TSTP Solution File: KLE084+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE084+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 02:22:09 EDT 2022
% Result : Theorem 8.10s 8.39s
% Output : Refutation 8.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE084+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 12:36:53 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.77/1.04 ============================== Prover9 ===============================
% 0.77/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.04 Process 3569 was started by sandbox2 on n009.cluster.edu,
% 0.77/1.04 Thu Jun 16 12:36:53 2022
% 0.77/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3414_n009.cluster.edu".
% 0.77/1.04 ============================== end of head ===========================
% 0.77/1.04
% 0.77/1.04 ============================== INPUT =================================
% 0.77/1.04
% 0.77/1.04 % Reading from file /tmp/Prover9_3414_n009.cluster.edu
% 0.77/1.04
% 0.77/1.04 set(prolog_style_variables).
% 0.77/1.04 set(auto2).
% 0.77/1.04 % set(auto2) -> set(auto).
% 0.77/1.04 % set(auto) -> set(auto_inference).
% 0.77/1.04 % set(auto) -> set(auto_setup).
% 0.77/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.04 % set(auto) -> set(auto_limits).
% 0.77/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.04 % set(auto) -> set(auto_denials).
% 0.77/1.04 % set(auto) -> set(auto_process).
% 0.77/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.04 % set(auto2) -> assign(stats, some).
% 0.77/1.04 % set(auto2) -> clear(echo_input).
% 0.77/1.04 % set(auto2) -> set(quiet).
% 0.77/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.04 % set(auto2) -> clear(print_given).
% 0.77/1.04 assign(lrs_ticks,-1).
% 0.77/1.04 assign(sos_limit,10000).
% 0.77/1.04 assign(order,kbo).
% 0.77/1.04 set(lex_order_vars).
% 0.77/1.04 clear(print_given).
% 0.77/1.04
% 0.77/1.04 % formulas(sos). % not echoed (21 formulas)
% 0.77/1.04
% 0.77/1.04 ============================== end of input ==========================
% 0.77/1.04
% 0.77/1.04 % From the command line: assign(max_seconds, 300).
% 0.77/1.04
% 0.77/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.04
% 0.77/1.04 % Formulas that are not ordinary clauses:
% 0.77/1.04 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 0.77/1.04 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].
% 0.77/1.04 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 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].
% 8.10/8.39 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 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].
% 8.10/8.39 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 21 -(all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.10/8.39
% 8.10/8.39 ============================== end of process non-clausal formulas ===
% 8.10/8.39
% 8.10/8.39 ============================== PROCESS INITIAL CLAUSES ===============
% 8.10/8.39
% 8.10/8.39 ============================== PREDICATE ELIMINATION =================
% 8.10/8.39 22 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 8.10/8.39 23 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 8.10/8.39
% 8.10/8.39 ============================== end predicate elimination =============
% 8.10/8.39
% 8.10/8.39 Auto_denials:
% 8.10/8.39 % copying label goals to answer in negative clause
% 8.10/8.39
% 8.10/8.39 Term ordering decisions:
% 8.10/8.39 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. antidomain=1. coantidomain=1. codomain=1. domain=1.
% 8.10/8.39
% 8.10/8.39 ============================== end of process initial clauses ========
% 8.10/8.39
% 8.10/8.39 ============================== CLAUSES FOR SEARCH ====================
% 8.10/8.39
% 8.10/8.39 ============================== end of clauses for search =============
% 8.10/8.39
% 8.10/8.39 ============================== SEARCH ================================
% 8.10/8.39
% 8.10/8.39 % Starting search at 0.01 seconds.
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=39.000, iters=3344
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=37.000, iters=3454
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=33.000, iters=3341
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=32.000, iters=3364
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=30.000, iters=3338
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=29.000, iters=3397
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=28.000, iters=3333
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=27.000, iters=3355
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=26.000, iters=3339
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=25.000, iters=3333
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=24.000, iters=3397
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=23.000, iters=3337
% 8.10/8.39
% 8.10/8.39 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.96 sec).
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=22.000, iters=3333
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=21.000, iters=3349
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=20.000, iters=3335
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=6229, wt=49.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=3655, wt=48.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=6892, wt=47.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=4626, wt=46.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=6893, wt=45.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=5859, wt=44.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=4308, wt=43.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=4788, wt=42.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=15493, wt=18.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=15513, wt=16.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=15521, wt=15.000
% 8.10/8.39
% 8.10/8.39 Low Water (displace): id=15895, wt=14.000
% 8.10/8.39
% 8.10/8.39 Low Water (keep): wt=19.000, iters=3349
% 8.10/8.39
% 8.10/8.39 ============================== PROOF =================================
% 8.10/8.39 % SZS status Theorem
% 8.10/8.39 % SZS output start Refutation
% 8.10/8.39
% 8.10/8.39 % Proof 1 at 7.09 (+ 0.27) seconds: goals.
