TSTP Solution File: KLE117+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE117+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 02:22:19 EDT 2022
% Result : Theorem 193.83s 194.14s
% Output : Refutation 193.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : KLE117+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 16 15:43:31 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.42/0.97 ============================== Prover9 ===============================
% 0.42/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.97 Process 18352 was started by sandbox2 on n018.cluster.edu,
% 0.42/0.97 Thu Jun 16 15:43:31 2022
% 0.42/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18198_n018.cluster.edu".
% 0.42/0.97 ============================== end of head ===========================
% 0.42/0.97
% 0.42/0.97 ============================== INPUT =================================
% 0.42/0.97
% 0.42/0.97 % Reading from file /tmp/Prover9_18198_n018.cluster.edu
% 0.42/0.97
% 0.42/0.97 set(prolog_style_variables).
% 0.42/0.97 set(auto2).
% 0.42/0.97 % set(auto2) -> set(auto).
% 0.42/0.97 % set(auto) -> set(auto_inference).
% 0.42/0.97 % set(auto) -> set(auto_setup).
% 0.42/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.97 % set(auto) -> set(auto_limits).
% 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.97 % set(auto) -> set(auto_denials).
% 0.42/0.97 % set(auto) -> set(auto_process).
% 0.42/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.97 % set(auto2) -> assign(stats, some).
% 0.42/0.97 % set(auto2) -> clear(echo_input).
% 0.42/0.97 % set(auto2) -> set(quiet).
% 0.42/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.97 % set(auto2) -> clear(print_given).
% 0.42/0.97 assign(lrs_ticks,-1).
% 0.42/0.97 assign(sos_limit,10000).
% 0.42/0.97 assign(order,kbo).
% 0.42/0.97 set(lex_order_vars).
% 0.42/0.97 clear(print_given).
% 0.42/0.97
% 0.42/0.97 % formulas(sos). % not echoed (27 formulas)
% 0.42/0.97
% 0.42/0.97 ============================== end of input ==========================
% 0.42/0.97
% 0.42/0.97 % From the command line: assign(max_seconds, 300).
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.97
% 0.42/0.97 % Formulas that are not ordinary clauses:
% 0.42/0.97 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 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].
% 0.42/0.97 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 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].
% 0.42/0.97 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 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].
% 0.42/0.97 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].
% 0.42/0.97 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 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].
% 4.12/4.40 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 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].
% 4.12/4.40 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.40 27 -(all X0 all X1 (addition(X0,X1) = X1 -> (all X2 addition(forward_diamond(X0,domain(X2)),forward_diamond(X1,domain(X2))) = forward_diamond(X1,domain(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.12/4.40
% 4.12/4.40 ============================== end of process non-clausal formulas ===
% 4.12/4.40
% 4.12/4.40 ============================== PROCESS INITIAL CLAUSES ===============
% 4.12/4.40
% 4.12/4.40 ============================== PREDICATE ELIMINATION =================
% 4.12/4.40 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 4.12/4.40 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 4.12/4.40
% 4.12/4.40 ============================== end predicate elimination =============
% 4.12/4.40
% 4.12/4.40 Auto_denials:
% 4.12/4.40 % copying label goals to answer in negative clause
% 4.12/4.40
% 4.12/4.40 Term ordering decisions:
% 4.12/4.40 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. backward_diamond=1. forward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. c=1. domain=1. codomain=1.
% 4.12/4.40
% 4.12/4.40 ============================== end of process initial clauses ========
% 4.12/4.40
% 4.12/4.40 ============================== CLAUSES FOR SEARCH ====================
% 4.12/4.40
% 4.12/4.40 ============================== end of clauses for search =============
% 4.12/4.40
% 4.12/4.40 ============================== SEARCH ================================
% 4.12/4.40
% 4.12/4.40 % Starting search at 0.01 seconds.
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=44.000, iters=3474
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=40.000, iters=3481
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=35.000, iters=3368
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=34.000, iters=3343
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=31.000, iters=3350
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=30.000, iters=3356
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=29.000, iters=3355
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=28.000, iters=3357
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=27.000, iters=3360
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=26.000, iters=3351
% 4.12/4.40
% 4.12/4.40 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 1.42 sec).
