TSTP Solution File: KLE116+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE116+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 02:22:18 EDT 2022
% Result : Theorem 37.62s 37.91s
% Output : Refutation 37.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE116+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 11:27:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.49/1.07 ============================== Prover9 ===============================
% 0.49/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.49/1.07 Process 10891 was started by sandbox2 on n006.cluster.edu,
% 0.49/1.07 Thu Jun 16 11:27:27 2022
% 0.49/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10736_n006.cluster.edu".
% 0.49/1.07 ============================== end of head ===========================
% 0.49/1.07
% 0.49/1.07 ============================== INPUT =================================
% 0.49/1.07
% 0.49/1.07 % Reading from file /tmp/Prover9_10736_n006.cluster.edu
% 0.49/1.07
% 0.49/1.07 set(prolog_style_variables).
% 0.49/1.07 set(auto2).
% 0.49/1.07 % set(auto2) -> set(auto).
% 0.49/1.07 % set(auto) -> set(auto_inference).
% 0.49/1.07 % set(auto) -> set(auto_setup).
% 0.49/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.49/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.49/1.07 % set(auto) -> set(auto_limits).
% 0.49/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.49/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.49/1.07 % set(auto) -> set(auto_denials).
% 0.49/1.07 % set(auto) -> set(auto_process).
% 0.49/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.49/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.49/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.49/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.49/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.49/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.49/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.49/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.49/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.49/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.49/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.49/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.49/1.07 % set(auto2) -> assign(stats, some).
% 0.49/1.07 % set(auto2) -> clear(echo_input).
% 0.49/1.07 % set(auto2) -> set(quiet).
% 0.49/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.49/1.07 % set(auto2) -> clear(print_given).
% 0.49/1.07 assign(lrs_ticks,-1).
% 0.49/1.07 assign(sos_limit,10000).
% 0.49/1.07 assign(order,kbo).
% 0.49/1.07 set(lex_order_vars).
% 0.49/1.07 clear(print_given).
% 0.49/1.07
% 0.49/1.07 % formulas(sos). % not echoed (27 formulas)
% 0.49/1.07
% 0.49/1.07 ============================== end of input ==========================
% 0.49/1.07
% 0.49/1.07 % From the command line: assign(max_seconds, 300).
% 0.49/1.07
% 0.49/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.49/1.07
% 0.49/1.07 % Formulas that are not ordinary clauses:
% 0.49/1.07 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 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].
% 0.49/1.07 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 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].
% 0.49/1.07 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 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].
% 0.49/1.07 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].
% 0.49/1.07 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 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].
% 5.25/5.61 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 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].
% 5.25/5.61 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 5.25/5.61 27 -(all X0 all X1 all X2 forward_box(X0,multiplication(domain(X1),domain(X2))) = multiplication(forward_box(X0,domain(X1)),forward_box(X0,domain(X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.25/5.61
% 5.25/5.61 ============================== end of process non-clausal formulas ===
% 5.25/5.61
% 5.25/5.61 ============================== PROCESS INITIAL CLAUSES ===============
% 5.25/5.61
% 5.25/5.61 ============================== PREDICATE ELIMINATION =================
% 5.25/5.61 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 5.25/5.61 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 5.25/5.61
% 5.25/5.61 ============================== end predicate elimination =============
% 5.25/5.61
% 5.25/5.61 Auto_denials:
% 5.25/5.61 % copying label goals to answer in negative clause
% 5.25/5.61
% 5.25/5.61 Term ordering decisions:
% 5.25/5.61 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.
% 5.25/5.61
% 5.25/5.61 ============================== end of process initial clauses ========
% 5.25/5.61
% 5.25/5.61 ============================== CLAUSES FOR SEARCH ====================
% 5.25/5.61
% 5.25/5.61 ============================== end of clauses for search =============
% 5.25/5.61
% 5.25/5.61 ============================== SEARCH ================================
% 5.25/5.61
% 5.25/5.61 % Starting search at 0.01 seconds.
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=36.000, iters=3371
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=33.000, iters=3334
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=32.000, iters=3363
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=31.000, iters=3361
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=30.000, iters=3341
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=29.000, iters=3400
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=28.000, iters=3336
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=27.000, iters=3356
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=26.000, iters=3342
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=25.000, iters=3336
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=23.000, iters=4381
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=22.000, iters=3937
% 5.25/5.61
% 5.25/5.61 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.98 sec).
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=21.000, iters=3340
% 5.25/5.61
% 5.25/5.61 Low Water (keep): wt=20.000, iters=3338
% 5.25/5.61
% 5.25/5.61 Low Water (displace): id=6267, wt=49.000
% 5.25/5.61
% 5.25/5.61 Low Water (displace): id=3689, wt=48.000
% 5.25/5.61
% 5.25/5.61 Low Water (displace): id=6915, wt=47.000
% 5.25/5.61
% 5.25/5.61 Low Water (displace): id=4651, wt=46.000
% 5.25/5.61
% 5.25/5.61 Low Water (displace): id=6916, wt=45.000
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=5877, wt=44.000
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=4319, wt=43.000
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=15543, wt=19.000
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=15545, wt=18.000
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=15558, wt=17.000
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=15588, wt=16.000
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=15643, wt=15.000
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=16033, wt=14.000
% 37.62/37.91
% 37.62/37.91 Low Water (keep): wt=19.000, iters=3338
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=16647, wt=13.000
% 37.62/37.91
% 37.62/37.91 Low Water (keep): wt=18.000, iters=3354
% 37.62/37.91
% 37.62/37.91 Low Water (displace): id=22431, wt=12.000
% 37.62/37.91
% 37.62/37.91 Low Water (keep): wt=17.000, iters=3341
% 37.62/37.91
% 37.62/37.91 Low Water (keep): wt=16.000, iters=5472
% 37.62/37.91
% 37.62/37.91 Low Water (keep): wt=15.000, iters=3955
% 37.62/37.91
% 37.62/37.91 ============================== PROOF =================================
% 37.62/37.91 % SZS status Theorem
% 37.62/37.91 % SZS output start Refutation
% 37.62/37.91
% 37.62/37.91 % Proof 1 at 35.59 (+ 1.26) seconds: goals.