% 8.10/8.39 % Length of proof is 130.
% 8.10/8.39 % Level of proof is 26.
% 8.10/8.39 % Maximum clause weight is 26.000.
% 8.10/8.39 % Given clauses 954.
% 8.10/8.39
% 8.10/8.39 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 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].
% 8.10/8.39 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 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].
% 8.10/8.39 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 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].
% 8.10/8.39 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].
% 8.10/8.39 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 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].
% 8.10/8.39 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 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].
% 8.10/8.39 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 8.10/8.39 21 -(all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.10/8.39 24 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 8.10/8.39 25 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 8.10/8.39 26 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 8.10/8.39 27 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 8.10/8.39 28 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 8.10/8.39 29 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 8.10/8.39 30 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 8.10/8.39 31 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 8.10/8.39 32 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 8.10/8.39 34 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 8.10/8.39 35 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 8.10/8.39 36 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(35),rewrite([34(4)])].
% 8.10/8.39 37 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 8.10/8.39 38 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(37),rewrite([34(4)])].
% 8.10/8.39 39 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 8.10/8.39 40 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(39),rewrite([34(2)]),flip(a)].
% 8.10/8.39 41 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 8.10/8.39 42 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 8.10/8.39 43 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(42),flip(a)].
% 8.10/8.39 44 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 8.10/8.39 45 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(44),flip(a)].
% 8.10/8.39 46 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 8.10/8.39 47 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(46),flip(a)].
% 8.10/8.39 48 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 8.10/8.39 49 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(48),flip(a)].
% 8.10/8.39 50 domain(multiplication(c1,domain(c2))) != domain(multiplication(c1,c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(21)].
% 8.10/8.39 51 antidomain(antidomain(multiplication(c1,antidomain(antidomain(c2))))) != antidomain(antidomain(multiplication(c1,c2))) # answer(goals). [copy(50),rewrite([31(3),31(6),31(11)])].
% 8.10/8.39 52 antidomain(one) = zero. [para(30(a,1),26(a,1)),flip(a)].
% 8.10/8.39 53 coantidomain(one) = zero. [para(32(a,1),27(a,1)),flip(a)].
% 8.10/8.39 54 addition(A,addition(A,B)) = addition(A,B). [para(40(a,1),25(a,1)),rewrite([34(1),34(2),40(2,R),25(1),34(3)])].
% 8.10/8.39 55 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(30(a,1),41(a,1,1)),rewrite([29(2)]),flip(a)].
% 8.10/8.39 58 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(24(a,1),43(a,2,2)),rewrite([28(3),34(3)])].
% 8.10/8.39 59 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(26(a,1),43(a,1,1)),rewrite([34(4)]),flip(a)].
% 8.10/8.39 60 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(30(a,1),43(a,1,1)),rewrite([58(4)]),flip(a)].
% 8.10/8.39 61 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(32(a,1),43(a,1,1)),rewrite([58(3),34(3)]),flip(a)].
% 8.10/8.39 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(27(a,1),45(a,1,1)),rewrite([34(4)]),flip(a)].
% 8.10/8.39 64 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(32(a,1),45(a,1,1)),rewrite([58(4),34(3)]),flip(a)].
% 8.10/8.39 72 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(32(a,1),47(a,1,1,1))].
% 8.10/8.39 73 addition(antidomain(multiplication(A,multiplication(B,C))),antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C)))))) = antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C))))). [para(41(a,1),47(a,1,1,1)),rewrite([41(7),41(13)])].
% 8.10/8.39 77 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(30(a,1),49(a,1,1,1))].
% 8.10/8.39 81 addition(zero,antidomain(zero)) = one. [para(52(a,1),36(a,1,1)),rewrite([52(3)])].
% 8.10/8.39 82 addition(zero,coantidomain(zero)) = one. [para(53(a,1),38(a,1,1)),rewrite([53(3)])].
% 8.10/8.39 85 multiplication(A,antidomain(zero)) = A. [para(81(a,1),43(a,2,2)),rewrite([28(2),58(5),26(5)])].
% 8.10/8.39 89 multiplication(A,coantidomain(zero)) = A. [para(82(a,1),43(a,2,2)),rewrite([28(2),58(5),26(5)])].
% 8.10/8.39 91 addition(one,antidomain(A)) = one. [para(36(a,1),54(a,1,2)),rewrite([34(3),36(7)])].
% 8.10/8.39 92 addition(one,coantidomain(A)) = one. [para(38(a,1),54(a,1,2)),rewrite([34(3),38(7)])].