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=25.000, iters=3358
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=24.000, iters=3405
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=23.000, iters=3425
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=22.000, iters=3386
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=21.000, iters=3345
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=20.000, iters=3343
% 4.12/4.40
% 4.12/4.40 Low Water (keep): wt=19.000, iters=5038
% 4.12/4.40
% 4.12/4.40 Low Water (displace): id=6591, wt=49.000
% 4.12/4.40
% 4.12/4.40 Low Water (displace): id=3698, wt=48.000
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=7159, wt=47.000
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=8574, wt=46.000
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=8164, wt=45.000
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=6264, wt=44.000
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=8517, wt=43.000
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=8589, wt=42.000
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=14786, wt=16.000
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=14792, wt=15.000
% 193.83/194.14
% 193.83/194.14 Low Water (keep): wt=18.000, iters=3335
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=17254, wt=14.000
% 193.83/194.14
% 193.83/194.14 Low Water (displace): id=17629, wt=12.000
% 193.83/194.14
% 193.83/194.14 Low Water (keep): wt=17.000, iters=3333
% 193.83/194.14
% 193.83/194.14 Low Water (keep): wt=16.000, iters=3336
% 193.83/194.14
% 193.83/194.14 Low Water (keep): wt=15.000, iters=3346
% 193.83/194.14
% 193.83/194.14 Low Water (keep): wt=14.000, iters=3338
% 193.83/194.14
% 193.83/194.14 ============================== PROOF =================================
% 193.83/194.14 % SZS status Theorem
% 193.83/194.14 % SZS output start Refutation
% 193.83/194.14
% 193.83/194.14 % Proof 1 at 186.30 (+ 6.87) seconds: goals.
% 193.83/194.14 % Length of proof is 230.
% 193.83/194.14 % Level of proof is 33.
% 193.83/194.14 % Maximum clause weight is 29.000.
% 193.83/194.14 % Given clauses 6511.
% 193.83/194.14
% 193.83/194.14 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 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].
% 193.83/194.14 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 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].
% 193.83/194.14 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 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].
% 193.83/194.14 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].
% 193.83/194.14 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 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].
% 193.83/194.14 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 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].
% 193.83/194.14 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 193.83/194.14 27 -(all X0 all X1 (addition(X0,X1) = X1 -> (all X2 addition(forward_diamond(X0,domain(X2)),forward_diamond(X1,domain(X2))) = forward_diamond(X1,domain(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 193.83/194.14 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 193.83/194.14 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 193.83/194.14 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 193.83/194.14 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 193.83/194.14 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 193.83/194.14 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 193.83/194.14 36 addition(c1,c2) = c2 # label(goals) # label(negated_conjecture). [clausify(27)].
% 193.83/194.14 37 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 193.83/194.14 38 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 193.83/194.14 39 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 193.83/194.14 43 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 193.83/194.14 44 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 193.83/194.14 45 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(44),rewrite([43(4)])].
% 193.83/194.14 46 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 193.83/194.14 47 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(46),rewrite([43(4)])].
% 193.83/194.14 50 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 193.83/194.14 51 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(50),rewrite([38(2),38(5)])].
% 193.83/194.14 58 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 193.83/194.14 59 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(58),rewrite([43(2)]),flip(a)].
% 193.83/194.14 60 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 193.83/194.14 61 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 193.83/194.14 62 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(61),flip(a)].
% 193.83/194.14 63 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 193.83/194.14 64 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(63),flip(a)].
% 193.83/194.14 65 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 193.83/194.14 66 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(65),flip(a)].
% 193.83/194.14 67 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 193.83/194.14 68 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(67),flip(a)].
% 193.83/194.14 69 forward_diamond(c2,domain(c3)) != addition(forward_diamond(c1,domain(c3)),forward_diamond(c2,domain(c3))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 193.83/194.14 70 addition(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c3))))))),antidomain(antidomain(multiplication(c2,antidomain(antidomain(antidomain(antidomain(c3)))))))) != antidomain(antidomain(multiplication(c2,antidomain(antidomain(antidomain(antidomain(c3))))))) # answer(goals). [copy(69),rewrite([38(3),51(5),38(12),51(14),38(21),51(23)]),flip(a)].
% 193.83/194.14 71 antidomain(one) = zero. [para(37(a,1),32(a,1)),flip(a)].
% 193.83/194.14 72 coantidomain(one) = zero. [para(39(a,1),33(a,1)),flip(a)].
% 193.83/194.14 73 addition(A,addition(A,B)) = addition(A,B). [para(59(a,1),31(a,1)),rewrite([43(1),43(2),59(2,R),31(1),43(3)])].
% 193.83/194.14 74 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(37(a,1),60(a,1,1)),rewrite([35(2)]),flip(a)].
% 193.83/194.14 75 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(60(a,1),39(a,1))].
% 193.83/194.14 76 multiplication(A,multiplication(coantidomain(A),B)) = zero. [para(39(a,1),60(a,1,1)),rewrite([35(2)]),flip(a)].
% 193.83/194.14 77 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),62(a,2,2)),rewrite([34(3),43(3)])].
% 193.83/194.14 78 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),62(a,1,1)),rewrite([43(4)]),flip(a)].
% 193.83/194.14 79 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(37(a,1),62(a,1,1)),rewrite([77(4)]),flip(a)].
% 193.83/194.14 80 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(39(a,1),62(a,1,1)),rewrite([77(3),43(3)]),flip(a)].
% 193.83/194.14 81 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),64(a,1,1)),rewrite([43(4)]),flip(a)].
% 193.83/194.14 82 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(37(a,1),64(a,1,1)),rewrite([77(3),43(3)]),flip(a)].
