0.03/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n020.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Aug 9 04:43:50 EDT 2022 0.13/0.35 % CPUTime : 0.47/1.00 ============================== Prover9 =============================== 0.47/1.00 Prover9 (32) version 2009-11A, November 2009. 0.47/1.00 Process 1154 was started by sandbox2 on n020.cluster.edu, 0.47/1.00 Tue Aug 9 04:43:50 2022 0.47/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_975_n020.cluster.edu". 0.47/1.00 ============================== end of head =========================== 0.47/1.00 0.47/1.00 ============================== INPUT ================================= 0.47/1.00 0.47/1.00 % Reading from file /tmp/Prover9_975_n020.cluster.edu 0.47/1.00 0.47/1.00 set(prolog_style_variables). 0.47/1.00 set(auto2). 0.47/1.00 % set(auto2) -> set(auto). 0.47/1.00 % set(auto) -> set(auto_inference). 0.47/1.00 % set(auto) -> set(auto_setup). 0.47/1.00 % set(auto_setup) -> set(predicate_elim). 0.47/1.00 % set(auto_setup) -> assign(eq_defs, unfold). 0.47/1.00 % set(auto) -> set(auto_limits). 0.47/1.00 % set(auto_limits) -> assign(max_weight, "100.000"). 0.47/1.00 % set(auto_limits) -> assign(sos_limit, 20000). 0.47/1.00 % set(auto) -> set(auto_denials). 0.47/1.00 % set(auto) -> set(auto_process). 0.47/1.00 % set(auto2) -> assign(new_constants, 1). 0.47/1.00 % set(auto2) -> assign(fold_denial_max, 3). 0.47/1.00 % set(auto2) -> assign(max_weight, "200.000"). 0.47/1.00 % set(auto2) -> assign(max_hours, 1). 0.47/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.47/1.00 % set(auto2) -> assign(max_seconds, 0). 0.47/1.00 % set(auto2) -> assign(max_minutes, 5). 0.47/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.47/1.00 % set(auto2) -> set(sort_initial_sos). 0.47/1.00 % set(auto2) -> assign(sos_limit, -1). 0.47/1.00 % set(auto2) -> assign(lrs_ticks, 3000). 0.47/1.00 % set(auto2) -> assign(max_megs, 400). 0.47/1.00 % set(auto2) -> assign(stats, some). 0.47/1.00 % set(auto2) -> clear(echo_input). 0.47/1.00 % set(auto2) -> set(quiet). 0.47/1.00 % set(auto2) -> clear(print_initial_clauses). 0.47/1.00 % set(auto2) -> clear(print_given). 0.47/1.00 assign(lrs_ticks,-1). 0.47/1.00 assign(sos_limit,10000). 0.47/1.00 assign(order,kbo). 0.47/1.00 set(lex_order_vars). 0.47/1.00 clear(print_given). 0.47/1.00 0.47/1.00 % formulas(sos). % not echoed (14 formulas) 0.47/1.00 0.47/1.00 ============================== end of input ========================== 0.47/1.00 0.47/1.00 % From the command line: assign(max_seconds, 960). 0.47/1.00 0.47/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.47/1.00 0.47/1.00 % Formulas that are not ordinary clauses: 0.47/1.00 1 (all X0 all X1 join(converse(X0),converse(X1)) = converse(join(X0,X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 2 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 3 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 4 (all X0 meet(X0,complement(X0)) = zero) # label(def_zero) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 5 (all X0 all X1 join(X1,X0) = join(X0,X1)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 6 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 7 (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]. 