TSTP Solution File: KLE101+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE101+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 02:22:14 EDT 2022
% Result : Theorem 56.83s 57.09s
% Output : Refutation 56.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE101+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 11:23:11 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.83/1.13 ============================== Prover9 ===============================
% 0.83/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.13 Process 12808 was started by sandbox on n015.cluster.edu,
% 0.83/1.13 Thu Jun 16 11:23:12 2022
% 0.83/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12655_n015.cluster.edu".
% 0.83/1.13 ============================== end of head ===========================
% 0.83/1.13
% 0.83/1.13 ============================== INPUT =================================
% 0.83/1.13
% 0.83/1.13 % Reading from file /tmp/Prover9_12655_n015.cluster.edu
% 0.83/1.13
% 0.83/1.13 set(prolog_style_variables).
% 0.83/1.13 set(auto2).
% 0.83/1.13 % set(auto2) -> set(auto).
% 0.83/1.13 % set(auto) -> set(auto_inference).
% 0.83/1.13 % set(auto) -> set(auto_setup).
% 0.83/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.13 % set(auto) -> set(auto_limits).
% 0.83/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.13 % set(auto) -> set(auto_denials).
% 0.83/1.13 % set(auto) -> set(auto_process).
% 0.83/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.13 % set(auto2) -> assign(stats, some).
% 0.83/1.13 % set(auto2) -> clear(echo_input).
% 0.83/1.13 % set(auto2) -> set(quiet).
% 0.83/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.13 % set(auto2) -> clear(print_given).
% 0.83/1.13 assign(lrs_ticks,-1).
% 0.83/1.13 assign(sos_limit,10000).
% 0.83/1.13 assign(order,kbo).
% 0.83/1.13 set(lex_order_vars).
% 0.83/1.13 clear(print_given).
% 0.83/1.13
% 0.83/1.13 % formulas(sos). % not echoed (27 formulas)
% 0.83/1.13
% 0.83/1.13 ============================== end of input ==========================
% 0.83/1.13
% 0.83/1.13 % From the command line: assign(max_seconds, 300).
% 0.83/1.13
% 0.83/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.13
% 0.83/1.13 % Formulas that are not ordinary clauses:
% 0.83/1.13 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 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].
% 0.83/1.13 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 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].
% 0.83/1.13 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 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].
% 0.83/1.13 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].
% 0.83/1.13 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 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].
% 3.79/4.05 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 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].
% 3.79/4.05 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 3.79/4.05 27 -(all X0 all X1 all X2 (multiplication(forward_diamond(X0,domain(X1)),domain(X2)) = zero -> multiplication(domain(X1),backward_diamond(X0,domain(X2))) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.79/4.05
% 3.79/4.05 ============================== end of process non-clausal formulas ===
% 3.79/4.05
% 3.79/4.05 ============================== PROCESS INITIAL CLAUSES ===============
% 3.79/4.05
% 3.79/4.05 ============================== PREDICATE ELIMINATION =================
% 3.79/4.05 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 3.79/4.05 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 3.79/4.05
% 3.79/4.05 ============================== end predicate elimination =============
% 3.79/4.05
% 3.79/4.05 Auto_denials:
% 3.79/4.05 % copying label goals to answer in negative clause
% 3.79/4.05
% 3.79/4.05 Term ordering decisions:
% 3.79/4.05 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. forward_diamond=1. backward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. domain=1. c=1. codomain=1.
% 3.79/4.05
% 3.79/4.05 ============================== end of process initial clauses ========
% 3.79/4.05
% 3.79/4.05 ============================== CLAUSES FOR SEARCH ====================
% 3.79/4.05
% 3.79/4.05 ============================== end of clauses for search =============
% 3.79/4.05
% 3.79/4.05 ============================== SEARCH ================================
% 3.79/4.05
% 3.79/4.05 % Starting search at 0.01 seconds.
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=44.000, iters=3383
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=41.000, iters=3340
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=40.000, iters=3415
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=37.000, iters=3355
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=36.000, iters=3340
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=35.000, iters=3345
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=34.000, iters=3356
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=33.000, iters=3340
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=32.000, iters=3370
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=31.000, iters=3415
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=30.000, iters=3383
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=29.000, iters=3347
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=28.000, iters=3335
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=27.000, iters=3355
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=26.000, iters=3333
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=25.000, iters=3339
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=24.000, iters=3379
% 3.79/4.05
% 3.79/4.05 Low Water (keep): wt=23.000, iters=3335
% 3.79/4.05
% 3.79/4.05 Low Water (displace): id=7520, wt=66.000
% 3.79/4.05
% 3.79/4.05 Low Water (displace): id=7519, wt=60.000
% 3.79/4.05
% 3.79/4.05 Low Water (displace): id=7548, wt=56.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=7482, wt=54.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=7510, wt=52.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=7687, wt=50.000
% 56.83/57.09
% 56.83/57.09 Low Water (keep): wt=22.000, iters=3336
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=7546, wt=48.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=8369, wt=47.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=8129, wt=46.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=7849, wt=45.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=8435, wt=44.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=7511, wt=43.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=8483, wt=42.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=14400, wt=20.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=14602, wt=19.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=14940, wt=18.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=14944, wt=17.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=15028, wt=16.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=15029, wt=15.000
% 56.83/57.09
% 56.83/57.09 Low Water (keep): wt=21.000, iters=3340
% 56.83/57.09
% 56.83/57.09 Low Water (keep): wt=20.000, iters=3338
% 56.83/57.09
% 56.83/57.09 Low Water (keep): wt=19.000, iters=3338
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=21062, wt=14.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=21617, wt=13.000
% 56.83/57.09
% 56.83/57.09 Low Water (displace): id=21958, wt=12.000
% 56.83/57.09
% 56.83/57.09 Low Water (keep): wt=18.000, iters=3335
% 56.83/57.09
% 56.83/57.09 Low Water (keep): wt=17.000, iters=3338
% 56.83/57.09
% 56.83/57.09 Low Water (keep): wt=16.000, iters=3333
% 56.83/57.09
% 56.83/57.09 ============================== PROOF =================================
% 56.83/57.09 % SZS status Theorem
% 56.83/57.09 % SZS output start Refutation
% 56.83/57.09
% 56.83/57.09 % Proof 1 at 54.41 (+ 1.56) seconds: goals.