% 193.83/194.14 83 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(39(a,1),64(a,1,1)),rewrite([77(4),43(3)]),flip(a)].
% 193.83/194.14 84 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(60(a,1),64(a,1,1)),rewrite([43(6)])].
% 193.83/194.14 87 addition(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(33(a,1),66(a,1,1,1)),rewrite([33(5),33(9)])].
% 193.83/194.14 89 addition(antidomain(zero),antidomain(multiplication(antidomain(A),antidomain(antidomain(A))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))). [para(37(a,1),66(a,1,1,1))].
% 193.83/194.14 91 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(39(a,1),66(a,1,1,1))].
% 193.83/194.14 96 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(37(a,1),68(a,1,1,1))].
% 193.83/194.14 99 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(60(a,1),68(a,1,1,1))].
% 193.83/194.14 100 addition(zero,antidomain(zero)) = one. [para(71(a,1),45(a,1,1)),rewrite([71(3)])].
% 193.83/194.14 101 addition(zero,coantidomain(zero)) = one. [para(72(a,1),47(a,1,1)),rewrite([72(3)])].
% 193.83/194.14 104 multiplication(A,antidomain(zero)) = A. [para(100(a,1),62(a,2,2)),rewrite([34(2),77(5),32(5)])].
% 193.83/194.14 108 multiplication(A,coantidomain(zero)) = A. [para(101(a,1),62(a,2,2)),rewrite([34(2),77(5),32(5)])].
% 193.83/194.14 110 addition(one,antidomain(A)) = one. [para(45(a,1),73(a,1,2)),rewrite([43(3),45(7)])].
% 193.83/194.14 111 addition(one,coantidomain(A)) = one. [para(47(a,1),73(a,1,2)),rewrite([43(3),47(7)])].
% 193.83/194.14 112 antidomain(zero) = one. [para(104(a,1),33(a,1)),flip(a)].
% 193.83/194.14 113 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(91),rewrite([112(2),110(7)]),flip(a)].
% 193.83/194.14 114 antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))) = one. [back_rewrite(89),rewrite([112(2),110(7)]),flip(a)].
% 193.83/194.14 115 coantidomain(zero) = one. [para(108(a,1),33(a,1)),flip(a)].
% 193.83/194.14 117 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(96),rewrite([115(2),111(7)]),flip(a)].
% 193.83/194.14 118 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(60(a,1),74(a,1,2))].
% 193.83/194.14 121 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(74(a,1),66(a,1,1,1)),rewrite([112(2),110(8)]),flip(a)].
% 193.83/194.14 123 addition(A,multiplication(A,antidomain(B))) = A. [para(110(a,1),62(a,2,2)),rewrite([32(2),32(5)])].
% 193.83/194.14 124 addition(A,multiplication(antidomain(B),A)) = A. [para(110(a,1),64(a,2,1)),rewrite([33(2),33(5)])].
% 193.83/194.14 125 addition(A,multiplication(A,coantidomain(B))) = A. [para(111(a,1),62(a,2,2)),rewrite([32(2),32(5)])].
% 193.83/194.14 126 addition(A,multiplication(coantidomain(B),A)) = A. [para(111(a,1),64(a,2,1)),rewrite([33(2),33(5)])].
% 193.83/194.14 128 multiplication(A,addition(B,multiplication(coantidomain(A),C))) = multiplication(A,B). [para(76(a,1),62(a,1,1)),rewrite([77(3),43(4)]),flip(a)].
% 193.83/194.14 129 multiplication(addition(A,B),multiplication(coantidomain(B),C)) = multiplication(A,multiplication(coantidomain(B),C)). [para(76(a,1),64(a,1,1)),rewrite([77(5),43(4)]),flip(a)].
% 193.83/194.14 133 addition(A,addition(B,multiplication(A,antidomain(C)))) = addition(A,B). [para(123(a,1),59(a,2,2)),rewrite([43(3),43(5)])].
% 193.83/194.14 136 multiplication(addition(A,B),multiplication(C,coantidomain(multiplication(B,C)))) = multiplication(A,multiplication(C,coantidomain(multiplication(B,C)))). [para(75(a,1),64(a,1,1)),rewrite([77(6),43(5)]),flip(a)].
% 193.83/194.14 160 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(113(a,1),37(a,1,1)),rewrite([33(6)])].
% 193.83/194.14 164 multiplication(A,multiplication(B,antidomain(antidomain(coantidomain(multiplication(A,B)))))) = zero. [para(160(a,1),60(a,1)),flip(a)].
% 193.83/194.14 165 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(160(a,1),62(a,1,1)),rewrite([77(3),43(5)]),flip(a)].
% 193.83/194.14 168 multiplication(antidomain(A),antidomain(antidomain(A))) = zero. [para(114(a,1),37(a,1,1)),rewrite([33(6)])].
% 193.83/194.14 171 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(47(a,1),79(a,1,2)),rewrite([32(4)]),flip(a)].