0.47/1.00 8 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 9 (all X0 all X1 complement(join(complement(X0),complement(X1))) = meet(X0,X1)) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 10 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 11 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 12 (all X0 all X1 all X2 join(composition(X0,X2),composition(X1,X2)) = composition(join(X0,X1),X2)) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.47/1.00 13 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 14 -(all X0 (join(X0,one) = one -> X0 = converse(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 4.68/4.98 4.68/4.98 ============================== end of process non-clausal formulas === 4.68/4.98 4.68/4.98 ============================== PROCESS INITIAL CLAUSES =============== 4.68/4.98 4.68/4.98 ============================== PREDICATE ELIMINATION ================= 4.68/4.98 4.68/4.98 ============================== end predicate elimination ============= 4.68/4.98 4.68/4.98 Auto_denials: 4.68/4.98 % copying label goals to answer in negative clause 4.68/4.98 4.68/4.98 Term ordering decisions: 4.68/4.98 Function symbol KB weights: one=1. top=1. zero=1. c1=1. join=1. composition=1. meet=1. complement=1. converse=1. 4.68/4.98 4.68/4.98 ============================== end of process initial clauses ======== 4.68/4.98 4.68/4.98 ============================== CLAUSES FOR SEARCH ==================== 4.68/4.98 4.68/4.98 ============================== end of clauses for search ============= 4.68/4.98 4.68/4.98 ============================== SEARCH ================================ 4.68/4.98 4.68/4.98 % Starting search at 0.01 seconds. 4.68/4.98 4.68/4.98 Low Water (keep): wt=43.000, iters=3345 4.68/4.98 4.68/4.98 Low Water (keep): wt=37.000, iters=3393 4.68/4.98 4.68/4.98 Low Water (keep): wt=34.000, iters=3335 4.68/4.98 4.68/4.98 Low Water (keep): wt=33.000, iters=3336 4.68/4.98 4.68/4.98 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 1.22 sec). 4.68/4.98 4.68/4.98 Low Water (keep): wt=32.000, iters=3418 4.68/4.98 4.68/4.98 Low Water (keep): wt=31.000, iters=3363 4.68/4.98 4.68/4.98 Low Water (keep): wt=30.000, iters=3406 4.68/4.98 4.68/4.98 Low Water (keep): wt=29.000, iters=3348 4.68/4.98 4.68/4.98 Low Water (keep): wt=28.000, iters=3380 4.68/4.98 4.68/4.98 Low Water (keep): wt=27.000, iters=3342 4.68/4.98 4.68/4.98 Low Water (keep): wt=26.000, iters=3358 4.68/4.98 4.68/4.98 Low Water (keep): wt=25.000, iters=3335 4.68/4.98 4.68/4.98 Low Water (keep): wt=24.000, iters=3340 4.68/4.98 4.68/4.98 Low Water (keep): wt=23.000, iters=3335 4.68/4.98 4.68/4.98 Low Water (keep): wt=22.000, iters=3383 4.68/4.98 4.68/4.98 Low Water (keep): wt=21.000, iters=3333 4.68/4.98 4.68/4.98 Low Water (keep): wt=20.000, iters=3343 4.68/4.98 4.68/4.98 Low Water (keep): wt=19.000, iters=3341 4.68/4.98 4.68/4.98 Low Water (displace): id=4391, wt=46.000 4.68/4.98 4.68/4.98 Low Water (displace): id=7181, wt=45.000 4.68/4.98 4.68/4.98 Low Water (displace): id=7364, wt=44.000 4.68/4.98 4.68/4.98 Low Water (displace): id=7049, wt=43.000 4.68/4.98 4.68/4.98 Low Water (displace): id=7353, wt=42.000 4.68/4.98 4.68/4.98 Low Water (displace): id=7333, wt=41.000 4.68/4.98 4.68/4.98 Low Water (displace): id=5403, wt=40.000 4.68/4.98 4.68/4.98 Low Water (displace): id=6578, wt=39.000 4.68/4.98 4.68/4.98 Low Water (displace): id=7365, wt=38.000 4.68/4.98 4.68/4.98 Low Water (displace): id=13617, wt=16.000 4.68/4.98 4.68/4.98 Low Water (displace): id=13620, wt=15.000 4.68/4.98 4.68/4.98 Low Water (displace): id=13624, wt=14.000 4.68/4.98 4.68/4.98 Low Water (displace): id=13811, wt=13.000 4.68/4.98 4.68/4.98 Low Water (keep): wt=18.000, iters=3333 4.68/4.98 4.68/4.98 ============================== PROOF ================================= 4.68/4.98 % SZS status Theorem 4.68/4.98 % SZS output start Refutation 4.68/4.98 4.68/4.98 % Proof 1 at 3.88 (+ 0.11) seconds: goals. 4.68/4.98 % Length of proof is 148. 4.68/4.98 % Level of proof is 34. 4.68/4.98 % Maximum clause weight is 21.000. 4.68/4.98 % Given clauses 989. 