TSTP Solution File: KLE121+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE121+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 02:22:20 EDT 2022
% Result : Theorem 262.33s 262.68s
% Output : Refutation 262.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE121+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 08:30:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.42/1.02 ============================== Prover9 ===============================
% 0.42/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.02 Process 13622 was started by sandbox2 on n020.cluster.edu,
% 0.42/1.02 Thu Jun 16 08:30:05 2022
% 0.42/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13469_n020.cluster.edu".
% 0.42/1.02 ============================== end of head ===========================
% 0.42/1.02
% 0.42/1.02 ============================== INPUT =================================
% 0.42/1.02
% 0.42/1.02 % Reading from file /tmp/Prover9_13469_n020.cluster.edu
% 0.42/1.02
% 0.42/1.02 set(prolog_style_variables).
% 0.42/1.02 set(auto2).
% 0.42/1.02 % set(auto2) -> set(auto).
% 0.42/1.02 % set(auto) -> set(auto_inference).
% 0.42/1.02 % set(auto) -> set(auto_setup).
% 0.42/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.02 % set(auto) -> set(auto_limits).
% 0.42/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.02 % set(auto) -> set(auto_denials).
% 0.42/1.02 % set(auto) -> set(auto_process).
% 0.42/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.02 % set(auto2) -> assign(stats, some).
% 0.42/1.02 % set(auto2) -> clear(echo_input).
% 0.42/1.02 % set(auto2) -> set(quiet).
% 0.42/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.02 % set(auto2) -> clear(print_given).
% 0.42/1.02 assign(lrs_ticks,-1).
% 0.42/1.02 assign(sos_limit,10000).
% 0.42/1.02 assign(order,kbo).
% 0.42/1.02 set(lex_order_vars).
% 0.42/1.02 clear(print_given).
% 0.42/1.02
% 0.42/1.02 % formulas(sos). % not echoed (27 formulas)
% 0.42/1.02
% 0.42/1.02 ============================== end of input ==========================
% 0.42/1.02
% 0.42/1.02 % From the command line: assign(max_seconds, 300).
% 0.42/1.02
% 0.42/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.02
% 0.42/1.02 % Formulas that are not ordinary clauses:
% 0.42/1.02 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 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].
% 0.42/1.02 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 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].
% 0.42/1.02 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 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].
% 0.42/1.02 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].
% 0.42/1.02 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 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].
% 4.95/5.28 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 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].
% 4.95/5.28 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 4.95/5.28 27 -(all X0 all X1 all X2 all X3 all X4 (addition(backward_diamond(X3,domain(X0)),domain(X1)) = domain(X1) & addition(backward_diamond(X4,domain(X1)),domain(X2)) = domain(X2) -> addition(backward_diamond(multiplication(X3,X4),domain(X0)),domain(X2)) = domain(X2))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.95/5.28
% 4.95/5.28 ============================== end of process non-clausal formulas ===
% 4.95/5.28
% 4.95/5.28 ============================== PROCESS INITIAL CLAUSES ===============
% 4.95/5.28
% 4.95/5.28 ============================== PREDICATE ELIMINATION =================
% 4.95/5.28 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 4.95/5.28 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 4.95/5.28
% 4.95/5.28 ============================== end predicate elimination =============
% 4.95/5.28
% 4.95/5.28 Auto_denials:
% 4.95/5.28 % copying label goals to answer in negative clause
% 4.95/5.28
% 4.95/5.28 Term ordering decisions:
% 4.95/5.28 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. c4=1. c5=1. multiplication=1. addition=1. backward_diamond=1. forward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. domain=1. c=1. codomain=1.
% 4.95/5.28
% 4.95/5.28 ============================== end of process initial clauses ========
% 4.95/5.28
% 4.95/5.28 ============================== CLAUSES FOR SEARCH ====================
% 4.95/5.28
% 4.95/5.28 ============================== end of clauses for search =============
% 4.95/5.28
% 4.95/5.28 ============================== SEARCH ================================
% 4.95/5.28
% 4.95/5.28 % Starting search at 0.01 seconds.
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=40.000, iters=3335
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=36.000, iters=3381
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=33.000, iters=3344
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=32.000, iters=3373
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=31.000, iters=3371
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=30.000, iters=3333
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=29.000, iters=3410
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=28.000, iters=3346
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=27.000, iters=3366
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=26.000, iters=3352
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=25.000, iters=3346
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=21.000, iters=4376
% 4.95/5.28
% 4.95/5.28 Low Water (keep): wt=20.000, iters=3998
% 4.95/5.28
% 4.95/5.28 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.82 sec).
% 4.95/5.28
% 4.95/5.28 Low Water (displace): id=6306, wt=49.000
% 4.95/5.28
% 4.95/5.28 Low Water (displace): id=3728, wt=48.000
% 4.95/5.28
% 4.95/5.28 Low Water (displace): id=6954, wt=47.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=4690, wt=46.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=6955, wt=45.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=5916, wt=44.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=4358, wt=43.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=15551, wt=19.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=15560, wt=17.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=15581, wt=16.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=15594, wt=15.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=15943, wt=14.000
% 262.33/262.68
% 262.33/262.68 Low Water (keep): wt=19.000, iters=3337
% 262.33/262.68
% 262.33/262.68 Low Water (keep): wt=18.000, iters=3372
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=20732, wt=13.000
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=22774, wt=12.000
% 262.33/262.68
% 262.33/262.68 Low Water (keep): wt=17.000, iters=3338
% 262.33/262.68
% 262.33/262.68 Low Water (displace): id=25385, wt=9.000
% 262.33/262.68
% 262.33/262.68 Low Water (keep): wt=16.000, iters=3340
% 262.33/262.68
% 262.33/262.68 Low Water (keep): wt=15.000, iters=3335
% 262.33/262.68
% 262.33/262.68 Low Water (keep): wt=14.000, iters=3657
% 262.33/262.68
% 262.33/262.68 ============================== PROOF =================================
% 262.33/262.68 % SZS status Theorem
% 262.33/262.68 % SZS output start Refutation
% 262.33/262.68
% 262.33/262.68 % Proof 1 at 252.75 (+ 8.93) seconds: goals.
% 262.33/262.68 % Length of proof is 347.
% 262.33/262.68 % Level of proof is 41.
% 262.33/262.68 % Maximum clause weight is 25.000.
% 262.33/262.68 % Given clauses 6899.
% 262.33/262.68
% 262.33/262.68 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 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].
% 262.33/262.68 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 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].
% 262.33/262.68 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 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].
% 262.33/262.68 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].
% 262.33/262.68 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 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].
% 262.33/262.68 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 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].
% 262.33/262.68 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 262.33/262.68 27 -(all X0 all X1 all X2 all X3 all X4 (addition(backward_diamond(X3,domain(X0)),domain(X1)) = domain(X1) & addition(backward_diamond(X4,domain(X1)),domain(X2)) = domain(X2) -> addition(backward_diamond(multiplication(X3,X4),domain(X0)),domain(X2)) = domain(X2))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 262.33/262.68 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 262.33/262.68 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 262.33/262.68 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 262.33/262.68 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 262.33/262.68 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 262.33/262.68 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 262.33/262.68 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 262.33/262.68 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 262.33/262.68 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 262.33/262.68 39 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(20)].
% 262.33/262.68 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 262.33/262.68 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 262.33/262.68 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 262.33/262.68 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 262.33/262.68 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 262.33/262.68 51 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(24)].
% 262.33/262.68 52 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(51),rewrite([39(2),39(5)])].
% 262.33/262.68 57 domain(c2) = addition(backward_diamond(c4,domain(c1)),domain(c2)) # label(goals) # label(negated_conjecture). [clausify(27)].
% 262.33/262.68 58 addition(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c1)))),c4)))) = antidomain(antidomain(c2)). [copy(57),rewrite([37(2),37(6),52(8),37(14),42(16)]),flip(a)].
