0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.09/0.30 % Computer : n016.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % DateTime : Thu Jul 2 07:34:35 EDT 2020 0.09/0.30 % CPUTime : 0.72/1.01 ============================== Prover9 =============================== 0.72/1.01 Prover9 (32) version 2009-11A, November 2009. 0.72/1.01 Process 29590 was started by sandbox2 on n016.cluster.edu, 0.72/1.01 Thu Jul 2 07:34:36 2020 0.72/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_29436_n016.cluster.edu". 0.72/1.01 ============================== end of head =========================== 0.72/1.01 0.72/1.01 ============================== INPUT ================================= 0.72/1.01 0.72/1.01 % Reading from file /tmp/Prover9_29436_n016.cluster.edu 0.72/1.01 0.72/1.01 set(prolog_style_variables). 0.72/1.01 set(auto2). 0.72/1.01 % set(auto2) -> set(auto). 0.72/1.01 % set(auto) -> set(auto_inference). 0.72/1.01 % set(auto) -> set(auto_setup). 0.72/1.01 % set(auto_setup) -> set(predicate_elim). 0.72/1.01 % set(auto_setup) -> assign(eq_defs, unfold). 0.72/1.01 % set(auto) -> set(auto_limits). 0.72/1.01 % set(auto_limits) -> assign(max_weight, "100.000"). 0.72/1.01 % set(auto_limits) -> assign(sos_limit, 20000). 0.72/1.01 % set(auto) -> set(auto_denials). 0.72/1.01 % set(auto) -> set(auto_process). 0.72/1.01 % set(auto2) -> assign(new_constants, 1). 0.72/1.01 % set(auto2) -> assign(fold_denial_max, 3). 0.72/1.01 % set(auto2) -> assign(max_weight, "200.000"). 0.72/1.01 % set(auto2) -> assign(max_hours, 1). 0.72/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.72/1.01 % set(auto2) -> assign(max_seconds, 0). 0.72/1.01 % set(auto2) -> assign(max_minutes, 5). 0.72/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.72/1.01 % set(auto2) -> set(sort_initial_sos). 0.72/1.01 % set(auto2) -> assign(sos_limit, -1). 0.72/1.01 % set(auto2) -> assign(lrs_ticks, 3000). 0.72/1.01 % set(auto2) -> assign(max_megs, 400). 0.72/1.01 % set(auto2) -> assign(stats, some). 0.72/1.01 % set(auto2) -> clear(echo_input). 0.72/1.01 % set(auto2) -> set(quiet). 0.72/1.01 % set(auto2) -> clear(print_initial_clauses). 0.72/1.01 % set(auto2) -> clear(print_given). 0.72/1.01 assign(lrs_ticks,-1). 0.72/1.01 assign(sos_limit,10000). 0.72/1.01 assign(order,kbo). 0.72/1.01 set(lex_order_vars). 0.72/1.01 clear(print_given). 0.72/1.01 0.72/1.01 % formulas(sos). % not echoed (17 formulas) 0.72/1.01 0.72/1.01 ============================== end of input ========================== 0.72/1.01 0.72/1.01 % From the command line: assign(max_seconds, 960). 0.72/1.01 0.72/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.72/1.01 0.72/1.01 % Formulas that are not ordinary clauses: 0.72/1.01 1 (all X0 all X1 complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 2 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 3 (all X0 all X1 join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 4 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 5 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 6 (all X0 all X1 complement(join(complement(X0),complement(X1))) = meet(X0,X1)) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 7 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 8 (all X0 X0 = converse(converse(X0))) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 9 (all X0 all X1 all X2 composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2))) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 10 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 11 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 12 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption]. 