters=3355
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=26.000, iters=3339
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=25.000, iters=3333
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=24.000, iters=3397
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=23.000, iters=3337
% 72.09/72.37
% 72.09/72.37 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.87 sec).
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=22.000, iters=3333
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=21.000, iters=3349
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=20.000, iters=3335
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=6229, wt=49.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=3655, wt=48.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=6892, wt=47.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=4626, wt=46.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=6893, wt=45.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=5859, wt=44.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=4308, wt=43.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=4788, wt=42.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=15493, wt=18.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=15513, wt=16.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=15521, wt=15.000
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=15895, wt=14.000
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=19.000, iters=3349
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=18.000, iters=3341
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=22734, wt=13.000
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=17.000, iters=3338
% 72.09/72.37
% 72.09/72.37 Low Water (displace): id=23979, wt=12.000
% 72.09/72.37
% 72.09/72.37 Low Water (keep): wt=16.000, iters=3339
% 72.09/72.37
% 72.09/72.37 ============================== PROOF =================================
% 72.09/72.37 % SZS status Theorem
% 72.09/72.37 % SZS output start Refutation
% 72.09/72.37
% 72.09/72.37 % Proof 1 at 69.11 (+ 2.30) seconds: goals.
% 72.09/72.37 % Length of proof is 255.
% 72.09/72.37 % Level of proof is 37.
% 72.09/72.37 % Maximum clause weight is 26.000.
% 72.09/72.37 % Given clauses 3032.
% 72.09/72.37
% 72.09/72.37 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 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].
% 72.09/72.37 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 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].
% 72.09/72.37 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 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].
% 72.09/72.37 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].
% 72.09/72.37 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 14 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 18 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 72.09/72.37 21 -(all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 72.09/72.37 24 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 72.09/72.37 25 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 72.09/72.37 26 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 72.09/72.37 27 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 72.09/72.37 28 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 72.09/72.37 29 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 72.09/72.37 30 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 72.09/72.37 31 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 72.09/72.37 32 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 72.09/72.37 34 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 72.09/72.37 35 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 72.09/72.37 36 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(35),rewrite([34(4)])].
% 72.09/72.37 37 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 72.09/72.37 38 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(37),rewrite([34(4)])].
% 72.09/72.37 39 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 72.09/72.37 40 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(39),rewrite([34(2)]),flip(a)].
% 72.09/72.37 41 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 72.09/72.37 42 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 72.09/72.37 43 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(42),flip(a)].
% 72.09/72.37 44 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 72.09/72.37 45 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(44),flip(a)].
% 72.09/72.37 46 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 72.09/72.37 47 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(46),flip(a)].
% 72.09/72.37 48 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 72.09/72.37 49 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(48),flip(a)].
% 72.09/72.37 50 domain(addition(c1,c2)) != addition(domain(c1),domain(c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(21)].
% 72.09/72.37 51 addition(antidomain(antidomain(c1)),antidomain(antidomain(c2))) != antidomain(antidomain(addition(c1,c2))) # answer(goals). [copy(50),rewrite([31(4),31(7),31(10)]),flip(a)].
% 72.09/72.37 52 antidomain(one) = zero. [para(30(a,1),26(a,1)),flip(a)].
% 72.09/72.37 53 coantidomain(one) = zero. [para(32(a,1),27(a,1)),flip(a)].
% 72.09/72.37 54 addition(A,addition(A,B)) = addition(A,B). [para(40(a,1),25(a,1)),rewrite([34(1),34(2),40(2,R),25(1),34(3)])].
% 72.09/72.37 55 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(30(a,1),41(a,1,1)),rewrite([29(2)]),flip(a)].
% 72.09/72.37 57 multiplication(A,multiplication(coantidomain(A),B)) = zero. [para(32(a,1),41(a,1,1)),rewrite([29(2)]),flip(a)].
% 72.09/72.37 58 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(24(a,1),43(a,2,2)),rewrite([28(3),34(3)])].
% 72.09/72.37 59 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(26(a,1),43(a,1,1)),rewrite([34(4)]),flip(a)].
% 72.09/72.37 60 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(30(a,1),43(a,1,1)),rewrite([58(4)]),flip(a)].
% 72.09/72.37 61 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(32(a,1),43(a,1,1)),rewrite([58(3),34(3)]),flip(a)].
% 72.09/72.37 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(27(a,1),45(a,1,1)),rewrite([34(4)]),flip(a)].
% 72.09/72.37 63 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(30(a,1),45(a,1,1)),rewrite([58(3),34(3)]),flip(a)].
% 72.09/72.37 64 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(32(a,1),45(a,1,1)),rewrite([58(4),34(3)]),flip(a)].
% 72.09/72.37 72 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(32(a,1),47(a,1,1,1))].
