TSTP Solution File: KLE099+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE099+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 02:22:13 EDT 2022
% Result : Theorem 2.71s 2.98s
% Output : Refutation 2.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : KLE099+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jun 16 15:23:20 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.69/0.99 ============================== Prover9 ===============================
% 0.69/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.69/0.99 Process 10558 was started by sandbox on n014.cluster.edu,
% 0.69/0.99 Thu Jun 16 15:23:21 2022
% 0.69/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10214_n014.cluster.edu".
% 0.69/0.99 ============================== end of head ===========================
% 0.69/0.99
% 0.69/0.99 ============================== INPUT =================================
% 0.69/0.99
% 0.69/0.99 % Reading from file /tmp/Prover9_10214_n014.cluster.edu
% 0.69/0.99
% 0.69/0.99 set(prolog_style_variables).
% 0.69/0.99 set(auto2).
% 0.69/0.99 % set(auto2) -> set(auto).
% 0.69/0.99 % set(auto) -> set(auto_inference).
% 0.69/0.99 % set(auto) -> set(auto_setup).
% 0.69/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.69/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.69/0.99 % set(auto) -> set(auto_limits).
% 0.69/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.69/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.69/0.99 % set(auto) -> set(auto_denials).
% 0.69/0.99 % set(auto) -> set(auto_process).
% 0.69/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.69/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.69/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.69/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.69/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.69/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.69/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.69/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.69/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.69/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.69/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.69/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.69/0.99 % set(auto2) -> assign(stats, some).
% 0.69/0.99 % set(auto2) -> clear(echo_input).
% 0.69/0.99 % set(auto2) -> set(quiet).
% 0.69/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.69/0.99 % set(auto2) -> clear(print_given).
% 0.69/0.99 assign(lrs_ticks,-1).
% 0.69/0.99 assign(sos_limit,10000).
% 0.69/0.99 assign(order,kbo).
% 0.69/0.99 set(lex_order_vars).
% 0.69/0.99 clear(print_given).
% 0.69/0.99
% 0.69/0.99 % formulas(sos). % not echoed (27 formulas)
% 0.69/0.99
% 0.69/0.99 ============================== end of input ==========================
% 0.69/0.99
% 0.69/0.99 % From the command line: assign(max_seconds, 300).
% 0.69/0.99
% 0.69/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.69/0.99
% 0.69/0.99 % Formulas that are not ordinary clauses:
% 0.69/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 0.69/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 0.69/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 0.69/0.99 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].
% 0.69/0.99 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 2.71/2.98 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 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].
% 2.71/2.98 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 27 -(all X0 all X1 all X2 (addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) -> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.71/2.98
% 2.71/2.98 ============================== end of process non-clausal formulas ===
% 2.71/2.98
% 2.71/2.98 ============================== PROCESS INITIAL CLAUSES ===============
% 2.71/2.98
% 2.71/2.98 ============================== PREDICATE ELIMINATION =================
% 2.71/2.98 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.71/2.98 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.71/2.98
% 2.71/2.98 ============================== end predicate elimination =============
% 2.71/2.98
% 2.71/2.98 Auto_denials:
% 2.71/2.98 % copying label goals to answer in negative clause
% 2.71/2.98
% 2.71/2.98 Term ordering decisions:
% 2.71/2.98 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.
% 2.71/2.98
% 2.71/2.98 ============================== end of process initial clauses ========
% 2.71/2.98
% 2.71/2.98 ============================== CLAUSES FOR SEARCH ====================
% 2.71/2.98
% 2.71/2.98 ============================== end of clauses for search =============
% 2.71/2.98
% 2.71/2.98 ============================== SEARCH ================================
% 2.71/2.98
% 2.71/2.98 % Starting search at 0.01 seconds.
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=41.000, iters=3380
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=39.000, iters=3403
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=36.000, iters=3366
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=31.000, iters=3336
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=30.000, iters=3345
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=29.000, iters=3349
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=28.000, iters=3335
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=27.000, iters=3387
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=26.000, iters=3333
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=25.000, iters=3337
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=24.000, iters=3374
% 2.71/2.98
% 2.71/2.98 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.76 sec).