0.72/1.01 13 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) # label(modular_law_2) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 15 (all X0 all X1 all X2 composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) = join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))))) # label(dedekind_law) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 16 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) # label(modular_law_1) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 17 -(all X0 composition(complement(composition(X0,top)),top) = complement(composition(X0,top))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 7.42/7.72 7.42/7.72 ============================== end of process non-clausal formulas === 7.42/7.72 7.42/7.72 ============================== PROCESS INITIAL CLAUSES =============== 7.42/7.72 7.42/7.72 ============================== PREDICATE ELIMINATION ================= 7.42/7.72 7.42/7.72 ============================== end predicate elimination ============= 7.42/7.72 7.42/7.72 Auto_denials: 7.42/7.72 % copying label goals to answer in negative clause 7.42/7.72 7.42/7.72 Term ordering decisions: 7.42/7.72 Function symbol KB weights: one=1. top=1. zero=1. c1=1. composition=1. join=1. meet=1. converse=1. complement=1. 7.42/7.72 7.42/7.72 ============================== end of process initial clauses ======== 7.42/7.72 7.42/7.72 ============================== CLAUSES FOR SEARCH ==================== 7.42/7.72 7.42/7.72 ============================== end of clauses for search ============= 7.42/7.72 7.42/7.72 ============================== SEARCH ================================ 7.42/7.72 7.42/7.72 % Starting search at 0.01 seconds. 7.42/7.72 7.42/7.72 Low Water (keep): wt=86.000, iters=3408 7.42/7.72 7.42/7.72 Low Water (keep): wt=77.000, iters=3340 7.42/7.72 7.42/7.72 Low Water (keep): wt=76.000, iters=3442 7.42/7.72 7.42/7.72 Low Water (keep): wt=74.000, iters=3361 7.42/7.72 7.42/7.72 Low Water (keep): wt=73.000, iters=3348 7.42/7.72 7.42/7.72 Low Water (keep): wt=72.000, iters=3345 7.42/7.72 7.42/7.72 Low Water (keep): wt=71.000, iters=3370 7.42/7.72 7.42/7.72 Low Water (keep): wt=70.000, iters=3337 7.42/7.72 7.42/7.72 Low Water (keep): wt=69.000, iters=3343 7.42/7.72 7.42/7.72 Low Water (keep): wt=68.000, iters=3441 7.42/7.72 7.42/7.72 Low Water (keep): wt=67.000, iters=3401 7.42/7.72 7.42/7.72 Low Water (keep): wt=66.000, iters=3400 7.42/7.72 7.42/7.72 Low Water (keep): wt=64.000, iters=3397 7.42/7.72 7.42/7.72 Low Water (keep): wt=63.000, iters=3451 7.42/7.72 7.42/7.72 Low Water (keep): wt=62.000, iters=3496 7.42/7.72 7.42/7.72 Low Water (keep): wt=61.000, iters=3447 7.42/7.72 7.42/7.72 Low Water (keep): wt=60.000, iters=3369 7.42/7.72 7.42/7.72 Low Water (keep): wt=59.000, iters=3356 7.42/7.72 7.42/7.72 Low Water (keep): wt=57.000, iters=3390 7.42/7.72 7.42/7.72 Low Water (keep): wt=56.000, iters=3409 7.42/7.72 7.42/7.72 Low Water (keep): wt=54.000, iters=3376 7.42/7.72 7.42/7.72 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 3.98 sec). 7.42/7.72 7.42/7.72 Low Water (keep): wt=53.000, iters=3348 7.42/7.72 7.42/7.72 Low Water (keep): wt=51.000, iters=3377 7.42/7.72 7.42/7.72 Low Water (keep): wt=48.000, iters=3349 7.42/7.72 7.42/7.72 Low Water (keep): wt=47.000, iters=3569 7.42/7.72 7.42/7.72 Low Water (keep): wt=45.000, iters=3494 7.42/7.72 7.42/7.72 Low Water (keep): wt=38.000, iters=3351 7.42/7.72 7.42/7.72 Low Water (keep): wt=35.000, iters=3346 7.42/7.72 7.42/7.72 Low Water (keep): wt=34.000, iters=3355 7.42/7.72 7.42/7.72 Low Water (keep): wt=33.000, iters=3390 7.42/7.72 7.42/7.72 Low Water (keep): wt=32.000, iters=3352 7.42/7.72 7.42/7.72 