% 56.83/57.09 % Length of proof is 281.
% 56.83/57.09 % Level of proof is 36.
% 56.83/57.09 % Maximum clause weight is 30.000.
% 56.83/57.09 % Given clauses 2549.
% 56.83/57.09
% 56.83/57.09 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 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].
% 56.83/57.09 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 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].
% 56.83/57.09 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 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].
% 56.83/57.09 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].
% 56.83/57.09 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 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].
% 56.83/57.09 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 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].
% 56.83/57.09 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 56.83/57.09 27 -(all X0 all X1 all X2 (multiplication(forward_diamond(X0,domain(X1)),domain(X2)) = zero -> multiplication(domain(X1),backward_diamond(X0,domain(X2))) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 56.83/57.09 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 56.83/57.09 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 56.83/57.09 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 56.83/57.09 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 56.83/57.09 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 56.83/57.09 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 56.83/57.09 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 56.83/57.09 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 56.83/57.09 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 56.83/57.09 39 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(20)].
% 56.83/57.09 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 56.83/57.09 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 56.83/57.09 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 56.83/57.09 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 56.83/57.09 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 56.83/57.09 47 domain_difference(A,B) = multiplication(domain(A),antidomain(B)) # label(domain_difference) # label(axiom). [clausify(22)].
% 56.83/57.09 48 domain_difference(A,B) = multiplication(antidomain(antidomain(A)),antidomain(B)). [copy(47),rewrite([37(2)])].
% 56.83/57.09 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 56.83/57.09 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])].
% 56.83/57.09 51 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(24)].
% 56.83/57.09 52 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(51),rewrite([39(2),39(5)])].
% 56.83/57.09 57 multiplication(forward_diamond(c1,domain(c2)),domain(c3)) = zero # label(goals) # label(negated_conjecture). [clausify(27)].
% 56.83/57.09 58 zero = multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))). [copy(57),rewrite([37(3),50(5),37(11)]),flip(a)].
% 56.83/57.09 59 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 56.83/57.09 60 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(59),rewrite([42(2)]),flip(a)].
% 56.83/57.09 61 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 56.83/57.09 62 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 56.83/57.09 63 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(62),flip(a)].
% 56.83/57.09 64 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 56.83/57.09 65 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(64),flip(a)].
% 56.83/57.09 66 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 56.83/57.09 67 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(66),flip(a)].
% 56.83/57.09 68 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 56.83/57.09 69 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(68),flip(a)].
% 56.83/57.09 70 multiplication(domain(c2),backward_diamond(c1,domain(c3))) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 56.83/57.09 71 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))) != multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) # answer(goals). [copy(70),rewrite([37(2),37(6),52(8),58(14)]),flip(a)].
% 56.83/57.09 72 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))) = multiplication(A,coantidomain(A)). [back_rewrite(38),rewrite([58(3)]),flip(a)].
% 56.83/57.09 73 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))) = multiplication(antidomain(A),A). [back_rewrite(36),rewrite([58(3)]),flip(a)].
% 56.83/57.09 74 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),multiplication(antidomain(antidomain(c3)),A)) = multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))). [back_rewrite(35),rewrite([58(1),61(14),58(15)])].
% 56.83/57.09 75 multiplication(A,multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3)))) = multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))). [back_rewrite(34),rewrite([58(1),58(15)])].
% 56.83/57.09 76 addition(A,multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3)))) = A. [back_rewrite(30),rewrite([58(1)])].
% 56.83/57.09 77 addition(A,addition(A,B)) = addition(A,B). [para(60(a,1),31(a,1)),rewrite([42(1),42(2),60(2,R),31(1),42(3)])].
% 56.83/57.09 78 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),63(a,1,1)),rewrite([42(4)]),flip(a)].
% 56.83/57.09 79 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),65(a,1,1)),rewrite([42(4)]),flip(a)].
% 56.83/57.09 84 addition(antidomain(multiplication(A,multiplication(B,C))),antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C)))))) = antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C))))). [para(61(a,1),67(a,1,1,1)),rewrite([61(7),61(13)])].
% 56.83/57.09 87 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(61(a,1),69(a,1,1,1))].
% 56.83/57.09 88 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))) = coantidomain(one). [para(72(a,2),33(a,1))].
% 56.83/57.09 89 multiplication(A,coantidomain(A)) = coantidomain(one). [para(72(a,1),48(a,2)),rewrite([48(10),88(13)]),flip(a)].
% 56.83/57.09 90 multiplication(coantidomain(one),A) = coantidomain(one). [para(72(a,1),61(a,1,1)),rewrite([89(2),74(17),88(16)])].
% 56.83/57.09 91 multiplication(A,multiplication(coantidomain(A),B)) = coantidomain(one). [para(72(a,2),61(a,1,1)),rewrite([88(13),90(3)]),flip(a)].
% 56.83/57.09 93 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),addition(A,antidomain(antidomain(c3)))) = addition(coantidomain(one),multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),A)). [para(72(a,1),63(a,1,1)),rewrite([89(2),42(26)]),flip(a)].
% 56.83/57.09 94 multiplication(A,addition(B,coantidomain(A))) = addition(coantidomain(one),multiplication(A,B)). [para(72(a,2),63(a,1,1)),rewrite([88(13),42(6)]),flip(a)].
% 56.83/57.09 96 multiplication(addition(A,B),coantidomain(B)) = addition(coantidomain(one),multiplication(A,coantidomain(B))). [para(72(a,2),65(a,1,1)),rewrite([88(13),42(6)]),flip(a)].