% 262.33/262.68 59 domain(c3) = addition(backward_diamond(c5,domain(c2)),domain(c3)) # label(goals) # label(negated_conjecture). [clausify(27)].
% 262.33/262.68 60 addition(antidomain(antidomain(c3)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c2)))),c5)))) = antidomain(antidomain(c3)). [copy(59),rewrite([37(2),37(6),52(8),37(14),42(16)]),flip(a)].
% 262.33/262.68 61 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 262.33/262.68 62 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(61),rewrite([42(2)]),flip(a)].
% 262.33/262.68 63 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 262.33/262.68 64 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 262.33/262.68 65 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(64),flip(a)].
% 262.33/262.68 66 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 262.33/262.68 67 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(66),flip(a)].
% 262.33/262.68 68 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 262.33/262.68 69 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(68),flip(a)].
% 262.33/262.68 70 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 262.33/262.68 71 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(70),flip(a)].
% 262.33/262.68 72 domain(c3) != addition(backward_diamond(multiplication(c4,c5),domain(c1)),domain(c3)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 262.33/262.68 73 addition(antidomain(antidomain(c3)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c1)))),multiplication(c4,c5))))) != antidomain(antidomain(c3)) # answer(goals). [copy(72),rewrite([37(2),37(8),52(10),37(16),42(18)]),flip(a)].
% 262.33/262.68 74 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 262.33/262.68 75 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 262.33/262.68 76 addition(A,addition(A,B)) = addition(A,B). [para(62(a,1),31(a,1)),rewrite([42(1),42(2),62(2,R),31(1),42(3)])].
% 262.33/262.68 77 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),63(a,1,1)),rewrite([35(2)]),flip(a)].
% 262.33/262.68 78 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(63(a,1),38(a,1))].
% 262.33/262.68 79 multiplication(A,multiplication(coantidomain(A),B)) = zero. [para(38(a,1),63(a,1,1)),rewrite([35(2)]),flip(a)].
% 262.33/262.68 80 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),65(a,2,2)),rewrite([34(3),42(3)])].
% 262.33/262.68 81 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),65(a,1,1)),rewrite([42(4)]),flip(a)].
% 262.33/262.68 82 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),65(a,1,1)),rewrite([80(4)]),flip(a)].
% 262.33/262.68 83 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(38(a,1),65(a,1,1)),rewrite([80(3),42(3)]),flip(a)].
% 262.33/262.68 84 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),67(a,1,1)),rewrite([42(4)]),flip(a)].
% 262.33/262.68 85 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(36(a,1),67(a,1,1)),rewrite([80(3),42(3)]),flip(a)].
% 262.33/262.68 86 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(38(a,1),67(a,1,1)),rewrite([80(4),42(3)]),flip(a)].
% 262.33/262.68 87 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(63(a,1),67(a,1,1)),rewrite([42(6)])].
% 262.33/262.68 94 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(38(a,1),69(a,1,1,1))].
% 262.33/262.68 95 addition(antidomain(multiplication(A,multiplication(B,C))),antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C)))))) = antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C))))). [para(63(a,1),69(a,1,1,1)),rewrite([63(7),63(13)])].
% 262.33/262.68 99 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),71(a,1,1,1))].
% 262.33/262.68 100 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(A)))) = coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(A))). [para(38(a,1),71(a,1,1,1))].
% 262.33/262.68 102 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(63(a,1),71(a,1,1,1))].
% 262.33/262.68 103 addition(zero,antidomain(zero)) = one. [para(74(a,1),44(a,1,1)),rewrite([74(3)])].
% 262.33/262.68 104 addition(zero,coantidomain(zero)) = one. [para(75(a,1),46(a,1,1)),rewrite([75(3)])].
% 262.33/262.68 107 multiplication(A,antidomain(zero)) = A. [para(103(a,1),65(a,2,2)),rewrite([34(2),80(5),32(5)])].
% 262.33/262.68 111 multiplication(A,coantidomain(zero)) = A. [para(104(a,1),65(a,2,2)),rewrite([34(2),80(5),32(5)])].
% 262.33/262.68 113 addition(one,antidomain(A)) = one. [para(44(a,1),76(a,1,2)),rewrite([42(3),44(7)])].
% 262.33/262.68 114 addition(one,coantidomain(A)) = one. [para(46(a,1),76(a,1,2)),rewrite([42(3),46(7)])].
% 262.33/262.68 115 antidomain(zero) = one. [para(107(a,1),33(a,1)),flip(a)].
% 262.33/262.68 116 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(94),rewrite([115(2),113(7)]),flip(a)].
% 262.33/262.68 118 coantidomain(zero) = one. [para(111(a,1),33(a,1)),flip(a)].
% 262.33/262.68 119 coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(A))) = one. [back_rewrite(100),rewrite([118(2),114(7)]),flip(a)].
% 262.33/262.68 120 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(99),rewrite([118(2),114(7)]),flip(a)].
% 262.33/262.68 121 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(63(a,1),77(a,1,2))].
% 262.33/262.68 124 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(77(a,1),69(a,1,1,1)),rewrite([115(2),113(8)]),flip(a)].
% 262.33/262.68 126 addition(A,multiplication(A,antidomain(B))) = A. [para(113(a,1),65(a,2,2)),rewrite([32(2),32(5)])].
% 262.33/262.68 127 addition(A,multiplication(antidomain(B),A)) = A. [para(113(a,1),67(a,2,1)),rewrite([33(2),33(5)])].
% 262.33/262.68 128 addition(A,multiplication(A,coantidomain(B))) = A. [para(114(a,1),65(a,2,2)),rewrite([32(2),32(5)])].
% 262.33/262.68 129 addition(A,multiplication(coantidomain(B),A)) = A. [para(114(a,1),67(a,2,1)),rewrite([33(2),33(5)])].
% 262.33/262.68 131 multiplication(A,addition(B,multiplication(coantidomain(A),C))) = multiplication(A,B). [para(79(a,1),65(a,1,1)),rewrite([80(3),42(4)]),flip(a)].
% 262.33/262.68 132 multiplication(addition(A,B),multiplication(coantidomain(B),C)) = multiplication(A,multiplication(coantidomain(B),C)). [para(79(a,1),67(a,1,1)),rewrite([80(5),42(4)]),flip(a)].
% 262.33/262.68 133 antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))) = one. [para(79(a,1),69(a,1,1,1)),rewrite([115(2),113(8)]),flip(a)].
% 262.33/262.68 136 addition(A,addition(B,multiplication(A,antidomain(C)))) = addition(A,B). [para(126(a,1),62(a,2,2)),rewrite([42(3),42(5)])].
% 262.33/262.68 145 addition(A,addition(B,multiplication(A,coantidomain(C)))) = addition(A,B). [para(128(a,1),62(a,2,2)),rewrite([42(3),42(5)])].
% 262.33/262.68 151 multiplication(addition(A,multiplication(A,B)),C) = multiplication(A,multiplication(addition(B,one),C)). [para(81(a,1),63(a,1,1))].
% 262.33/262.68 153 addition(addition(A,multiplication(A,B)),multiplication(A,C)) = multiplication(A,addition(B,addition(C,one))). [para(81(a,1),65(a,1,1)),rewrite([42(7),62(7,R),42(6)])].
% 262.33/262.68 155 addition(addition(A,multiplication(A,B)),multiplication(C,addition(B,one))) = multiplication(addition(A,C),addition(B,one)). [para(81(a,1),67(a,1,1))].
% 262.33/262.68 157 multiplication(addition(A,multiplication(A,B)),B) = multiplication(A,multiplication(B,addition(B,one))). [para(81(a,2),67(a,1)),rewrite([63(4)]),flip(a)].
% 262.33/262.68 159 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,antidomain(antidomain(addition(B,one)))))) = antidomain(multiplication(A,antidomain(antidomain(addition(B,one))))). [para(81(a,1),69(a,1,1,1))].