Low Water (keep): wt=31.000, iters=3349 7.42/7.72 7.42/7.72 Low Water (keep): wt=30.000, iters=3413 7.42/7.72 7.42/7.72 Low Water (keep): wt=29.000, iters=3370 7.42/7.72 7.42/7.72 Low Water (keep): wt=28.000, iters=3376 7.42/7.72 7.42/7.72 Low Water (keep): wt=27.000, iters=3351 7.42/7.72 7.42/7.72 Low Water (keep): wt=26.000, iters=3376 7.42/7.72 7.42/7.72 Low Water (keep): wt=25.000, iters=3409 7.42/7.72 7.42/7.72 Low Water (displace): id=4733, wt=87.000 7.42/7.72 7.42/7.72 Low Water (displace): id=5890, wt=86.000 7.42/7.72 7.42/7.72 Low Water (keep): wt=24.000, iters=3345 7.42/7.72 7.42/7.72 Low Water (displace): id=16581, wt=23.000 7.42/7.72 7.42/7.72 Low Water (displace): id=16586, wt=22.000 7.42/7.72 7.42/7.72 Low Water (displace): id=16600, wt=21.000 7.42/7.72 7.42/7.72 Low Water (displace): id=16656, wt=18.000 7.42/7.72 7.42/7.72 Low Water (keep): wt=23.000, iters=3342 7.42/7.72 7.42/7.72 Low Water (displace): id=16996, wt=17.000 7.42/7.72 7.42/7.72 Low Water (displace): id=17095, wt=16.000 7.42/7.72 7.42/7.72 Low Water (keep): wt=22.000, iters=3335 7.42/7.72 7.42/7.72 ============================== PROOF ================================= 7.42/7.72 % SZS status Theorem 7.42/7.72 % SZS output start Refutation 7.42/7.72 7.42/7.72 % Proof 1 at 6.59 (+ 0.12) seconds: goals. 7.42/7.72 % Length of proof is 142. 7.42/7.72 % Level of proof is 36. 7.42/7.72 % Maximum clause weight is 48.000. 7.42/7.72 % Given clauses 696. 7.42/7.72 7.42/7.72 1 (all X0 all X1 complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 2 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 3 (all X0 all X1 join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 4 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 5 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 6 (all X0 all X1 complement(join(complement(X0),complement(X1))) = meet(X0,X1)) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 7 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 8 (all X0 X0 = converse(converse(X0))) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 9 (all X0 all X1 all X2 composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2))) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 10 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 11 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 12 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 13 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) # label(modular_law_2) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 15 (all X0 all X1 all X2 composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) = join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))))) # label(dedekind_law) # label(axiom) # label(non_clause). [assumption]. 7.42/7.72 17 -(all X0 composition(complement(composition(X0,top)),top) = complement(composition(X0,top))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 7.42/7.72 18 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)]. 7.42/7.72 19 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(11)]. 7.42/7.72 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(4)]. 7.42/7.72 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(12)]. 7.42/7.72 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(7)]. 7.42/7.72 23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(2)]. 7.42/7.72 24 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(23),flip(a)]. 7.42/7.72 25 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(6)]. 7.42/7.72 26 join(converse(A),converse(B)) = converse(join(A,B)) # label(converse_additivity) # label(axiom). [clausify(13)]. 7.42/7.72 27 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(9)]. 