% 37.62/37.91 % Length of proof is 272.
% 37.62/37.91 % Level of proof is 37.
% 37.62/37.91 % Maximum clause weight is 51.000.
% 37.62/37.91 % Given clauses 2154.
% 37.62/37.91
% 37.62/37.91 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 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].
% 37.62/37.91 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 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].
% 37.62/37.91 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 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].
% 37.62/37.91 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].
% 37.62/37.91 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 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].
% 37.62/37.91 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 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].
% 37.62/37.91 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 37.62/37.91 27 -(all X0 all X1 all X2 forward_box(X0,multiplication(domain(X1),domain(X2))) = multiplication(forward_box(X0,domain(X1)),forward_box(X0,domain(X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 37.62/37.91 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 37.62/37.91 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 37.62/37.91 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 37.62/37.91 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 37.62/37.91 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 37.62/37.91 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 37.62/37.91 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 37.62/37.91 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 37.62/37.91 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 37.62/37.91 40 c(A) = antidomain(domain(A)) # label(complement) # label(axiom). [clausify(21)].
% 37.62/37.91 41 c(A) = antidomain(antidomain(antidomain(A))). [copy(40),rewrite([37(2)])].
% 37.62/37.91 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 37.62/37.91 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 37.62/37.91 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 37.62/37.91 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 37.62/37.91 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 37.62/37.91 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 37.62/37.91 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])].
% 37.62/37.91 53 forward_box(A,B) = c(forward_diamond(A,c(B))) # label(forward_box) # label(axiom). [clausify(25)].
% 37.62/37.91 54 forward_box(A,B) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(antidomain(antidomain(antidomain(B))))))))))). [copy(53),rewrite([41(2),50(5),41(10)])].
% 37.62/37.91 57 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 37.62/37.91 58 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(57),rewrite([42(2)]),flip(a)].
% 37.62/37.91 59 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 37.62/37.91 60 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 37.62/37.91 61 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(60),flip(a)].
% 37.62/37.91 62 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 37.62/37.91 63 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(62),flip(a)].
% 37.62/37.91 64 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 37.62/37.91 65 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(64),flip(a)].
% 37.62/37.91 66 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 37.62/37.91 67 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(66),flip(a)].
% 37.62/37.91 68 forward_box(c1,multiplication(domain(c2),domain(c3))) != multiplication(forward_box(c1,domain(c2)),forward_box(c1,domain(c3))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 37.62/37.91 69 multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))))))))),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3)))))))))))))) != antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(antidomain(antidomain(c2)),antidomain(antidomain(c3)))))))))))))) # answer(goals). [copy(68),rewrite([37(3),37(6),54(9),37(22),54(24),37(37),54(39)]),flip(a)].
% 37.62/37.91 70 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 37.62/37.91 71 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 37.62/37.91 72 addition(A,addition(A,B)) = addition(A,B). [para(58(a,1),31(a,1)),rewrite([42(1),42(2),58(2,R),31(1),42(3)])].
% 37.62/37.91 73 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),59(a,1,1)),rewrite([35(2)]),flip(a)].
% 37.62/37.91 74 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(59(a,1),38(a,1))].
% 37.62/37.91 75 multiplication(A,multiplication(coantidomain(A),B)) = zero. [para(38(a,1),59(a,1,1)),rewrite([35(2)]),flip(a)].
% 37.62/37.91 76 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),61(a,2,2)),rewrite([34(3),42(3)])].
% 37.62/37.91 77 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),61(a,1,1)),rewrite([42(4)]),flip(a)].
% 37.62/37.91 78 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),61(a,1,1)),rewrite([76(4)]),flip(a)].
% 37.62/37.91 79 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(38(a,1),61(a,1,1)),rewrite([76(3),42(3)]),flip(a)].
% 37.62/37.91 80 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),63(a,1,1)),rewrite([42(4)]),flip(a)].
% 37.62/37.91 81 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(36(a,1),63(a,1,1)),rewrite([76(3),42(3)]),flip(a)].
% 37.62/37.91 82 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(38(a,1),63(a,1,1)),rewrite([76(4),42(3)]),flip(a)].
% 37.62/37.91 83 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(59(a,1),63(a,1,1)),rewrite([42(6)])].
% 37.62/37.91 90 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(38(a,1),65(a,1,1,1))].
% 37.62/37.91 91 addition(antidomain(multiplication(A,multiplication(B,C))),antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C)))))) = antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C))))). [para(59(a,1),65(a,1,1,1)),rewrite([59(7),59(13)])].
% 37.62/37.91 95 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),67(a,1,1,1))].
% 37.62/37.91 98 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(59(a,1),67(a,1,1,1))].
% 37.62/37.91 99 addition(zero,antidomain(zero)) = one. [para(70(a,1),44(a,1,1)),rewrite([70(3)])].
% 37.62/37.91 100 addition(zero,coantidomain(zero)) = one. [para(71(a,1),46(a,1,1)),rewrite([71(3)])].
% 37.62/37.91 103 multiplication(A,antidomain(zero)) = A. [para(99(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 37.62/37.91 107 multiplication(A,coantidomain(zero)) = A. [para(100(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 37.62/37.91 109 addition(one,antidomain(A)) = one. [para(44(a,1),72(a,1,2)),rewrite([42(3),44(7)])].
