0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s 0.15/0.46 % Computer : n016.cluster.edu 0.15/0.46 % Model : x86_64 x86_64 0.15/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.46 % Memory : 8042.1875MB 0.15/0.46 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.46 % CPULimit : 1200 0.15/0.46 % DateTime : Tue Jul 13 16:01:53 EDT 2021 0.15/0.46 % CPUTime : 0.64/1.02 ============================== Prover9 =============================== 0.64/1.02 Prover9 (32) version 2009-11A, November 2009. 0.64/1.02 Process 27502 was started by sandbox2 on n016.cluster.edu, 0.64/1.02 Tue Jul 13 16:01:54 2021 0.64/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_27168_n016.cluster.edu". 0.64/1.02 ============================== end of head =========================== 0.64/1.02 0.64/1.02 ============================== INPUT ================================= 0.64/1.02 0.64/1.02 % Reading from file /tmp/Prover9_27168_n016.cluster.edu 0.64/1.02 0.64/1.02 set(prolog_style_variables). 0.64/1.02 set(auto2). 0.64/1.02 % set(auto2) -> set(auto). 0.64/1.02 % set(auto) -> set(auto_inference). 0.64/1.02 % set(auto) -> set(auto_setup). 0.64/1.02 % set(auto_setup) -> set(predicate_elim). 0.64/1.02 % set(auto_setup) -> assign(eq_defs, unfold). 0.64/1.02 % set(auto) -> set(auto_limits). 0.64/1.02 % set(auto_limits) -> assign(max_weight, "100.000"). 0.64/1.02 % set(auto_limits) -> assign(sos_limit, 20000). 0.64/1.02 % set(auto) -> set(auto_denials). 0.64/1.02 % set(auto) -> set(auto_process). 0.64/1.02 % set(auto2) -> assign(new_constants, 1). 0.64/1.02 % set(auto2) -> assign(fold_denial_max, 3). 0.64/1.02 % set(auto2) -> assign(max_weight, "200.000"). 0.64/1.02 % set(auto2) -> assign(max_hours, 1). 0.64/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.64/1.02 % set(auto2) -> assign(max_seconds, 0). 0.64/1.02 % set(auto2) -> assign(max_minutes, 5). 0.64/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.64/1.02 % set(auto2) -> set(sort_initial_sos). 0.64/1.02 % set(auto2) -> assign(sos_limit, -1). 0.64/1.02 % set(auto2) -> assign(lrs_ticks, 3000). 0.64/1.02 % set(auto2) -> assign(max_megs, 400). 0.64/1.02 % set(auto2) -> assign(stats, some). 0.64/1.02 % set(auto2) -> clear(echo_input). 0.64/1.02 % set(auto2) -> set(quiet). 0.64/1.02 % set(auto2) -> clear(print_initial_clauses). 0.64/1.02 % set(auto2) -> clear(print_given). 0.64/1.02 assign(lrs_ticks,-1). 0.64/1.02 assign(sos_limit,10000). 0.64/1.02 assign(order,kbo). 0.64/1.02 set(lex_order_vars). 0.64/1.02 clear(print_given). 0.64/1.02 0.64/1.02 % formulas(sos). % not echoed (27 formulas) 0.64/1.02 0.64/1.02 ============================== end of input ========================== 0.64/1.02 0.64/1.02 % From the command line: assign(max_seconds, 1200). 0.64/1.02 0.64/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.64/1.02 0.64/1.02 % Formulas that are not ordinary clauses: 0.64/1.02 1 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 2 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 3 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 5 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 6 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 7 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 8 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 9 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 10 (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]. 0.64/1.02 11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 13 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 14 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 0.64/1.02 15 (all X0 coantidomain(coantidomain(X0)) = codomain(X0)) # label(codomain4) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 16 (all X0 zero = multiplication(X0,coantidomain(X0))) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 17 (all X0 all X1 antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))) # label(domain2) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 18 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 19 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 20 (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]. 