0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.34 % Computer : n016.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1200 0.12/0.34 % DateTime : Tue Jul 13 16:02:08 EDT 2021 0.12/0.34 % CPUTime : 0.44/1.08 ============================== Prover9 =============================== 0.44/1.08 Prover9 (32) version 2009-11A, November 2009. 0.44/1.08 Process 28307 was started by sandbox on n016.cluster.edu, 0.44/1.08 Tue Jul 13 16:02:08 2021 0.44/1.08 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_28154_n016.cluster.edu". 0.44/1.08 ============================== end of head =========================== 0.44/1.08 0.44/1.08 ============================== INPUT ================================= 0.44/1.08 0.44/1.08 % Reading from file /tmp/Prover9_28154_n016.cluster.edu 0.44/1.08 0.44/1.08 set(prolog_style_variables). 0.44/1.08 set(auto2). 0.44/1.08 % set(auto2) -> set(auto). 0.44/1.08 % set(auto) -> set(auto_inference). 0.44/1.08 % set(auto) -> set(auto_setup). 0.44/1.08 % set(auto_setup) -> set(predicate_elim). 0.44/1.08 % set(auto_setup) -> assign(eq_defs, unfold). 0.44/1.08 % set(auto) -> set(auto_limits). 0.44/1.08 % set(auto_limits) -> assign(max_weight, "100.000"). 0.44/1.08 % set(auto_limits) -> assign(sos_limit, 20000). 0.44/1.08 % set(auto) -> set(auto_denials). 0.44/1.08 % set(auto) -> set(auto_process). 0.44/1.08 % set(auto2) -> assign(new_constants, 1). 0.44/1.08 % set(auto2) -> assign(fold_denial_max, 3). 0.44/1.08 % set(auto2) -> assign(max_weight, "200.000"). 0.44/1.08 % set(auto2) -> assign(max_hours, 1). 0.44/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.44/1.08 % set(auto2) -> assign(max_seconds, 0). 0.44/1.08 % set(auto2) -> assign(max_minutes, 5). 0.44/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.44/1.08 % set(auto2) -> set(sort_initial_sos). 0.44/1.08 % set(auto2) -> assign(sos_limit, -1). 0.44/1.08 % set(auto2) -> assign(lrs_ticks, 3000). 0.44/1.08 % set(auto2) -> assign(max_megs, 400). 0.44/1.08 % set(auto2) -> assign(stats, some). 0.44/1.08 % set(auto2) -> clear(echo_input). 0.44/1.08 % set(auto2) -> set(quiet). 0.44/1.08 % set(auto2) -> clear(print_initial_clauses). 0.44/1.08 % set(auto2) -> clear(print_given). 0.44/1.08 assign(lrs_ticks,-1). 0.44/1.08 assign(sos_limit,10000). 0.44/1.08 assign(order,kbo). 0.44/1.08 set(lex_order_vars). 0.44/1.08 clear(print_given). 0.44/1.08 0.44/1.08 % formulas(sos). % not echoed (27 formulas) 0.44/1.08 0.44/1.08 ============================== end of input ========================== 0.44/1.08 0.44/1.08 % From the command line: assign(max_seconds, 1200). 0.44/1.08 0.44/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.44/1.08 0.44/1.08 % Formulas that are not ordinary clauses: 0.44/1.08 1 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 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]. 0.44/1.08 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]. 0.44/1.08 4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 5 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 6 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 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]. 0.44/1.08 8 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 9 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 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]. 0.44/1.08 11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 13 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 14 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 0.44/1.08 15 (all X0 coantidomain(coantidomain(X0)) = codomain(X0)) # label(codomain4) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 16 (all X0 zero = multiplication(X0,coantidomain(X0))) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 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]. 4.74/5.08 18 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 19 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 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]. 4.74/5.08 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 24 (all X0 all X1 c(backward_diamond(X0,c(X1))) = backward_box(X0,X1)) # label(backward_box) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 26 (all X0 all X1 codomain(multiplication(codomain(X1),X0)) = backward_diamond(X0,X1)) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption]. 