4.68/4.98 4.68/4.98 1 (all X0 all X1 join(converse(X0),converse(X1)) = converse(join(X0,X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 2 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 3 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 4 (all X0 meet(X0,complement(X0)) = zero) # label(def_zero) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 5 (all X0 all X1 join(X1,X0) = join(X0,X1)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 6 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 7 (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]. 4.68/4.98 8 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 9 (all X0 all X1 complement(join(complement(X0),complement(X1))) = meet(X0,X1)) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 10 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 11 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 12 (all X0 all X1 all X2 join(composition(X0,X2),composition(X1,X2)) = composition(join(X0,X1),X2)) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 13 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption]. 4.68/4.98 14 -(all X0 (join(X0,one) = one -> X0 = converse(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 4.68/4.98 15 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(3)]. 4.68/4.98 16 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(8)]. 4.68/4.98 17 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(14)]. 4.68/4.98 18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(4)]. 4.68/4.98 19 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(6)]. 4.68/4.98 20 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(5)]. 4.68/4.98 21 join(converse(A),converse(B)) = converse(join(A,B)) # label(converse_additivity) # label(axiom). [clausify(1)]. 4.68/4.98 22 composition(converse(A),converse(B)) = converse(composition(B,A)) # label(converse_multiplicativity) # label(axiom). [clausify(2)]. 4.68/4.98 23 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(9)]. 4.68/4.98 24 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(7)]. 4.68/4.98 25 join(A,join(B,C)) = join(C,join(A,B)). [copy(24),rewrite([20(2)]),flip(a)]. 4.68/4.98 26 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(10)]. 4.68/4.98 27 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(12)]. 4.68/4.98 28 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(27),flip(a)]. 4.68/4.98 29 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(13)]. 4.68/4.98 30 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(29),rewrite([20(7)]),flip(a)]. 4.68/4.98 31 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(11)]. 4.68/4.98 32 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(31),rewrite([20(6),20(8)]),rewrite([20(6)])]. 4.68/4.98 33 converse(c1) != c1 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)]. 4.68/4.98 34 join(one,c1) = one. [back_rewrite(17),rewrite([20(3)])]. 4.68/4.98 35 complement(top) = zero. [back_rewrite(18),rewrite([23(2),19(4)])]. 4.68/4.98 36 converse(join(A,converse(B))) = join(B,converse(A)). [para(15(a,1),21(a,1,1)),rewrite([20(4)]),flip(a)]. 4.68/4.98 37 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(15(a,1),22(a,1,1)),flip(a)]. 4.68/4.98 38 converse(composition(converse(A),B)) = composition(converse(B),A). [para(15(a,1),22(a,1,2)),flip(a)]. 4.68/4.98 39 join(A,join(B,complement(A))) = join(B,top). [para(19(a,1),25(a,2,2)),rewrite([20(2)])]. 4.68/4.98 40 composition(A,composition(one,B)) = composition(A,B). [para(16(a,1),26(a,1,1)),flip(a)]. 4.68/4.98 42 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(22(a,1),28(a,1,1)),rewrite([20(7)])]. 