5.13/5.55 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 24 (all X0 all X1 c(backward_diamond(X0,c(X1))) = backward_box(X0,X1)) # label(backward_box) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 26 (all X0 all X1 codomain(multiplication(codomain(X1),X0)) = backward_diamond(X0,X1)) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption]. 5.13/5.55 27 -(all X0 all X1 all X2 (backward_box(X0,domain(X2)) = addition(domain(X1),backward_box(X0,domain(X2))) -> addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 5.13/5.55 5.13/5.55 ============================== end of process non-clausal formulas === 5.13/5.55 5.13/5.55 ============================== PROCESS INITIAL CLAUSES =============== 5.13/5.55 5.13/5.55 ============================== PREDICATE ELIMINATION ================= 5.13/5.55 28 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom). [clausify(8)]. 5.13/5.55 29 addition(A,B) != B | leq(A,B) # label(order) # label(axiom). [clausify(8)]. 5.13/5.55 5.13/5.55 ============================== end predicate elimination ============= 5.13/5.55 5.13/5.55 Auto_denials: 5.13/5.55 % copying label goals to answer in negative clause 5.13/5.55 5.13/5.55 Term ordering decisions: 5.13/5.55 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. backward_box=1. backward_diamond=1. forward_diamond=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. domain=1. c=1. codomain=1. 5.13/5.55 5.13/5.55 ============================== end of process initial clauses ======== 5.13/5.55 5.13/5.55 ============================== CLAUSES FOR SEARCH ==================== 5.13/5.55 5.13/5.55 ============================== end of clauses for search ============= 5.13/5.55 5.13/5.55 ============================== SEARCH ================================ 5.13/5.55 5.13/5.55 % Starting search at 0.02 seconds. 5.13/5.55 5.13/5.55 Low Water (keep): wt=41.000, iters=3425 5.13/5.55 5.13/5.55 Low Water (keep): wt=37.000, iters=3430 5.13/5.55 5.13/5.55 Low Water (keep): wt=32.000, iters=3340 5.13/5.55 5.13/5.55 Low Water (keep): wt=30.000, iters=3348 5.13/5.55 5.13/5.55 Low Water (keep): wt=29.000, iters=3374 5.13/5.55 5.13/5.55 Low Water (keep): wt=28.000, iters=3366 5.13/5.55 5.13/5.55 Low Water (keep): wt=27.000, iters=3335 5.13/5.55 5.13/5.55 Low Water (keep): wt=26.000, iters=3364 5.13/5.55 5.13/5.55 Low Water (keep): wt=23.000, iters=4288 5.13/5.55 5.13/5.55 Low Water (keep): wt=22.000, iters=3830 5.13/5.55 5.13/5.55 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 2.15 sec). 5.13/5.55 5.13/5.55 Low Water (keep): wt=21.000, iters=3344 5.13/5.55 5.13/5.55 Low Water (keep): wt=20.000, iters=3335 5.13/5.55 5.13/5.55 Low Water (displace): id=6362, wt=49.000 5.13/5.55 5.13/5.55 Low Water (displace): id=3792, wt=48.000 5.13/5.55 5.13/5.55 Low Water (displace): id=6999, wt=47.000 5.13/5.55 5.13/5.55 Low Water (displace): id=4752, wt=46.000 5.13/5.55 5.13/5.55 Low Water (displace): id=7000, wt=45.000 5.13/5.55 5.13/5.55 Low Water (displace): id=5957, wt=44.000 5.13/5.55 5.13/5.55 Low Water (displace): id=4417, wt=43.000 13.57/13.96 13.57/13.96 Low Water (displace): id=15528, wt=19.000 13.57/13.96 13.57/13.96 Low Water (displace): id=15550, wt=17.000 13.57/13.96 13.57/13.96 Low Water (displace): id=15552, wt=15.000 13.57/13.96 13.57/13.96 Low Water (displace): id=15627, wt=14.000 13.57/13.96 13.57/13.96 Low Water (keep): wt=19.000, iters=3335 13.57/13.96 13.57/13.96 Low Water (displace): id=17045, wt=13.000 13.57/13.96 13.57/13.96 Low Water (keep): wt=18.000, iters=3340 13.57/13.96 13.57/13.96 Low Water (keep): wt=17.000, iters=3336 13.57/13.96 13.57/13.96 ============================== PROOF ================================= 13.57/13.96 % SZS status Theorem 13.57/13.96 % SZS output start Refutation 13.57/13.96 13.57/13.96 % Proof 1 at 12.50 (+ 0.46) seconds: goals. 