% 262.33/262.68 163 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(116(a,1),36(a,1,1)),rewrite([33(6)])].
% 262.33/262.68 168 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(163(a,1),65(a,1,1)),rewrite([80(3),42(5)]),flip(a)].
% 262.33/262.68 174 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),82(a,1,2)),rewrite([32(4)]),flip(a)].
% 262.33/262.68 179 addition(multiplication(antidomain(A),B),multiplication(C,addition(A,B))) = multiplication(addition(C,antidomain(A)),addition(A,B)). [para(82(a,1),67(a,1,1)),rewrite([42(7)])].
% 262.33/262.68 180 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(67(a,1),82(a,1,2))].
% 262.33/262.68 181 addition(antidomain(multiplication(antidomain(A),B)),antidomain(multiplication(antidomain(A),antidomain(antidomain(addition(A,B)))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(addition(A,B))))). [para(82(a,1),69(a,1,1,1))].
% 262.33/262.68 184 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(127(a,1),82(a,1,2)),rewrite([36(2)]),flip(a)].
% 262.33/262.68 185 multiplication(antidomain(A),multiplication(coantidomain(B),A)) = zero. [para(129(a,1),82(a,1,2)),rewrite([36(2)]),flip(a)].
% 262.33/262.68 190 multiplication(coantidomain(coantidomain(A)),coantidomain(A)) = zero. [para(119(a,1),38(a,1,2)),rewrite([32(6)])].
% 262.33/262.68 196 addition(zero,coantidomain(A)) = coantidomain(A). [para(190(a,1),129(a,1,2)),rewrite([42(3)])].
% 262.33/262.68 197 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(46(a,1),83(a,1,2)),rewrite([32(3)]),flip(a)].
% 262.33/262.68 198 multiplication(A,multiplication(addition(B,coantidomain(A)),C)) = multiplication(A,multiplication(B,C)). [para(83(a,1),63(a,1,1)),rewrite([63(2)]),flip(a)].
% 262.33/262.68 200 multiplication(A,addition(B,addition(C,coantidomain(A)))) = multiplication(A,addition(B,C)). [para(83(a,1),65(a,1,1)),rewrite([65(3),42(5),62(5,R),42(4)]),flip(a)].
% 262.33/262.68 204 multiplication(coantidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(71(a,1),83(a,1,2)),rewrite([38(8),63(7)]),flip(a)].
% 262.33/262.68 206 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(197(a,1),65(a,1,1)),rewrite([81(4,R),42(7)]),flip(a)].
% 262.33/262.68 211 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(120(a,1),38(a,1,2)),rewrite([32(6)])].
% 262.33/262.68 215 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(211(a,1),67(a,1,1)),rewrite([80(3),42(5)]),flip(a)].
% 262.33/262.68 219 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(184(a,1),67(a,1,1)),rewrite([80(5),42(5)]),flip(a)].
% 262.33/262.68 222 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(82(a,1),184(a,1,2))].
% 262.33/262.68 235 addition(coantidomain(addition(A,multiplication(B,A))),coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A))) = coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A)). [para(84(a,1),71(a,1,1,1))].
% 262.33/262.68 245 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(83(a,1),84(a,2,2)),rewrite([42(9),62(9),42(8),62(9,R),42(8)])].
% 262.33/262.68 248 multiplication(addition(A,antidomain(B)),multiplication(coantidomain(C),B)) = multiplication(A,multiplication(coantidomain(C),B)). [para(185(a,1),67(a,1,1)),rewrite([80(5),42(5)]),flip(a)].
% 262.33/262.68 262 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(44(a,1),85(a,1,1)),rewrite([33(3)]),flip(a)].
% 262.33/262.68 264 multiplication(addition(A,addition(B,antidomain(C))),C) = multiplication(addition(A,B),C). [para(85(a,1),67(a,1,1)),rewrite([67(3),42(5),62(5,R),42(4)]),flip(a)].
% 262.33/262.68 269 multiplication(addition(A,antidomain(B)),addition(B,one)) = addition(A,addition(antidomain(B),multiplication(A,B))). [para(85(a,1),81(a,2,2)),rewrite([42(9),62(9),42(8),62(9,R),42(8)])].
% 262.33/262.68 270 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),86(a,1,1))].
% 262.33/262.68 271 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),86(a,1,1)),rewrite([33(5)]),flip(a)].
% 262.33/262.68 272 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),86(a,1,1)),rewrite([33(5)]),flip(a)].
% 262.33/262.68 281 multiplication(A,coantidomain(addition(A,B))) = zero. [para(76(a,1),86(a,1,1)),rewrite([38(4)]),flip(a)].
% 262.33/262.68 285 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(262(a,1),63(a,1,1)),flip(a)].
% 262.33/262.68 286 multiplication(antidomain(A),addition(B,antidomain(A))) = multiplication(antidomain(A),addition(B,one)). [para(262(a,1),65(a,1,1)),rewrite([81(4,R),42(7)]),flip(a)].
% 262.33/262.68 287 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(262(a,1),67(a,1,1)),rewrite([84(4,R),42(6)]),flip(a)].
% 262.33/262.68 291 coantidomain(addition(A,one)) = zero. [para(281(a,1),33(a,1)),rewrite([42(3)]),flip(a)].
% 262.33/262.68 301 coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B)))) = one. [para(281(a,1),71(a,1,1,1)),rewrite([118(2),114(8)]),flip(a)].
% 262.33/262.68 303 multiplication(A,coantidomain(multiplication(A,addition(B,one)))) = zero. [para(81(a,2),281(a,1,2,1))].
% 262.33/262.68 308 addition(coantidomain(A),coantidomain(addition(A,multiplication(B,A)))) = coantidomain(A). [back_rewrite(235),rewrite([291(6),118(5),33(5),42(5),291(8),118(7),33(7)])].
% 262.33/262.68 311 multiplication(addition(A,multiplication(B,antidomain(C))),C) = multiplication(A,C). [para(36(a,1),87(a,1,1,2)),rewrite([34(2),80(3)]),flip(a)].
% 262.33/262.68 333 addition(multiplication(A,multiplication(antidomain(B),C)),multiplication(D,addition(B,C))) = multiplication(addition(D,multiplication(A,antidomain(B))),addition(B,C)). [para(82(a,1),87(a,1,1,2))].
% 262.33/262.68 334 addition(multiplication(antidomain(A),B),multiplication(C,multiplication(D,addition(A,B)))) = multiplication(addition(antidomain(A),multiplication(C,D)),addition(A,B)). [para(82(a,1),87(a,1,2)),rewrite([42(6)])].
% 262.33/262.68 342 multiplication(addition(A,multiplication(B,coantidomain(C))),coantidomain(C)) = multiplication(addition(B,A),coantidomain(C)). [para(197(a,1),87(a,1,1,2)),rewrite([67(5)]),flip(a)].
% 262.33/262.68 446 antidomain(addition(A,one)) = zero. [para(36(a,1),303(a,1,2,1)),rewrite([118(5),32(5)])].
% 262.33/262.68 456 addition(antidomain(A),antidomain(addition(A,multiplication(A,B)))) = antidomain(A). [back_rewrite(159),rewrite([446(6),115(5),32(5),42(5),446(8),115(7),32(7)])].
% 262.33/262.68 457 addition(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(A). [para(446(a,1),69(a,1,2,1,2,1)),rewrite([115(6),32(6),42(6),446(9),115(8),32(8)])].
% 262.33/262.68 488 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,addition(B,multiplication(B,C))))) = antidomain(multiplication(A,B)). [para(81(a,1),95(a,1,1,1,2)),rewrite([446(7),115(6),32(6),42(7),446(10),115(9),32(9)])].
% 262.33/262.68 523 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(124(a,1),36(a,1,1)),rewrite([33(7)])].