4.68/4.98 44 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(26(a,1),28(a,1,1)),rewrite([20(6)])]. 4.68/4.98 47 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(16(a,1),30(a,1,2,2,1))]. 4.68/4.98 48 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(30(a,1),21(a,2,1)),rewrite([38(7)])]. 4.68/4.98 49 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(22(a,1),30(a,1,2,2,1)),rewrite([15(4)])]. 4.68/4.98 51 join(zero,complement(join(complement(A),complement(A)))) = A. [para(19(a,1),32(a,1,1,1)),rewrite([35(2)])]. 4.68/4.98 55 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(32(a,1),32(a,1,2,1)),rewrite([20(10)])]. 4.68/4.98 59 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(35(a,1),32(a,1,2,1,1))]. 4.68/4.98 60 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(36(a,1),21(a,1,1)),rewrite([20(7),25(7,R),20(6)]),flip(a)]. 4.68/4.98 61 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(36(a,1),21(a,1,2)),rewrite([25(4,R),20(3),21(3),60(7)]),flip(a)]. 4.68/4.98 65 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(36(a,1),36(a,2,2)),rewrite([61(4),36(4),25(6,R),20(5)])]. 4.68/4.98 66 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(60),rewrite([65(8),21(7)])]. 4.68/4.98 68 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(37(a,1),21(a,1,1)),rewrite([20(7)]),flip(a)]. 4.68/4.98 72 composition(converse(one),A) = A. [para(16(a,1),38(a,1,1)),rewrite([15(2)]),flip(a)]. 4.68/4.98 78 converse(one) = one. [para(72(a,1),16(a,1)),flip(a)]. 4.68/4.98 80 composition(join(A,one),B) = join(B,composition(A,B)). [para(72(a,1),28(a,1,1)),rewrite([78(4),20(4)]),flip(a)]. 4.68/4.98 82 join(complement(A),complement(composition(one,A))) = complement(A). [para(72(a,1),30(a,1,2))]. 4.68/4.98 83 composition(one,A) = A. [para(72(a,1),40(a,2)),rewrite([78(2),40(4)])]. 4.68/4.98 84 join(complement(A),complement(A)) = complement(A). [back_rewrite(82),rewrite([83(3)])]. 4.68/4.98 85 join(zero,complement(complement(A))) = A. [back_rewrite(51),rewrite([84(4)])]. 4.68/4.98 86 converse(join(A,one)) = join(one,converse(A)). [para(78(a,1),21(a,1,1)),rewrite([20(5)]),flip(a)]. 4.68/4.98 90 join(top,complement(A)) = top. [para(84(a,1),39(a,1,2)),rewrite([19(2),20(4)]),flip(a)]. 4.68/4.98 91 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(59),rewrite([90(3),35(2)])]. 4.68/4.98 92 join(top,top) = join(A,top). [para(90(a,1),39(a,1,2)),flip(a)]. 4.68/4.98 97 join(A,top) = join(B,top). [para(92(a,1),39(a,2)),rewrite([90(3)])]. 4.68/4.98 98 join(A,top) = c_0. [new_symbol(97)]. 4.68/4.98 101 join(A,join(B,complement(A))) = c_0. [back_rewrite(39),rewrite([98(5)])]. 4.68/4.98 112 c_0 = top. [para(85(a,1),101(a,1,2)),rewrite([20(2),19(2)]),flip(a)]. 4.68/4.98 113 join(A,join(B,complement(A))) = top. [back_rewrite(101),rewrite([112(4)])]. 4.68/4.98 115 join(A,top) = top. [back_rewrite(98),rewrite([112(3)])]. 4.68/4.98 125 converse(join(A,join(B,one))) = join(one,converse(join(A,B))). [para(86(a,1),21(a,1,1)),rewrite([65(5),21(4),20(7),25(7,R),20(6)]),flip(a)]. 4.68/4.98 136 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(83(a,1),44(a,1,2)),rewrite([20(3)]),flip(a)]. 4.68/4.98 140 join(zero,complement(A)) = complement(A). [para(85(a,1),91(a,1,2,1))]. 4.68/4.98 141 complement(complement(A)) = A. [back_rewrite(91),rewrite([140(4),140(4)])]. 4.68/4.98 142 join(A,zero) = A. [back_rewrite(85),rewrite([141(3),20(2)])]. 4.68/4.98 147 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(141(a,1),32(a,1,1,1,2)),rewrite([141(5),20(4)])]. 4.68/4.98 149 join(A,A) = A. [para(141(a,1),84(a,1,1)),rewrite([141(2),141(3)])]. 4.68/4.98 153 join(A,join(A,B)) = join(A,B). [para(149(a,1),25(a,1)),rewrite([20(3),25(4,R),20(3),25(3,R),149(2)]),flip(a)]. 