% 193.83/194.14 174 addition(multiplication(antidomain(A),B),multiplication(C,addition(A,B))) = multiplication(addition(C,antidomain(A)),addition(A,B)). [para(79(a,1),64(a,1,1)),rewrite([43(7)])].
% 193.83/194.14 175 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(64(a,1),79(a,1,2))].
% 193.83/194.14 179 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(124(a,1),79(a,1,2)),rewrite([37(2)]),flip(a)].
% 193.83/194.14 183 multiplication(addition(A,antidomain(B)),antidomain(antidomain(B))) = multiplication(A,antidomain(antidomain(B))). [para(168(a,1),64(a,1,1)),rewrite([77(5),43(5)]),flip(a)].
% 193.83/194.14 192 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(47(a,1),80(a,1,2)),rewrite([32(3)]),flip(a)].
% 193.83/194.14 199 multiplication(coantidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(68(a,1),80(a,1,2)),rewrite([39(8),60(7)]),flip(a)].
% 193.83/194.14 201 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(192(a,1),62(a,1,1)),rewrite([78(4,R),43(7)]),flip(a)].
% 193.83/194.14 202 multiplication(addition(A,coantidomain(B)),coantidomain(B)) = multiplication(addition(A,one),coantidomain(B)). [para(192(a,1),64(a,1,1)),rewrite([81(4,R),43(6)]),flip(a)].
% 193.83/194.14 206 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(117(a,1),39(a,1,2)),rewrite([32(6)])].
% 193.83/194.14 210 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(206(a,1),64(a,1,1)),rewrite([77(3),43(5)]),flip(a)].
% 193.83/194.14 214 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(179(a,1),64(a,1,1)),rewrite([77(5),43(5)]),flip(a)].
% 193.83/194.14 240 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(80(a,1),81(a,2,2)),rewrite([43(9),59(9),43(8),59(9,R),43(8)])].
% 193.83/194.14 257 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(45(a,1),82(a,1,1)),rewrite([33(3)]),flip(a)].
% 193.83/194.14 260 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(addition(A,antidomain(antidomain(antidomain(B)))),B))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [para(82(a,1),66(a,1,2,1)),rewrite([43(11),82(18)])].
% 193.83/194.14 264 multiplication(addition(A,antidomain(B)),addition(B,one)) = addition(A,addition(antidomain(B),multiplication(A,B))). [para(82(a,1),78(a,2,2)),rewrite([43(9),59(9),43(8),59(9,R),43(8)])].
% 193.83/194.14 266 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(43(a,1),83(a,1,1))].
% 193.83/194.14 268 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(47(a,1),83(a,1,1)),rewrite([33(5)]),flip(a)].
% 193.83/194.14 271 addition(multiplication(A,coantidomain(B)),multiplication(addition(A,B),C)) = multiplication(addition(A,B),addition(C,coantidomain(B))). [para(83(a,1),62(a,1,1)),rewrite([43(8)])].
% 193.83/194.14 277 multiplication(A,coantidomain(addition(A,B))) = zero. [para(73(a,1),83(a,1,1)),rewrite([39(4)]),flip(a)].
% 193.83/194.14 287 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(257(a,1),60(a,1,1)),flip(a)].
% 193.83/194.14 288 multiplication(antidomain(A),addition(B,antidomain(A))) = multiplication(antidomain(A),addition(B,one)). [para(257(a,1),62(a,1,1)),rewrite([78(4,R),43(7)]),flip(a)].
% 193.83/194.14 298 multiplication(A,multiplication(B,coantidomain(multiplication(A,addition(B,C))))) = zero. [para(62(a,1),277(a,1,2,1)),rewrite([60(5)])].
% 193.83/194.14 302 antidomain(multiplication(A,antidomain(antidomain(coantidomain(addition(A,B)))))) = one. [para(277(a,1),66(a,1,1,1)),rewrite([112(2),110(8)]),flip(a)].
% 193.83/194.14 313 multiplication(addition(antidomain(A),multiplication(B,C)),A) = multiplication(B,multiplication(C,A)). [para(37(a,1),84(a,1,2)),rewrite([43(4),77(4)]),flip(a)].
% 193.83/194.14 577 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(37(a,1),99(a,1,1,1)),rewrite([115(2),111(9)]),flip(a)].
% 193.83/194.14 578 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one. [para(39(a,1),99(a,1,1,1,2)),rewrite([34(2),115(2),111(8)]),flip(a)].
% 193.83/194.14 598 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [para(179(a,1),99(a,1,1,1)),rewrite([115(2),111(9)]),flip(a)].
% 193.83/194.14 677 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(121(a,1),37(a,1,1)),rewrite([33(7)])].
% 193.83/194.14 684 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(677(a,1),62(a,1,1)),rewrite([77(4),43(7)]),flip(a)].
% 193.83/194.14 790 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(171(a,1),124(a,1,2)),rewrite([43(5)])].