% 262.33/262.68 531 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(523(a,1),65(a,1,1)),rewrite([80(4),42(7)]),flip(a)].
% 262.33/262.68 540 multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))) = zero. [para(133(a,1),36(a,1,1)),rewrite([33(7)])].
% 262.33/262.68 549 multiplication(addition(A,B),antidomain(antidomain(multiplication(coantidomain(B),C)))) = multiplication(A,antidomain(antidomain(multiplication(coantidomain(B),C)))). [para(540(a,1),67(a,1,1)),rewrite([80(7),42(6)]),flip(a)].
% 262.33/262.68 573 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B)) = one. [para(36(a,1),102(a,1,1,1,2)),rewrite([34(2),118(2),114(8)]),flip(a)].
% 262.33/262.68 574 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(36(a,1),102(a,1,1,1)),rewrite([118(2),114(9)]),flip(a)].
% 262.33/262.68 575 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one. [para(38(a,1),102(a,1,1,1,2)),rewrite([34(2),118(2),114(8)]),flip(a)].
% 262.33/262.68 587 multiplication(coantidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = zero. [para(102(a,1),83(a,1,2)),rewrite([38(10),63(9)]),flip(a)].
% 262.33/262.68 595 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [para(184(a,1),102(a,1,1,1)),rewrite([118(2),114(9)]),flip(a)].
% 262.33/262.68 600 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [para(185(a,1),102(a,1,1,1)),rewrite([118(2),114(9)]),flip(a)].
% 262.33/262.68 662 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(174(a,1),127(a,1,2)),rewrite([42(5)])].
% 262.33/262.68 760 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(42(a,1),222(a,1,1,1))].
% 262.33/262.68 859 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),270(a,1,1)),rewrite([33(4)]),flip(a)].
% 262.33/262.68 860 multiplication(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c1)))),c4))),coantidomain(antidomain(antidomain(c2)))) = zero. [para(58(a,1),270(a,1,1)),rewrite([38(8)]),flip(a)].
% 262.33/262.68 861 multiplication(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c2)))),c5))),coantidomain(antidomain(antidomain(c3)))) = zero. [para(60(a,1),270(a,1,1)),rewrite([38(8)]),flip(a)].
% 262.33/262.68 865 multiplication(addition(A,B),multiplication(C,coantidomain(multiplication(A,C)))) = multiplication(B,multiplication(C,coantidomain(multiplication(A,C)))). [para(67(a,1),270(a,1,1)),rewrite([63(5),63(9)])].
% 262.33/262.68 867 multiplication(A,multiplication(antidomain(B),coantidomain(A))) = zero. [para(126(a,1),270(a,1,1)),rewrite([38(2),63(5)]),flip(a)].
% 262.33/262.68 869 multiplication(A,multiplication(coantidomain(B),coantidomain(A))) = zero. [para(128(a,1),270(a,1,1)),rewrite([38(2),63(5)]),flip(a)].
% 262.33/262.68 893 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [para(867(a,1),102(a,1,1,1)),rewrite([118(2),114(9)]),flip(a)].
% 262.33/262.68 898 multiplication(A,addition(B,addition(C,multiplication(coantidomain(A),D)))) = multiplication(A,addition(B,C)). [para(131(a,1),65(a,1,1)),rewrite([65(3),42(6),62(6,R),42(5)]),flip(a)].
% 262.33/262.68 938 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [para(869(a,1),102(a,1,1,1)),rewrite([118(2),114(9)]),flip(a)].
% 262.33/262.68 967 multiplication(addition(A,B),multiplication(coantidomain(A),C)) = multiplication(B,multiplication(coantidomain(A),C)). [para(42(a,1),132(a,1,1))].
% 262.33/262.68 1044 multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [para(301(a,1),38(a,1,2)),rewrite([32(7)])].
% 262.33/262.68 1059 addition(A,multiplication(addition(A,B),antidomain(C))) = addition(A,multiplication(B,antidomain(C))). [para(67(a,1),136(a,1,2)),rewrite([42(1)])].
% 262.33/262.68 1107 multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [para(573(a,1),38(a,1,2)),rewrite([32(7)])].
% 262.33/262.68 1122 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [para(575(a,1),38(a,1,2)),rewrite([32(7)])].
% 262.33/262.68 1136 multiplication(coantidomain(coantidomain(addition(A,multiplication(B,A)))),coantidomain(A)) = zero. [para(84(a,1),1122(a,1,1,1,1))].
% 262.33/262.68 1194 multiplication(antidomain(addition(A,B)),A) = zero. [para(76(a,1),760(a,1,1,1)),rewrite([285(6)])].
% 262.33/262.68 1437 addition(one,addition(coantidomain(A),coantidomain(B))) = one. [para(114(a,1),145(a,2)),rewrite([33(5)])].
% 262.33/262.68 1454 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(859(a,1),128(a,1,2))].
% 262.33/262.68 2318 addition(A,addition(B,multiplication(addition(A,B),C))) = multiplication(addition(A,B),addition(C,one)). [para(81(a,1),155(a,1,2)),rewrite([62(5,R),62(4,R),67(3),62(4,R),42(3)])].
% 262.33/262.68 2407 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),168(a,1,2)),rewrite([32(2)]),flip(a)].
% 262.33/262.68 2429 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2407(a,1),63(a,1,1)),flip(a)].
% 262.33/262.68 2430 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2407(a,1),63(a,1)),flip(a)].
% 262.33/262.68 2431 multiplication(A,addition(B,antidomain(coantidomain(A)))) = addition(A,multiplication(A,B)). [para(2407(a,1),65(a,1,1)),rewrite([42(5)]),flip(a)].
% 262.33/262.68 2437 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2407(a,1),129(a,1,2)),rewrite([42(5)])].
% 262.33/262.68 2536 multiplication(A,coantidomain(coantidomain(A))) = A. [para(174(a,1),2429(a,1,2)),rewrite([2407(3)]),flip(a)].
% 262.33/262.68 2569 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(272),rewrite([2536(5)]),flip(a)].
% 262.33/262.68 2598 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2569(a,1),662(a,1,2)),rewrite([42(5),2437(5),2569(6)])].
% 262.33/262.68 2627 multiplication(addition(A,multiplication(A,B)),addition(B,coantidomain(A))) = multiplication(A,multiplication(B,addition(B,one))). [para(83(a,1),157(a,1,1,2)),rewrite([42(11),62(11,R),42(10),114(10),198(11)])].
% 262.33/262.68 2701 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2598(a,1),44(a,1,1)),rewrite([2598(4)])].
% 262.33/262.68 2707 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2598(a,1),859(a,1,1,1)),rewrite([2598(5),174(5),2598(5)]),flip(a)].
% 262.33/262.68 2709 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2598(a,1),859(a,2,1)),rewrite([2707(2),2707(6),859(9),2707(6)])].
% 262.33/262.68 2716 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2569(a,1),2598(a,1,1,1)),rewrite([2707(2),2707(5)]),flip(a)].
% 262.33/262.68 2717 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2569(a,1),2598(a,2)),rewrite([2707(2),2716(3),2709(4)])].
% 262.33/262.68 2953 multiplication(antidomain(coantidomain(addition(A,multiplication(B,A)))),coantidomain(A)) = zero. [back_rewrite(1136),rewrite([2707(4)])].
% 262.33/262.68 2960 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [back_rewrite(1122),rewrite([2707(3)])].
% 262.33/262.68 2973 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [back_rewrite(1107),rewrite([2707(4)])].
% 262.33/262.68 2993 multiplication(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [back_rewrite(1044),rewrite([2707(2)])].
% 262.33/262.68 2998 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [back_rewrite(938),rewrite([2707(4)])].
% 262.33/262.68 3001 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [back_rewrite(893),rewrite([2707(4)])].