4.74/5.08 27 -(all X0 all X1 addition(backward_diamond(X0,forward_box(X0,domain(X1))),domain(X1)) = domain(X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 4.74/5.08 4.74/5.08 ============================== end of process non-clausal formulas === 4.74/5.08 4.74/5.08 ============================== PROCESS INITIAL CLAUSES =============== 4.74/5.08 4.74/5.08 ============================== PREDICATE ELIMINATION ================= 4.74/5.08 28 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom). [clausify(8)]. 4.74/5.08 29 addition(A,B) != B | leq(A,B) # label(order) # label(axiom). [clausify(8)]. 4.74/5.08 4.74/5.08 ============================== end predicate elimination ============= 4.74/5.08 4.74/5.08 Auto_denials: 4.74/5.08 % copying label goals to answer in negative clause 4.74/5.08 4.74/5.08 Term ordering decisions: 4.74/5.08 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. backward_diamond=1. forward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. c=1. domain=1. codomain=1. 4.74/5.08 4.74/5.08 ============================== end of process initial clauses ======== 4.74/5.08 4.74/5.08 ============================== CLAUSES FOR SEARCH ==================== 4.74/5.08 4.74/5.08 ============================== end of clauses for search ============= 4.74/5.08 4.74/5.08 ============================== SEARCH ================================ 4.74/5.08 4.74/5.08 % Starting search at 0.01 seconds. 4.74/5.08 4.74/5.08 Low Water (keep): wt=41.000, iters=3418 4.74/5.08 4.74/5.08 Low Water (keep): wt=37.000, iters=3423 4.74/5.08 4.74/5.08 Low Water (keep): wt=34.000, iters=3406 4.74/5.08 4.74/5.08 Low Water (keep): wt=32.000, iters=3365 4.74/5.08 4.74/5.08 Low Water (keep): wt=30.000, iters=3340 4.74/5.08 4.74/5.08 Low Water (keep): wt=29.000, iters=3366 4.74/5.08 4.74/5.08 Low Water (keep): wt=28.000, iters=3358 4.74/5.08 4.74/5.08 Low Water (keep): wt=27.000, iters=3396 4.74/5.08 4.74/5.08 Low Water (keep): wt=26.000, iters=3357 4.74/5.08 4.74/5.08 Low Water (keep): wt=21.000, iters=4242 4.74/5.08 4.74/5.08 Low Water (keep): wt=20.000, iters=3863 4.74/5.08 4.74/5.08 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 1.73 sec). 4.74/5.08 4.74/5.08 Low Water (displace): id=6314, wt=49.000 4.74/5.08 4.74/5.08 Low Water (displace): id=3744, wt=48.000 4.74/5.08 4.74/5.08 Low Water (displace): id=6951, wt=47.000 4.74/5.08 4.74/5.08 Low Water (displace): id=4704, wt=46.000 4.74/5.08 4.74/5.08 Low Water (displace): id=6952, wt=45.000 4.74/5.08 4.74/5.08 Low Water (displace): id=5909, wt=44.000 4.74/5.08 4.74/5.08 Low Water (displace): id=4369, wt=43.000 4.74/5.08 4.74/5.08 Low Water (displace): id=4871, wt=42.000 4.74/5.08 4.74/5.08 Low Water (displace): id=6995, wt=41.000 4.74/5.08 4.74/5.08 Low Water (displace): id=15503, wt=19.000 8.14/8.41 8.14/8.41 Low Water (displace): id=15506, wt=16.000 8.14/8.41 8.14/8.41 Low Water (displace): id=15527, wt=15.000 8.14/8.41 8.14/8.41 Low Water (displace): id=16041, wt=14.000 8.14/8.41 8.14/8.41 Low Water (keep): wt=19.000, iters=3341 8.14/8.41 8.14/8.41 Low Water (displace): id=16675, wt=13.000 8.14/8.41 8.14/8.41 ============================== PROOF ================================= 8.14/8.41 % SZS status Theorem 8.14/8.41 % SZS output start Refutation 8.14/8.41 8.14/8.41 % Proof 1 at 7.04 (+ 0.31) seconds: goals. 8.14/8.41 % Length of proof is 137. 8.14/8.41 % Level of proof is 26. 8.14/8.41 % Maximum clause weight is 29.000. 8.14/8.41 % Given clauses 1007. 8.14/8.41 8.14/8.41 1 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 8.14/8.41 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]. 8.14/8.41 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]. 8.14/8.41 4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 5 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 6 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 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]. 8.14/8.42 9 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 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]. 8.14/8.42 11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 13 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 14 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 15 (all X0 coantidomain(coantidomain(X0)) = codomain(X0)) # label(codomain4) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 16 (all X0 zero = multiplication(X0,coantidomain(X0))) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 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]. 