% 72.09/72.37 73 addition(antidomain(multiplication(A,multiplication(B,C))),antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C)))))) = antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C))))). [para(41(a,1),47(a,1,1,1)),rewrite([41(7),41(13)])].
% 72.09/72.37 77 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(30(a,1),49(a,1,1,1))].
% 72.09/72.37 80 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(41(a,1),49(a,1,1,1))].
% 72.09/72.37 81 addition(zero,antidomain(zero)) = one. [para(52(a,1),36(a,1,1)),rewrite([52(3)])].
% 72.09/72.37 82 addition(zero,coantidomain(zero)) = one. [para(53(a,1),38(a,1,1)),rewrite([53(3)])].
% 72.09/72.37 85 multiplication(A,antidomain(zero)) = A. [para(81(a,1),43(a,2,2)),rewrite([28(2),58(5),26(5)])].
% 72.09/72.37 89 multiplication(A,coantidomain(zero)) = A. [para(82(a,1),43(a,2,2)),rewrite([28(2),58(5),26(5)])].
% 72.09/72.37 91 addition(one,antidomain(A)) = one. [para(36(a,1),54(a,1,2)),rewrite([34(3),36(7)])].
% 72.09/72.37 92 addition(one,coantidomain(A)) = one. [para(38(a,1),54(a,1,2)),rewrite([34(3),38(7)])].
% 72.09/72.37 93 antidomain(zero) = one. [para(85(a,1),27(a,1)),flip(a)].
% 72.09/72.37 94 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(72),rewrite([93(2),91(7)]),flip(a)].
% 72.09/72.37 96 coantidomain(zero) = one. [para(89(a,1),27(a,1)),flip(a)].
% 72.09/72.37 98 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(77),rewrite([96(2),92(7)]),flip(a)].
% 72.09/72.37 99 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(41(a,1),55(a,1,2))].
% 72.09/72.37 102 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(55(a,1),47(a,1,1,1)),rewrite([93(2),91(8)]),flip(a)].
% 72.09/72.37 105 addition(A,multiplication(antidomain(B),A)) = A. [para(91(a,1),45(a,2,1)),rewrite([27(2),27(5)])].
% 72.09/72.37 106 addition(A,multiplication(A,coantidomain(B))) = A. [para(92(a,1),43(a,2,2)),rewrite([26(2),26(5)])].
% 72.09/72.37 107 addition(A,multiplication(coantidomain(B),A)) = A. [para(92(a,1),45(a,2,1)),rewrite([27(2),27(5)])].
% 72.09/72.37 110 multiplication(addition(A,B),multiplication(coantidomain(B),C)) = multiplication(A,multiplication(coantidomain(B),C)). [para(57(a,1),45(a,1,1)),rewrite([58(5),34(4)]),flip(a)].
% 72.09/72.37 111 antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))) = one. [para(57(a,1),47(a,1,1,1)),rewrite([93(2),91(8)]),flip(a)].
% 72.09/72.37 129 multiplication(addition(A,multiplication(A,B)),C) = multiplication(A,multiplication(addition(B,one),C)). [para(59(a,1),41(a,1,1))].
% 72.09/72.37 131 addition(addition(A,multiplication(A,B)),multiplication(A,C)) = multiplication(A,addition(B,addition(C,one))). [para(59(a,1),43(a,1,1)),rewrite([34(7),40(7,R),34(6)])].
% 72.09/72.37 133 addition(addition(A,multiplication(A,B)),multiplication(C,addition(B,one))) = multiplication(addition(A,C),addition(B,one)). [para(59(a,1),45(a,1,1))].
% 72.09/72.37 137 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,antidomain(antidomain(addition(B,one)))))) = antidomain(multiplication(A,antidomain(antidomain(addition(B,one))))). [para(59(a,1),47(a,1,1,1))].
% 72.09/72.37 141 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(94(a,1),30(a,1,1)),rewrite([27(6)])].
% 72.09/72.37 146 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(141(a,1),43(a,1,1)),rewrite([58(3),34(5)]),flip(a)].
% 72.09/72.37 152 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(38(a,1),60(a,1,2)),rewrite([26(4)]),flip(a)].
% 72.09/72.37 155 addition(multiplication(antidomain(A),B),multiplication(C,addition(A,B))) = multiplication(addition(C,antidomain(A)),addition(A,B)). [para(60(a,1),45(a,1,1)),rewrite([34(7)])].
% 72.09/72.37 156 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(45(a,1),60(a,1,2))].
% 72.09/72.37 160 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(105(a,1),60(a,1,2)),rewrite([30(2)]),flip(a)].
% 72.09/72.37 161 multiplication(antidomain(A),multiplication(coantidomain(B),A)) = zero. [para(107(a,1),60(a,1,2)),rewrite([30(2)]),flip(a)].
% 72.09/72.37 173 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(38(a,1),61(a,1,2)),rewrite([26(3)]),flip(a)].