% 56.83/57.09 99 addition(antidomain(coantidomain(one)),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(72(a,2),67(a,1,1,1)),rewrite([88(13)])].
% 56.83/57.09 103 multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) != coantidomain(one) # answer(goals). [para(72(a,1),71(a,1)),rewrite([89(2)]),flip(a)].
% 56.83/57.09 104 addition(A,coantidomain(one)) = A. [back_rewrite(76),rewrite([88(13)])].
% 56.83/57.09 105 multiplication(A,coantidomain(one)) = coantidomain(one). [back_rewrite(75),rewrite([88(13),88(16)])].
% 56.83/57.09 107 multiplication(antidomain(A),A) = coantidomain(one). [back_rewrite(73),rewrite([88(13)]),flip(a)].
% 56.83/57.09 109 addition(one,antidomain(A)) = one. [para(44(a,1),77(a,1,2)),rewrite([42(3),44(7)])].
% 56.83/57.09 110 addition(one,coantidomain(A)) = one. [para(46(a,1),77(a,1,2)),rewrite([42(3),46(7)])].
% 56.83/57.09 111 addition(coantidomain(one),multiplication(A,B)) = multiplication(A,B). [para(104(a,1),63(a,2,2)),rewrite([105(4),42(4)])].
% 56.83/57.09 112 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [back_rewrite(96),rewrite([111(8)])].
% 56.83/57.09 114 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [back_rewrite(94),rewrite([111(7)])].
% 56.83/57.09 115 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),addition(A,antidomain(antidomain(c3)))) = multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),A). [back_rewrite(93),rewrite([111(27)])].
% 56.83/57.09 116 addition(A,multiplication(A,antidomain(B))) = A. [para(109(a,1),63(a,2,2)),rewrite([32(2),32(5)])].
% 56.83/57.09 117 addition(A,multiplication(antidomain(B),A)) = A. [para(109(a,1),65(a,2,1)),rewrite([33(2),33(5)])].
% 56.83/57.09 118 addition(A,multiplication(A,coantidomain(B))) = A. [para(110(a,1),63(a,2,2)),rewrite([32(2),32(5)])].
% 56.83/57.09 119 addition(A,multiplication(coantidomain(B),A)) = A. [para(110(a,1),65(a,2,1)),rewrite([33(2),33(5)])].
% 56.83/57.09 125 multiplication(A,addition(B,addition(C,one))) = addition(A,multiplication(A,addition(B,C))). [para(78(a,1),63(a,1,2)),rewrite([60(4,R),63(3),42(1)]),flip(a)].
% 56.83/57.09 130 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,antidomain(antidomain(addition(B,one)))))) = antidomain(multiplication(A,antidomain(antidomain(addition(B,one))))). [para(78(a,1),67(a,1,1,1))].
% 56.83/57.09 135 coantidomain(one) = antidomain(one). [para(107(a,1),32(a,1))].
% 56.83/57.09 136 multiplication(antidomain(A),multiplication(A,B)) = multiplication(antidomain(one),B). [para(107(a,1),61(a,1,1)),rewrite([135(2)]),flip(a)].
% 56.83/57.09 137 multiplication(antidomain(A),addition(A,B)) = addition(antidomain(one),multiplication(antidomain(A),B)). [para(107(a,1),63(a,1,1)),rewrite([135(2)]),flip(a)].
% 56.83/57.09 138 multiplication(addition(A,antidomain(B)),B) = addition(antidomain(one),multiplication(A,B)). [para(107(a,1),65(a,1,1)),rewrite([135(2),42(6)]),flip(a)].
% 56.83/57.09 141 addition(coantidomain(antidomain(one)),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(107(a,1),69(a,1,1,1)),rewrite([135(2)])].
% 56.83/57.09 145 addition(antidomain(one),multiplication(A,B)) = multiplication(A,B). [back_rewrite(111),rewrite([135(2)])].
% 56.83/57.09 147 multiplication(antidomain(A),A) = antidomain(one). [back_rewrite(107),rewrite([135(4)])].
% 56.83/57.09 149 multiplication(A,antidomain(one)) = antidomain(one). [back_rewrite(105),rewrite([135(2),135(5)])].
% 56.83/57.09 151 multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) != antidomain(one) # answer(goals). [back_rewrite(103),rewrite([135(15)])].
% 56.83/57.09 155 addition(antidomain(antidomain(one)),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [back_rewrite(99),rewrite([135(2)])].
% 56.83/57.09 159 multiplication(A,multiplication(coantidomain(A),B)) = antidomain(one). [back_rewrite(91),rewrite([135(5)])].
% 56.83/57.09 160 multiplication(antidomain(one),A) = antidomain(one). [back_rewrite(90),rewrite([135(2),135(5)])].
% 56.83/57.09 161 multiplication(A,coantidomain(A)) = antidomain(one). [back_rewrite(89),rewrite([135(4)])].
% 56.83/57.09 164 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [back_rewrite(138),rewrite([145(7)])].
% 56.83/57.09 165 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [back_rewrite(137),rewrite([145(8)])].
% 56.83/57.09 166 multiplication(antidomain(A),multiplication(A,B)) = antidomain(one). [back_rewrite(136),rewrite([160(6)])].
% 56.83/57.09 177 addition(coantidomain(addition(A,multiplication(B,A))),coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A))) = coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A)). [para(79(a,1),69(a,1,1,1))].
% 56.83/57.09 181 addition(antidomain(one),coantidomain(antidomain(one))) = one. [para(135(a,1),46(a,1,1)),rewrite([135(4)])].
% 56.83/57.09 199 addition(antidomain(one),antidomain(antidomain(A))) = antidomain(antidomain(A)). [para(147(a,1),116(a,1,2)),rewrite([42(5)])].