% 37.62/37.91 110 addition(one,coantidomain(A)) = one. [para(46(a,1),72(a,1,2)),rewrite([42(3),46(7)])].
% 37.62/37.91 111 antidomain(zero) = one. [para(103(a,1),33(a,1)),flip(a)].
% 37.62/37.91 112 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(90),rewrite([111(2),109(7)]),flip(a)].
% 37.62/37.91 114 coantidomain(zero) = one. [para(107(a,1),33(a,1)),flip(a)].
% 37.62/37.91 116 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(95),rewrite([114(2),110(7)]),flip(a)].
% 37.62/37.91 117 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(59(a,1),73(a,1,2))].
% 37.62/37.91 120 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(73(a,1),65(a,1,1,1)),rewrite([111(2),109(8)]),flip(a)].
% 37.62/37.91 123 addition(A,multiplication(antidomain(B),A)) = A. [para(109(a,1),63(a,2,1)),rewrite([33(2),33(5)])].
% 37.62/37.91 124 addition(A,multiplication(A,coantidomain(B))) = A. [para(110(a,1),61(a,2,2)),rewrite([32(2),32(5)])].
% 37.62/37.91 125 addition(A,multiplication(coantidomain(B),A)) = A. [para(110(a,1),63(a,2,1)),rewrite([33(2),33(5)])].
% 37.62/37.91 127 multiplication(A,addition(B,multiplication(coantidomain(A),C))) = multiplication(A,B). [para(75(a,1),61(a,1,1)),rewrite([76(3),42(4)]),flip(a)].
% 37.62/37.91 129 antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))) = one. [para(75(a,1),65(a,1,1,1)),rewrite([111(2),109(8)]),flip(a)].
% 37.62/37.91 141 addition(A,addition(B,multiplication(A,coantidomain(C)))) = addition(A,B). [para(124(a,1),58(a,2,2)),rewrite([42(3),42(5)])].
% 37.62/37.91 147 multiplication(addition(A,multiplication(A,B)),C) = multiplication(A,multiplication(addition(B,one),C)). [para(77(a,1),59(a,1,1))].
% 37.62/37.91 149 addition(addition(A,multiplication(A,B)),multiplication(A,C)) = multiplication(A,addition(B,addition(C,one))). [para(77(a,1),61(a,1,1)),rewrite([42(7),58(7,R),42(6)])].
% 37.62/37.91 151 addition(addition(A,multiplication(A,B)),multiplication(C,addition(B,one))) = multiplication(addition(A,C),addition(B,one)). [para(77(a,1),63(a,1,1))].
% 37.62/37.91 155 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,antidomain(antidomain(addition(B,one)))))) = antidomain(multiplication(A,antidomain(antidomain(addition(B,one))))). [para(77(a,1),65(a,1,1,1))].
% 37.62/37.91 159 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(112(a,1),36(a,1,1)),rewrite([33(6)])].
% 37.62/37.91 164 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(159(a,1),61(a,1,1)),rewrite([76(3),42(5)]),flip(a)].
% 37.62/37.91 170 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),78(a,1,2)),rewrite([32(4)]),flip(a)].
% 37.62/37.91 173 addition(multiplication(antidomain(A),B),multiplication(C,addition(A,B))) = multiplication(addition(C,antidomain(A)),addition(A,B)). [para(78(a,1),63(a,1,1)),rewrite([42(7)])].
% 37.62/37.91 174 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(63(a,1),78(a,1,2))].
% 37.62/37.91 178 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(123(a,1),78(a,1,2)),rewrite([36(2)]),flip(a)].
% 37.62/37.91 179 multiplication(antidomain(A),multiplication(coantidomain(B),A)) = zero. [para(125(a,1),78(a,1,2)),rewrite([36(2)]),flip(a)].
% 37.62/37.91 191 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(46(a,1),79(a,1,2)),rewrite([32(3)]),flip(a)].
% 37.62/37.91 194 multiplication(A,addition(B,addition(C,coantidomain(A)))) = multiplication(A,addition(B,C)). [para(79(a,1),61(a,1,1)),rewrite([61(3),42(5),58(5,R),42(4)]),flip(a)].
% 37.62/37.91 198 multiplication(coantidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(67(a,1),79(a,1,2)),rewrite([38(8),59(7)]),flip(a)].
% 37.62/37.91 200 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(191(a,1),61(a,1,1)),rewrite([77(4,R),42(7)]),flip(a)].
% 37.62/37.91 205 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(116(a,1),38(a,1,2)),rewrite([32(6)])].
% 37.62/37.91 209 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(205(a,1),63(a,1,1)),rewrite([76(3),42(5)]),flip(a)].
% 37.62/37.91 213 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(178(a,1),63(a,1,1)),rewrite([76(5),42(5)]),flip(a)].
% 37.62/37.91 216 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(78(a,1),178(a,1,2))].
% 37.62/37.91 229 addition(coantidomain(addition(A,multiplication(B,A))),coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A))) = coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A)). [para(80(a,1),67(a,1,1,1))].
% 37.62/37.91 239 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(79(a,1),80(a,2,2)),rewrite([42(9),58(9),42(8),58(9,R),42(8)])].
% 37.62/37.91 242 multiplication(addition(A,antidomain(B)),multiplication(coantidomain(C),B)) = multiplication(A,multiplication(coantidomain(C),B)). [para(179(a,1),63(a,1,1)),rewrite([76(5),42(5)]),flip(a)].
% 37.62/37.91 256 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(44(a,1),81(a,1,1)),rewrite([33(3)]),flip(a)].