7.42/7.72 28 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(10)]. 7.42/7.72 29 join(A,join(B,C)) = join(C,join(A,B)). [copy(28),rewrite([22(2)]),flip(a)]. 7.42/7.72 30 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity) # label(axiom). [clausify(1)]. 7.42/7.72 31 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(30),rewrite([22(6)])]. 7.42/7.72 32 join(composition(A,B),composition(C,B)) = composition(join(A,C),B) # label(composition_distributivity) # label(axiom). [clausify(5)]. 7.42/7.72 33 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)]. 7.42/7.72 34 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(33),rewrite([22(6),22(8)]),rewrite([22(6)])]. 7.42/7.72 35 meet(composition(meet(A,composition(B,converse(C))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)) # label(modular_law_2) # label(axiom). [clausify(14)]. 7.42/7.72 36 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C))))) = complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C)))). [copy(35),rewrite([25(3),25(8),22(10),25(13),22(15),25(19),25(24),22(26)]),flip(a)]. 7.42/7.72 39 join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))) # label(dedekind_law) # label(axiom). [clausify(15)]. 7.42/7.72 40 join(complement(join(complement(A),complement(composition(B,C)))),composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A))))). [copy(39),rewrite([25(2),22(4),25(8),25(14),25(22),25(28)])]. 7.42/7.72 41 complement(composition(c1,top)) != composition(complement(composition(c1,top)),top) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)]. 7.42/7.72 42 composition(complement(composition(c1,top)),top) != complement(composition(c1,top)) # answer(goals). [copy(41),flip(a)]. 7.42/7.72 43 complement(top) = zero. [back_rewrite(21),rewrite([25(2),20(4)])]. 7.42/7.72 44 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(18(a,1),24(a,1,1)),flip(a)]. 7.42/7.72 45 converse(composition(converse(A),B)) = composition(converse(B),A). [para(18(a,1),24(a,1,2)),flip(a)]. 7.42/7.72 46 converse(join(A,converse(B))) = join(B,converse(A)). [para(18(a,1),26(a,1,1)),rewrite([22(4)]),flip(a)]. 7.42/7.72 47 composition(A,composition(one,B)) = composition(A,B). [para(19(a,1),27(a,1,1)),flip(a)]. 7.42/7.72 49 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),29(a,2,2)),rewrite([22(2)])]. 7.42/7.72 50 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(18(a,1),31(a,1,2,1))]. 7.42/7.72 51 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(19(a,1),31(a,1,2,2,1))]. 7.42/7.72 53 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(31(a,1),26(a,2,1)),rewrite([45(7)])]. 7.42/7.72 55 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(24(a,1),32(a,1,1)),rewrite([22(7)])]. 7.42/7.72 57 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(27(a,1),32(a,1,1)),rewrite([22(6)])]. 7.42/7.72 58 join(composition(A,B),composition(C,composition(D,B))) = composition(join(A,composition(C,D)),B). [para(27(a,1),32(a,1,2))]. 7.42/7.72 59 join(zero,complement(join(complement(A),complement(A)))) = A. [para(20(a,1),34(a,1,1,1)),rewrite([43(2)])]. 7.42/7.72 63 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(34(a,1),34(a,1,2,1)),rewrite([22(10)])]. 7.42/7.72 89 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(43(a,1),31(a,1,1)),rewrite([43(9)])]. 7.42/7.72 91 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(43(a,1),34(a,1,2,1,1))]. 7.42/7.72 101 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(44(a,1),26(a,1,1)),rewrite([22(7)]),flip(a)]. 7.42/7.72 113 composition(converse(one),A) = A. [para(19(a,1),45(a,1,1)),rewrite([18(2)]),flip(a)]. 