% 2.71/2.98
% 2.71/2.98 Low Water (keep): wt=23.000, iters=3337
% 2.71/2.98
% 2.71/2.98 ============================== PROOF =================================
% 2.71/2.98 % SZS status Theorem
% 2.71/2.98 % SZS output start Refutation
% 2.71/2.98
% 2.71/2.98 % Proof 1 at 1.92 (+ 0.08) seconds: goals.
% 2.71/2.98 % Length of proof is 127.
% 2.71/2.98 % Level of proof is 23.
% 2.71/2.98 % Maximum clause weight is 18.000.
% 2.71/2.98 % Given clauses 524.
% 2.71/2.98
% 2.71/2.98 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 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].
% 2.71/2.98 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 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].
% 2.71/2.98 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 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].
% 2.71/2.98 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].
% 2.71/2.98 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 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].
% 2.71/2.98 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 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].
% 2.71/2.98 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 2.71/2.98 27 -(all X0 all X1 all X2 (addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) -> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.71/2.98 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.71/2.98 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.71/2.98 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.71/2.98 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.71/2.98 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.71/2.98 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 2.71/2.98 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 2.71/2.98 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 2.71/2.98 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 2.71/2.98 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.71/2.98 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 2.71/2.98 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 2.71/2.98 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 2.71/2.98 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 2.71/2.98 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 2.71/2.98 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])].
% 2.71/2.98 57 domain(c3) = addition(forward_diamond(c1,domain(c2)),domain(c3)) # label(goals) # label(negated_conjecture). [clausify(27)].
% 2.71/2.98 58 addition(antidomain(antidomain(c3)),antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))) = antidomain(antidomain(c3)). [copy(57),rewrite([37(2),37(6),50(8),37(14),42(16)]),flip(a)].
% 2.71/2.98 59 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 2.71/2.98 60 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(59),rewrite([42(2)]),flip(a)].
% 2.71/2.98 61 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.71/2.98 62 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.71/2.98 63 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(62),flip(a)].
% 2.71/2.98 64 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.71/2.98 65 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(64),flip(a)].
% 2.71/2.98 66 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 2.71/2.98 67 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(66),flip(a)].
% 2.71/2.98 68 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 2.71/2.98 69 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(68),flip(a)].
% 2.71/2.98 70 multiplication(antidomain(c3),multiplication(c1,domain(c2))) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 2.71/2.98 71 multiplication(antidomain(c3),multiplication(c1,antidomain(antidomain(c2)))) != zero # answer(goals). [copy(70),rewrite([37(5)])].
% 2.71/2.98 72 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 2.71/2.98 73 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 2.71/2.98 74 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)])].
% 2.71/2.98 75 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),61(a,1,1)),rewrite([35(2)]),flip(a)].
% 2.71/2.98 78 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),63(a,2,2)),rewrite([34(3),42(3)])].
% 2.71/2.98 79 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),63(a,1,1)),rewrite([42(4)]),flip(a)].
% 2.71/2.98 80 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),63(a,1,1)),rewrite([78(4)]),flip(a)].
% 2.71/2.98 81 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(38(a,1),63(a,1,1)),rewrite([78(3),42(3)]),flip(a)].
% 2.71/2.98 82 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),65(a,1,1)),rewrite([42(4)]),flip(a)].
% 2.71/2.98 83 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(36(a,1),65(a,1,1)),rewrite([78(3),42(3)]),flip(a)].
% 2.71/2.98 84 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(38(a,1),65(a,1,1)),rewrite([78(4),42(3)]),flip(a)].
% 2.71/2.98 92 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(38(a,1),67(a,1,1,1))].
% 2.71/2.98 97 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),69(a,1,1,1))].
% 2.71/2.98 101 addition(zero,antidomain(zero)) = one. [para(72(a,1),44(a,1,1)),rewrite([72(3)])].
% 2.71/2.98 102 addition(zero,coantidomain(zero)) = one. [para(73(a,1),46(a,1,1)),rewrite([73(3)])].
% 2.71/2.98 105 multiplication(A,antidomain(zero)) = A. [para(101(a,1),63(a,2,2)),rewrite([34(2),78(5),32(5)])].
% 2.71/2.98 109 multiplication(A,coantidomain(zero)) = A. [para(102(a,1),63(a,2,2)),rewrite([34(2),78(5),32(5)])].
% 2.71/2.98 111 addition(one,antidomain(A)) = one. [para(44(a,1),74(a,1,2)),rewrite([42(3),44(7)])].