% 72.09/72.37 176 multiplication(A,addition(B,addition(C,coantidomain(A)))) = multiplication(A,addition(B,C)). [para(61(a,1),43(a,1,1)),rewrite([43(3),34(5),40(5,R),34(4)]),flip(a)].
% 72.09/72.37 180 multiplication(coantidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(49(a,1),61(a,1,2)),rewrite([32(8),41(7)]),flip(a)].
% 72.09/72.37 182 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(173(a,1),43(a,1,1)),rewrite([59(4,R),34(7)]),flip(a)].
% 72.09/72.37 187 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(98(a,1),32(a,1,2)),rewrite([26(6)])].
% 72.09/72.37 191 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(187(a,1),45(a,1,1)),rewrite([58(3),34(5)]),flip(a)].
% 72.09/72.37 195 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(160(a,1),45(a,1,1)),rewrite([58(5),34(5)]),flip(a)].
% 72.09/72.37 198 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(60(a,1),160(a,1,2))].
% 72.09/72.37 211 addition(coantidomain(addition(A,multiplication(B,A))),coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A))) = coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A)). [para(62(a,1),49(a,1,1,1))].
% 72.09/72.37 221 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(61(a,1),62(a,2,2)),rewrite([34(9),40(9),34(8),40(9,R),34(8)])].
% 72.09/72.37 224 multiplication(addition(A,antidomain(B)),multiplication(coantidomain(C),B)) = multiplication(A,multiplication(coantidomain(C),B)). [para(161(a,1),45(a,1,1)),rewrite([58(5),34(5)]),flip(a)].
% 72.09/72.37 238 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(36(a,1),63(a,1,1)),rewrite([27(3)]),flip(a)].
% 72.09/72.37 242 multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = zero. [para(47(a,1),63(a,1,1)),rewrite([30(8)]),flip(a)].
% 72.09/72.37 245 multiplication(addition(A,antidomain(B)),addition(B,one)) = addition(A,addition(antidomain(B),multiplication(A,B))). [para(63(a,1),59(a,2,2)),rewrite([34(9),40(9),34(8),40(9,R),34(8)])].
% 72.09/72.37 246 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(34(a,1),64(a,1,1))].
% 72.09/72.37 247 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(36(a,1),64(a,1,1)),rewrite([27(5)]),flip(a)].
% 72.09/72.37 248 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(38(a,1),64(a,1,1)),rewrite([27(5)]),flip(a)].
% 72.09/72.37 252 multiplication(A,multiplication(addition(B,C),coantidomain(multiplication(A,C)))) = multiplication(A,multiplication(B,coantidomain(multiplication(A,C)))). [para(43(a,1),64(a,1,1)),rewrite([41(5),41(9)])].
% 72.09/72.37 257 multiplication(A,coantidomain(addition(A,B))) = zero. [para(54(a,1),64(a,1,1)),rewrite([32(4)]),flip(a)].
% 72.09/72.37 261 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(238(a,1),41(a,1,1)),flip(a)].
% 72.09/72.37 262 multiplication(antidomain(A),addition(B,antidomain(A))) = multiplication(antidomain(A),addition(B,one)). [para(238(a,1),43(a,1,1)),rewrite([59(4,R),34(7)]),flip(a)].
% 72.09/72.37 263 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(238(a,1),45(a,1,1)),rewrite([62(4,R),34(6)]),flip(a)].
% 72.09/72.37 267 coantidomain(addition(A,one)) = zero. [para(257(a,1),27(a,1)),rewrite([34(3)]),flip(a)].
% 72.09/72.37 276 coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B)))) = one. [para(257(a,1),49(a,1,1,1)),rewrite([96(2),92(8)]),flip(a)].
% 72.09/72.37 278 multiplication(A,coantidomain(multiplication(A,addition(B,one)))) = zero. [para(59(a,2),257(a,1,2,1))].
% 72.09/72.37 283 addition(coantidomain(A),coantidomain(addition(A,multiplication(B,A)))) = coantidomain(A). [back_rewrite(211),rewrite([267(6),96(5),27(5),34(5),267(8),96(7),27(7)])].
% 72.09/72.37 419 antidomain(addition(A,one)) = zero. [para(30(a,1),278(a,1,2,1)),rewrite([96(5),26(5)])].
% 72.09/72.37 429 addition(antidomain(A),antidomain(addition(A,multiplication(A,B)))) = antidomain(A). [back_rewrite(137),rewrite([419(6),93(5),26(5),34(5),419(8),93(7),26(7)])].
% 72.09/72.38 430 addition(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(A). [para(419(a,1),47(a,1,2,1,2,1)),rewrite([93(6),26(6),34(6),419(9),93(8),26(8)])].