7.42/7.72 121 converse(one) = one. [para(113(a,1),19(a,1)),flip(a)]. 7.42/7.72 123 join(complement(A),composition(one,complement(A))) = complement(A). [para(113(a,1),31(a,1,2,2,1)),rewrite([121(3),121(3)])]. 7.42/7.72 125 join(A,composition(B,A)) = composition(join(B,one),A). [para(113(a,1),32(a,1,1)),rewrite([121(4),22(4)])]. 7.42/7.72 139 composition(one,A) = A. [para(113(a,1),47(a,2)),rewrite([121(2),47(4)])]. 7.42/7.72 142 join(complement(A),complement(A)) = complement(A). [back_rewrite(123),rewrite([139(4)])]. 7.42/7.72 146 join(zero,complement(complement(A))) = A. [back_rewrite(59),rewrite([142(4)])]. 7.42/7.72 149 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(46(a,1),26(a,1,1)),rewrite([22(7),29(7,R),22(6)]),flip(a)]. 7.42/7.72 150 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(46(a,1),26(a,1,2)),rewrite([29(4,R),22(3),26(3),149(7)]),flip(a)]. 7.42/7.72 156 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(46(a,1),46(a,2,2)),rewrite([150(4),46(4),29(6,R),22(5)])]. 7.42/7.72 157 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(149),rewrite([156(8),26(7)])]. 7.42/7.72 158 converse(join(A,one)) = join(one,converse(A)). [para(121(a,1),26(a,1,1)),rewrite([22(5)]),flip(a)]. 7.42/7.72 174 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(158(a,1),24(a,1,1))]. 7.42/7.72 187 join(top,complement(A)) = top. [para(142(a,1),49(a,1,2)),rewrite([20(2),22(4)]),flip(a)]. 7.42/7.72 188 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(91),rewrite([187(3),43(2)])]. 7.42/7.72 189 join(top,top) = join(A,top). [para(187(a,1),49(a,1,2)),flip(a)]. 7.42/7.72 190 join(complement(one),composition(A,complement(converse(A)))) = complement(one). [para(19(a,1),50(a,1,2,2,1))]. 7.42/7.72 198 join(A,top) = join(B,top). [para(189(a,1),49(a,2)),rewrite([187(3)])]. 7.42/7.72 199 join(A,top) = c_0. [new_symbol(198)]. 7.42/7.72 202 join(A,join(B,complement(A))) = c_0. [back_rewrite(49),rewrite([199(5)])]. 7.42/7.72 207 c_0 = top. [para(36(a,1),202(a,1,2)),rewrite([20(22)]),flip(a)]. 7.42/7.72 208 join(A,join(B,complement(A))) = top. [back_rewrite(202),rewrite([207(4)])]. 7.42/7.72 210 join(A,top) = top. [back_rewrite(199),rewrite([207(3)])]. 7.42/7.72 218 join(zero,complement(A)) = complement(A). [para(146(a,1),188(a,1,2,1))]. 7.42/7.72 219 complement(complement(A)) = A. [back_rewrite(188),rewrite([218(4),218(4)])]. 7.42/7.72 220 join(A,zero) = A. [back_rewrite(146),rewrite([219(3),22(2)])]. 7.42/7.72 242 join(A,composition(converse(B),complement(composition(B,complement(A))))) = A. [para(219(a,1),31(a,1,1)),rewrite([219(8)])]. 7.42/7.72 243 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(219(a,1),34(a,1,1,1,2)),rewrite([219(5),22(4)])]. 7.42/7.72 251 complement(zero) = top. [para(43(a,1),219(a,1,1))]. 7.42/7.72 252 join(A,A) = A. [para(219(a,1),142(a,1,1)),rewrite([219(2),219(3)])]. 7.42/7.72 254 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(219(a,1),51(a,1,2,2))]. 7.42/7.72 261 join(A,join(A,B)) = join(A,B). [para(252(a,1),29(a,1)),rewrite([22(3),29(4,R),22(3),29(3,R),252(2)]),flip(a)]. 7.42/7.72 263 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(43(a,1),53(a,1,1,1)),rewrite([43(10)])]. 7.42/7.72 267 join(A,complement(join(B,complement(A)))) = A. [para(34(a,1),261(a,1,2)),rewrite([22(4),34(12)])]. 7.42/7.72 272 join(complement(A),complement(join(A,B))) = complement(A). [para(219(a,1),267(a,1,2,1,2)),rewrite([22(2)])]. 7.42/7.72 292 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(158(a,1),89(a,1,2,1))]. 7.42/7.72 298 converse(join(A,composition(A,B))) = converse(composition(A,join(B,one))). [para(139(a,1),55(a,1,2)),rewrite([22(4),26(4),174(8)])]. 