% 262.33/262.68 3003 multiplication(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(c2)))),c5))),coantidomain(antidomain(antidomain(c3)))) = zero. [back_rewrite(861),rewrite([2707(5),2707(9)])].
% 262.33/262.68 3004 multiplication(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(c1)))),c4))),coantidomain(antidomain(antidomain(c2)))) = zero. [back_rewrite(860),rewrite([2707(5),2707(9)])].
% 262.33/262.68 3045 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [back_rewrite(600),rewrite([2707(5)])].
% 262.33/262.68 3050 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [back_rewrite(595),rewrite([2707(5)])].
% 262.33/262.68 3055 multiplication(antidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = zero. [back_rewrite(587),rewrite([2707(3)])].
% 262.33/262.68 3061 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(574),rewrite([2707(5)])].
% 262.33/262.68 3080 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(215),rewrite([2707(3)])].
% 262.33/262.68 3084 multiplication(antidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [back_rewrite(204),rewrite([2707(2)])].
% 262.33/262.68 3087 addition(antidomain(antidomain(c3)),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(c1)))),multiplication(c4,c5))))) != antidomain(antidomain(c3)) # answer(goals). [back_rewrite(73),rewrite([2707(8),2707(14)])].
% 262.33/262.68 3090 backward_diamond(A,B) = antidomain(coantidomain(multiplication(antidomain(coantidomain(B)),A))). [back_rewrite(52),rewrite([2707(3),2707(6)])].
% 262.33/262.68 3374 addition(multiplication(antidomain(antidomain(A)),B),multiplication(antidomain(A),addition(B,one))) = addition(B,antidomain(A)). [para(44(a,1),179(a,2,1)),rewrite([42(6),286(7),42(11),33(12)])].
% 262.33/262.68 3409 multiplication(A,multiplication(addition(coantidomain(A),antidomain(B)),addition(B,C))) = multiplication(A,multiplication(antidomain(B),C)). [para(179(a,1),131(a,1,2))].
% 262.33/262.68 3502 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(44(a,1),180(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 262.33/262.68 3595 multiplication(antidomain(multiplication(coantidomain(A),B)),multiplication(antidomain(coantidomain(A)),B)) = multiplication(antidomain(multiplication(coantidomain(A),B)),B). [para(2701(a,1),180(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 262.33/262.68 3996 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(271(a,1),128(a,1,2))].
% 262.33/262.68 4503 multiplication(A,addition(coantidomain(A),coantidomain(B))) = multiplication(A,coantidomain(B)). [para(308(a,1),200(a,2,2)),rewrite([42(6),62(7,R),42(6),308(6)])].
% 262.33/262.68 4578 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,multiplication(addition(B,one),addition(C,one))))) = antidomain(addition(A,multiplication(A,B))). [para(151(a,1),456(a,1,2,1,2)),rewrite([153(10),42(8),2318(9)])].
% 262.33/262.68 4969 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(1454(a,1),206(a,1,2)),rewrite([42(11),113(11),32(9)])].
% 262.33/262.68 4974 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3996(a,1),206(a,1,2)),rewrite([42(11),113(11),32(10)])].
% 262.33/262.68 4976 multiplication(coantidomain(addition(A,multiplication(B,A))),coantidomain(A)) = coantidomain(addition(A,multiplication(B,A))). [para(308(a,1),206(a,1,2)),rewrite([42(11),114(11),32(10)])].
% 262.33/262.68 5188 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(44(a,1),219(a,1,1)),rewrite([33(5)]),flip(a)].
% 262.33/262.68 7607 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(4969(a,1),245(a,2,2,2)),rewrite([42(4),114(4),2707(6),33(8),2707(11),42(14),2701(14),42(10),113(10)])].
% 262.33/262.68 7935 multiplication(antidomain(A),multiplication(coantidomain(B),antidomain(A))) = multiplication(coantidomain(B),antidomain(A)). [para(44(a,1),248(a,1,1)),rewrite([33(5)]),flip(a)].
% 262.33/262.68 8600 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A)) = zero. [para(2998(a,1),38(a,1,2)),rewrite([32(8)])].
% 262.33/262.68 8615 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(addition(A,B))) = zero. [para(86(a,1),8600(a,1,1,1,1))].
% 262.33/262.68 8629 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A)) = zero. [para(3001(a,1),38(a,1,2)),rewrite([32(8)])].
% 262.33/262.68 8758 multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A) = zero. [para(3045(a,1),38(a,1,2)),rewrite([32(8)])].
% 262.33/262.68 9146 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = zero. [para(3050(a,1),38(a,1,2)),rewrite([32(8)])].
% 262.33/262.68 9179 multiplication(coantidomain(antidomain(A)),A) = A. [para(2701(a,1),3080(a,1,1)),rewrite([33(2)]),flip(a)].
% 262.33/262.68 9189 multiplication(antidomain(antidomain(A)),A) = A. [para(7607(a,1),3080(a,1,1)),rewrite([33(2)]),flip(a)].
% 262.33/262.68 9193 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(4974),rewrite([9179(5)]),flip(a)].
% 262.33/262.68 9207 addition(antidomain(antidomain(c3)),antidomain(coantidomain(multiplication(antidomain(antidomain(c1)),multiplication(c4,c5))))) != antidomain(antidomain(c3)) # answer(goals). [back_rewrite(3087),rewrite([9193(7)])].
% 262.33/262.68 9208 multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(c1)),c4))),antidomain(c2)) = zero. [back_rewrite(3004),rewrite([9193(4),9193(11)])].
% 262.33/262.68 9209 multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(c2)),c5))),antidomain(c3)) = zero. [back_rewrite(3003),rewrite([9193(4),9193(11)])].
% 262.33/262.68 9257 multiplication(antidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B). [para(9189(a,1),63(a,1,1)),flip(a)].
% 262.33/262.68 9266 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(9189(a,1),121(a,1,2,2))].
% 262.33/262.68 9297 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9193(a,1),2707(a,1,1)),rewrite([9193(5)])].
% 262.33/262.68 9298 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9193(a,1),2707(a,2,1)),rewrite([9297(3),9297(4)])].
% 262.33/262.68 9299 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9193(a,1),2717(a,2)),rewrite([9297(3),9298(4)])].
% 262.33/262.68 9540 multiplication(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(multiplication(A,addition(B,one))). [para(457(a,1),287(a,1,1)),rewrite([42(9),113(9),33(12)])].
% 262.33/262.68 11791 multiplication(antidomain(antidomain(c1)),multiplication(c4,antidomain(c2))) = zero. [para(9208(a,1),2429(a,1,2)),rewrite([34(7),63(9)]),flip(a)].
% 262.33/262.68 11795 multiplication(antidomain(antidomain(c1)),multiplication(c4,multiplication(antidomain(c2),A))) = zero. [para(11791(a,1),63(a,1,1)),rewrite([35(2),63(9)]),flip(a)].
% 262.33/262.68 11818 multiplication(antidomain(antidomain(c2)),multiplication(c5,antidomain(c3))) = zero. [para(9209(a,1),2429(a,1,2)),rewrite([34(7),63(9)]),flip(a)].
% 262.33/262.68 12745 multiplication(addition(coantidomain(A),coantidomain(B)),coantidomain(A)) = coantidomain(A). [para(129(a,1),342(a,1,1)),rewrite([197(3),42(4)]),flip(a)].
% 262.33/262.68 12780 addition(coantidomain(A),addition(coantidomain(B),antidomain(coantidomain(A)))) = one. [para(12745(a,1),269(a,2,2,2)),rewrite([42(6),62(6,R),42(9),114(9),32(8),42(13),2701(13),42(11),1437(11)])].
% 262.33/262.68 12787 addition(antidomain(A),addition(antidomain(antidomain(A)),coantidomain(B))) = one. [para(9297(a,1),12780(a,1,1)),rewrite([9297(5),9299(6),62(6)])].