% 37.62/37.91 258 multiplication(addition(A,addition(B,antidomain(C))),C) = multiplication(addition(A,B),C). [para(81(a,1),63(a,1,1)),rewrite([63(3),42(5),58(5,R),42(4)]),flip(a)].
% 37.62/37.91 260 multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = zero. [para(65(a,1),81(a,1,1)),rewrite([36(8)]),flip(a)].
% 37.62/37.91 263 multiplication(addition(A,antidomain(B)),addition(B,one)) = addition(A,addition(antidomain(B),multiplication(A,B))). [para(81(a,1),77(a,2,2)),rewrite([42(9),58(9),42(8),58(9,R),42(8)])].
% 37.62/37.91 264 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),82(a,1,1))].
% 37.62/37.91 265 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),82(a,1,1)),rewrite([33(5)]),flip(a)].
% 37.62/37.91 266 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),82(a,1,1)),rewrite([33(5)]),flip(a)].
% 37.62/37.91 270 multiplication(A,multiplication(addition(B,C),coantidomain(multiplication(A,C)))) = multiplication(A,multiplication(B,coantidomain(multiplication(A,C)))). [para(61(a,1),82(a,1,1)),rewrite([59(5),59(9)])].
% 37.62/37.91 275 multiplication(A,coantidomain(addition(A,B))) = zero. [para(72(a,1),82(a,1,1)),rewrite([38(4)]),flip(a)].
% 37.62/37.91 279 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(256(a,1),59(a,1,1)),flip(a)].
% 37.62/37.91 281 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(256(a,1),63(a,1,1)),rewrite([80(4,R),42(6)]),flip(a)].
% 37.62/37.91 285 coantidomain(addition(A,one)) = zero. [para(275(a,1),33(a,1)),rewrite([42(3)]),flip(a)].
% 37.62/37.91 295 coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B)))) = one. [para(275(a,1),67(a,1,1,1)),rewrite([114(2),110(8)]),flip(a)].
% 37.62/37.91 297 multiplication(A,coantidomain(multiplication(A,addition(B,one)))) = zero. [para(77(a,2),275(a,1,2,1))].
% 37.62/37.91 302 addition(coantidomain(A),coantidomain(addition(A,multiplication(B,A)))) = coantidomain(A). [back_rewrite(229),rewrite([285(6),114(5),33(5),42(5),285(8),114(7),33(7)])].
% 37.62/37.91 336 multiplication(addition(A,multiplication(B,coantidomain(C))),coantidomain(C)) = multiplication(addition(B,A),coantidomain(C)). [para(191(a,1),83(a,1,1,2)),rewrite([63(5)]),flip(a)].
% 37.62/37.91 440 antidomain(addition(A,one)) = zero. [para(36(a,1),297(a,1,2,1)),rewrite([114(5),32(5)])].
% 37.62/37.91 450 addition(antidomain(A),antidomain(addition(A,multiplication(A,B)))) = antidomain(A). [back_rewrite(155),rewrite([440(6),111(5),32(5),42(5),440(8),111(7),32(7)])].
% 37.62/37.91 451 addition(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(A). [para(440(a,1),65(a,1,2,1,2,1)),rewrite([111(6),32(6),42(6),440(9),111(8),32(8)])].
% 37.62/37.91 482 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,addition(B,multiplication(B,C))))) = antidomain(multiplication(A,B)). [para(77(a,1),91(a,1,1,1,2)),rewrite([440(7),111(6),32(6),42(7),440(10),111(9),32(9)])].
% 37.62/37.91 517 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(120(a,1),36(a,1,1)),rewrite([33(7)])].
% 37.62/37.91 525 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(517(a,1),61(a,1,1)),rewrite([76(4),42(7)]),flip(a)].
% 37.62/37.91 534 multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))) = zero. [para(129(a,1),36(a,1,1)),rewrite([33(7)])].
% 37.62/37.91 542 multiplication(A,addition(B,antidomain(antidomain(multiplication(coantidomain(A),C))))) = multiplication(A,B). [para(534(a,1),61(a,1,1)),rewrite([76(3),42(6)]),flip(a)].
% 37.62/37.91 543 multiplication(addition(A,B),antidomain(antidomain(multiplication(coantidomain(B),C)))) = multiplication(A,antidomain(antidomain(multiplication(coantidomain(B),C)))). [para(534(a,1),63(a,1,1)),rewrite([76(7),42(6)]),flip(a)].
% 37.62/37.91 567 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B)) = one. [para(36(a,1),98(a,1,1,1,2)),rewrite([34(2),114(2),110(8)]),flip(a)].
% 37.62/37.91 568 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(36(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 37.62/37.91 569 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one. [para(38(a,1),98(a,1,1,1,2)),rewrite([34(2),114(2),110(8)]),flip(a)].
% 37.62/37.91 589 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [para(178(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 37.62/37.91 594 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [para(179(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 37.62/37.91 656 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(170(a,1),123(a,1,2)),rewrite([42(5)])].
% 37.62/37.91 754 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(42(a,1),216(a,1,1,1))].
% 37.62/37.91 853 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),264(a,1,1)),rewrite([33(4)]),flip(a)].
% 37.62/37.91 861 multiplication(A,multiplication(coantidomain(B),coantidomain(A))) = zero. [para(124(a,1),264(a,1,1)),rewrite([38(2),59(5)]),flip(a)].
% 37.62/37.91 890 multiplication(A,addition(B,addition(C,multiplication(coantidomain(A),D)))) = multiplication(A,addition(B,C)). [para(127(a,1),61(a,1,1)),rewrite([61(3),42(6),58(6,R),42(5)]),flip(a)].