% 56.83/57.09 209 addition(antidomain(one),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(161(a,1),117(a,1,2)),rewrite([42(5)])].
% 56.83/57.09 210 coantidomain(antidomain(one)) = one. [back_rewrite(181),rewrite([209(6)])].
% 56.83/57.09 213 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(141),rewrite([210(3),110(7)]),flip(a)].
% 56.83/57.09 215 addition(antidomain(one),antidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(147(a,1),118(a,1,2)),rewrite([42(5)])].
% 56.83/57.09 223 addition(antidomain(antidomain(one)),antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))))) = antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))). [para(159(a,1),67(a,1,1,1))].
% 56.83/57.09 228 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = antidomain(one). [para(61(a,1),166(a,1,2))].
% 56.83/57.09 248 multiplication(coantidomain(coantidomain(antidomain(A))),A) = antidomain(one). [para(213(a,1),161(a,1,2)),rewrite([32(6)])].
% 56.83/57.09 272 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(248(a,1),65(a,1,1)),rewrite([145(4),42(5)]),flip(a)].
% 56.83/57.09 287 multiplication(A,addition(B,addition(C,coantidomain(A)))) = multiplication(A,addition(B,C)). [para(114(a,1),63(a,1,1)),rewrite([63(3),42(5),60(5,R),42(4)]),flip(a)].
% 56.83/57.09 292 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(114(a,1),79(a,2,2)),rewrite([42(9),60(9),42(8),60(9,R),42(8)])].
% 56.83/57.09 307 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(44(a,1),164(a,1,1)),rewrite([33(3)]),flip(a)].
% 56.83/57.09 326 multiplication(antidomain(multiplication(A,multiplication(B,C))),multiplication(A,multiplication(B,antidomain(antidomain(C))))) = antidomain(one). [para(84(a,1),164(a,1,1)),rewrite([147(10)]),flip(a)].
% 56.83/57.09 327 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(307(a,1),61(a,1,1)),flip(a)].
% 56.83/57.09 329 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(307(a,1),65(a,1,1)),rewrite([79(4,R),42(6)]),flip(a)].
% 56.83/57.09 345 antidomain(antidomain(one)) = one. [para(199(a,1),44(a,1))].
% 56.83/57.09 357 antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))) = one. [back_rewrite(223),rewrite([345(3),109(8)]),flip(a)].
% 56.83/57.09 359 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(155),rewrite([345(3),109(7)]),flip(a)].
% 56.83/57.09 367 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B)) = one. [para(147(a,1),87(a,1,1,1,2)),rewrite([149(3),210(3),110(8)]),flip(a)].
% 56.83/57.09 368 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(147(a,1),87(a,1,1,1)),rewrite([210(3),110(9)]),flip(a)].
% 56.83/57.09 369 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one. [para(161(a,1),87(a,1,1,1,2)),rewrite([149(3),210(3),110(8)]),flip(a)].
% 56.83/57.09 376 multiplication(coantidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = antidomain(one). [para(87(a,1),114(a,1,2)),rewrite([161(10),61(10)]),flip(a)].
% 56.83/57.09 387 multiplication(A,antidomain(antidomain(coantidomain(A)))) = antidomain(one). [para(359(a,1),147(a,1,1)),rewrite([33(6)])].
% 56.83/57.09 390 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(387(a,1),63(a,1,1)),rewrite([145(4),42(5)]),flip(a)].
% 56.83/57.09 398 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),112(a,1,1))].
% 56.83/57.09 399 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),112(a,1,1)),rewrite([33(5)]),flip(a)].
% 56.83/57.09 400 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),112(a,1,1)),rewrite([33(5)]),flip(a)].
% 56.83/57.09 410 multiplication(A,coantidomain(addition(A,B))) = antidomain(one). [para(77(a,1),112(a,1,1)),rewrite([161(4)]),flip(a)].
% 56.83/57.09 428 coantidomain(addition(A,one)) = antidomain(one). [para(410(a,1),33(a,1)),rewrite([42(4)]),flip(a)].
% 56.83/57.09 440 multiplication(A,coantidomain(multiplication(A,addition(B,one)))) = antidomain(one). [para(78(a,2),410(a,1,2,1))].
% 56.83/57.09 450 addition(coantidomain(A),coantidomain(addition(A,multiplication(B,A)))) = coantidomain(A). [back_rewrite(177),rewrite([428(6),210(6),33(5),42(5),428(8),210(8),33(7)])].
% 56.83/57.09 484 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),165(a,1,2)),rewrite([32(4)]),flip(a)].
% 56.83/57.09 488 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(65(a,1),165(a,1,2))].
% 56.83/57.09 496 multiplication(antidomain(A),multiplication(antidomain(B),A)) = antidomain(one). [para(117(a,1),165(a,1,2)),rewrite([147(2)]),flip(a)].
% 56.83/57.09 497 multiplication(antidomain(A),multiplication(coantidomain(B),A)) = antidomain(one). [para(119(a,1),165(a,1,2)),rewrite([147(2)]),flip(a)].
% 56.83/57.09 503 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(496(a,1),65(a,1,1)),rewrite([145(6),42(5)]),flip(a)].
% 56.83/57.09 513 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [para(496(a,1),87(a,1,1,1)),rewrite([210(3),110(9)]),flip(a)].
% 56.83/57.09 514 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = antidomain(one). [para(165(a,1),496(a,1,2))].
% 56.83/57.09 517 multiplication(addition(A,antidomain(B)),multiplication(coantidomain(C),B)) = multiplication(A,multiplication(coantidomain(C),B)). [para(497(a,1),65(a,1,1)),rewrite([145(6),42(5)]),flip(a)].
% 56.83/57.09 527 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [para(497(a,1),87(a,1,1,1)),rewrite([210(3),110(9)]),flip(a)].
% 56.83/57.09 536 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),addition(antidomain(antidomain(c3)),antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))) = antidomain(one). [para(147(a,1),115(a,2)),rewrite([42(21)])].