% 262.33/262.68 12799 addition(antidomain(A),addition(antidomain(antidomain(A)),antidomain(coantidomain(B)))) = one. [para(2707(a,1),12787(a,1,2,2))].
% 262.33/262.68 12864 addition(antidomain(A),addition(antidomain(B),antidomain(antidomain(A)))) = one. [para(9297(a,1),12799(a,1,2,2,1)),rewrite([9299(6),42(5)])].
% 262.33/262.68 12870 multiplication(addition(antidomain(A),antidomain(B)),antidomain(A)) = antidomain(A). [para(12864(a,1),264(a,1,1)),rewrite([33(3)]),flip(a)].
% 262.33/262.68 12886 multiplication(antidomain(antidomain(addition(antidomain(A),antidomain(B)))),antidomain(A)) = antidomain(A). [para(12870(a,1),9257(a,1,2)),rewrite([12870(12)])].
% 262.33/262.68 13490 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero. [para(3061(a,1),38(a,1,2)),rewrite([32(8)])].
% 262.33/262.68 15529 addition(antidomain(antidomain(A)),antidomain(antidomain(addition(antidomain(A),antidomain(B))))) = one. [para(12886(a,1),269(a,2,2,2)),rewrite([42(8),42(11),113(11),32(10),42(17),44(17),42(15),113(15)])].
% 262.33/262.68 16637 multiplication(antidomain(A),antidomain(antidomain(addition(antidomain(A),antidomain(B))))) = antidomain(A). [para(15529(a,1),82(a,1,2)),rewrite([9299(3),32(3),9299(4)]),flip(a)].
% 262.33/262.68 16785 antidomain(multiplication(A,addition(B,one))) = antidomain(addition(A,multiplication(A,B))). [para(81(a,1),488(a,1,1,1)),rewrite([81(9,R),4578(11)]),flip(a)].
% 262.33/262.68 17189 multiplication(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,B)). [para(69(a,1),16637(a,1,2,1,1)),rewrite([9299(8)])].
% 262.33/262.68 17365 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(44(a,1),531(a,1,2)),rewrite([32(3)]),flip(a)].
% 262.33/262.68 17369 antidomain(multiplication(A,addition(B,one))) = antidomain(A). [back_rewrite(9540),rewrite([17365(6)]),flip(a)].
% 262.33/262.68 17371 antidomain(addition(A,multiplication(A,B))) = antidomain(A). [back_rewrite(16785),rewrite([17369(4)]),flip(a)].
% 262.33/262.68 17505 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17365(a,1),127(a,1,2)),rewrite([42(4)])].
% 262.33/262.68 17515 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(17365(a,1),2429(a,1,2)),rewrite([2407(3)]),flip(a)].
% 262.33/262.68 17525 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(17365(a,1),245(a,2,2,2)),rewrite([42(3),113(3),9297(5),42(6),33(7),9297(9),42(11),44(11),42(9),113(9)])].
% 262.33/262.68 17538 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17365(a,1),2430(a,1,2,2,1,1)),rewrite([9297(5),9299(6),5188(6),17365(8)])].
% 262.33/262.68 17727 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17538(a,1),63(a,1,1)),flip(a)].
% 262.33/262.68 17756 multiplication(antidomain(multiplication(coantidomain(A),B)),B) = multiplication(antidomain(coantidomain(A)),B). [back_rewrite(3595),rewrite([17727(7)]),flip(a)].
% 262.33/262.68 17757 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3502),rewrite([17727(7)]),flip(a)].
% 262.33/262.68 18811 multiplication(antidomain(antidomain(A)),multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(184(a,1),17757(a,1,1,1)),rewrite([115(2),33(4)]),flip(a)].
% 262.33/262.68 18816 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(1194(a,1),17757(a,1,1,1)),rewrite([115(2),33(2)]),flip(a)].
% 262.33/262.68 18824 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(2960(a,1),17757(a,1,1,1)),rewrite([115(2),33(3),2717(5)]),flip(a)].
% 262.33/262.68 18825 multiplication(coantidomain(multiplication(A,antidomain(B))),B) = B. [para(2973(a,1),17757(a,1,1,1)),rewrite([115(2),33(2),2717(5)]),flip(a)].
% 262.33/262.68 18826 multiplication(coantidomain(A),coantidomain(addition(A,B))) = coantidomain(addition(A,B)). [para(2993(a,1),17757(a,1,1,1)),rewrite([115(2),33(4),2717(5)]),flip(a)].
% 262.33/262.68 18842 coantidomain(addition(A,multiplication(B,A))) = coantidomain(A). [para(2953(a,1),17757(a,1,1,1)),rewrite([115(2),33(3),2717(6),4976(6)]),flip(a)].
% 262.33/262.68 18850 multiplication(coantidomain(multiplication(A,coantidomain(B))),coantidomain(A)) = coantidomain(A). [para(8600(a,1),17757(a,1,1,1)),rewrite([115(2),33(3),2717(6)]),flip(a)].
% 262.33/262.68 18851 multiplication(coantidomain(multiplication(A,antidomain(B))),coantidomain(A)) = coantidomain(A). [para(8629(a,1),17757(a,1,1,1)),rewrite([115(2),33(3),2717(6)]),flip(a)].
% 262.33/262.68 18852 multiplication(coantidomain(multiplication(antidomain(A),coantidomain(B))),A) = A. [para(8758(a,1),17757(a,1,1,1)),rewrite([115(2),33(2),2717(6)]),flip(a)].
% 262.33/262.68 18853 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A. [para(9146(a,1),17757(a,1,1,1)),rewrite([115(2),33(2),2717(6)]),flip(a)].
% 262.33/262.68 18855 multiplication(coantidomain(A),multiplication(B,coantidomain(multiplication(A,B)))) = multiplication(B,coantidomain(multiplication(A,B))). [para(3084(a,1),17757(a,1,1,1)),rewrite([115(2),33(5),2717(6)]),flip(a)].
% 262.33/262.68 18870 multiplication(antidomain(c2),multiplication(c5,antidomain(c3))) = multiplication(c5,antidomain(c3)). [para(11818(a,1),17757(a,1,1,1)),rewrite([115(2),33(6),9299(8)]),flip(a)].
% 262.33/262.68 18887 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(13490(a,1),17757(a,1,1,1)),rewrite([115(2),33(2),2717(6)]),flip(a)].
% 262.33/262.68 18956 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(42(a,1),18816(a,1,1,1,1))].
% 262.33/262.68 18987 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(18816(a,1),17538(a,1,1,1)),rewrite([9299(5),9299(8)])].
% 262.33/262.68 18988 addition(antidomain(A),antidomain(addition(A,B))) = antidomain(A). [para(18816(a,1),17505(a,1,2,1)),rewrite([9299(4),42(4),18816(8)])].
% 262.33/262.68 19034 addition(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = one. [para(18825(a,1),17525(a,1,2,1)),rewrite([2717(5),42(5)])].
% 262.33/262.68 19035 multiplication(antidomain(A),antidomain(coantidomain(multiplication(B,antidomain(A))))) = antidomain(coantidomain(multiplication(B,antidomain(A)))). [para(18825(a,1),17538(a,1,1,1))].
% 262.33/262.68 19081 coantidomain(addition(A,multiplication(B,multiplication(C,A)))) = coantidomain(A). [para(63(a,1),18842(a,1,1,2))].
% 262.33/262.68 19104 coantidomain(addition(A,antidomain(multiplication(coantidomain(A),B)))) = antidomain(antidomain(multiplication(coantidomain(A),B))). [para(17515(a,1),18842(a,1,1,2)),rewrite([42(4),9297(9)])].
% 262.33/262.68 19162 addition(antidomain(A),antidomain(addition(B,A))) = antidomain(A). [para(18956(a,1),17505(a,1,2,1)),rewrite([9299(4),42(4),18956(8)])].