% 37.62/37.91 930 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [para(861(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 37.62/37.91 1036 multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [para(295(a,1),38(a,1,2)),rewrite([32(7)])].
% 37.62/37.91 1099 multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [para(567(a,1),38(a,1,2)),rewrite([32(7)])].
% 37.62/37.91 1114 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [para(569(a,1),38(a,1,2)),rewrite([32(7)])].
% 37.62/37.91 1186 multiplication(antidomain(addition(A,B)),A) = zero. [para(72(a,1),754(a,1,1,1)),rewrite([279(6)])].
% 37.62/37.91 1425 addition(one,addition(coantidomain(A),coantidomain(B))) = one. [para(110(a,1),141(a,2)),rewrite([33(5)])].
% 37.62/37.91 1442 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(853(a,1),124(a,1,2))].
% 37.62/37.91 2298 addition(A,addition(B,multiplication(addition(A,B),C))) = multiplication(addition(A,B),addition(C,one)). [para(77(a,1),151(a,1,2)),rewrite([58(5,R),58(4,R),63(3),58(4,R),42(3)])].
% 37.62/37.91 2387 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),164(a,1,2)),rewrite([32(2)]),flip(a)].
% 37.62/37.91 2409 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2387(a,1),59(a,1,1)),flip(a)].
% 37.62/37.91 2410 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2387(a,1),59(a,1)),flip(a)].
% 37.62/37.91 2417 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2387(a,1),125(a,1,2)),rewrite([42(5)])].
% 37.62/37.91 2516 multiplication(A,coantidomain(coantidomain(A))) = A. [para(170(a,1),2409(a,1,2)),rewrite([2387(3)]),flip(a)].
% 37.62/37.91 2549 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(266),rewrite([2516(5)]),flip(a)].
% 37.62/37.91 2578 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2549(a,1),656(a,1,2)),rewrite([42(5),2417(5),2549(6)])].
% 37.62/37.91 2679 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2578(a,1),44(a,1,1)),rewrite([2578(4)])].
% 37.62/37.91 2685 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2578(a,1),853(a,1,1,1)),rewrite([2578(5),170(5),2578(5)]),flip(a)].
% 37.62/37.91 2687 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2578(a,1),853(a,2,1)),rewrite([2685(2),2685(6),853(9),2685(6)])].
% 37.62/37.91 2694 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2549(a,1),2578(a,1,1,1)),rewrite([2685(2),2685(5)]),flip(a)].
% 37.62/37.91 2695 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2549(a,1),2578(a,2)),rewrite([2685(2),2694(3),2687(4)])].
% 37.62/37.91 2926 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [back_rewrite(1114),rewrite([2685(3)])].
% 37.62/37.91 2939 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [back_rewrite(1099),rewrite([2685(4)])].
% 37.62/37.91 2959 multiplication(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [back_rewrite(1036),rewrite([2685(2)])].
% 37.62/37.91 2964 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [back_rewrite(930),rewrite([2685(4)])].
% 37.62/37.91 3009 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [back_rewrite(594),rewrite([2685(5)])].
% 37.62/37.91 3014 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [back_rewrite(589),rewrite([2685(5)])].
% 37.62/37.91 3025 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(568),rewrite([2685(5)])].
% 37.62/37.91 3044 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(209),rewrite([2685(3)])].
% 37.62/37.91 3048 multiplication(antidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [back_rewrite(198),rewrite([2685(2)])].
% 37.62/37.91 3370 multiplication(A,multiplication(addition(coantidomain(A),antidomain(B)),addition(B,C))) = multiplication(A,multiplication(antidomain(B),C)). [para(173(a,1),127(a,1,2))].
% 37.62/37.91 3463 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(44(a,1),174(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 37.62/37.91 3935 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),antidomain(antidomain(B))) = zero. [para(2939(a,1),260(a,1,1,1)),rewrite([111(2),33(9)])].
% 37.62/37.91 3957 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(265(a,1),124(a,1,2))].
% 37.62/37.91 4464 multiplication(A,addition(coantidomain(A),coantidomain(B))) = multiplication(A,coantidomain(B)). [para(302(a,1),194(a,2,2)),rewrite([42(6),58(7,R),42(6),302(6)])].
% 37.62/37.91 4539 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,multiplication(addition(B,one),addition(C,one))))) = antidomain(addition(A,multiplication(A,B))). [para(147(a,1),450(a,1,2,1,2)),rewrite([149(10),42(8),2298(9)])].
% 37.62/37.91 4930 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(1442(a,1),200(a,1,2)),rewrite([42(11),109(11),32(9)])].
% 37.62/37.91 4935 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3957(a,1),200(a,1,2)),rewrite([42(11),109(11),32(10)])].
% 37.62/37.91 5149 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(44(a,1),213(a,1,1)),rewrite([33(5)]),flip(a)].
% 37.62/37.91 7569 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(4930(a,1),239(a,2,2,2)),rewrite([42(4),110(4),2685(6),33(8),2685(11),42(14),2679(14),42(10),109(10)])].
% 37.62/37.91 7897 multiplication(antidomain(A),multiplication(coantidomain(B),antidomain(A))) = multiplication(coantidomain(B),antidomain(A)). [para(44(a,1),242(a,1,1)),rewrite([33(5)]),flip(a)].
% 37.62/37.91 8564 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A)) = zero. [para(2964(a,1),38(a,1,2)),rewrite([32(8)])].
% 37.62/37.91 8579 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(addition(A,B))) = zero. [para(82(a,1),8564(a,1,1,1,1))].
% 37.62/37.91 8722 multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A) = zero. [para(3009(a,1),38(a,1,2)),rewrite([32(8)])].