% 56.83/57.09 644 multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))) = antidomain(one). [para(357(a,1),147(a,1,1)),rewrite([33(7)])].
% 56.83/57.09 647 multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B) = antidomain(one). [para(367(a,1),161(a,1,2)),rewrite([32(7)])].
% 56.83/57.09 718 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = antidomain(one). [para(369(a,1),161(a,1,2)),rewrite([32(7)])].
% 56.83/57.09 738 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),398(a,1,1)),rewrite([33(4)]),flip(a)].
% 56.83/57.09 741 multiplication(A,multiplication(addition(B,C),coantidomain(multiplication(A,B)))) = multiplication(A,multiplication(C,coantidomain(multiplication(A,B)))). [para(63(a,1),398(a,1,1)),rewrite([61(5),61(9)])].
% 56.83/57.09 977 multiplication(antidomain(addition(A,B)),addition(A,addition(B,one))) = addition(antidomain(one),antidomain(addition(A,B))). [para(147(a,1),125(a,2,2)),rewrite([42(11)])].
% 56.83/57.09 1007 antidomain(addition(A,one)) = antidomain(one). [para(147(a,1),440(a,1,2,1)),rewrite([210(6),32(5)])].
% 56.83/57.09 1016 addition(antidomain(A),antidomain(addition(A,multiplication(A,B)))) = antidomain(A). [back_rewrite(130),rewrite([1007(6),345(6),32(5),42(5),1007(8),345(8),32(7)])].
% 56.83/57.09 1017 addition(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(A). [para(1007(a,1),67(a,1,2,1,2,1)),rewrite([345(7),32(6),42(6),1007(9),345(9),32(8)])].
% 56.83/57.09 1036 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(484(a,1),79(a,2,2)),rewrite([42(4),109(4),33(4),42(7)]),flip(a)].
% 56.83/57.09 1246 multiplication(A,addition(B,antidomain(antidomain(multiplication(coantidomain(A),C))))) = multiplication(A,B). [para(644(a,1),63(a,1,1)),rewrite([145(4),42(6)]),flip(a)].
% 56.83/57.09 2030 multiplication(coantidomain(antidomain(A)),A) = A. [para(46(a,1),272(a,1,1)),rewrite([33(2)]),flip(a)].
% 56.83/57.09 2059 multiplication(antidomain(coantidomain(antidomain(A))),A) = antidomain(one). [para(1036(a,1),272(a,1,1)),rewrite([248(4)]),flip(a)].
% 56.83/57.09 2060 multiplication(coantidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B). [para(2030(a,1),61(a,1,1)),flip(a)].
% 56.83/57.09 2070 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(2030(a,1),116(a,1,2)),rewrite([42(5)])].
% 56.83/57.09 2075 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(coantidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [para(2030(a,1),84(a,1,2,1)),rewrite([42(13),2030(22)])].
% 56.83/57.09 2102 multiplication(antidomain(coantidomain(antidomain(addition(A,B)))),addition(A,addition(B,one))) = antidomain(coantidomain(antidomain(addition(A,B)))). [para(2059(a,1),125(a,2,2)),rewrite([42(15),215(15)])].
% 56.83/57.09 2514 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),390(a,1,2)),rewrite([32(2)]),flip(a)].
% 56.83/57.09 2545 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2514(a,1),61(a,1,1)),flip(a)].
% 56.83/57.09 2546 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2514(a,1),61(a,1)),flip(a)].
% 56.83/57.09 2557 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2514(a,1),119(a,1,2)),rewrite([42(5)])].
% 56.83/57.09 2596 multiplication(A,coantidomain(coantidomain(A))) = A. [para(484(a,1),2545(a,1,2)),rewrite([2514(3)]),flip(a)].
% 56.83/57.09 2620 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(400),rewrite([2596(5)]),flip(a)].
% 56.83/57.09 2692 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2620(a,1),1036(a,1,2)),rewrite([42(5),2557(5),2620(6)])].
% 56.83/57.09 2715 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2692(a,1),738(a,1,1,1)),rewrite([2692(5),484(5),2692(5)]),flip(a)].
% 56.83/57.09 2717 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2692(a,1),738(a,2,1)),rewrite([2715(2),2715(6),738(9),2715(6)])].
% 56.83/57.09 2726 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2620(a,1),2692(a,1,1,1)),rewrite([2715(2),2715(5)]),flip(a)].
% 56.83/57.09 2727 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2620(a,1),2692(a,2)),rewrite([2715(2),2726(3),2717(4)])].
% 56.83/57.09 2969 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = antidomain(one). [back_rewrite(718),rewrite([2715(3)])].
% 56.83/57.09 2978 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),B) = antidomain(one). [back_rewrite(647),rewrite([2715(4)])].
% 56.83/57.09 2983 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [back_rewrite(527),rewrite([2715(5)])].
% 56.83/57.09 2986 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [back_rewrite(513),rewrite([2715(5)])].
% 56.83/57.09 2999 multiplication(antidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = antidomain(one). [back_rewrite(376),rewrite([2715(3)])].
% 56.83/57.09 3001 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(368),rewrite([2715(5)])].
% 56.83/57.09 3013 multiplication(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) != antidomain(one) # answer(goals). [back_rewrite(151),rewrite([2715(8),2715(12)])].
% 56.83/57.09 3014 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(antidomain(coantidomain(A)),B))) = coantidomain(multiplication(antidomain(coantidomain(A)),B)). [back_rewrite(69),rewrite([2715(4),2715(9)])].
% 56.83/57.09 3639 coantidomain(antidomain(antidomain(A))) = antidomain(A). [para(399(a,1),78(a,2,2)),rewrite([42(6),110(6),32(3),2070(6)]),flip(a)].