13.57/13.96 % Length of proof is 168. 13.57/13.96 % Level of proof is 27. 13.57/13.96 % Maximum clause weight is 35.000. 13.57/13.96 % Given clauses 1381. 13.57/13.96 13.57/13.96 1 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 2 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 3 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 5 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 6 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 7 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 9 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 10 (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]. 13.57/13.96 11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 13 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 14 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 15 (all X0 coantidomain(coantidomain(X0)) = codomain(X0)) # label(codomain4) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 16 (all X0 zero = multiplication(X0,coantidomain(X0))) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 17 (all X0 all X1 antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))) # label(domain2) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 18 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 19 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 20 (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]. 13.57/13.96 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 24 (all X0 all X1 c(backward_diamond(X0,c(X1))) = backward_box(X0,X1)) # label(backward_box) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 26 (all X0 all X1 codomain(multiplication(codomain(X1),X0)) = backward_diamond(X0,X1)) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption]. 13.57/13.96 27 -(all X0 all X1 all X2 (backward_box(X0,domain(X2)) = addition(domain(X1),backward_box(X0,domain(X2))) -> addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 13.57/13.96 30 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(1)]. 13.57/13.96 31 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(4)]. 13.57/13.96 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(5)]. 13.57/13.96 33 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(6)]. 13.57/13.96 34 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)]. 13.57/13.96 35 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(12)]. 13.57/13.96 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)]. 13.57/13.96 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(14)]. 13.57/13.96 38 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(15)]. 13.57/13.96 39 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(16)]. 13.57/13.96 40 c(A) = antidomain(domain(A)) # label(complement) # label(axiom). [clausify(21)]. 13.57/13.96 41 c(A) = antidomain(antidomain(antidomain(A))). [copy(40),rewrite([37(2)])]. 13.57/13.96 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(9)]. 13.57/13.96 43 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(18)]. 13.57/13.96 44 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(43),rewrite([42(4)])]. 13.57/13.96 45 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(19)]. 13.57/13.96 46 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(45),rewrite([42(4)])]. 13.57/13.96 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)]. 13.57/13.96 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])]. 13.57/13.96 51 backward_box(A,B) = c(backward_diamond(A,c(B))) # label(backward_box) # label(axiom). [clausify(24)]. 13.57/13.96 52 backward_box(A,B) = antidomain(antidomain(antidomain(backward_diamond(A,antidomain(antidomain(antidomain(B))))))). [copy(51),rewrite([41(2),41(6)])]. 13.57/13.96 55 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(26)]. 13.57/13.96 56 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(55),rewrite([38(2),38(5)])]. 