% 262.33/262.68 19181 addition(antidomain(coantidomain(A)),coantidomain(multiplication(B,A))) = one. [para(18824(a,1),269(a,2,2,2)),rewrite([42(5),42(8),114(8),32(7),42(11),2701(11),42(9),114(9)])].
% 262.33/262.68 19188 coantidomain(addition(A,coantidomain(multiplication(B,A)))) = zero. [para(18824(a,1),8615(a,1,1,1,1)),rewrite([2707(2),2717(3),42(4),18826(6)])].
% 262.33/262.68 19211 coantidomain(addition(A,coantidomain(A))) = zero. [para(33(a,1),19188(a,1,1,2,1))].
% 262.33/262.68 19257 multiplication(A,coantidomain(multiplication(addition(B,coantidomain(B)),A))) = zero. [para(19211(a,1),3084(a,1,1,1)),rewrite([115(2),33(7)])].
% 262.33/262.68 19342 multiplication(coantidomain(A),antidomain(B)) = multiplication(antidomain(B),coantidomain(A)). [para(18852(a,1),17515(a,1,2,1)),rewrite([63(5),7935(5)])].
% 262.33/262.68 19345 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))). [para(18852(a,1),17538(a,1,1,1))].
% 262.33/262.68 19421 multiplication(coantidomain(A),antidomain(coantidomain(multiplication(A,antidomain(B))))) = zero. [back_rewrite(8629),rewrite([19342(6,R)])].
% 262.33/262.68 19474 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(18853(a,1),17515(a,1,2,1)),rewrite([63(5),5188(5)])].
% 262.33/262.68 19477 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),antidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))). [para(18853(a,1),17538(a,1,1,1))].
% 262.33/262.68 19760 addition(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = one. [para(2717(a,1),19034(a,1,1)),rewrite([2717(4)])].
% 262.33/262.68 19788 addition(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(multiplication(antidomain(B),A)). [para(127(a,1),19162(a,1,2,1)),rewrite([42(5)])].
% 262.33/262.68 19810 multiplication(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(A). [para(19181(a,1),82(a,1,2)),rewrite([2717(3),32(3),2717(4)]),flip(a)].
% 262.33/262.68 19888 multiplication(coantidomain(A),antidomain(coantidomain(multiplication(B,coantidomain(A))))) = antidomain(coantidomain(multiplication(B,coantidomain(A)))). [para(19760(a,1),86(a,1,1)),rewrite([2707(5),33(6),2707(9)]),flip(a)].
% 262.33/262.68 19890 multiplication(A,coantidomain(multiplication(B,coantidomain(A)))) = A. [para(19760(a,1),4503(a,1,2)),rewrite([32(2)]),flip(a)].
% 262.33/262.68 20031 multiplication(A,multiplication(coantidomain(B),antidomain(coantidomain(A)))) = multiplication(A,coantidomain(B)). [para(18850(a,1),17515(a,1,2,1)),rewrite([63(5)])].
% 262.33/262.68 20319 addition(antidomain(A),coantidomain(multiplication(antidomain(multiplication(B,A)),B))) = one. [para(18887(a,1),17525(a,1,2,1)),rewrite([2717(6),42(6)])].
% 262.33/262.68 20567 coantidomain(addition(antidomain(coantidomain(A)),multiplication(B,A))) = coantidomain(A). [para(2407(a,1),19081(a,1,1,2,2)),rewrite([9297(8),2717(8)])].
% 262.33/262.68 20775 coantidomain(multiplication(addition(A,coantidomain(A)),B)) = coantidomain(B). [para(19257(a,1),18887(a,1,1,1,1,1)),rewrite([115(2),33(2),19810(6)]),flip(a)].
% 262.33/262.68 20781 coantidomain(multiplication(antidomain(coantidomain(A)),B)) = coantidomain(multiplication(A,B)). [para(132(a,1),20775(a,1,1)),rewrite([2707(2),2429(4),2707(4)]),flip(a)].
% 262.33/262.68 20812 coantidomain(multiplication(A,antidomain(antidomain(multiplication(antidomain(coantidomain(A)),B))))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [para(549(a,1),20775(a,1,1)),rewrite([2707(2),2707(9),9297(13),9299(13)])].
% 262.33/262.68 20838 backward_diamond(A,B) = antidomain(coantidomain(multiplication(B,A))). [back_rewrite(3090),rewrite([20781(5)])].
% 262.33/262.68 21059 multiplication(coantidomain(A),coantidomain(B)) = multiplication(coantidomain(B),coantidomain(A)). [para(2717(a,1),19342(a,1,2)),rewrite([2717(6)])].
% 262.33/262.68 21087 antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))) = multiplication(coantidomain(B),antidomain(A)). [para(19342(a,1),2430(a,1,2,2,1,1)),rewrite([19345(8),19888(7)])].
% 262.33/262.68 21148 multiplication(A,coantidomain(multiplication(coantidomain(A),antidomain(B)))) = A. [para(19342(a,2),19890(a,1,2,1))].
% 262.33/262.68 21159 antidomain(coantidomain(multiplication(coantidomain(A),antidomain(B)))) = multiplication(coantidomain(A),antidomain(B)). [para(19342(a,1),20838(a,2,1,1)),rewrite([20838(3),21087(10)])].
% 262.33/262.68 21170 multiplication(coantidomain(A),coantidomain(multiplication(A,antidomain(B)))) = coantidomain(A). [back_rewrite(18851),rewrite([21059(5)])].
% 262.33/262.68 21329 antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))) = multiplication(antidomain(A),antidomain(B)). [para(19474(a,1),2430(a,1,2,2,1,1)),rewrite([19474(5),19035(8),19477(7)])].
% 262.33/262.68 21332 multiplication(antidomain(A),addition(antidomain(A),antidomain(B))) = antidomain(A). [para(19474(a,1),2431(a,2,2)),rewrite([9297(4),9299(5),42(4),19474(9),81(10,R),42(9),113(9),32(8)])].
% 262.33/262.68 21351 multiplication(antidomain(A),antidomain(multiplication(antidomain(B),antidomain(A)))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(19474(a,1),17757(a,2)),rewrite([19474(6)])].
% 262.33/262.68 21850 antidomain(antidomain(multiplication(coantidomain(A),antidomain(B)))) = multiplication(coantidomain(A),antidomain(B)). [para(21148(a,1),20567(a,1,1,2)),rewrite([2707(5),21159(5),42(5),19104(6),2707(10),21159(10)])].
% 262.33/262.68 21910 coantidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [para(19474(a,1),20781(a,1,1))].
% 262.33/262.68 22022 multiplication(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = multiplication(coantidomain(B),antidomain(A)). [para(17756(a,1),21170(a,1,2,1)),rewrite([9297(5),21850(5),19474(7),21910(8),63(7),18855(7),9297(10),21850(10)])].
% 262.33/262.68 22181 multiplication(antidomain(A),addition(antidomain(A),coantidomain(B))) = antidomain(A). [para(2717(a,1),21332(a,1,2,2))].
% 262.33/262.68 22348 addition(antidomain(A),multiplication(antidomain(antidomain(A)),coantidomain(B))) = addition(antidomain(A),coantidomain(B)). [para(22181(a,1),179(a,1,2)),rewrite([42(6),44(10),33(11)])].
% 262.33/262.68 23680 multiplication(A,coantidomain(multiplication(B,antidomain(coantidomain(A))))) = multiplication(A,coantidomain(B)). [para(2429(a,1),865(a,2)),rewrite([22022(8),967(6),20031(5)]),flip(a)].
% 262.33/262.68 24138 multiplication(A,addition(coantidomain(A),antidomain(B))) = multiplication(A,antidomain(B)). [para(269(a,2),898(a,1,2)),rewrite([3409(7),32(3)]),flip(a)].