% 37.62/37.91 8963 multiplication(A,multiplication(antidomain(antidomain(B)),coantidomain(multiplication(A,antidomain(coantidomain(antidomain(B))))))) = multiplication(A,coantidomain(multiplication(A,antidomain(coantidomain(antidomain(B)))))). [para(7569(a,1),270(a,1,2,1)),rewrite([33(7)]),flip(a)].
% 37.62/37.91 9110 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = zero. [para(3014(a,1),38(a,1,2)),rewrite([32(8)])].
% 37.62/37.91 9143 multiplication(coantidomain(antidomain(A)),A) = A. [para(2679(a,1),3044(a,1,1)),rewrite([33(2)]),flip(a)].
% 37.62/37.91 9153 multiplication(antidomain(antidomain(A)),A) = A. [para(7569(a,1),3044(a,1,1)),rewrite([33(2)]),flip(a)].
% 37.62/37.91 9157 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(4935),rewrite([9143(5)]),flip(a)].
% 37.62/37.91 9251 multiplication(antidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B). [para(9153(a,1),59(a,1,1)),flip(a)].
% 37.62/37.91 9260 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(9153(a,1),117(a,1,2,2))].
% 37.62/37.91 9291 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9157(a,1),2685(a,1,1)),rewrite([9157(5)])].
% 37.62/37.91 9292 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9157(a,1),2685(a,2,1)),rewrite([9291(3),9291(4)])].
% 37.62/37.91 9293 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9157(a,1),2695(a,2)),rewrite([9291(3),9292(4)])].
% 37.62/37.91 9341 multiplication(A,multiplication(antidomain(antidomain(B)),coantidomain(multiplication(A,antidomain(B))))) = multiplication(A,coantidomain(multiplication(A,antidomain(B)))). [back_rewrite(8963),rewrite([9291(4),9293(5),9291(9),9293(10)])].
% 37.62/37.91 9482 antidomain(multiplication(c1,antidomain(multiplication(antidomain(antidomain(c2)),antidomain(antidomain(c3)))))) != multiplication(antidomain(multiplication(c1,antidomain(c2))),antidomain(multiplication(c1,antidomain(c3)))) # answer(goals). [back_rewrite(69),rewrite([9293(5),9293(5),9293(5),9293(7),9293(7),9293(10),9293(10),9293(10),9293(12),9293(12),9293(22),9293(22),9293(24),9293(24)]),flip(a)].
% 37.62/37.91 9547 multiplication(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(multiplication(A,addition(B,one))). [para(451(a,1),281(a,1,1)),rewrite([42(9),109(9),33(12)])].
% 37.62/37.91 13000 multiplication(addition(coantidomain(A),coantidomain(B)),coantidomain(A)) = coantidomain(A). [para(125(a,1),336(a,1,1)),rewrite([191(3),42(4)]),flip(a)].
% 37.62/37.91 13039 addition(coantidomain(A),addition(coantidomain(B),antidomain(coantidomain(A)))) = one. [para(13000(a,1),263(a,2,2,2)),rewrite([42(6),58(6,R),42(9),110(9),32(8),42(13),2679(13),42(11),1425(11)])].
% 37.62/37.91 13046 addition(antidomain(A),addition(antidomain(antidomain(A)),coantidomain(B))) = one. [para(9291(a,1),13039(a,1,1)),rewrite([9291(5),9293(6),58(6)])].
% 37.62/37.91 13058 addition(antidomain(A),addition(antidomain(antidomain(A)),antidomain(coantidomain(B)))) = one. [para(2685(a,1),13046(a,1,2,2))].
% 37.62/37.91 13121 addition(antidomain(A),addition(antidomain(B),antidomain(antidomain(A)))) = one. [para(9291(a,1),13058(a,1,2,2,1)),rewrite([9293(6),42(5)])].
% 37.62/37.91 13127 multiplication(addition(antidomain(A),antidomain(B)),antidomain(A)) = antidomain(A). [para(13121(a,1),258(a,1,1)),rewrite([33(3)]),flip(a)].
% 37.62/37.91 13143 multiplication(antidomain(antidomain(addition(antidomain(A),antidomain(B)))),antidomain(A)) = antidomain(A). [para(13127(a,1),9251(a,1,2)),rewrite([13127(12)])].
% 37.62/37.91 13409 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero. [para(3025(a,1),38(a,1,2)),rewrite([32(8)])].
% 37.62/37.91 15435 addition(antidomain(antidomain(A)),antidomain(antidomain(addition(antidomain(A),antidomain(B))))) = one. [para(13143(a,1),263(a,2,2,2)),rewrite([42(8),42(11),109(11),32(10),42(17),44(17),42(15),109(15)])].
% 37.62/37.91 16484 multiplication(antidomain(A),antidomain(antidomain(addition(antidomain(A),antidomain(B))))) = antidomain(A). [para(15435(a,1),78(a,1,2)),rewrite([9293(3),32(3),9293(4)]),flip(a)].
% 37.62/37.91 16775 antidomain(multiplication(A,addition(B,one))) = antidomain(addition(A,multiplication(A,B))). [para(77(a,1),482(a,1,1,1)),rewrite([77(9,R),4539(11)]),flip(a)].
% 37.62/37.91 16929 multiplication(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,B)). [para(65(a,1),16484(a,1,2,1,1)),rewrite([9293(8)])].
% 37.62/37.91 17240 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(44(a,1),542(a,1,2)),rewrite([32(2)]),flip(a)].
% 37.62/37.91 17243 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(44(a,1),525(a,1,2)),rewrite([32(3)]),flip(a)].
% 37.62/37.91 17244 antidomain(multiplication(A,addition(B,one))) = antidomain(A). [back_rewrite(9547),rewrite([17243(6)]),flip(a)].