% 72.09/72.38 461 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,addition(B,multiplication(B,C))))) = antidomain(multiplication(A,B)). [para(59(a,1),73(a,1,1,1,2)),rewrite([419(7),93(6),26(6),34(7),419(10),93(9),26(9)])].
% 72.09/72.38 496 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(102(a,1),30(a,1,1)),rewrite([27(7)])].
% 72.09/72.38 504 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(496(a,1),43(a,1,1)),rewrite([58(4),34(7)]),flip(a)].
% 72.09/72.38 513 multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))) = zero. [para(111(a,1),30(a,1,1)),rewrite([27(7)])].
% 72.09/72.38 522 multiplication(addition(A,B),antidomain(antidomain(multiplication(coantidomain(B),C)))) = multiplication(A,antidomain(antidomain(multiplication(coantidomain(B),C)))). [para(513(a,1),45(a,1,1)),rewrite([58(7),34(6)]),flip(a)].
% 72.09/72.38 546 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B)) = one. [para(30(a,1),80(a,1,1,1,2)),rewrite([28(2),96(2),92(8)]),flip(a)].
% 72.09/72.38 547 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(30(a,1),80(a,1,1,1)),rewrite([96(2),92(9)]),flip(a)].
% 72.09/72.38 548 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one. [para(32(a,1),80(a,1,1,1,2)),rewrite([28(2),96(2),92(8)]),flip(a)].
% 72.09/72.38 568 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [para(160(a,1),80(a,1,1,1)),rewrite([96(2),92(9)]),flip(a)].
% 72.09/72.38 573 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [para(161(a,1),80(a,1,1,1)),rewrite([96(2),92(9)]),flip(a)].
% 72.09/72.38 635 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(152(a,1),105(a,1,2)),rewrite([34(5)])].
% 72.09/72.38 733 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(34(a,1),198(a,1,1,1))].
% 72.09/72.38 832 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(36(a,1),246(a,1,1)),rewrite([27(4)]),flip(a)].
% 72.09/72.38 840 multiplication(A,multiplication(coantidomain(B),coantidomain(A))) = zero. [para(106(a,1),246(a,1,1)),rewrite([32(2),41(5)]),flip(a)].
% 72.09/72.38 909 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [para(840(a,1),80(a,1,1,1)),rewrite([96(2),92(9)]),flip(a)].
% 72.09/72.38 1013 multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [para(276(a,1),32(a,1,2)),rewrite([26(7)])].
% 72.09/72.38 1076 multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [para(546(a,1),32(a,1,2)),rewrite([26(7)])].
% 72.09/72.38 1091 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [para(548(a,1),32(a,1,2)),rewrite([26(7)])].
% 72.09/72.38 1163 multiplication(antidomain(addition(A,B)),A) = zero. [para(54(a,1),733(a,1,1,1)),rewrite([261(6)])].
% 72.09/72.38 1419 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(832(a,1),106(a,1,2))].
% 72.09/72.38 2270 addition(A,addition(B,multiplication(addition(A,B),C))) = multiplication(addition(A,B),addition(C,one)). [para(59(a,1),133(a,1,2)),rewrite([40(5,R),40(4,R),45(3),40(4,R),34(3)])].
% 72.09/72.38 2359 multiplication(A,antidomain(coantidomain(A))) = A. [para(36(a,1),146(a,1,2)),rewrite([26(2)]),flip(a)].
% 72.09/72.38 2381 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2359(a,1),41(a,1,1)),flip(a)].
% 72.09/72.38 2382 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2359(a,1),41(a,1)),flip(a)].
% 72.09/72.38 2383 multiplication(A,addition(B,antidomain(coantidomain(A)))) = addition(A,multiplication(A,B)). [para(2359(a,1),43(a,1,1)),rewrite([34(5)]),flip(a)].
% 72.09/72.38 2389 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2359(a,1),107(a,1,2)),rewrite([34(5)])].
% 72.09/72.38 2488 multiplication(A,coantidomain(coantidomain(A))) = A. [para(152(a,1),2381(a,1,2)),rewrite([2359(3)]),flip(a)].
% 72.09/72.38 2521 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(248),rewrite([2488(5)]),flip(a)].
% 72.09/72.38 2550 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2521(a,1),635(a,1,2)),rewrite([34(5),2389(5),2521(6)])].
% 72.09/72.38 2649 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2550(a,1),36(a,1,1)),rewrite([2550(4)])].
% 72.09/72.38 2655 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2550(a,1),832(a,1,1,1)),rewrite([2550(5),152(5),2550(5)]),flip(a)].
% 72.09/72.38 2657 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2550(a,1),832(a,2,1)),rewrite([2655(2),2655(6),832(9),2655(6)])].
% 72.09/72.38 2664 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2521(a,1),2550(a,1,1,1)),rewrite([2655(2),2655(5)]),flip(a)].
% 72.09/72.38 2665 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2521(a,1),2550(a,2)),rewrite([2655(2),2664(3),2657(4)])].