8.14/8.42 18 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 19 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 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]. 8.14/8.42 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 26 (all X0 all X1 codomain(multiplication(codomain(X1),X0)) = backward_diamond(X0,X1)) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption]. 8.14/8.42 27 -(all X0 all X1 addition(backward_diamond(X0,forward_box(X0,domain(X1))),domain(X1)) = domain(X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 8.14/8.42 30 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(1)]. 8.14/8.42 31 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(4)]. 8.14/8.42 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(5)]. 8.14/8.42 33 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(6)]. 8.14/8.42 34 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)]. 8.14/8.42 35 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(12)]. 8.14/8.42 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)]. 8.14/8.42 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(14)]. 8.14/8.42 38 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(15)]. 8.14/8.42 39 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(16)]. 8.14/8.42 40 c(A) = antidomain(domain(A)) # label(complement) # label(axiom). [clausify(21)]. 8.14/8.42 41 c(A) = antidomain(antidomain(antidomain(A))). [copy(40),rewrite([37(2)])]. 8.14/8.42 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(9)]. 8.14/8.42 43 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(18)]. 8.14/8.42 44 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(43),rewrite([42(4)])]. 8.14/8.42 45 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(19)]. 8.14/8.42 46 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(45),rewrite([42(4)])]. 8.14/8.42 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)]. 8.14/8.42 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])]. 8.14/8.42 53 forward_box(A,B) = c(forward_diamond(A,c(B))) # label(forward_box) # label(axiom). [clausify(25)]. 8.14/8.42 54 forward_box(A,B) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(antidomain(antidomain(antidomain(B))))))))))). [copy(53),rewrite([41(2),50(5),41(10)])]. 8.14/8.42 55 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(26)]. 8.14/8.42 56 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(55),rewrite([38(2),38(5)])]. 8.14/8.42 57 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)]. 8.14/8.42 58 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(57),rewrite([42(2)]),flip(a)]. 8.14/8.42 59 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(10)]. 8.14/8.42 60 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom). [clausify(3)]. 8.14/8.42 61 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom). [clausify(7)]. 8.14/8.42 62 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(17)]. 8.14/8.42 63 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(62),flip(a)]. 8.14/8.42 64 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(20)]. 8.14/8.42 65 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(64),flip(a)]. 8.14/8.42 66 domain(c2) != addition(backward_diamond(c1,forward_box(c1,domain(c2))),domain(c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)]. 8.14/8.42 67 addition(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))))))))))),c1)))) != antidomain(antidomain(c2)) # answer(goals). [copy(66),rewrite([37(2),37(7),54(9),56(20),37(26),42(28)]),flip(a)]. 8.14/8.42 69 antidomain(one) = zero. [para(36(a,1),30(a,1)),flip(a)]. 8.14/8.42 70 coantidomain(one) = zero. [para(39(a,1),31(a,1)),flip(a)]. 8.14/8.42 71 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)])]. 8.14/8.42 72 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),59(a,1,1)),rewrite([34(2)]),flip(a)]. 8.14/8.42 75 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)). [para(30(a,1),60(a,1,1)),rewrite([42(4)])]. 8.14/8.42 76 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(32(a,1),60(a,2,2)),rewrite([33(3),42(3)])]. 8.14/8.42 77 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),60(a,1,1)),rewrite([76(4)]),flip(a)]. 8.14/8.42 78 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(39(a,1),60(a,1,1)),rewrite([76(3),42(3)]),flip(a)]. 8.14/8.42 81 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(39(a,1),61(a,1,1)),rewrite([76(4),42(3)]),flip(a)]. 8.14/8.42 89 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(39(a,1),63(a,1,1,1))]. 