% 193.83/194.14 818 multiplication(A,addition(B,addition(C,multiplication(coantidomain(A),D)))) = multiplication(A,addition(B,C)). [para(128(a,1),62(a,1,1)),rewrite([62(3),43(6),59(6,R),43(5)]),flip(a)].
% 193.83/194.14 959 addition(A,multiplication(addition(A,B),antidomain(C))) = addition(A,multiplication(B,antidomain(C))). [para(64(a,1),133(a,1,2)),rewrite([43(1)])].
% 193.83/194.14 1023 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(45(a,1),266(a,1,1)),rewrite([33(4)]),flip(a)].
% 193.83/194.14 1029 multiplication(A,multiplication(antidomain(B),coantidomain(A))) = zero. [para(123(a,1),266(a,1,1)),rewrite([39(2),60(5)]),flip(a)].
% 193.83/194.14 1031 multiplication(A,multiplication(coantidomain(B),coantidomain(A))) = zero. [para(125(a,1),266(a,1,1)),rewrite([39(2),60(5)]),flip(a)].
% 193.83/194.14 1045 multiplication(addition(A,B),multiplication(antidomain(C),coantidomain(B))) = multiplication(A,multiplication(antidomain(C),coantidomain(B))). [para(1029(a,1),64(a,1,1)),rewrite([77(6),43(5)]),flip(a)].
% 193.83/194.14 1054 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [para(1029(a,1),99(a,1,1,1)),rewrite([115(2),111(9)]),flip(a)].
% 193.83/194.14 1110 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [para(1031(a,1),99(a,1,1,1)),rewrite([115(2),111(9)]),flip(a)].
% 193.83/194.14 1150 multiplication(antidomain(A),multiplication(B,coantidomain(multiplication(antidomain(antidomain(A)),B)))) = multiplication(B,coantidomain(multiplication(antidomain(antidomain(A)),B))). [para(45(a,1),136(a,1,1)),rewrite([33(7)]),flip(a)].
% 193.83/194.14 1338 multiplication(A,antidomain(antidomain(coantidomain(addition(A,B))))) = zero. [para(302(a,1),37(a,1,1)),rewrite([33(7)])].
% 193.83/194.14 1561 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [para(578(a,1),39(a,1,2)),rewrite([32(7)])].
% 193.83/194.14 2588 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(1023(a,1),125(a,1,2))].
% 193.83/194.14 2820 multiplication(A,antidomain(coantidomain(A))) = A. [para(45(a,1),165(a,1,2)),rewrite([32(2)]),flip(a)].
% 193.83/194.14 2843 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2820(a,1),60(a,1,1)),flip(a)].
% 193.83/194.14 2851 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2820(a,1),126(a,1,2)),rewrite([43(5)])].
% 193.83/194.14 3262 multiplication(A,multiplication(addition(coantidomain(A),antidomain(B)),addition(B,C))) = multiplication(A,multiplication(antidomain(B),C)). [para(174(a,1),128(a,1,2))].
% 193.83/194.14 3422 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(45(a,1),175(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 193.83/194.14 3998 multiplication(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(45(a,1),183(a,1,1)),rewrite([33(5)]),flip(a)].
% 193.83/194.14 4897 multiplication(A,coantidomain(coantidomain(A))) = A. [para(171(a,1),2843(a,1,2)),rewrite([2820(3)]),flip(a)].
% 193.83/194.14 4940 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(268),rewrite([4897(5)]),flip(a)].
% 193.83/194.14 5056 multiplication(coantidomain(coantidomain(A)),antidomain(antidomain(coantidomain(addition(A,B))))) = zero. [para(1338(a,1),199(a,1,2,2,1)),rewrite([115(8),32(8)])].
% 193.83/194.14 5071 multiplication(coantidomain(coantidomain(A)),multiplication(B,antidomain(antidomain(coantidomain(multiplication(A,B)))))) = zero. [para(164(a,1),199(a,1,2,2,1)),rewrite([115(9),32(9)])].
% 193.83/194.14 5112 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(4940(a,1),790(a,1,2)),rewrite([43(5),2851(5),4940(6)])].
% 193.83/194.14 5124 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(5112(a,1),45(a,1,1)),rewrite([5112(4)])].
% 193.83/194.14 5130 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(5112(a,1),1023(a,1,1,1)),rewrite([5112(5),171(5),5112(5)]),flip(a)].
% 193.83/194.14 5132 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(5112(a,1),1023(a,2,1)),rewrite([5130(2),5130(6),1023(9),5130(6)])].
% 193.83/194.14 5143 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(4940(a,1),5112(a,1,1,1)),rewrite([5130(2),5130(5)]),flip(a)].
% 193.83/194.14 5144 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(4940(a,1),5112(a,2)),rewrite([5130(2),5143(3),5132(4)])].
% 193.83/194.14 5180 multiplication(antidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [back_rewrite(5071),rewrite([5130(2),5144(6)])].
% 193.83/194.14 5195 multiplication(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [back_rewrite(5056),rewrite([5130(2),5144(6)])].