% 8.10/8.39 93 antidomain(zero) = one. [para(85(a,1),27(a,1)),flip(a)].
% 8.10/8.39 94 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(72),rewrite([93(2),91(7)]),flip(a)].
% 8.10/8.39 96 coantidomain(zero) = one. [para(89(a,1),27(a,1)),flip(a)].
% 8.10/8.39 98 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(77),rewrite([96(2),92(7)]),flip(a)].
% 8.10/8.39 99 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(41(a,1),55(a,1,2))].
% 8.10/8.39 102 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(55(a,1),47(a,1,1,1)),rewrite([93(2),91(8)]),flip(a)].
% 8.10/8.39 105 addition(A,multiplication(antidomain(B),A)) = A. [para(91(a,1),45(a,2,1)),rewrite([27(2),27(5)])].
% 8.10/8.39 106 addition(A,multiplication(A,coantidomain(B))) = A. [para(92(a,1),43(a,2,2)),rewrite([26(2),26(5)])].
% 8.10/8.39 107 addition(A,multiplication(coantidomain(B),A)) = A. [para(92(a,1),45(a,2,1)),rewrite([27(2),27(5)])].
% 8.10/8.39 141 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(94(a,1),30(a,1,1)),rewrite([27(6)])].
% 8.10/8.39 146 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(141(a,1),43(a,1,1)),rewrite([58(3),34(5)]),flip(a)].
% 8.10/8.39 152 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(38(a,1),60(a,1,2)),rewrite([26(4)]),flip(a)].
% 8.10/8.39 156 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(45(a,1),60(a,1,2))].
% 8.10/8.39 160 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(105(a,1),60(a,1,2)),rewrite([30(2)]),flip(a)].
% 8.10/8.39 173 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(38(a,1),61(a,1,2)),rewrite([26(3)]),flip(a)].
% 8.10/8.39 182 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(173(a,1),43(a,1,1)),rewrite([59(4,R),34(7)]),flip(a)].
% 8.10/8.39 187 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(98(a,1),32(a,1,2)),rewrite([26(6)])].
% 8.10/8.39 191 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(187(a,1),45(a,1,1)),rewrite([58(3),34(5)]),flip(a)].
% 8.10/8.39 195 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(160(a,1),45(a,1,1)),rewrite([58(5),34(5)]),flip(a)].
% 8.10/8.39 221 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(61(a,1),62(a,2,2)),rewrite([34(9),40(9),34(8),40(9,R),34(8)])].
% 8.10/8.39 246 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(34(a,1),64(a,1,1))].
% 8.10/8.39 247 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(36(a,1),64(a,1,1)),rewrite([27(5)]),flip(a)].
% 8.10/8.39 248 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(38(a,1),64(a,1,1)),rewrite([27(5)]),flip(a)].
% 8.10/8.39 496 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(102(a,1),30(a,1,1)),rewrite([27(7)])].
% 8.10/8.39 504 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(496(a,1),43(a,1,1)),rewrite([58(4),34(7)]),flip(a)].
% 8.10/8.39 635 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(152(a,1),105(a,1,2)),rewrite([34(5)])].
% 8.10/8.39 832 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(36(a,1),246(a,1,1)),rewrite([27(4)]),flip(a)].
% 8.10/8.39 1419 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(832(a,1),106(a,1,2))].
% 8.10/8.39 2359 multiplication(A,antidomain(coantidomain(A))) = A. [para(36(a,1),146(a,1,2)),rewrite([26(2)]),flip(a)].
% 8.10/8.39 2381 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2359(a,1),41(a,1,1)),flip(a)].
% 8.10/8.39 2382 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2359(a,1),41(a,1)),flip(a)].
% 8.10/8.39 2389 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2359(a,1),107(a,1,2)),rewrite([34(5)])].
% 8.10/8.39 2488 multiplication(A,coantidomain(coantidomain(A))) = A. [para(152(a,1),2381(a,1,2)),rewrite([2359(3)]),flip(a)].
% 8.10/8.39 2521 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(248),rewrite([2488(5)]),flip(a)].
% 8.10/8.39 2550 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2521(a,1),635(a,1,2)),rewrite([34(5),2389(5),2521(6)])].
% 8.10/8.39 2649 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2550(a,1),36(a,1,1)),rewrite([2550(4)])].
% 8.10/8.39 2655 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2550(a,1),832(a,1,1,1)),rewrite([2550(5),152(5),2550(5)]),flip(a)].
% 8.10/8.39 2657 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2550(a,1),832(a,2,1)),rewrite([2655(2),2655(6),832(9),2655(6)])].