7.42/7.72 321 join(complement(A),complement(composition(join(B,one),A))) = complement(A). [para(125(a,1),272(a,1,2,1))]. 7.42/7.72 328 join(complement(one),converse(complement(one))) = complement(one). [para(19(a,1),254(a,1,2))]. 7.42/7.72 338 converse(complement(one)) = complement(one). [para(328(a,1),26(a,2,1)),rewrite([18(7),22(6),328(6)]),flip(a)]. 7.42/7.72 347 converse(top) = top. [para(338(a,1),158(a,2,2)),rewrite([22(4),20(4),20(6)])]. 7.42/7.72 354 join(top,converse(A)) = top. [para(347(a,1),26(a,1,1)),rewrite([22(5),210(5),347(5)])]. 7.42/7.72 358 join(top,composition(A,converse(B))) = top. [para(44(a,1),354(a,1,2))]. 7.42/7.72 366 join(top,composition(A,B)) = top. [para(18(a,1),358(a,1,2,2))]. 7.42/7.72 367 composition(join(A,one),top) = top. [para(347(a,1),358(a,1,2,2)),rewrite([125(4)])]. 7.42/7.72 368 composition(join(one,converse(A)),zero) = zero. [back_rewrite(292),rewrite([367(8),43(6),125(7),22(5),261(5)])]. 7.42/7.72 391 composition(top,zero) = zero. [para(338(a,1),368(a,1,1,2)),rewrite([20(4)])]. 7.42/7.72 401 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(391(a,1),40(a,1,1,1,2,1)),rewrite([251(3),22(3),187(3),43(2),43(3),218(7),219(6),251(6),347(7),187(9),43(6),27(6),43(9),218(13),219(12),251(12),347(13),187(15),43(12),27(12)])]. 7.42/7.72 406 join(zero,composition(A,composition(B,zero))) = zero. [para(391(a,1),57(a,1,2)),rewrite([22(5),366(8),391(8)])]. 7.42/7.72 408 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(401),rewrite([406(7)]),flip(a)]. 7.42/7.72 440 join(complement(A),complement(join(B,A))) = complement(A). [para(267(a,1),63(a,2)),rewrite([219(2),219(4),219(8),63(13)])]. 7.42/7.72 475 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(408(a,1),27(a,1,1)),rewrite([27(7)]),flip(a)]. 7.42/7.72 476 composition(A,zero) = zero. [para(408(a,1),27(a,1)),rewrite([408(6)]),flip(a)]. 7.42/7.72 477 composition(converse(zero),A) = converse(zero). [para(408(a,1),45(a,1,1)),rewrite([476(6)]),flip(a)]. 7.42/7.72 482 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(475),rewrite([477(5)]),flip(a)]. 7.42/7.72 514 join(composition(A,B),composition(C,converse(zero))) = composition(join(A,composition(C,converse(zero))),B). [para(477(a,1),58(a,1,2,2))]. 7.42/7.72 516 converse(zero) = zero. [para(477(a,1),476(a,1))]. 7.42/7.72 518 join(zero,composition(converse(complement(composition(A,top))),A)) = zero. [back_rewrite(263),rewrite([516(2),516(9)])]. 7.42/7.72 519 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(514),rewrite([516(3),476(3),22(3),516(5),476(5),220(5)])]. 7.42/7.72 523 composition(zero,A) = zero. [back_rewrite(482),rewrite([516(4),476(4)])]. 7.42/7.72 524 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(518),rewrite([519(7)])]. 7.42/7.72 625 composition(converse(complement(composition(A,top))),composition(A,B)) = zero. [para(524(a,1),27(a,1,1)),rewrite([523(2)]),flip(a)]. 7.42/7.72 696 join(one,complement(composition(A,complement(converse(A))))) = complement(composition(A,complement(converse(A)))). [para(190(a,1),440(a,1,2,1)),rewrite([219(7),22(6)])]. 7.42/7.72 3570 join(complement(A),composition(join(B,one),A)) = top. [para(321(a,1),208(a,1,2)),rewrite([22(5)])]. 7.42/7.72 3648 join(A,composition(join(B,one),complement(A))) = top. [para(219(a,1),3570(a,1,1))]. 7.42/7.72 3651 join(A,join(B,composition(join(C,one),complement(A)))) = top. [para(3648(a,1),29(a,2,2)),rewrite([22(5),210(8)])]. 7.42/7.72 7742 join(complement(A),composition(join(one,converse(B)),A)) = top. [para(50(a,1),3651(a,1,2)),rewrite([158(3),22(6)])]. 7.42/7.72 7752 join(converse(complement(converse(A))),composition(A,join(B,one))) = top. [para(7742(a,1),101(a,1,1)),rewrite([347(2),46(5),121(3),22(8)]),flip(a)]. 