% 262.33/262.68 25282 multiplication(antidomain(antidomain(c1)),multiplication(c4,multiplication(c5,antidomain(c3)))) = zero. [para(18870(a,1),11795(a,1,2,2))].
% 262.33/262.68 25306 coantidomain(multiplication(addition(one,c5),antidomain(c3))) = antidomain(antidomain(c3)). [para(18870(a,1),19081(a,1,1,2)),rewrite([84(7,R),42(3),9297(10)])].
% 262.33/262.68 25359 multiplication(antidomain(c3),coantidomain(addition(one,c5))) = zero. [para(25306(a,1),19421(a,1,2,1)),rewrite([9299(8),19342(7)])].
% 262.33/262.68 25372 coantidomain(addition(one,c5)) = zero. [para(25359(a,1),84(a,2,2)),rewrite([42(4),113(4),281(6),42(7),196(7)]),flip(a)].
% 262.33/262.68 25373 multiplication(addition(A,antidomain(c3)),addition(zero,c3)) = multiplication(A,addition(zero,c3)). [para(25359(a,1),179(a,1,1)),rewrite([25372(6),42(4),80(6),25372(12),42(10)]),flip(a)].
% 262.33/262.68 25374 antidomain(multiplication(antidomain(c3),antidomain(antidomain(addition(zero,c3))))) = one. [para(25359(a,1),181(a,1,1,1)),rewrite([115(2),25372(8),42(6),113(11),25372(8),42(6)]),flip(a)].
% 262.33/262.68 25543 multiplication(antidomain(c3),addition(zero,c3)) = zero. [para(25374(a,1),9266(a,1,1)),rewrite([33(8)])].
% 262.33/262.68 25558 multiplication(A,addition(zero,c3)) = multiplication(A,c3). [para(25543(a,1),333(a,1,2)),rewrite([115(2),33(3),42(4),80(4),115(6),32(6),42(5),25373(9)]),flip(a)].
% 262.33/262.68 25559 addition(zero,c3) = c3. [para(25543(a,1),334(a,1,2,2)),rewrite([115(2),33(3),34(3),42(3),115(5),25558(12),311(10),33(6)])].
% 262.33/262.68 25991 addition(antidomain(A),multiplication(antidomain(B),antidomain(addition(A,C)))) = antidomain(A). [para(18988(a,1),1059(a,1,2,1)),rewrite([81(5,R),42(4),113(4),32(3),19474(6)]),flip(a)].
% 262.33/262.68 29491 addition(coantidomain(A),antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = one. [para(78(a,1),20319(a,1,2,1,1,1)),rewrite([115(6),33(6),42(6)])].
% 262.33/262.68 34736 multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = A. [para(29491(a,1),24138(a,1,2)),rewrite([32(2)]),flip(a)].
% 262.33/262.68 34770 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [para(9266(a,1),34736(a,1,2,1,2,1)),rewrite([118(7),32(7),19474(7),17189(7)]),flip(a)].
% 262.33/262.68 35801 multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(c1)),c4))),multiplication(c5,antidomain(c3))) = zero. [para(25282(a,1),3055(a,1,2,2,1)),rewrite([118(13),32(13)])].
% 262.33/262.68 36308 antidomain(addition(antidomain(antidomain(A)),multiplication(antidomain(B),A))) = antidomain(A). [para(18811(a,1),17371(a,1,1,2)),rewrite([9299(9)])].
% 262.33/262.68 36317 antidomain(antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(21148(a,1),36308(a,1,1,2)),rewrite([9297(2),19474(4),21329(6),34770(5),42(5),19788(5),9297(6),19474(8),21329(10)])].
% 262.33/262.68 36319 coantidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [back_rewrite(20812),rewrite([36317(5),2429(6)])].
% 262.33/262.68 37447 antidomain(multiplication(antidomain(coantidomain(A)),B)) = addition(antidomain(B),coantidomain(A)). [para(23680(a,1),3374(a,1,1)),rewrite([9297(8),9299(8),36319(9),42(11),113(11),32(7),42(6),22348(6),9297(6),9299(6),36319(7),42(9),19788(9)]),flip(a)].
% 262.33/262.68 37929 addition(antidomain(A),antidomain(coantidomain(B))) = antidomain(multiplication(coantidomain(B),A)). [para(2707(a,1),37447(a,1,1,1,1)),rewrite([2717(3),2707(6)]),flip(a)].
% 262.33/262.68 37935 addition(antidomain(A),antidomain(antidomain(B))) = antidomain(multiplication(antidomain(B),A)). [para(9297(a,1),37447(a,1,1,1,1)),rewrite([9299(3),9297(6)]),flip(a)].
% 262.33/262.68 38064 antidomain(multiplication(antidomain(c3),coantidomain(multiplication(antidomain(antidomain(c1)),multiplication(c4,c5))))) != antidomain(antidomain(c3)) # answer(goals). [back_rewrite(9207),rewrite([37929(13),19342(11)])].
% 262.33/262.68 38553 addition(antidomain(antidomain(A)),antidomain(addition(A,B))) = antidomain(multiplication(antidomain(A),B)). [para(82(a,1),37935(a,2,1)),rewrite([42(5)])].
% 262.33/262.68 38554 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(B)). [para(37935(a,1),85(a,1,1)),rewrite([19474(5),19474(8)])].
% 262.33/262.68 39324 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)). [para(25991(a,1),2627(a,1,1)),rewrite([9297(5),42(6),38553(6),38554(5),42(10),113(10),32(8),18987(7)])].
% 262.33/262.68 39471 antidomain(addition(A,antidomain(addition(A,B)))) = antidomain(addition(A,antidomain(B))). [back_rewrite(21351),rewrite([19474(4),39324(4),39324(5),39324(8)])].
% 262.33/262.68 39560 antidomain(addition(A,antidomain(coantidomain(B)))) = multiplication(coantidomain(B),antidomain(A)). [para(2717(a,1),39324(a,1,1)),rewrite([42(6)]),flip(a)].
% 262.33/262.68 44404 antidomain(addition(c3,coantidomain(multiplication(antidomain(antidomain(c1)),multiplication(c4,c5))))) = zero. [para(35801(a,1),3055(a,1,2,2,1)),rewrite([20781(10),63(7),118(13),32(13),39324(12),42(10)])].
% 262.33/262.68 44405 multiplication(antidomain(c3),coantidomain(multiplication(antidomain(antidomain(c1)),multiplication(c4,c5)))) = antidomain(c3). [para(44404(a,1),39471(a,1,1,2)),rewrite([42(3),25559(3),39560(14),19342(13)]),flip(a)].
% 262.33/262.68 44406 $F # answer(goals). [back_rewrite(38064),rewrite([44405(11)]),xx(a)].
% 262.33/262.68
% 262.33/262.68 % SZS output end Refutation
% 262.33/262.68 ============================== end of proof ==========================
% 262.33/262.68
% 262.33/262.68 ============================== STATISTICS ============================
% 262.33/262.68
% 262.33/262.68 Given=6899. Generated=16996753. Kept=44360. proofs=1.
% 262.33/262.68 Usable=5051. Sos=6263. Demods=11150. Limbo=1, Disabled=33075. Hints=0.
% 262.33/262.68 Megabytes=31.18.
% 262.33/262.68 User_CPU=252.76, System_CPU=8.93, Wall_clock=261.
% 262.33/262.68
% 262.33/262.68 ============================== end of statistics =====================
% 262.33/262.68
% 262.33/262.68 ============================== end of search =========================
% 262.33/262.68
% 262.33/262.68 THEOREM PROVED
% 262.33/262.68 % SZS status Theorem
% 262.33/262.68
% 262.33/262.68 Exiting with 1 proof.
% 262.33/262.68
% 262.33/262.68 Process 13622 exit (max_proofs) Thu Jun 16 08:34:26 2022
% 262.33/262.68 Prover9 interrupted
%------------------------------------------------------------------------------