% 72.09/72.38 2893 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [back_rewrite(1091),rewrite([2655(3)])].
% 72.09/72.38 2906 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [back_rewrite(1076),rewrite([2655(4)])].
% 72.09/72.38 2926 multiplication(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [back_rewrite(1013),rewrite([2655(2)])].
% 72.09/72.38 2931 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [back_rewrite(909),rewrite([2655(4)])].
% 72.09/72.38 2976 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [back_rewrite(573),rewrite([2655(5)])].
% 72.09/72.38 2981 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [back_rewrite(568),rewrite([2655(5)])].
% 72.09/72.38 2992 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(547),rewrite([2655(5)])].
% 72.09/72.38 3011 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(191),rewrite([2655(3)])].
% 72.09/72.38 3015 multiplication(antidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [back_rewrite(180),rewrite([2655(2)])].
% 72.09/72.38 3301 addition(multiplication(antidomain(antidomain(A)),B),multiplication(antidomain(A),addition(B,one))) = addition(B,antidomain(A)). [para(36(a,1),155(a,2,1)),rewrite([34(6),262(7),34(11),27(12)])].
% 72.09/72.38 3429 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(36(a,1),156(a,1,2,1)),rewrite([27(5)]),flip(a)].
% 72.09/72.38 3899 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),antidomain(antidomain(B))) = zero. [para(2906(a,1),242(a,1,1,1)),rewrite([93(2),27(9)])].
% 72.09/72.38 3921 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(247(a,1),106(a,1,2))].
% 72.09/72.38 4450 multiplication(A,addition(coantidomain(A),coantidomain(B))) = multiplication(A,coantidomain(B)). [para(283(a,1),176(a,2,2)),rewrite([34(6),40(7,R),34(6),283(6)])].
% 72.09/72.38 4500 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,multiplication(addition(B,one),addition(C,one))))) = antidomain(addition(A,multiplication(A,B))). [para(129(a,1),429(a,1,2,1,2)),rewrite([131(10),34(8),2270(9)])].
% 72.09/72.38 4909 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(1419(a,1),182(a,1,2)),rewrite([34(11),91(11),26(9)])].
% 72.09/72.38 4914 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3921(a,1),182(a,1,2)),rewrite([34(11),91(11),26(10)])].
% 72.09/72.38 5167 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(36(a,1),195(a,1,1)),rewrite([27(5)]),flip(a)].
% 72.09/72.38 7574 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(4909(a,1),221(a,2,2,2)),rewrite([34(4),92(4),2655(6),27(8),2655(11),34(14),2649(14),34(10),91(10)])].
% 72.09/72.38 7862 multiplication(antidomain(A),multiplication(coantidomain(B),antidomain(A))) = multiplication(coantidomain(B),antidomain(A)). [para(36(a,1),224(a,1,1)),rewrite([27(5)]),flip(a)].
% 72.09/72.38 8521 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A)) = zero. [para(2931(a,1),32(a,1,2)),rewrite([26(8)])].
% 72.09/72.38 8536 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(addition(A,B))) = zero. [para(64(a,1),8521(a,1,1,1,1))].
% 72.09/72.38 8679 multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A) = zero. [para(2976(a,1),32(a,1,2)),rewrite([26(8)])].
% 72.09/72.38 8955 multiplication(A,multiplication(antidomain(antidomain(B)),coantidomain(multiplication(A,antidomain(coantidomain(antidomain(B))))))) = multiplication(A,coantidomain(multiplication(A,antidomain(coantidomain(antidomain(B)))))). [para(7574(a,1),252(a,1,2,1)),rewrite([27(7)]),flip(a)].
% 72.09/72.38 9020 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = zero. [para(2981(a,1),32(a,1,2)),rewrite([26(8)])].
% 72.09/72.38 9100 multiplication(coantidomain(antidomain(A)),A) = A. [para(2649(a,1),3011(a,1,1)),rewrite([27(2)]),flip(a)].
% 72.09/72.38 9110 multiplication(antidomain(antidomain(A)),A) = A. [para(7574(a,1),3011(a,1,1)),rewrite([27(2)]),flip(a)].
% 72.09/72.38 9114 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(4914),rewrite([9100(5)]),flip(a)].
% 72.09/72.38 9169 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [para(9110(a,1),73(a,1,2,1)),rewrite([34(13),9110(22)])].
% 72.09/72.38 9170 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(9110(a,1),99(a,1,2,2))].
% 72.09/72.38 9249 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9114(a,1),2655(a,1,1)),rewrite([9114(5)])].
% 72.09/72.38 9250 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9114(a,1),2655(a,2,1)),rewrite([9249(3),9249(4)])].
% 72.09/72.38 9251 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9114(a,1),2665(a,2)),rewrite([9249(3),9250(4)])].