8.14/8.42 94 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),65(a,1,1,1))]. 8.14/8.42 97 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(59(a,1),65(a,1,1,1))]. 8.14/8.42 98 addition(zero,antidomain(zero)) = one. [para(69(a,1),46(a,1,1)),rewrite([69(3)])]. 8.14/8.42 99 addition(zero,coantidomain(zero)) = one. [para(70(a,1),44(a,1,1)),rewrite([70(3)])]. 8.14/8.42 102 multiplication(A,antidomain(zero)) = A. [para(98(a,1),60(a,2,2)),rewrite([33(2),76(5),30(5)])]. 8.14/8.42 106 multiplication(A,coantidomain(zero)) = A. [para(99(a,1),60(a,2,2)),rewrite([33(2),76(5),30(5)])]. 8.14/8.42 108 addition(one,coantidomain(A)) = one. [para(44(a,1),71(a,1,2)),rewrite([42(3),44(7)])]. 8.14/8.42 109 addition(one,antidomain(A)) = one. [para(46(a,1),71(a,1,2)),rewrite([42(3),46(7)])]. 8.14/8.42 110 antidomain(zero) = one. [para(102(a,1),31(a,1)),flip(a)]. 8.14/8.42 111 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(89),rewrite([110(2),109(7)]),flip(a)]. 8.14/8.42 113 coantidomain(zero) = one. [para(106(a,1),31(a,1)),flip(a)]. 8.14/8.42 115 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(94),rewrite([113(2),108(7)]),flip(a)]. 8.14/8.42 119 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(72(a,1),63(a,1,1,1)),rewrite([110(2),109(8)]),flip(a)]. 8.14/8.42 121 addition(A,multiplication(A,coantidomain(B))) = A. [para(108(a,1),60(a,2,2)),rewrite([30(2),30(5)])]. 8.14/8.42 122 addition(A,multiplication(coantidomain(B),A)) = A. [para(108(a,1),61(a,2,1)),rewrite([31(2),31(5)])]. 8.14/8.42 124 addition(A,multiplication(antidomain(B),A)) = A. [para(109(a,1),61(a,2,1)),rewrite([31(2),31(5)])]. 8.14/8.42 158 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(111(a,1),36(a,1,1)),rewrite([31(6)])]. 8.14/8.42 163 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(158(a,1),60(a,1,1)),rewrite([76(3),42(5)]),flip(a)]. 8.14/8.42 168 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(44(a,1),77(a,1,2)),rewrite([30(4)]),flip(a)]. 8.14/8.42 173 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(61(a,1),77(a,1,2))]. 8.14/8.42 178 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(124(a,1),77(a,1,2)),rewrite([36(2)]),flip(a)]. 8.14/8.42 190 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(44(a,1),78(a,1,2)),rewrite([30(3)]),flip(a)]. 8.14/8.42 199 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(190(a,1),60(a,1,1)),rewrite([75(4),42(7)]),flip(a)]. 8.14/8.42 204 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(115(a,1),39(a,1,2)),rewrite([30(6)])]. 8.14/8.42 208 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(204(a,1),61(a,1,1)),rewrite([76(3),42(5)]),flip(a)]. 8.14/8.42 240 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(178(a,1),61(a,1,1)),rewrite([76(5),42(5)]),flip(a)]. 8.14/8.42 263 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),81(a,1,1))]. 8.14/8.42 264 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(44(a,1),81(a,1,1)),rewrite([31(5)]),flip(a)]. 8.14/8.42 265 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(46(a,1),81(a,1,1)),rewrite([31(5)]),flip(a)]. 8.14/8.42 517 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(119(a,1),36(a,1,1)),rewrite([31(7)])]. 8.14/8.42 525 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(517(a,1),60(a,1,1)),rewrite([76(4),42(7)]),flip(a)]. 8.14/8.42 568 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(36(a,1),97(a,1,1,1)),rewrite([113(2),108(9)]),flip(a)]. 8.14/8.42 656 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(168(a,1),124(a,1,2)),rewrite([42(5)])]. 8.14/8.42 853 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(46(a,1),263(a,1,1)),rewrite([31(4)]),flip(a)]. 8.14/8.42 2400 multiplication(A,antidomain(coantidomain(A))) = A. [para(46(a,1),163(a,1,2)),rewrite([30(2)]),flip(a)]. 8.14/8.42 2423 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2400(a,1),59(a,1,1)),flip(a)]. 8.14/8.42 2424 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2400(a,1),59(a,1)),flip(a)]. 8.14/8.42 2430 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2400(a,1),122(a,1,2)),rewrite([42(5)])]. 8.14/8.42 2590 multiplication(A,coantidomain(coantidomain(A))) = A. [para(168(a,1),2423(a,1,2)),rewrite([2400(3)]),flip(a)]. 8.14/8.42 2622 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(264),rewrite([2590(5)]),flip(a)]. 8.14/8.42 2651 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2622(a,1),656(a,1,2)),rewrite([42(5),2430(5),2622(6)])]. 