% 193.83/194.14 5710 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [back_rewrite(1561),rewrite([5130(3)])].
% 193.83/194.14 5770 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [back_rewrite(1110),rewrite([5130(4)])].
% 193.83/194.14 5775 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [back_rewrite(1054),rewrite([5130(4)])].
% 193.83/194.14 5827 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [back_rewrite(598),rewrite([5130(5)])].
% 193.83/194.14 5838 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(577),rewrite([5130(5)])].
% 193.83/194.14 5853 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(210),rewrite([5130(3)])].
% 193.83/194.14 5906 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(2588(a,1),201(a,1,2)),rewrite([43(11),110(11),32(9)])].
% 193.83/194.14 5991 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(45(a,1),214(a,1,1)),rewrite([33(5)]),flip(a)].
% 193.83/194.14 7853 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(5906(a,1),240(a,2,2,2)),rewrite([43(4),111(4),5130(6),33(8),5130(11),43(14),5124(14),43(10),110(10)])].
% 193.83/194.14 9338 addition(multiplication(A,antidomain(coantidomain(B))),multiplication(addition(A,one),coantidomain(B))) = addition(A,coantidomain(B)). [para(202(a,1),271(a,1,2)),rewrite([5130(2),5130(13),5124(14),32(12)])].
% 193.83/194.14 9918 multiplication(antidomain(multiplication(addition(A,antidomain(antidomain(antidomain(B)))),B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(addition(A,antidomain(antidomain(antidomain(B)))),B)). [para(260(a,1),288(a,1,2)),rewrite([43(23),110(23),32(19)])].
% 193.83/194.14 10201 multiplication(addition(antidomain(A),antidomain(B)),A) = multiplication(antidomain(B),A). [para(257(a,1),313(a,1,1,2)),rewrite([287(8)])].
% 193.83/194.14 13224 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(3998(a,1),123(a,1,2)),rewrite([87(5)])].
% 193.83/194.14 13254 multiplication(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,B)). [back_rewrite(9918),rewrite([13224(3),82(3),13224(10),82(10)])].
% 193.83/194.14 13262 addition(antidomain(antidomain(multiplication(c1,antidomain(antidomain(c3))))),antidomain(antidomain(multiplication(c2,antidomain(antidomain(c3)))))) != antidomain(antidomain(multiplication(c2,antidomain(antidomain(c3))))) # answer(goals). [back_rewrite(70),rewrite([13224(5),13224(12),13224(20)])].
% 193.83/194.14 14675 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A)) = zero. [para(5770(a,1),39(a,1,2)),rewrite([32(8)])].
% 193.83/194.14 14694 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(addition(A,B))) = zero. [para(83(a,1),14675(a,1,1,1,1))].
% 193.83/194.14 14711 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A)) = zero. [para(5775(a,1),39(a,1,2)),rewrite([32(8)])].
% 193.83/194.14 14955 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = zero. [para(5827(a,1),39(a,1,2)),rewrite([32(8)])].
% 193.83/194.14 14967 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(5906(a,1),5853(a,2)),rewrite([13224(5),5124(6),33(4)]),flip(a)].
% 193.83/194.14 14968 multiplication(antidomain(antidomain(A)),A) = A. [para(7853(a,1),5853(a,1,1)),rewrite([33(2)]),flip(a)].
% 193.83/194.14 15113 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(14968(a,1),118(a,1,2,2))].
% 193.83/194.14 19102 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(45(a,1),684(a,1,2)),rewrite([32(3)]),flip(a)].
% 193.83/194.14 19294 multiplication(antidomain(antidomain(multiplication(A,B))),antidomain(A)) = zero. [para(19102(a,1),179(a,1,2))].
% 193.83/194.14 19303 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(19102(a,1),2843(a,1,2)),rewrite([2820(3)]),flip(a)].
% 193.83/194.14 19306 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(19102(a,1),240(a,2,2,2)),rewrite([43(3),110(3),14967(5),43(6),33(7),14967(9),43(11),45(11),43(9),110(9)])].
% 193.83/194.14 19510 multiplication(antidomain(antidomain(multiplication(antidomain(A),B))),A) = zero. [para(19294(a,1),15113(a,1,1,1)),rewrite([112(2),33(7)])].
% 193.83/194.14 19518 addition(antidomain(A),antidomain(multiplication(antidomain(A),B))) = one. [para(79(a,1),19306(a,1,2,1)),rewrite([13224(3)])].
% 193.83/194.14 19524 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(19306(a,1),266(a,1,1)),rewrite([14967(4),13224(4),33(3),14967(6),13224(6)]),flip(a)].
% 193.83/194.14 19618 multiplication(antidomain(antidomain(multiplication(antidomain(addition(A,B)),C))),A) = zero. [para(19510(a,1),298(a,1,2,2,1)),rewrite([115(7),32(7)])].
% 193.83/194.14 19645 multiplication(antidomain(multiplication(antidomain(A),B)),A) = A. [para(19518(a,1),10201(a,1,1)),rewrite([33(2)]),flip(a)].