13.57/13.96 57 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)]. 13.57/13.96 58 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(57),rewrite([42(2)]),flip(a)]. 13.57/13.96 59 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(10)]. 13.57/13.96 60 backward_box(c1,domain(c3)) = addition(domain(c2),backward_box(c1,domain(c3))) # label(goals) # label(negated_conjecture). [clausify(27)]. 13.57/13.96 61 addition(antidomain(antidomain(c2)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1))))))) = antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1)))))). [copy(60),rewrite([37(3),52(5),56(8),37(17),37(21),52(23),56(26)]),flip(a)]. 13.57/13.96 62 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom). [clausify(3)]. 13.57/13.96 63 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom). [clausify(7)]. 13.57/13.96 64 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(17)]. 13.57/13.96 65 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(64),flip(a)]. 13.57/13.96 66 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(20)]. 13.57/13.96 67 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(66),flip(a)]. 13.57/13.96 68 domain(c3) != addition(forward_diamond(c1,domain(c2)),domain(c3)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)]. 13.57/13.96 69 addition(antidomain(antidomain(c3)),antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))) != antidomain(antidomain(c3)) # answer(goals). [copy(68),rewrite([37(2),37(6),50(8),37(14),42(16)]),flip(a)]. 13.57/13.96 71 antidomain(one) = zero. [para(36(a,1),30(a,1)),flip(a)]. 13.57/13.96 72 coantidomain(one) = zero. [para(39(a,1),31(a,1)),flip(a)]. 13.57/13.96 73 addition(A,addition(A,B)) = addition(A,B). [para(58(a,1),35(a,1)),rewrite([42(1),42(2),58(2,R),35(1),42(3)])]. 13.57/13.96 74 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),59(a,1,1)),rewrite([34(2)]),flip(a)]. 13.57/13.96 77 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)). [para(30(a,1),62(a,1,1)),rewrite([42(4)])]. 13.57/13.96 78 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(32(a,1),62(a,2,2)),rewrite([33(3),42(3)])]. 13.57/13.96 79 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),62(a,1,1)),rewrite([78(4)]),flip(a)]. 13.57/13.96 80 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(39(a,1),62(a,1,1)),rewrite([78(3),42(3)]),flip(a)]. 13.57/13.96 81 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A). [para(31(a,1),63(a,1,1)),rewrite([42(4)])]. 13.57/13.96 82 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(36(a,1),63(a,1,1)),rewrite([78(3),42(3)]),flip(a)]. 13.57/13.96 83 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(39(a,1),63(a,1,1)),rewrite([78(4),42(3)]),flip(a)]. 13.57/13.96 84 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)])]. 13.57/13.96 91 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(39(a,1),65(a,1,1,1))]. 13.57/13.96 92 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)])]. 13.57/13.96 96 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))]. 13.57/13.96 100 addition(zero,antidomain(zero)) = one. [para(71(a,1),46(a,1,1)),rewrite([71(3)])]. 13.57/13.96 101 addition(zero,coantidomain(zero)) = one. [para(72(a,1),44(a,1,1)),rewrite([72(3)])]. 13.57/13.96 104 multiplication(A,antidomain(zero)) = A. [para(100(a,1),62(a,2,2)),rewrite([33(2),78(5),30(5)])]. 13.57/13.96 108 multiplication(A,coantidomain(zero)) = A. [para(101(a,1),62(a,2,2)),rewrite([33(2),78(5),30(5)])]. 13.57/13.96 110 addition(one,coantidomain(A)) = one. [para(44(a,1),73(a,1,2)),rewrite([42(3),44(7)])]. 13.57/13.96 111 addition(one,antidomain(A)) = one. [para(46(a,1),73(a,1,2)),rewrite([42(3),46(7)])]. 13.57/13.96 112 antidomain(zero) = one. [para(104(a,1),31(a,1)),flip(a)]. 13.57/13.96 113 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(91),rewrite([112(2),111(7)]),flip(a)]. 13.57/13.96 115 coantidomain(zero) = one. [para(108(a,1),31(a,1)),flip(a)]. 