8.14/8.42 2748 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2651(a,1),46(a,1,1)),rewrite([2651(4)])]. 8.14/8.42 2754 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2651(a,1),853(a,1,1,1)),rewrite([2651(5),168(5),2651(5)]),flip(a)]. 8.14/8.42 2756 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2651(a,1),853(a,2,1)),rewrite([2754(2),2754(6),853(9),2754(6)])]. 8.14/8.42 2763 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2622(a,1),2651(a,1,1,1)),rewrite([2754(2),2754(5)]),flip(a)]. 8.14/8.42 2764 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2622(a,1),2651(a,2)),rewrite([2754(2),2763(3),2756(4)])]. 8.14/8.42 3114 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(568),rewrite([2754(5)])]. 8.14/8.42 3133 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(208),rewrite([2754(3)])]. 8.14/8.42 3140 addition(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))))))))))),c1)))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(67),rewrite([2754(20),2754(24)])]. 8.14/8.42 3513 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(46(a,1),173(a,1,2,1)),rewrite([31(5)]),flip(a)]. 8.14/8.42 4007 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(265(a,1),121(a,1,2))]. 8.14/8.42 4964 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(4007(a,1),199(a,1,2)),rewrite([42(11),109(11),30(10)])]. 8.14/8.42 7876 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(46(a,1),240(a,1,1)),rewrite([31(5)]),flip(a)]. 8.14/8.42 9085 multiplication(coantidomain(antidomain(A)),A) = A. [para(2748(a,1),3133(a,1,1)),rewrite([31(2)]),flip(a)]. 8.14/8.42 9099 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(4964),rewrite([9085(5)]),flip(a)]. 8.14/8.42 9110 addition(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))))))))),c1)))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(3140),rewrite([9099(19)])]. 8.14/8.42 9208 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9099(a,1),2754(a,1,1)),rewrite([9099(5)])]. 8.14/8.42 9209 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9099(a,1),2754(a,2,1)),rewrite([9208(3),9208(4)])]. 8.14/8.42 9210 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9099(a,1),2764(a,2)),rewrite([9208(3),9209(4)])]. 8.14/8.42 9358 addition(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(multiplication(c1,antidomain(c2))),c1)))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(9110),rewrite([9210(8),9210(8),9210(8),9210(10),9210(10)])]. 8.14/8.42 13404 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero. [para(3114(a,1),39(a,1,2)),rewrite([30(8)])]. 8.14/8.42 17271 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(46(a,1),525(a,1,2)),rewrite([30(3)]),flip(a)]. 8.14/8.42 17401 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17271(a,1),124(a,1,2)),rewrite([42(4)])]. 8.14/8.42 17426 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17271(a,1),2424(a,1,2,2,1,1)),rewrite([9208(5),9210(6),7876(6),17271(8)])]. 8.14/8.42 17599 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17426(a,1),59(a,1,1)),flip(a)]. 8.14/8.42 17628 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3513),rewrite([17599(7)]),flip(a)]. 8.14/8.42 18666 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(13404(a,1),17628(a,1,1,1)),rewrite([110(2),31(2),2764(6)]),flip(a)]. 8.14/8.42 19924 addition(antidomain(A),antidomain(coantidomain(multiplication(antidomain(multiplication(B,A)),B)))) = antidomain(A). [para(18666(a,1),17401(a,1,2,1)),rewrite([42(7),18666(12)])]. 8.14/8.42 19925 $F # answer(goals). [resolve(19924,a,9358,a)]. 8.14/8.42 8.14/8.42 % SZS output end Refutation 8.14/8.42 ============================== end of proof ========================== 8.14/8.42 8.14/8.42 ============================== STATISTICS ============================ 8.14/8.42 8.14/8.42 Given=1007. Generated=518693. Kept=19883. proofs=1. 8.14/8.42 Usable=676. Sos=9564. Demods=9834. Limbo=72, Disabled=9598. Hints=0. 8.14/8.42 Megabytes=18.67. 8.14/8.42 User_CPU=7.04, System_CPU=0.31, Wall_clock=8. 8.14/8.42 8.14/8.42 ============================== end of statistics ===================== 8.14/8.42 8.14/8.42 ============================== end of search ========================= 8.14/8.42 8.14/8.42 THEOREM PROVED 8.14/8.42 % SZS status Theorem 8.14/8.42 8.14/8.42 Exiting with 1 proof. 8.14/8.42 8.14/8.42 Process 28307 exit (max_proofs) Tue Jul 13 16:02:16 2021 8.14/8.42 Prover9 interrupted 8.14/8.42 EOF