% 56.83/57.09 3640 multiplication(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(antidomain(c3)),c1)))) != antidomain(one) # answer(goals). [back_rewrite(3013),rewrite([3639(7)])].
% 56.83/57.09 3643 multiplication(antidomain(antidomain(A)),addition(B,antidomain(A))) = multiplication(antidomain(antidomain(A)),B). [para(3639(a,1),114(a,1,2,2))].
% 56.83/57.09 3646 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(3639(a,1),2715(a,1,1)),rewrite([3639(5)])].
% 56.83/57.09 3647 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(3639(a,1),2715(a,2,1)),rewrite([3646(3),3646(4)])].
% 56.83/57.09 3648 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(3639(a,1),2727(a,2)),rewrite([3646(3),3647(4)])].
% 56.83/57.09 3649 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(c2))))),antidomain(antidomain(c3))) = antidomain(one). [back_rewrite(536),rewrite([3648(5),3648(15),3643(18)])].
% 56.83/57.09 3702 addition(antidomain(one),antidomain(addition(A,B))) = antidomain(addition(A,B)). [back_rewrite(2102),rewrite([3646(3),3648(4),977(6),3646(8),3648(9)])].
% 56.83/57.09 3712 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [back_rewrite(2075),rewrite([3646(9)])].
% 56.83/57.09 3720 multiplication(antidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B). [back_rewrite(2060),rewrite([3646(2)])].
% 56.83/57.09 3721 multiplication(antidomain(antidomain(A)),A) = A. [back_rewrite(2030),rewrite([3646(2)])].
% 56.83/57.09 3804 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),antidomain(antidomain(B))) = antidomain(one). [para(3646(a,1),2969(a,1,2))].
% 56.83/57.09 4491 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = antidomain(one). [para(42(a,1),514(a,1,1,1))].
% 56.83/57.09 5636 multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A) = antidomain(one). [para(2983(a,1),161(a,1,2)),rewrite([32(8)])].
% 56.83/57.09 5643 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = antidomain(one). [para(2986(a,1),161(a,1,2)),rewrite([32(8)])].
% 56.83/57.10 5822 addition(antidomain(one),antidomain(multiplication(A,addition(B,C)))) = antidomain(multiplication(A,addition(B,C))). [para(63(a,1),3702(a,1,2,1)),rewrite([63(9)])].
% 56.83/57.10 5824 antidomain(multiplication(A,addition(B,one))) = antidomain(addition(A,multiplication(A,B))). [para(78(a,2),3702(a,1,2,1)),rewrite([5822(7)])].
% 56.83/57.10 6141 multiplication(antidomain(addition(A,B)),A) = antidomain(one). [para(77(a,1),4491(a,1,1,1)),rewrite([327(6)])].
% 56.83/57.10 6489 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = antidomain(one). [para(3721(a,1),228(a,1,2,2))].
% 56.83/57.10 8472 multiplication(A,addition(coantidomain(A),coantidomain(B))) = multiplication(A,coantidomain(B)). [para(450(a,1),287(a,2,2)),rewrite([42(6),60(7,R),42(6),450(6)])].
% 56.83/57.10 11254 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = antidomain(one). [para(3001(a,1),161(a,1,2)),rewrite([32(8)])].
% 56.83/57.10 11628 multiplication(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(multiplication(A,addition(B,one))). [para(1017(a,1),329(a,1,1)),rewrite([42(9),109(9),33(12)])].
% 56.83/57.10 11872 addition(antidomain(multiplication(A,addition(B,one))),antidomain(multiplication(addition(A,multiplication(A,B)),addition(C,one)))) = antidomain(addition(A,multiplication(A,B))). [para(5824(a,2),1016(a,1,1)),rewrite([78(10,R)])].
% 56.83/57.10 15212 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(44(a,1),488(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 56.83/57.10 15801 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(44(a,1),503(a,1,1)),rewrite([33(5)]),flip(a)].
% 56.83/57.10 15960 multiplication(antidomain(A),multiplication(coantidomain(B),antidomain(A))) = multiplication(coantidomain(B),antidomain(A)). [para(44(a,1),517(a,1,1)),rewrite([33(5)]),flip(a)].
% 56.83/57.10 16035 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(44(a,1),1246(a,1,2)),rewrite([32(2)]),flip(a)].
% 56.83/57.10 16052 addition(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(multiplication(antidomain(antidomain(A)),B)). [para(16035(a,1),117(a,1,2)),rewrite([3646(2),42(6),3646(8)])].
% 56.83/57.10 16054 multiplication(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(A). [para(16035(a,1),165(a,2)),rewrite([3646(3),165(7)])].
% 56.83/57.10 16081 antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [back_rewrite(3712),rewrite([16052(13)])].
% 56.83/57.10 16134 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(3720(a,1),16054(a,1,2,1))].
% 56.83/57.10 16147 antidomain(multiplication(A,addition(B,one))) = antidomain(A). [back_rewrite(11628),rewrite([16134(6)]),flip(a)].
% 56.83/57.10 16183 antidomain(addition(A,multiplication(A,B))) = antidomain(A). [back_rewrite(11872),rewrite([16147(4),16147(7),1016(5)]),flip(a)].
% 56.83/57.10 16312 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(16134(a,1),79(a,2,2)),rewrite([42(3),109(3),33(4),42(6)]),flip(a)].
% 56.83/57.10 16327 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(16134(a,1),292(a,2,2,2)),rewrite([42(3),109(3),3646(5),42(6),33(7),3646(9),42(11),44(11),42(9),109(9)])].
% 56.83/57.10 16328 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(16134(a,1),2546(a,1,2,2,1,1)),rewrite([3646(5),3648(6),15801(6),16134(8)])].
% 56.83/57.10 16429 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(16328(a,1),61(a,1,1)),flip(a)].
% 56.83/57.10 16469 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(15212),rewrite([16429(7)]),flip(a)].