% 193.83/194.14 19675 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(19524(a,1),60(a,1,1)),flip(a)].
% 193.83/194.14 19703 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3422),rewrite([19675(7)]),flip(a)].
% 193.83/194.14 20750 multiplication(A,addition(coantidomain(A),antidomain(B))) = multiplication(A,antidomain(B)). [para(264(a,2),818(a,1,2)),rewrite([3262(7),32(3)]),flip(a)].
% 193.83/194.14 22445 addition(coantidomain(A),multiplication(antidomain(coantidomain(A)),antidomain(B))) = addition(coantidomain(A),antidomain(B)). [para(5124(a,1),959(a,1,2,1)),rewrite([33(4)]),flip(a)].
% 193.83/194.14 25065 multiplication(antidomain(multiplication(antidomain(addition(A,B)),C)),A) = A. [para(19618(a,1),1150(a,1,2,2,1)),rewrite([115(6),32(6),19618(11),115(7),32(7)])].
% 193.83/194.14 25075 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(32(a,1),25065(a,1,1,1))].
% 193.83/194.14 25104 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(43(a,1),25075(a,1,1,1,1))].
% 193.83/194.14 25138 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(25075(a,1),19645(a,1,1,1))].
% 193.83/194.14 25164 addition(antidomain(A),antidomain(antidomain(addition(B,A)))) = one. [para(25104(a,1),19306(a,1,2,1)),rewrite([13224(4),43(5)])].
% 193.83/194.14 25282 addition(antidomain(antidomain(A)),antidomain(multiplication(antidomain(B),A))) = one. [para(124(a,1),25164(a,1,2,1,1)),rewrite([43(6)])].
% 193.83/194.14 25552 multiplication(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(A). [para(25282(a,1),79(a,1,2)),rewrite([13224(3),32(3),13224(4)]),flip(a)].
% 193.83/194.14 29798 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero. [para(5838(a,1),39(a,1,2)),rewrite([32(8)])].
% 193.83/194.14 31977 multiplication(coantidomain(A),coantidomain(addition(A,B))) = coantidomain(addition(A,B)). [para(5195(a,1),19703(a,1,1,1)),rewrite([112(2),33(4),5144(5)]),flip(a)].
% 193.83/194.14 31981 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(5710(a,1),19703(a,1,1,1)),rewrite([112(2),33(3),5144(5)]),flip(a)].
% 193.83/194.14 32008 multiplication(coantidomain(multiplication(A,antidomain(B))),coantidomain(A)) = coantidomain(A). [para(14711(a,1),19703(a,1,1,1)),rewrite([112(2),33(3),5144(6)]),flip(a)].
% 193.83/194.14 32010 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A. [para(14955(a,1),19703(a,1,1,1)),rewrite([112(2),33(2),5144(6)]),flip(a)].
% 193.83/194.14 32117 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(29798(a,1),19703(a,1,1,1)),rewrite([112(2),33(2),5144(6)]),flip(a)].
% 193.83/194.14 32395 addition(antidomain(coantidomain(A)),coantidomain(multiplication(B,A))) = one. [para(31981(a,1),264(a,2,2,2)),rewrite([43(5),43(8),111(8),32(7),43(11),5124(11),43(9),111(9)])].
% 193.83/194.14 32423 coantidomain(addition(A,coantidomain(multiplication(B,A)))) = zero. [para(31981(a,1),14694(a,1,1,1,1)),rewrite([5130(2),5144(3),43(4),31977(6)])].
% 193.83/194.14 32436 coantidomain(addition(A,coantidomain(A))) = zero. [para(33(a,1),32423(a,1,1,2,1))].
% 193.83/194.14 32474 multiplication(A,coantidomain(multiplication(addition(B,coantidomain(B)),A))) = zero. [para(32436(a,1),5180(a,1,1,1)),rewrite([112(2),33(7)])].
% 193.83/194.14 32752 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(32010(a,1),19303(a,1,2,1)),rewrite([60(5),5991(5)])].
% 193.83/194.14 32861 addition(coantidomain(A),multiplication(antidomain(B),antidomain(coantidomain(A)))) = addition(coantidomain(A),antidomain(B)). [back_rewrite(22445),rewrite([32752(5)])].
% 193.83/194.14 33119 multiplication(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(A). [para(32395(a,1),79(a,1,2)),rewrite([5144(3),32(3),5144(4)]),flip(a)].
% 193.83/194.14 33303 addition(coantidomain(A),coantidomain(multiplication(A,antidomain(B)))) = coantidomain(multiplication(A,antidomain(B))). [para(32008(a,1),125(a,1,2)),rewrite([43(5)])].
% 193.83/194.14 33306 multiplication(A,multiplication(antidomain(B),antidomain(coantidomain(A)))) = multiplication(A,antidomain(B)). [para(32008(a,1),19303(a,1,2,1)),rewrite([60(5)])].