13.57/13.96 117 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(96),rewrite([115(2),110(7)]),flip(a)]. 13.57/13.96 118 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(59(a,1),74(a,1,2))]. 13.57/13.96 121 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(74(a,1),65(a,1,1,1)),rewrite([112(2),111(8)]),flip(a)]. 13.57/13.96 123 addition(A,multiplication(A,coantidomain(B))) = A. [para(110(a,1),62(a,2,2)),rewrite([30(2),30(5)])]. 13.57/13.96 124 addition(A,multiplication(coantidomain(B),A)) = A. [para(110(a,1),63(a,2,1)),rewrite([31(2),31(5)])]. 13.57/13.96 126 addition(A,multiplication(antidomain(B),A)) = A. [para(111(a,1),63(a,2,1)),rewrite([31(2),31(5)])]. 13.57/13.96 160 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(113(a,1),36(a,1,1)),rewrite([31(6)])]. 13.57/13.96 165 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(160(a,1),62(a,1,1)),rewrite([78(3),42(5)]),flip(a)]. 13.57/13.96 170 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(44(a,1),79(a,1,2)),rewrite([30(4)]),flip(a)]. 13.57/13.96 175 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(63(a,1),79(a,1,2))]. 13.57/13.96 180 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(126(a,1),79(a,1,2)),rewrite([36(2)]),flip(a)]. 13.57/13.96 192 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(44(a,1),80(a,1,2)),rewrite([30(3)]),flip(a)]. 13.57/13.96 201 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(192(a,1),62(a,1,1)),rewrite([77(4),42(7)]),flip(a)]. 13.57/13.96 206 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(117(a,1),39(a,1,2)),rewrite([30(6)])]. 13.57/13.96 210 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(206(a,1),63(a,1,1)),rewrite([78(3),42(5)]),flip(a)]. 13.57/13.96 239 addition(A,addition(coantidomain(B),multiplication(B,A))) = multiplication(addition(B,one),addition(A,coantidomain(B))). [para(80(a,1),81(a,1,2)),rewrite([42(4),58(4),42(3),58(4,R),42(3)])]. 13.57/13.96 242 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(180(a,1),63(a,1,1)),rewrite([78(5),42(5)]),flip(a)]. 13.57/13.96 245 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(79(a,1),180(a,1,2))]. 13.57/13.96 257 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(46(a,1),82(a,1,1)),rewrite([31(3)]),flip(a)]. 13.57/13.96 266 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),83(a,1,1))]. 13.57/13.96 267 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(44(a,1),83(a,1,1)),rewrite([31(5)]),flip(a)]. 13.57/13.96 268 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(46(a,1),83(a,1,1)),rewrite([31(5)]),flip(a)]. 13.57/13.96 282 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(257(a,1),59(a,1,1)),flip(a)]. 13.57/13.96 310 multiplication(addition(antidomain(A),multiplication(B,C)),A) = multiplication(B,multiplication(C,A)). [para(36(a,1),84(a,1,2)),rewrite([42(4),78(4)]),flip(a)]. 13.57/13.96 523 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(121(a,1),36(a,1,1)),rewrite([31(7)])]. 13.57/13.96 531 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(523(a,1),62(a,1,1)),rewrite([78(4),42(7)]),flip(a)]. 13.57/13.96 662 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(170(a,1),126(a,1,2)),rewrite([42(5)])]. 13.57/13.96 800 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(42(a,1),245(a,1,1,1))]. 13.57/13.96 860 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(46(a,1),266(a,1,1)),rewrite([31(4)]),flip(a)]. 13.57/13.96 1190 multiplication(antidomain(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1))))))),antidomain(antidomain(c2))) = zero. [para(61(a,1),800(a,1,1,1)),rewrite([282(37)])]. 13.57/13.96 1458 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(860(a,1),123(a,1,2))]. 13.57/13.96 2421 multiplication(A,antidomain(coantidomain(A))) = A. [para(46(a,1),165(a,1,2)),rewrite([30(2)]),flip(a)]. 13.57/13.96 2444 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2421(a,1),59(a,1,1)),flip(a)]. 