% 56.83/57.10 17478 multiplication(antidomain(antidomain(A)),multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(496(a,1),16469(a,1,1,1)),rewrite([345(3),33(4)]),flip(a)].
% 56.83/57.10 17486 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(2969(a,1),16469(a,1,1,1)),rewrite([345(3),33(3),2727(5)]),flip(a)].
% 56.83/57.10 17487 multiplication(coantidomain(multiplication(A,antidomain(B))),B) = B. [para(2978(a,1),16469(a,1,1,1)),rewrite([345(3),33(2),2727(5)]),flip(a)].
% 56.83/57.10 17493 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(6141(a,1),16469(a,1,1,1)),rewrite([345(3),33(2)]),flip(a)].
% 56.83/57.10 17503 multiplication(coantidomain(multiplication(antidomain(A),coantidomain(B))),A) = A. [para(5636(a,1),16469(a,1,1,1)),rewrite([345(3),33(2),2727(6)]),flip(a)].
% 56.83/57.10 17504 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A. [para(5643(a,1),16469(a,1,1,1)),rewrite([345(3),33(2),2727(6)]),flip(a)].
% 56.83/57.10 17523 multiplication(coantidomain(multiplication(A,antidomain(B))),antidomain(antidomain(B))) = antidomain(antidomain(B)). [para(3804(a,1),16469(a,1,1,1)),rewrite([345(3),33(4),2727(7)]),flip(a)].
% 56.83/57.10 17538 multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)) = multiplication(A,B). [para(6489(a,1),16469(a,1,1,1)),rewrite([345(3),33(3)]),flip(a)].
% 56.83/57.10 17553 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(11254(a,1),16469(a,1,1,1)),rewrite([345(3),33(2),2727(6)]),flip(a)].
% 56.83/57.10 17578 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [back_rewrite(16081),rewrite([17538(7)]),flip(a)].
% 56.83/57.10 17643 multiplication(antidomain(antidomain(multiplication(c1,c2))),antidomain(antidomain(c3))) = antidomain(one). [back_rewrite(3649),rewrite([17578(6)])].
% 56.83/57.10 17676 addition(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = one. [para(17487(a,1),16327(a,1,2,1)),rewrite([2727(5),42(5)])].
% 56.83/57.10 17677 multiplication(antidomain(A),antidomain(coantidomain(multiplication(B,antidomain(A))))) = antidomain(coantidomain(multiplication(B,antidomain(A)))). [para(17487(a,1),16328(a,1,1,1))].
% 56.83/57.10 17689 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(42(a,1),17493(a,1,1,1,1))].
% 56.83/57.10 17718 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(17493(a,1),16328(a,1,1,1)),rewrite([3648(5),3648(8)])].
% 56.83/57.10 17810 multiplication(antidomain(addition(A,B)),antidomain(B)) = antidomain(addition(A,B)). [para(17689(a,1),16054(a,1,2,1))].
% 56.83/57.10 17814 addition(antidomain(A),antidomain(addition(B,A))) = antidomain(A). [para(17689(a,1),16312(a,1,2,1)),rewrite([3648(4),42(4),17689(8)])].
% 56.83/57.10 17823 addition(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(multiplication(B,A)). [para(17486(a,1),78(a,2,2)),rewrite([42(5),110(5),32(4),42(6)]),flip(a)].
% 56.83/57.10 17885 multiplication(coantidomain(A),antidomain(B)) = multiplication(antidomain(B),coantidomain(A)). [para(17503(a,1),16035(a,1,2,1)),rewrite([61(5),15960(5)])].
% 56.83/57.10 17914 multiplication(antidomain(antidomain(A)),coantidomain(multiplication(B,antidomain(A)))) = antidomain(antidomain(A)). [back_rewrite(17523),rewrite([17885(6)])].
% 56.83/57.10 18004 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(17504(a,1),16035(a,1,2,1)),rewrite([61(5),15801(5)])].
% 56.83/57.10 18007 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),antidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))). [para(17504(a,1),16134(a,1,2,1)),rewrite([18004(7)])].
% 56.83/57.10 18022 multiplication(antidomain(A),antidomain(addition(B,A))) = antidomain(addition(B,A)). [back_rewrite(17810),rewrite([18004(4)])].
% 56.83/57.10 18024 multiplication(antidomain(antidomain(c3)),antidomain(antidomain(multiplication(c1,c2)))) = antidomain(one). [back_rewrite(17643),rewrite([18004(9)])].
% 56.83/57.10 18180 addition(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = one. [para(2727(a,1),17676(a,1,1)),rewrite([2727(4)])].
% 56.83/57.10 18312 addition(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(multiplication(antidomain(B),A)). [para(117(a,1),17814(a,1,2,1)),rewrite([42(5)])].
% 56.83/57.10 18380 multiplication(A,coantidomain(multiplication(B,coantidomain(A)))) = A. [para(18180(a,1),8472(a,1,2)),rewrite([32(2)]),flip(a)].
% 56.83/57.10 19076 multiplication(A,antidomain(multiplication(antidomain(B),coantidomain(A)))) = A. [para(17885(a,1),16035(a,1,2,1))].
% 56.83/57.10 19103 multiplication(A,coantidomain(multiplication(coantidomain(A),antidomain(B)))) = A. [para(17885(a,2),18380(a,1,2,1))].
% 56.83/57.10 19110 antidomain(multiplication(antidomain(antidomain(A)),coantidomain(B))) = antidomain(multiplication(coantidomain(B),A)). [para(17885(a,1),17578(a,1,1))].
% 56.83/57.10 19135 multiplication(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(A). [para(19076(a,1),165(a,2)),rewrite([3646(4),17578(6),165(6)])].
% 56.83/57.10 19297 antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))) = multiplication(antidomain(A),antidomain(B)). [para(18004(a,1),2546(a,1,2,2,1,1)),rewrite([18004(5),17677(8),18007(7)])].