% 2.71/2.98 112 addition(one,coantidomain(A)) = one. [para(46(a,1),74(a,1,2)),rewrite([42(3),46(7)])].
% 2.71/2.98 113 antidomain(zero) = one. [para(105(a,1),33(a,1)),flip(a)].
% 2.71/2.98 114 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(92),rewrite([113(2),111(7)]),flip(a)].
% 2.71/2.98 116 coantidomain(zero) = one. [para(109(a,1),33(a,1)),flip(a)].
% 2.71/2.98 118 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(97),rewrite([116(2),112(7)]),flip(a)].
% 2.71/2.98 119 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(61(a,1),75(a,1,2))].
% 2.71/2.98 125 addition(A,multiplication(antidomain(B),A)) = A. [para(111(a,1),65(a,2,1)),rewrite([33(2),33(5)])].
% 2.71/2.98 126 addition(A,multiplication(A,coantidomain(B))) = A. [para(112(a,1),63(a,2,2)),rewrite([32(2),32(5)])].
% 2.71/2.98 127 addition(A,multiplication(coantidomain(B),A)) = A. [para(112(a,1),65(a,2,1)),rewrite([33(2),33(5)])].
% 2.71/2.98 161 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(114(a,1),36(a,1,1)),rewrite([33(6)])].
% 2.71/2.98 166 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(161(a,1),63(a,1,1)),rewrite([78(3),42(5)]),flip(a)].
% 2.71/2.98 172 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),80(a,1,2)),rewrite([32(4)]),flip(a)].
% 2.71/2.98 181 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(125(a,1),80(a,1,2)),rewrite([36(2)]),flip(a)].
% 2.71/2.98 194 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(46(a,1),81(a,1,2)),rewrite([32(3)]),flip(a)].
% 2.71/2.98 203 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(194(a,1),63(a,1,1)),rewrite([79(4,R),42(7)]),flip(a)].
% 2.71/2.98 208 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(118(a,1),38(a,1,2)),rewrite([32(6)])].
% 2.71/2.98 212 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(208(a,1),65(a,1,1)),rewrite([78(3),42(5)]),flip(a)].
% 2.71/2.98 219 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(80(a,1),181(a,1,2))].
% 2.71/2.98 242 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(81(a,1),82(a,2,2)),rewrite([42(9),60(9),42(8),60(9,R),42(8)])].
% 2.71/2.98 259 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(44(a,1),83(a,1,1)),rewrite([33(3)]),flip(a)].
% 2.71/2.98 267 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),84(a,1,1))].
% 2.71/2.98 268 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),84(a,1,1)),rewrite([33(5)]),flip(a)].
% 2.71/2.98 269 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),84(a,1,1)),rewrite([33(5)]),flip(a)].
% 2.71/2.98 282 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(259(a,1),61(a,1,1)),flip(a)].
% 2.71/2.98 660 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(172(a,1),125(a,1,2)),rewrite([42(5)])].
% 2.71/2.98 758 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(42(a,1),219(a,1,1,1))].
% 2.71/2.98 857 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),267(a,1,1)),rewrite([33(4)]),flip(a)].
% 2.71/2.98 1190 multiplication(antidomain(addition(A,B)),A) = zero. [para(74(a,1),758(a,1,1,1)),rewrite([282(6)])].
% 2.71/2.98 1210 multiplication(antidomain(addition(A,B)),multiplication(A,C)) = zero. [para(1190(a,1),61(a,1,1)),rewrite([35(2)]),flip(a)].
% 2.71/2.98 1448 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(857(a,1),126(a,1,2))].
% 2.71/2.98 1461 multiplication(antidomain(addition(A,antidomain(antidomain(B)))),coantidomain(antidomain(B))) = zero. [para(857(a,1),1210(a,1,2)),rewrite([42(3)])].
% 2.71/2.98 2397 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),166(a,1,2)),rewrite([32(2)]),flip(a)].
% 2.71/2.98 2419 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2397(a,1),61(a,1,1)),flip(a)].
% 2.71/2.98 2427 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2397(a,1),127(a,1,2)),rewrite([42(5)])].
% 2.71/2.98 2526 multiplication(A,coantidomain(coantidomain(A))) = A. [para(172(a,1),2419(a,1,2)),rewrite([2397(3)]),flip(a)].