7.42/7.72 9380 join(A,converse(complement(converse(A)))) = top. [para(252(a,1),7752(a,1,2,2)),rewrite([19(5),22(4)])]. 7.42/7.72 9411 join(complement(converse(A)),converse(join(B,A))) = top. [para(9380(a,1),157(a,1,1,2)),rewrite([210(2),347(2)]),flip(a)]. 7.42/7.72 9415 complement(join(complement(A),converse(complement(converse(A))))) = complement(converse(complement(converse(A)))). [para(9380(a,1),243(a,1,1,1)),rewrite([43(2),22(6),218(8)])]. 7.42/7.72 9474 join(complement(one),complement(composition(converse(complement(A)),A))) = top. [para(51(a,1),9411(a,1,2,1)),rewrite([45(4),338(7),22(7)])]. 7.42/7.72 9481 join(complement(one),complement(converse(composition(A,complement(converse(A)))))) = top. [para(190(a,1),9411(a,1,2,1)),rewrite([338(8),22(8)])]. 7.42/7.72 9568 complement(join(complement(A),complement(converse(complement(converse(A)))))) = zero. [para(9474(a,1),36(a,1,2,1,2,1,1,1)),rewrite([139(6),22(6),43(13),523(13),251(13),22(13),187(13),43(9),22(9),218(9),24(18),9481(19),43(13),523(13),251(13),22(13),187(13),43(9)])]. 7.42/7.72 9711 complement(join(A,complement(converse(complement(converse(A)))))) = converse(complement(converse(A))). [para(9568(a,1),34(a,1,1)),rewrite([219(3),218(8)])]. 7.42/7.72 9727 complement(converse(complement(converse(A)))) = A. [para(9568(a,1),243(a,1,2)),rewrite([22(5),9415(6),22(6),218(6),219(6)])]. 7.42/7.72 9728 converse(complement(converse(A))) = complement(A). [back_rewrite(9711),rewrite([9727(4),252(1)]),flip(a)]. 7.42/7.72 9765 complement(converse(A)) = converse(complement(A)). [para(9728(a,1),18(a,1,1)),flip(a)]. 7.42/7.72 9768 converse(complement(composition(A,converse(B)))) = complement(composition(B,converse(A))). [para(44(a,1),9728(a,1,1,1))]. 7.42/7.72 9769 converse(complement(composition(converse(A),B))) = complement(composition(converse(B),A)). [para(45(a,1),9728(a,1,1,1))]. 7.42/7.72 10710 join(one,complement(composition(A,converse(complement(A))))) = complement(composition(A,converse(complement(A)))). [back_rewrite(696),rewrite([9765(3),9765(8)])]. 7.42/7.72 14078 composition(complement(composition(complement(A),converse(A))),A) = A. [para(242(a,1),298(a,1,1)),rewrite([18(2),9765(3),22(7),10710(7),45(7),9768(5)]),flip(a)]. 7.42/7.72 14236 composition(A,complement(composition(converse(A),complement(A)))) = A. [para(14078(a,1),44(a,1,1)),rewrite([18(2),9765(2),18(4),9769(5)]),flip(a)]. 7.42/7.72 14312 composition(complement(A),complement(composition(converse(complement(A)),A))) = complement(A). [para(219(a,1),14236(a,1,2,1,2))]. 7.42/7.72 17701 composition(complement(composition(A,top)),top) = complement(composition(A,top)). [para(625(a,1),14312(a,1,2,1)),rewrite([251(5)])]. 7.42/7.72 17702 $F # answer(goals). [resolve(17701,a,42,a)]. 7.42/7.72 7.42/7.72 % SZS output end Refutation 7.42/7.72 ============================== end of proof ========================== 7.42/7.72 7.42/7.72 ============================== STATISTICS ============================ 7.42/7.72 7.42/7.72 Given=696. Generated=128133. Kept=17676. proofs=1. 7.42/7.72 Usable=524. Sos=9996. Demods=10218. Limbo=2, Disabled=7170. Hints=0. 7.42/7.72 Megabytes=28.25. 7.42/7.72 User_CPU=6.59, System_CPU=0.12, Wall_clock=6. 7.42/7.72 7.42/7.72 ============================== end of statistics ===================== 7.42/7.72 7.42/7.72 ============================== end of search ========================= 7.42/7.72 7.42/7.72 THEOREM PROVED 7.42/7.72 % SZS status Theorem 7.42/7.72 7.42/7.72 Exiting with 1 proof. 7.42/7.72 7.42/7.72 Process 29590 exit (max_proofs) Thu Jul 2 07:34:42 2020 7.42/7.72 Prover9 interrupted 7.42/7.72 EOF