% 37.62/37.91 17248 antidomain(addition(A,multiplication(A,B))) = antidomain(A). [back_rewrite(16775),rewrite([17244(4)]),flip(a)].
% 37.62/37.91 17422 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17243(a,1),123(a,1,2)),rewrite([42(4)])].
% 37.62/37.91 17437 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(17243(a,1),239(a,2,2,2)),rewrite([42(3),109(3),9291(5),42(6),33(7),9291(9),42(11),44(11),42(9),109(9)])].
% 37.62/37.91 17444 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17243(a,1),2410(a,1,2,2,1,1)),rewrite([9291(5),9293(6),5149(6),17243(8)])].
% 37.62/37.91 17577 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17444(a,1),59(a,1,1)),flip(a)].
% 37.62/37.91 17608 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3463),rewrite([17577(7)]),flip(a)].
% 37.62/37.91 18565 multiplication(antidomain(antidomain(A)),multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(178(a,1),17608(a,1,1,1)),rewrite([111(2),33(4)]),flip(a)].
% 37.62/37.91 18570 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(1186(a,1),17608(a,1,1,1)),rewrite([111(2),33(2)]),flip(a)].
% 37.62/37.91 18578 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(2926(a,1),17608(a,1,1,1)),rewrite([111(2),33(3),2695(5)]),flip(a)].
% 37.62/37.91 18579 multiplication(coantidomain(multiplication(A,antidomain(B))),B) = B. [para(2939(a,1),17608(a,1,1,1)),rewrite([111(2),33(2),2695(5)]),flip(a)].
% 37.62/37.91 18580 multiplication(coantidomain(A),coantidomain(addition(A,B))) = coantidomain(addition(A,B)). [para(2959(a,1),17608(a,1,1,1)),rewrite([111(2),33(4),2695(5)]),flip(a)].
% 37.62/37.91 18606 multiplication(coantidomain(multiplication(antidomain(A),coantidomain(B))),A) = A. [para(8722(a,1),17608(a,1,1,1)),rewrite([111(2),33(2),2695(6)]),flip(a)].
% 37.62/37.91 18607 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A. [para(9110(a,1),17608(a,1,1,1)),rewrite([111(2),33(2),2695(6)]),flip(a)].
% 37.62/37.91 18613 multiplication(coantidomain(multiplication(A,antidomain(B))),antidomain(antidomain(B))) = antidomain(antidomain(B)). [para(3935(a,1),17608(a,1,1,1)),rewrite([111(2),33(4),2695(7)]),flip(a)].
% 37.62/37.91 18633 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(13409(a,1),17608(a,1,1,1)),rewrite([111(2),33(2),2695(6)]),flip(a)].
% 37.62/37.91 18679 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(42(a,1),18570(a,1,1,1,1))].
% 37.62/37.91 18710 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(18570(a,1),17444(a,1,1,1)),rewrite([9293(5),9293(8)])].
% 37.62/37.91 18758 addition(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = one. [para(18579(a,1),17437(a,1,2,1)),rewrite([2695(5),42(5)])].
% 37.62/37.91 18759 multiplication(antidomain(A),antidomain(coantidomain(multiplication(B,antidomain(A))))) = antidomain(coantidomain(multiplication(B,antidomain(A)))). [para(18579(a,1),17444(a,1,1,1))].
% 37.62/37.91 18879 addition(antidomain(A),antidomain(addition(B,A))) = antidomain(A). [para(18679(a,1),17422(a,1,2,1)),rewrite([9293(4),42(4),18679(8)])].
% 37.62/37.91 18898 addition(antidomain(coantidomain(A)),coantidomain(multiplication(B,A))) = one. [para(18578(a,1),263(a,2,2,2)),rewrite([42(5),42(8),110(8),32(7),42(11),2679(11),42(9),110(9)])].
% 37.62/37.91 18903 coantidomain(addition(A,coantidomain(multiplication(B,A)))) = zero. [para(18578(a,1),8579(a,1,1,1,1)),rewrite([2685(2),2695(3),42(4),18580(6)])].
% 37.62/37.91 18922 coantidomain(addition(A,coantidomain(A))) = zero. [para(33(a,1),18903(a,1,1,2,1))].
% 37.62/37.91 18968 multiplication(A,coantidomain(multiplication(addition(B,coantidomain(B)),A))) = zero. [para(18922(a,1),3048(a,1,1,1)),rewrite([111(2),33(7)])].
% 37.62/37.91 19047 multiplication(coantidomain(A),antidomain(B)) = multiplication(antidomain(B),coantidomain(A)). [para(18606(a,1),17240(a,1,2,1)),rewrite([59(5),7897(5)])].
% 37.62/37.91 19081 multiplication(antidomain(antidomain(A)),coantidomain(multiplication(B,antidomain(A)))) = antidomain(antidomain(A)). [back_rewrite(18613),rewrite([19047(6)])].
% 37.62/37.91 19138 multiplication(A,coantidomain(multiplication(A,antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [back_rewrite(9341),rewrite([19081(6)]),flip(a)].
% 37.62/37.91 19169 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(18607(a,1),17240(a,1,2,1)),rewrite([59(5),5149(5)])].
% 37.62/37.91 19172 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),antidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))). [para(18607(a,1),17243(a,1,2,1)),rewrite([19169(7)])].
% 37.62/37.91 19459 addition(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = one. [para(2695(a,1),18758(a,1,1)),rewrite([2695(4)])].
% 37.62/37.91 19484 addition(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(multiplication(antidomain(B),A)). [para(123(a,1),18879(a,1,2,1)),rewrite([42(5)])].