% 2.71/2.98 2559 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(269),rewrite([2526(5)]),flip(a)].
% 2.71/2.98 2588 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2559(a,1),660(a,1,2)),rewrite([42(5),2427(5),2559(6)])].
% 2.71/2.98 2689 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2588(a,1),44(a,1,1)),rewrite([2588(4)])].
% 2.71/2.98 2695 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2588(a,1),857(a,1,1,1)),rewrite([2588(5),172(5),2588(5)]),flip(a)].
% 2.71/2.98 2697 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2588(a,1),857(a,2,1)),rewrite([2695(2),2695(6),857(9),2695(6)])].
% 2.71/2.98 2704 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2559(a,1),2588(a,1,1,1)),rewrite([2695(2),2695(5)]),flip(a)].
% 2.71/2.98 2705 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2559(a,1),2588(a,2)),rewrite([2695(2),2704(3),2697(4)])].
% 2.71/2.98 3055 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(212),rewrite([2695(3)])].
% 2.71/2.98 3958 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(268(a,1),126(a,1,2))].
% 2.71/2.98 5022 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(1448(a,1),203(a,1,2)),rewrite([42(11),111(11),32(9)])].
% 2.71/2.98 5027 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3958(a,1),203(a,1,2)),rewrite([42(11),111(11),32(10)])].
% 2.71/2.98 6336 multiplication(antidomain(antidomain(antidomain(c3))),coantidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))) = zero. [para(58(a,1),1461(a,1,1,1))].
% 2.71/2.98 7710 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(5022(a,1),242(a,2,2,2)),rewrite([42(4),112(4),2695(6),33(8),2695(11),42(14),2689(14),42(10),111(10)])].
% 2.71/2.98 9044 multiplication(coantidomain(antidomain(A)),A) = A. [para(2689(a,1),3055(a,1,1)),rewrite([33(2)]),flip(a)].
% 2.71/2.98 9054 multiplication(antidomain(antidomain(A)),A) = A. [para(7710(a,1),3055(a,1,1)),rewrite([33(2)]),flip(a)].
% 2.71/2.98 9058 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(5027),rewrite([9044(5)]),flip(a)].
% 2.71/2.98 9174 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(9054(a,1),119(a,1,2,2))].
% 2.71/2.98 9206 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9058(a,1),2695(a,1,1)),rewrite([9058(5)])].
% 2.71/2.98 9207 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9058(a,1),2695(a,2,1)),rewrite([9206(3),9206(4)])].
% 2.71/2.98 9208 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9058(a,1),2705(a,2)),rewrite([9206(3),9207(4)])].
% 2.71/2.98 9279 multiplication(antidomain(c3),antidomain(antidomain(multiplication(c1,antidomain(antidomain(c2)))))) = zero. [back_rewrite(6336),rewrite([9208(4),9208(7),9206(9)])].
% 2.71/2.98 11912 multiplication(antidomain(c3),multiplication(c1,antidomain(antidomain(c2)))) = zero. [para(9279(a,1),9174(a,1,1,1)),rewrite([113(2),33(10)])].
% 2.71/2.98 11913 $F # answer(goals). [resolve(11912,a,71,a)].
% 2.71/2.98
% 2.71/2.98 % SZS output end Refutation
% 2.71/2.98 ============================== end of proof ==========================
% 2.71/2.98
% 2.71/2.98 ============================== STATISTICS ============================
% 2.71/2.98
% 2.71/2.98 Given=524. Generated=119363. Kept=11868. proofs=1.
% 2.71/2.98 Usable=361. Sos=7482. Demods=7334. Limbo=2, Disabled=4051. Hints=0.
% 2.71/2.98 Megabytes=12.94.
% 2.71/2.98 User_CPU=1.92, System_CPU=0.08, Wall_clock=2.
% 2.71/2.98
% 2.71/2.98 ============================== end of statistics =====================
% 2.71/2.98
% 2.71/2.98 ============================== end of search =========================
% 2.71/2.98
% 2.71/2.98 THEOREM PROVED
% 2.71/2.98 % SZS status Theorem
% 2.71/2.98
% 2.71/2.98 Exiting with 1 proof.
% 2.71/2.98
% 2.71/2.98 Process 10558 exit (max_proofs) Thu Jun 16 15:23:23 2022
% 2.71/2.98 Prover9 interrupted
%------------------------------------------------------------------------------