% 72.09/72.38 9298 multiplication(A,multiplication(antidomain(antidomain(B)),coantidomain(multiplication(A,antidomain(B))))) = multiplication(A,coantidomain(multiplication(A,antidomain(B)))). [back_rewrite(8955),rewrite([9249(4),9251(5),9249(9),9251(10)])].
% 72.09/72.38 9628 multiplication(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(multiplication(A,addition(B,one))). [para(430(a,1),263(a,1,1)),rewrite([34(9),91(9),27(12)])].
% 72.09/72.38 13368 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero. [para(2992(a,1),32(a,1,2)),rewrite([26(8)])].
% 72.09/72.38 16809 antidomain(multiplication(A,addition(B,one))) = antidomain(addition(A,multiplication(A,B))). [para(59(a,1),461(a,1,1,1)),rewrite([59(9,R),4500(11)]),flip(a)].
% 72.09/72.38 17437 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(36(a,1),504(a,1,2)),rewrite([26(3)]),flip(a)].
% 72.09/72.38 17438 antidomain(multiplication(A,addition(B,one))) = antidomain(A). [back_rewrite(9628),rewrite([17437(6)]),flip(a)].
% 72.09/72.38 17440 antidomain(addition(A,multiplication(A,B))) = antidomain(A). [back_rewrite(16809),rewrite([17438(4)]),flip(a)].
% 72.09/72.38 17584 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17437(a,1),105(a,1,2)),rewrite([34(4)])].
% 72.09/72.38 17594 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(17437(a,1),2381(a,1,2)),rewrite([2359(3)]),flip(a)].
% 72.09/72.38 17604 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(17437(a,1),221(a,2,2,2)),rewrite([34(3),91(3),9249(5),34(6),27(7),9249(9),34(11),36(11),34(9),91(9)])].
% 72.09/72.38 17620 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17437(a,1),2382(a,1,2,2,1,1)),rewrite([9249(5),9251(6),5167(6),17437(8)])].
% 72.09/72.38 17670 addition(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(multiplication(antidomain(antidomain(A)),B)). [para(17594(a,1),105(a,1,2)),rewrite([9249(2),34(6),9249(8)])].
% 72.09/72.38 17706 antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [back_rewrite(9169),rewrite([17670(13)])].
% 72.09/72.38 17809 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17620(a,1),41(a,1,1)),flip(a)].
% 72.09/72.38 17842 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3429),rewrite([17809(7)]),flip(a)].
% 72.09/72.38 18828 multiplication(antidomain(antidomain(A)),multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(160(a,1),17842(a,1,1,1)),rewrite([93(2),27(4)]),flip(a)].
% 72.09/72.38 18833 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(1163(a,1),17842(a,1,1,1)),rewrite([93(2),27(2)]),flip(a)].
% 72.09/72.38 18841 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(2893(a,1),17842(a,1,1,1)),rewrite([93(2),27(3),2665(5)]),flip(a)].
% 72.09/72.38 18842 multiplication(coantidomain(multiplication(A,antidomain(B))),B) = B. [para(2906(a,1),17842(a,1,1,1)),rewrite([93(2),27(2),2665(5)]),flip(a)].
% 72.09/72.38 18843 multiplication(coantidomain(A),coantidomain(addition(A,B))) = coantidomain(addition(A,B)). [para(2926(a,1),17842(a,1,1,1)),rewrite([93(2),27(4),2665(5)]),flip(a)].
% 72.09/72.38 18869 multiplication(coantidomain(multiplication(antidomain(A),coantidomain(B))),A) = A. [para(8679(a,1),17842(a,1,1,1)),rewrite([93(2),27(2),2665(6)]),flip(a)].
% 72.09/72.38 18870 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A. [para(9020(a,1),17842(a,1,1,1)),rewrite([93(2),27(2),2665(6)]),flip(a)].
% 72.09/72.38 18876 multiplication(coantidomain(multiplication(A,antidomain(B))),antidomain(antidomain(B))) = antidomain(antidomain(B)). [para(3899(a,1),17842(a,1,1,1)),rewrite([93(2),27(4),2665(7)]),flip(a)].
% 72.09/72.38 18885 multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)) = multiplication(A,B). [para(9170(a,1),17842(a,1,1,1)),rewrite([93(2),27(3)]),flip(a)].
% 72.09/72.38 18896 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(13368(a,1),17842(a,1,1,1)),rewrite([93(2),27(2),2665(6)]),flip(a)].
% 72.09/72.38 18936 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [back_rewrite(17706),rewrite([18885(7)]),flip(a)].
% 72.09/72.38 18965 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(34(a,1),18833(a,1,1,1,1))].
% 72.09/72.38 18994 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(18833(a,1),17620(a,1,1,1)),rewrite([9251(5),9251(8)])].