% 37.62/37.91 19503 multiplication(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(A). [para(18898(a,1),78(a,1,2)),rewrite([2695(3),32(3),2695(4)]),flip(a)].
% 37.62/37.91 19586 multiplication(A,coantidomain(multiplication(B,coantidomain(A)))) = A. [para(19459(a,1),4464(a,1,2)),rewrite([32(2)]),flip(a)].
% 37.62/37.91 20011 addition(antidomain(A),coantidomain(multiplication(antidomain(multiplication(B,A)),B))) = one. [para(18633(a,1),17437(a,1,2,1)),rewrite([2695(6),42(6)])].
% 37.62/37.91 20456 coantidomain(multiplication(addition(A,coantidomain(A)),B)) = coantidomain(B). [para(18968(a,1),18633(a,1,1,1,1,1)),rewrite([111(2),33(2),19503(6)]),flip(a)].
% 37.62/37.91 20519 coantidomain(multiplication(A,antidomain(antidomain(multiplication(antidomain(coantidomain(A)),B))))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [para(543(a,1),20456(a,1,1)),rewrite([2685(2),2685(9),9291(13),9293(13)])].
% 37.62/37.91 20824 multiplication(A,coantidomain(multiplication(coantidomain(A),antidomain(B)))) = A. [para(19047(a,2),19586(a,1,2,1))].
% 37.62/37.91 21000 antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))) = multiplication(antidomain(A),antidomain(B)). [para(19169(a,1),2410(a,1,2,2,1,1)),rewrite([19169(5),18759(8),19172(7)])].
% 37.62/37.91 24013 multiplication(A,addition(coantidomain(A),antidomain(B))) = multiplication(A,antidomain(B)). [para(263(a,2),890(a,1,2)),rewrite([3370(7),32(3)]),flip(a)].
% 37.62/37.91 24015 addition(coantidomain(A),antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = one. [para(74(a,1),20011(a,1,2,1,1,1)),rewrite([111(6),33(6),42(6)])].
% 37.62/37.91 26745 multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = A. [para(24015(a,1),24013(a,1,2)),rewrite([32(2)]),flip(a)].
% 37.62/37.91 26788 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [para(9260(a,1),26745(a,1,2,1,2,1)),rewrite([114(7),32(7),19169(7),16929(7)]),flip(a)].
% 37.62/37.91 26899 multiplication(antidomain(multiplication(c1,antidomain(c2))),antidomain(multiplication(c1,antidomain(c3)))) != antidomain(multiplication(c1,antidomain(multiplication(antidomain(antidomain(c2)),c3)))) # answer(goals). [back_rewrite(9482),rewrite([26788(9)]),flip(a)].
% 37.62/37.91 28372 antidomain(addition(antidomain(antidomain(A)),multiplication(antidomain(B),A))) = antidomain(A). [para(18565(a,1),17248(a,1,1,2)),rewrite([9293(9)])].
% 37.62/37.91 28391 antidomain(antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(20824(a,1),28372(a,1,1,2)),rewrite([9291(2),19169(4),21000(6),26788(5),42(5),19484(5),9291(6),19169(8),21000(10)])].
% 37.62/37.91 28395 coantidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [back_rewrite(20519),rewrite([28391(5),2409(6)])].
% 37.62/37.91 28947 multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B))) = multiplication(A,antidomain(B)). [para(9293(a,1),19138(a,2,2)),rewrite([28395(4)])].
% 37.62/37.91 32082 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(B)). [para(28947(a,1),78(a,2)),rewrite([9291(3),9293(4),78(6)])].
% 37.62/37.91 32094 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)). [para(18710(a,1),28947(a,2)),rewrite([9291(3),9293(4),78(4),32082(5)])].
% 37.62/37.91 32183 antidomain(multiplication(c1,antidomain(multiplication(antidomain(antidomain(c2)),c3)))) != antidomain(multiplication(c1,addition(antidomain(c2),antidomain(c3)))) # answer(goals). [back_rewrite(26899),rewrite([32094(11),61(9)]),flip(a)].
% 37.62/37.91 32352 antidomain(antidomain(addition(A,antidomain(B)))) = antidomain(multiplication(antidomain(A),B)). [para(32094(a,1),26788(a,1,1))].
% 37.62/37.91 33405 antidomain(multiplication(A,antidomain(multiplication(antidomain(B),C)))) = antidomain(multiplication(A,addition(B,antidomain(C)))). [para(32352(a,1),26788(a,1,1,2))].
% 37.62/37.91 33406 $F # answer(goals). [resolve(33405,a,32183,a)].
% 37.62/37.91
% 37.62/37.91 % SZS output end Refutation
% 37.62/37.91 ============================== end of proof ==========================
% 37.62/37.91
% 37.62/37.91 ============================== STATISTICS ============================
% 37.62/37.91
% 37.62/37.91 Given=2154. Generated=2283802. Kept=33362. proofs=1.
% 37.62/37.91 Usable=1106. Sos=7183. Demods=8111. Limbo=9, Disabled=25091. Hints=0.
% 37.62/37.91 Megabytes=25.32.
% 37.62/37.91 User_CPU=35.60, System_CPU=1.26, Wall_clock=36.
% 37.62/37.91
% 37.62/37.91 ============================== end of statistics =====================
% 37.62/37.91
% 37.62/37.91 ============================== end of search =========================
% 37.62/37.91
% 37.62/37.91 THEOREM PROVED
% 37.62/37.91 % SZS status Theorem
% 37.62/37.91
% 37.62/37.91 Exiting with 1 proof.
% 37.62/37.91
% 37.62/37.91 Process 10891 exit (max_proofs) Thu Jun 16 11:28:03 2022
% 37.62/37.91 Prover9 interrupted
%------------------------------------------------------------------------------