% 56.83/57.10 19326 multiplication(coantidomain(multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B)))),B) = B. [para(18004(a,1),17553(a,1,1,1))].
% 56.83/57.10 20758 coantidomain(multiplication(antidomain(coantidomain(A)),B)) = coantidomain(multiplication(A,B)). [para(2545(a,1),17823(a,1,2,1)),rewrite([42(7),3014(7),2545(8)])].
% 56.83/57.10 20862 coantidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [para(18004(a,1),20758(a,1,1))].
% 56.83/57.10 20939 antidomain(multiplication(antidomain(antidomain(c3)),multiplication(c1,c2))) = one. [para(18024(a,1),17578(a,1,1)),rewrite([345(3)]),flip(a)].
% 56.83/57.10 20944 multiplication(antidomain(antidomain(c3)),multiplication(c1,antidomain(antidomain(c2)))) = antidomain(one). [para(20939(a,1),326(a,1,1)),rewrite([33(11)])].
% 56.83/57.10 21700 multiplication(A,coantidomain(multiplication(A,antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [para(44(a,1),741(a,1,2,1)),rewrite([33(5),17914(10)])].
% 56.83/57.10 26752 antidomain(addition(antidomain(antidomain(A)),multiplication(antidomain(B),A))) = antidomain(A). [para(17478(a,1),16183(a,1,1,2)),rewrite([3648(9)])].
% 56.83/57.10 26780 antidomain(antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(19103(a,1),26752(a,1,1,2)),rewrite([3646(2),18004(4),19297(6),17578(5),42(5),18312(5),3646(6),18004(8),19297(10)])].
% 56.83/57.10 29445 antidomain(multiplication(antidomain(antidomain(A)),antidomain(coantidomain(B)))) = antidomain(multiplication(antidomain(coantidomain(B)),A)). [para(2715(a,1),19110(a,1,1,2)),rewrite([2715(8)])].
% 56.83/57.10 29447 antidomain(multiplication(antidomain(antidomain(A)),B)) = antidomain(multiplication(antidomain(antidomain(B)),A)). [para(3646(a,1),19110(a,1,1,2)),rewrite([17578(6),3646(6)])].
% 56.83/57.10 29471 coantidomain(multiplication(antidomain(A),antidomain(B))) = antidomain(multiplication(antidomain(A),antidomain(B))). [para(19297(a,1),2727(a,1,1)),flip(a)].
% 56.83/57.10 29566 antidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [back_rewrite(20862),rewrite([29471(5)])].
% 56.83/57.10 29567 multiplication(antidomain(multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B)))),B) = B. [back_rewrite(19326),rewrite([29471(6)])].
% 56.83/57.10 29585 coantidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [back_rewrite(29445),rewrite([29566(6)])].
% 56.83/57.10 35142 multiplication(antidomain(multiplication(antidomain(antidomain(A)),B)),A) = multiplication(antidomain(B),A). [para(29447(a,1),16469(a,1,1)),rewrite([3648(8)])].
% 56.83/57.10 35226 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(B)). [para(29567(a,1),16134(a,1,2,1)),rewrite([26780(7),26780(5),17578(6),61(7),18004(6),19135(6),26780(10),26780(8),17578(9)]),flip(a)].
% 56.83/57.10 35243 multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B))) = multiplication(A,antidomain(B)). [para(29585(a,1),21700(a,1,2)),rewrite([3648(8)])].
% 56.83/57.10 36617 multiplication(antidomain(addition(A,antidomain(B))),B) = multiplication(antidomain(A),B). [para(114(a,1),35142(a,1,1,1)),rewrite([35142(5),3646(5),3648(5)]),flip(a)].
% 56.83/57.10 36706 multiplication(antidomain(A),antidomain(coantidomain(B))) = antidomain(addition(A,coantidomain(B))). [para(2727(a,1),36617(a,1,1,1,2)),rewrite([18004(6),18022(6)]),flip(a)].
% 56.83/57.10 36798 antidomain(addition(antidomain(c2),coantidomain(multiplication(antidomain(antidomain(c3)),c1)))) != antidomain(one) # answer(goals). [back_rewrite(3640),rewrite([36706(11)])].
% 56.83/57.10 37219 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)). [para(17718(a,1),35243(a,2)),rewrite([3646(3),3648(4),165(4),35226(5)])].
% 56.83/57.10 39598 antidomain(addition(antidomain(c2),coantidomain(multiplication(antidomain(antidomain(c3)),c1)))) = antidomain(one). [para(20944(a,1),2999(a,1,2,2,1)),rewrite([3646(13),345(13),32(12),37219(11),42(9)])].
% 56.83/57.10 39599 $F # answer(goals). [resolve(39598,a,36798,a)].
% 56.83/57.10
% 56.83/57.10 % SZS output end Refutation
% 56.83/57.10 ============================== end of proof ==========================
% 56.83/57.10
% 56.83/57.10 ============================== STATISTICS ============================
% 56.83/57.10
% 56.83/57.10 Given=2549. Generated=2853142. Kept=39554. proofs=1.
% 56.83/57.10 Usable=1594. Sos=7981. Demods=9276. Limbo=8, Disabled=29999. Hints=0.
% 56.83/57.10 Megabytes=30.56.
% 56.83/57.10 User_CPU=54.42, System_CPU=1.56, Wall_clock=56.
% 56.83/57.10
% 56.83/57.10 ============================== end of statistics =====================
% 56.83/57.10
% 56.83/57.10 ============================== end of search =========================
% 56.83/57.10
% 56.83/57.10 THEOREM PROVED
% 56.83/57.10 % SZS status Theorem
% 56.83/57.10
% 56.83/57.10 Exiting with 1 proof.
% 56.83/57.10
% 56.83/57.10 Process 12808 exit (max_proofs) Thu Jun 16 11:24:08 2022
% 56.83/57.10 Prover9 interrupted
%------------------------------------------------------------------------------