% 72.09/72.38 19043 addition(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = one. [para(18842(a,1),17604(a,1,2,1)),rewrite([2665(5),34(5)])].
% 72.09/72.38 19044 multiplication(antidomain(A),antidomain(coantidomain(multiplication(B,antidomain(A))))) = antidomain(coantidomain(multiplication(B,antidomain(A)))). [para(18842(a,1),17620(a,1,1,1))].
% 72.09/72.38 19157 addition(antidomain(A),antidomain(addition(B,A))) = antidomain(A). [para(18965(a,1),17584(a,1,2,1)),rewrite([9251(4),34(4),18965(8)])].
% 72.09/72.38 19176 addition(antidomain(coantidomain(A)),coantidomain(multiplication(B,A))) = one. [para(18841(a,1),245(a,2,2,2)),rewrite([34(5),34(8),92(8),26(7),34(11),2649(11),34(9),92(9)])].
% 72.09/72.38 19182 coantidomain(addition(A,coantidomain(multiplication(B,A)))) = zero. [para(18841(a,1),8536(a,1,1,1,1)),rewrite([2655(2),2665(3),34(4),18843(6)])].
% 72.09/72.38 19202 coantidomain(addition(A,coantidomain(A))) = zero. [para(27(a,1),19182(a,1,1,2,1))].
% 72.09/72.38 19250 multiplication(A,coantidomain(multiplication(addition(B,coantidomain(B)),A))) = zero. [para(19202(a,1),3015(a,1,1,1)),rewrite([93(2),27(7)])].
% 72.09/72.38 19333 multiplication(coantidomain(A),antidomain(B)) = multiplication(antidomain(B),coantidomain(A)). [para(18869(a,1),17594(a,1,2,1)),rewrite([41(5),7862(5)])].
% 72.09/72.38 19336 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))). [para(18869(a,1),17620(a,1,1,1))].
% 72.09/72.38 19367 multiplication(antidomain(antidomain(A)),coantidomain(multiplication(B,antidomain(A)))) = antidomain(antidomain(A)). [back_rewrite(18876),rewrite([19333(6)])].
% 72.09/72.38 19422 multiplication(A,coantidomain(multiplication(A,antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [back_rewrite(9298),rewrite([19367(6)]),flip(a)].
% 72.09/72.38 19458 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(18870(a,1),17594(a,1,2,1)),rewrite([41(5),5167(5)])].
% 72.09/72.38 19461 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),antidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))). [para(18870(a,1),17620(a,1,1,1))].
% 72.09/72.38 19729 addition(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = one. [para(2665(a,1),19043(a,1,1)),rewrite([2665(4)])].
% 72.09/72.38 19756 addition(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(multiplication(antidomain(B),A)). [para(105(a,1),19157(a,1,2,1)),rewrite([34(5)])].
% 72.09/72.38 19777 multiplication(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(A). [para(19176(a,1),60(a,1,2)),rewrite([2665(3),26(3),2665(4)]),flip(a)].
% 72.09/72.38 19840 multiplication(coantidomain(A),antidomain(coantidomain(multiplication(B,coantidomain(A))))) = antidomain(coantidomain(multiplication(B,coantidomain(A)))). [para(19729(a,1),64(a,1,1)),rewrite([2655(5),27(6),2655(9)]),flip(a)].
% 72.09/72.38 19842 multiplication(A,coantidomain(multiplication(B,coantidomain(A)))) = A. [para(19729(a,1),4450(a,1,2)),rewrite([26(2)]),flip(a)].
% 72.09/72.38 20777 coantidomain(multiplication(addition(A,coantidomain(A)),B)) = coantidomain(B). [para(19250(a,1),18896(a,1,1,1,1,1)),rewrite([93(2),27(2),19777(6)]),flip(a)].
% 72.09/72.38 20783 coantidomain(multiplication(antidomain(coantidomain(A)),B)) = coantidomain(multiplication(A,B)). [para(110(a,1),20777(a,1,1)),rewrite([2655(2),2381(4),2655(4)]),flip(a)].
% 72.09/72.38 20805 coantidomain(multiplication(A,antidomain(antidomain(multiplication(antidomain(coantidomain(A)),B))))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [para(522(a,1),20777(a,1,1)),rewrite([2655(2),2655(9),9249(13),9251(13)])].
% 72.09/72.38 21032 antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))) = multiplication(coantidomain(B),antidomain(A)). [para(19333(a,1),2382(a,1,2,2,1,1)),rewrite([19336(8),19840(7)])].
% 72.09/72.38 21058 multiplication(A,antidomain(multiplication(antidomain(B),coantidomain(A)))) = A. [para(19333(a,1),17594(a,1,2,1))].
% 72.09/72.38 21094 multiplication(A,coantidomain(multiplication(coantidomain(A),antidomain(B)))) = A. [para(19333(a,2),19842(a,1,2,1))].