% 193.83/194.14 33396 addition(antidomain(A),coantidomain(multiplication(antidomain(multiplication(B,A)),B))) = one. [para(32117(a,1),19306(a,1,2,1)),rewrite([5144(6),43(6)])].
% 193.83/194.14 33606 coantidomain(multiplication(addition(A,coantidomain(A)),B)) = coantidomain(B). [para(32474(a,1),32117(a,1,1,1,1,1)),rewrite([112(2),33(2),33119(6)]),flip(a)].
% 193.83/194.14 33607 coantidomain(multiplication(antidomain(coantidomain(A)),B)) = coantidomain(multiplication(A,B)). [para(129(a,1),33606(a,1,1)),rewrite([5130(2),2843(4),5130(4)]),flip(a)].
% 193.83/194.14 33612 coantidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [para(1045(a,1),33606(a,1,1)),rewrite([5130(3),33306(5),5130(6)]),flip(a)].
% 193.83/194.14 33854 multiplication(coantidomain(multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B)))),B) = B. [para(32752(a,1),32117(a,1,1,1))].
% 193.83/194.14 35002 addition(coantidomain(A),antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = one. [para(75(a,1),33396(a,1,2,1,1,1)),rewrite([112(6),33(6),43(6)])].
% 193.83/194.14 36019 multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = A. [para(35002(a,1),20750(a,1,2)),rewrite([32(2)]),flip(a)].
% 193.83/194.14 36198 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [para(15113(a,1),36019(a,1,2,1,2,1)),rewrite([115(7),32(7),32752(7),13254(7)]),flip(a)].
% 193.83/194.14 36311 addition(antidomain(antidomain(multiplication(c1,c3))),antidomain(antidomain(multiplication(c2,c3)))) != antidomain(antidomain(multiplication(c2,c3))) # answer(goals). [back_rewrite(13262),rewrite([36198(6),36198(11),36198(17)])].
% 193.83/194.14 39126 multiplication(coantidomain(multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B)))),B) = B. [para(33612(a,1),32117(a,1,1))].
% 193.83/194.14 39174 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(B)). [para(33854(a,1),19303(a,1,2,1)),rewrite([60(7),32752(6),25552(6)]),flip(a)].
% 193.83/194.14 40855 multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B))) = multiplication(A,antidomain(B)). [para(39126(a,1),19303(a,1,2,1)),rewrite([60(7),32752(6),25552(6)]),flip(a)].
% 193.83/194.14 41766 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)). [para(25138(a,1),40855(a,2)),rewrite([14967(3),13224(4),79(4),39174(5)])].
% 193.83/194.14 41772 antidomain(antidomain(addition(A,coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [para(40855(a,1),33607(a,1,1)),rewrite([32752(4),41766(4),14967(4),14967(7),5144(7),40855(9)])].
% 193.83/194.14 41916 addition(coantidomain(A),antidomain(addition(B,coantidomain(A)))) = addition(coantidomain(A),antidomain(B)). [back_rewrite(32861),rewrite([41766(5)])].
% 193.83/194.14 43451 addition(coantidomain(A),antidomain(antidomain(B))) = coantidomain(multiplication(A,antidomain(B))). [para(19703(a,1),9338(a,1,1)),rewrite([41766(5),41766(8),41772(8),43(9),111(9),33(7),43(6),41916(6),41766(8),41772(8),43(9),33303(9)])].
% 193.83/194.14 43561 addition(antidomain(antidomain(A)),antidomain(antidomain(B))) = antidomain(antidomain(addition(A,B))). [para(14967(a,1),43451(a,1,1)),rewrite([41766(8),14967(8)])].
% 193.83/194.14 43611 $F # answer(goals). [back_rewrite(36311),rewrite([43561(11),64(7),36(3)]),xx(a)].
% 193.83/194.14
% 193.83/194.14 % SZS output end Refutation
% 193.83/194.14 ============================== end of proof ==========================
% 193.83/194.14
% 193.83/194.14 ============================== STATISTICS ============================
% 193.83/194.14
% 193.83/194.14 Given=6511. Generated=13451909. Kept=43567. proofs=1.
% 193.83/194.14 Usable=3431. Sos=6413. Demods=9753. Limbo=50, Disabled=33702. Hints=0.
% 193.83/194.14 Megabytes=31.03.
% 193.83/194.14 User_CPU=186.30, System_CPU=6.87, Wall_clock=194.
% 193.83/194.14
% 193.83/194.14 ============================== end of statistics =====================
% 193.83/194.14
% 193.83/194.14 ============================== end of search =========================
% 193.83/194.14
% 193.83/194.14 THEOREM PROVED
% 193.83/194.14 % SZS status Theorem
% 193.83/194.14
% 193.83/194.14 Exiting with 1 proof.
% 193.83/194.14
% 193.83/194.14 Process 18352 exit (max_proofs) Thu Jun 16 15:46:45 2022
% 193.83/194.14 Prover9 interrupted
%------------------------------------------------------------------------------