% 8.10/8.39 2664 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2521(a,1),2550(a,1,1,1)),rewrite([2655(2),2655(5)]),flip(a)].
% 8.10/8.39 2665 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2521(a,1),2550(a,2)),rewrite([2655(2),2664(3),2657(4)])].
% 8.10/8.39 3011 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(191),rewrite([2655(3)])].
% 8.10/8.39 3429 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(36(a,1),156(a,1,2,1)),rewrite([27(5)]),flip(a)].
% 8.10/8.39 3921 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(247(a,1),106(a,1,2))].
% 8.10/8.39 4909 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(1419(a,1),182(a,1,2)),rewrite([34(11),91(11),26(9)])].
% 8.10/8.39 4914 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3921(a,1),182(a,1,2)),rewrite([34(11),91(11),26(10)])].
% 8.10/8.39 5167 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(36(a,1),195(a,1,1)),rewrite([27(5)]),flip(a)].
% 8.10/8.39 7574 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(4909(a,1),221(a,2,2,2)),rewrite([34(4),92(4),2655(6),27(8),2655(11),34(14),2649(14),34(10),91(10)])].
% 8.10/8.39 9100 multiplication(coantidomain(antidomain(A)),A) = A. [para(2649(a,1),3011(a,1,1)),rewrite([27(2)]),flip(a)].
% 8.10/8.39 9110 multiplication(antidomain(antidomain(A)),A) = A. [para(7574(a,1),3011(a,1,1)),rewrite([27(2)]),flip(a)].
% 8.10/8.39 9114 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(4914),rewrite([9100(5)]),flip(a)].
% 8.10/8.39 9169 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)))). [para(9110(a,1),73(a,1,2,1)),rewrite([34(13),9110(22)])].
% 8.10/8.39 9170 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(9110(a,1),99(a,1,2,2))].
% 8.10/8.39 9249 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9114(a,1),2655(a,1,1)),rewrite([9114(5)])].
% 8.10/8.39 9250 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9114(a,1),2655(a,2,1)),rewrite([9249(3),9249(4)])].
% 8.10/8.39 9251 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9114(a,1),2665(a,2)),rewrite([9249(3),9250(4)])].
% 8.10/8.39 17437 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(36(a,1),504(a,1,2)),rewrite([26(3)]),flip(a)].
% 8.10/8.39 17594 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(17437(a,1),2381(a,1,2)),rewrite([2359(3)]),flip(a)].
% 8.10/8.39 17620 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17437(a,1),2382(a,1,2,2,1,1)),rewrite([9249(5),9251(6),5167(6),17437(8)])].
% 8.10/8.39 17670 addition(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(multiplication(antidomain(antidomain(A)),B)). [para(17594(a,1),105(a,1,2)),rewrite([9249(2),34(6),9249(8)])].
% 8.10/8.39 17706 antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [back_rewrite(9169),rewrite([17670(13)])].
% 8.10/8.39 17809 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17620(a,1),41(a,1,1)),flip(a)].
% 8.10/8.39 17842 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3429),rewrite([17809(7)]),flip(a)].
% 8.10/8.39 18885 multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)) = multiplication(A,B). [para(9170(a,1),17842(a,1,1,1)),rewrite([93(2),27(3)]),flip(a)].
% 8.10/8.39 18936 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [back_rewrite(17706),rewrite([18885(7)]),flip(a)].
% 8.10/8.39 18965 $F # answer(goals). [back_rewrite(51),rewrite([18936(6)]),xx(a)].
% 8.10/8.39
% 8.10/8.39 % SZS output end Refutation
% 8.10/8.39 ============================== end of proof ==========================
% 8.10/8.39
% 8.10/8.39 ============================== STATISTICS ============================
% 8.10/8.39
% 8.10/8.39 Given=954. Generated=477489. Kept=18933. proofs=1.
% 8.10/8.39 Usable=686. Sos=8813. Demods=9091. Limbo=29, Disabled=9427. Hints=0.
% 8.10/8.39 Megabytes=18.19.
% 8.10/8.39 User_CPU=7.09, System_CPU=0.27, Wall_clock=8.
% 8.10/8.39
% 8.10/8.39 ============================== end of statistics =====================
% 8.10/8.39
% 8.10/8.39 ============================== end of search =========================
% 8.10/8.39
% 8.10/8.39 THEOREM PROVED
% 8.10/8.39 % SZS status Theorem
% 8.10/8.39
% 8.10/8.39 Exiting with 1 proof.
% 8.10/8.39
% 8.10/8.39 Process 3569 exit (max_proofs) Thu Jun 16 12:37:01 2022
% 8.10/8.39 Prover9 interrupted
%------------------------------------------------------------------------------