13.57/13.96 2445 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2421(a,1),59(a,1)),flip(a)]. 13.57/13.96 2451 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2421(a,1),124(a,1,2)),rewrite([42(5)])]. 13.57/13.96 2611 multiplication(A,coantidomain(coantidomain(A))) = A. [para(170(a,1),2444(a,1,2)),rewrite([2421(3)]),flip(a)]. 13.57/13.96 2643 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(267),rewrite([2611(5)]),flip(a)]. 13.57/13.96 2672 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2643(a,1),662(a,1,2)),rewrite([42(5),2451(5),2643(6)])]. 13.57/13.96 2693 multiplication(antidomain(antidomain(antidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1))))),antidomain(antidomain(c2))) = zero. [back_rewrite(1190),rewrite([2672(13)])]. 13.57/13.96 2785 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2672(a,1),46(a,1,1)),rewrite([2672(4)])]. 13.57/13.96 2791 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2672(a,1),860(a,1,1,1)),rewrite([2672(5),170(5),2672(5)]),flip(a)]. 13.57/13.96 2793 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2672(a,1),860(a,2,1)),rewrite([2791(2),2791(6),860(9),2791(6)])]. 13.57/13.96 2800 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2643(a,1),2672(a,1,1,1)),rewrite([2791(2),2791(5)]),flip(a)]. 13.57/13.96 2801 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2643(a,1),2672(a,2)),rewrite([2791(2),2800(3),2793(4)])]. 13.57/13.96 2819 multiplication(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1))),antidomain(antidomain(c2))) = zero. [back_rewrite(2693),rewrite([2791(8),2801(13)])]. 13.57/13.96 3182 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(210),rewrite([2791(3)])]. 13.57/13.96 3561 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(46(a,1),175(a,1,2,1)),rewrite([31(5)]),flip(a)]. 13.57/13.96 4055 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(268(a,1),123(a,1,2))]. 13.57/13.96 5006 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(1458(a,1),201(a,1,2)),rewrite([42(11),111(11),30(9)])]. 13.57/13.96 5012 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(4055(a,1),201(a,1,2)),rewrite([42(11),111(11),30(10)])]. 13.57/13.96 7634 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(5006(a,1),239(a,1,2,2)),rewrite([2791(5),42(8),2785(8),42(4),111(4),42(5),110(5),2791(7),31(9)]),flip(a)]. 13.57/13.96 7924 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(46(a,1),242(a,1,1)),rewrite([31(5)]),flip(a)]. 13.57/13.96 9118 multiplication(coantidomain(antidomain(A)),A) = A. [para(2785(a,1),3182(a,1,1)),rewrite([31(2)]),flip(a)]. 13.57/13.96 9128 multiplication(antidomain(antidomain(A)),A) = A. [para(7634(a,1),3182(a,1,1)),rewrite([31(2)]),flip(a)]. 13.57/13.96 9132 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(5012),rewrite([9118(5)]),flip(a)]. 13.57/13.96 9149 multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))),c1))),antidomain(antidomain(c2))) = zero. [back_rewrite(2819),rewrite([9132(7)])]. 13.57/13.96 9253 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(9128(a,1),92(a,1,2,1)),rewrite([42(13),9128(22)])]. 13.57/13.96 9254 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(9128(a,1),118(a,1,2,2))]. 13.57/13.96 9285 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9132(a,1),2791(a,1,1)),rewrite([9132(5)])]. 13.57/13.96 9286 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9132(a,1),2791(a,2,1)),rewrite([9285(3),9285(4)])]. 13.57/13.96 9287 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9132(a,1),2801(a,2)),rewrite([9285(3),9286(4)])]. 13.57/13.96 9437 multiplication(antidomain(coantidomain(multiplication(antidomain(c3),c1))),antidomain(antidomain(c2))) = zero. [back_rewrite(9149),rewrite([9287(4),9287(4)])]. 13.57/13.96 9445 addition(antidomain(antidomain(c3)),antidomain(antidomain(multiplication(c1,antidomain(antidomain(c2)))))) != antidomain(antidomain(c3)) # answer(goals). [back_rewrite(69),rewrite([9287(8)])]. 