% 72.09/72.38 21124 multiplication(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(A). [para(21058(a,1),60(a,2)),rewrite([9249(4),18936(6),60(6)])].
% 72.09/72.38 21310 antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))) = multiplication(antidomain(A),antidomain(B)). [para(19458(a,1),2382(a,1,2,2,1,1)),rewrite([19458(5),19044(8),19461(7)])].
% 72.09/72.38 21313 multiplication(antidomain(A),addition(antidomain(A),antidomain(B))) = antidomain(A). [para(19458(a,1),2383(a,2,2)),rewrite([9249(4),9251(5),34(4),19458(9),59(10,R),34(9),91(9),26(8)])].
% 72.09/72.38 21333 multiplication(coantidomain(multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B)))),B) = B. [para(19458(a,1),18896(a,1,1,1))].
% 72.09/72.38 21888 coantidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [para(19458(a,1),20783(a,1,1))].
% 72.09/72.38 22164 addition(antidomain(A),multiplication(antidomain(B),antidomain(antidomain(A)))) = addition(antidomain(A),antidomain(B)). [para(21313(a,1),155(a,1,2)),rewrite([19458(4),34(6),36(10),27(11)])].
% 72.09/72.38 29302 antidomain(addition(antidomain(antidomain(A)),multiplication(antidomain(B),A))) = antidomain(A). [para(18828(a,1),17440(a,1,1,2)),rewrite([9251(9)])].
% 72.09/72.38 29334 antidomain(antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(21094(a,1),29302(a,1,1,2)),rewrite([9249(2),19458(4),21310(6),18936(5),34(5),19756(5),9249(6),19458(8),21310(10)])].
% 72.09/72.38 29344 coantidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [back_rewrite(20805),rewrite([29334(5),2381(6)])].
% 72.09/72.38 30046 multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B))) = multiplication(A,antidomain(B)). [para(9251(a,1),19422(a,2,2)),rewrite([29344(4)])].
% 72.09/72.38 30774 antidomain(coantidomain(multiplication(A,antidomain(B)))) = multiplication(antidomain(B),antidomain(coantidomain(A))). [para(2655(a,1),21032(a,1,1,1,2)),rewrite([21888(5),2655(6),19458(8)])].
% 72.09/72.38 30961 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(B)). [para(21333(a,1),17437(a,1,2,1)),rewrite([30774(7),9249(5),9251(6),19458(5),41(7),19458(6),21124(6),30774(10),9249(8),9251(9),19458(8)]),flip(a)].
% 72.09/72.38 33149 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)). [para(18994(a,1),30046(a,2)),rewrite([9249(3),9251(4),60(4),30961(5)])].
% 72.09/72.38 33306 addition(antidomain(A),antidomain(addition(B,antidomain(A)))) = addition(antidomain(A),antidomain(B)). [back_rewrite(22164),rewrite([33149(5)])].
% 72.09/72.38 39008 antidomain(multiplication(antidomain(antidomain(A)),B)) = addition(antidomain(A),antidomain(B)). [para(30046(a,1),3301(a,1,1)),rewrite([33149(4),34(2),9249(7),9251(7),34(10),91(10),26(6),34(5),33306(5),9249(6),9251(6),34(9),17670(9)]),flip(a)].
% 72.09/72.38 39024 addition(antidomain(A),antidomain(antidomain(B))) = antidomain(multiplication(antidomain(B),A)). [para(9251(a,1),39008(a,1,1,1)),rewrite([34(7)]),flip(a)].
% 72.09/72.38 39062 $F # answer(goals). [back_rewrite(51),rewrite([39024(7),33149(5),34(3)]),xx(a)].
% 72.09/72.38
% 72.09/72.38 % SZS output end Refutation
% 72.09/72.38 ============================== end of proof ==========================
% 72.09/72.38
% 72.09/72.38 ============================== STATISTICS ============================
% 72.09/72.38
% 72.09/72.38 Given=3032. Generated=4330764. Kept=39030. proofs=1.
% 72.09/72.38 Usable=1714. Sos=7680. Demods=9255. Limbo=38, Disabled=29620. Hints=0.
% 72.09/72.38 Megabytes=28.40.
% 72.09/72.38 User_CPU=69.12, System_CPU=2.30, Wall_clock=72.
% 72.09/72.38
% 72.09/72.38 ============================== end of statistics =====================
% 72.09/72.38
% 72.09/72.38 ============================== end of search =========================
% 72.09/72.38
% 72.09/72.38 THEOREM PROVED
% 72.09/72.38 % SZS status Theorem
% 72.09/72.38
% 72.09/72.38 Exiting with 1 proof.
% 72.09/72.38
% 72.09/72.38 Process 27081 exit (max_proofs) Thu Jun 16 14:35:58 2022
% 72.09/72.38 Prover9 interrupted
%------------------------------------------------------------------------------