13.57/13.96 10211 multiplication(addition(antidomain(A),antidomain(B)),A) = multiplication(antidomain(B),A). [para(257(a,1),310(a,1,1,2)),rewrite([282(8)])]. 13.57/13.96 12084 multiplication(antidomain(coantidomain(multiplication(antidomain(c3),c1))),c2) = zero. [para(9437(a,1),9254(a,1,1,1)),rewrite([112(2),31(10)])]. 13.57/13.96 12155 multiplication(antidomain(c3),multiplication(c1,c2)) = zero. [para(12084(a,1),2444(a,1,2)),rewrite([33(6),59(7)]),flip(a)]. 13.57/13.96 17632 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(46(a,1),531(a,1,2)),rewrite([30(3)]),flip(a)]. 13.57/13.96 17801 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17632(a,1),126(a,1,2)),rewrite([42(4)])]. 13.57/13.96 17810 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(17632(a,1),2444(a,1,2)),rewrite([2421(3)]),flip(a)]. 13.57/13.96 17816 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(17632(a,1),239(a,1,2,2)),rewrite([9285(4),42(6),46(6),42(4),111(4),42(4),111(4),9285(6),42(7),31(8)]),flip(a)]. 13.57/13.96 17829 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17632(a,1),2445(a,1,2,2,1,1)),rewrite([9285(5),9287(6),7924(6),17632(8)])]. 13.57/13.96 17865 addition(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(multiplication(antidomain(antidomain(A)),B)). [para(17810(a,1),126(a,1,2)),rewrite([9285(2),42(6),9285(8)])]. 13.57/13.96 17901 antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [back_rewrite(9253),rewrite([17865(13)])]. 13.57/13.96 17958 addition(antidomain(A),antidomain(multiplication(antidomain(A),B))) = one. [para(79(a,1),17816(a,1,2,1)),rewrite([9287(3)])]. 13.57/13.96 18012 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17829(a,1),59(a,1,1)),flip(a)]. 13.57/13.96 18044 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3561),rewrite([18012(7)]),flip(a)]. 13.57/13.96 18087 multiplication(antidomain(multiplication(antidomain(A),B)),A) = A. [para(17958(a,1),10211(a,1,1)),rewrite([31(2)]),flip(a)]. 13.57/13.96 18652 addition(antidomain(A),antidomain(antidomain(multiplication(antidomain(A),B)))) = antidomain(A). [para(18087(a,1),17801(a,1,2,1)),rewrite([42(6),18087(10)])]. 13.57/13.96 22304 multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)) = multiplication(A,B). [para(9254(a,1),18044(a,1,1,1)),rewrite([112(2),31(3)]),flip(a)]. 13.57/13.96 22312 multiplication(antidomain(antidomain(c3)),multiplication(c1,c2)) = multiplication(c1,c2). [para(12155(a,1),18044(a,1,1,1)),rewrite([112(2),31(5)]),flip(a)]. 13.57/13.96 22377 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [back_rewrite(17901),rewrite([22304(7)]),flip(a)]. 13.57/13.97 22400 addition(antidomain(antidomain(c3)),antidomain(antidomain(multiplication(c1,c2)))) != antidomain(antidomain(c3)) # answer(goals). [back_rewrite(9445),rewrite([22377(9)])]. 13.57/13.97 23804 addition(antidomain(antidomain(c3)),antidomain(antidomain(multiplication(c1,c2)))) = antidomain(antidomain(c3)). [para(22312(a,1),18652(a,1,2,1,1))]. 13.57/13.97 23805 $F # answer(goals). [resolve(23804,a,22400,a)]. 13.57/13.97 13.57/13.97 % SZS output end Refutation 13.57/13.97 ============================== end of proof ========================== 13.57/13.97 13.57/13.97 ============================== STATISTICS ============================ 13.57/13.97 13.57/13.97 Given=1381. Generated=867672. Kept=23762. proofs=1. 13.57/13.97 Usable=924. Sos=8923. Demods=9504. Limbo=27, Disabled=13916. Hints=0. 13.57/13.97 Megabytes=20.61. 13.57/13.97 User_CPU=12.50, System_CPU=0.46, Wall_clock=13. 13.57/13.97 13.57/13.97 ============================== end of statistics ===================== 13.57/13.97 13.57/13.97 ============================== end of search ========================= 13.57/13.97 13.57/13.97 THEOREM PROVED 13.57/13.97 % SZS status Theorem 13.57/13.97 13.57/13.97 Exiting with 1 proof. 13.57/13.97 13.57/13.97 Process 27502 exit (max_proofs) Tue Jul 13 16:02:07 2021 13.57/13.97 Prover9 interrupted 13.57/13.97 EOF