4.68/4.98 154 join(A,complement(join(B,complement(A)))) = A. [para(32(a,1),153(a,1,2)),rewrite([20(4),32(12)])]. 4.68/4.98 156 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(154(a,1),25(a,2,2)),rewrite([20(4),20(6)])]. 4.68/4.98 159 join(complement(A),complement(join(A,B))) = complement(A). [para(141(a,1),154(a,1,2,1,2)),rewrite([20(2)])]. 4.68/4.98 167 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(21(a,1),159(a,1,2,1))]. 4.68/4.98 177 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(141(a,1),47(a,1,2,2))]. 4.68/4.98 181 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(35(a,1),48(a,1,1,1)),rewrite([35(10)])]. 4.68/4.98 198 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(80(a,1),28(a,1,2)),rewrite([25(4,R),28(3),20(1)]),flip(a)]. 4.68/4.98 230 join(complement(one),converse(complement(one))) = complement(one). [para(16(a,1),177(a,1,2))]. 4.68/4.98 241 converse(complement(one)) = complement(one). [para(230(a,1),21(a,2,1)),rewrite([15(7),20(6),230(6)]),flip(a)]. 4.68/4.98 242 converse(join(A,complement(one))) = join(complement(one),converse(A)). [para(241(a,1),21(a,1,1)),rewrite([20(7)]),flip(a)]. 4.68/4.98 246 converse(top) = top. [para(241(a,1),86(a,2,2)),rewrite([20(4),19(4),19(6)])]. 4.68/4.98 250 join(top,converse(A)) = top. [para(246(a,1),21(a,1,1)),rewrite([20(5),115(5),246(5)])]. 4.68/4.98 251 converse(composition(A,top)) = composition(top,converse(A)). [para(246(a,1),22(a,1,1)),flip(a)]. 4.68/4.98 255 join(top,composition(A,converse(B))) = top. [para(37(a,1),250(a,1,2))]. 4.68/4.98 264 join(complement(A),complement(join(B,A))) = complement(A). [para(154(a,1),55(a,2)),rewrite([141(2),141(4),141(8),55(13)])]. 4.68/4.98 265 join(A,complement(join(complement(A),complement(B)))) = A. [para(55(a,1),159(a,1,2,1)),rewrite([141(2),20(3),141(7)])]. 4.68/4.98 270 join(top,composition(A,B)) = top. [para(15(a,1),255(a,1,2,2))]. 4.68/4.98 274 converse(composition(A,composition(B,top))) = composition(top,converse(composition(A,B))). [para(251(a,1),22(a,1,1)),rewrite([26(5),22(4)]),flip(a)]. 4.68/4.98 279 composition(top,join(one,converse(A))) = top. [para(86(a,1),251(a,2,2)),rewrite([80(4),270(4),246(2)]),flip(a)]. 4.68/4.98 301 composition(top,join(A,one)) = top. [para(15(a,1),279(a,1,2,2)),rewrite([20(3)])]. 4.68/4.98 325 join(zero,composition(A,zero)) = zero. [para(301(a,1),49(a,1,2,2,1,1)),rewrite([246(2),35(2),246(5),35(5),80(5),153(6),246(6),35(6)])]. 4.68/4.98 327 join(A,composition(B,zero)) = A. [para(325(a,1),25(a,1,2)),rewrite([142(2),142(4),20(3)]),flip(a)]. 4.68/4.98 346 composition(join(A,B),zero) = composition(A,zero). [para(327(a,1),28(a,1)),flip(a)]. 4.68/4.98 348 composition(A,zero) = zero. [para(327(a,1),80(a,2)),rewrite([346(4)])]. 4.68/4.98 350 composition(converse(zero),A) = converse(zero). [para(348(a,1),38(a,1,1)),flip(a)]. 4.68/4.98 359 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(350(a,1),44(a,1,1,2)),flip(a)]. 4.68/4.98 363 converse(zero) = zero. [para(350(a,1),348(a,1))]. 4.68/4.98 366 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(359),rewrite([363(2),348(2),142(2),363(3),348(3)]),flip(a)]. 4.68/4.98 369 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(181),rewrite([363(2),366(7),363(7)])]. 4.68/4.98 376 join(zero,converse(A)) = converse(A). [para(363(a,1),21(a,1,1)),rewrite([20(5),142(5)])]. 4.68/4.98 462 converse(composition(A,join(B,complement(composition(converse(A),top))))) = converse(composition(A,B)). [para(369(a,1),42(a,1,2)),rewrite([20(4),376(4),20(9),21(9),22(10)]),flip(a)]. 4.68/4.98 539 join(complement(one),complement(c1)) = complement(c1). [para(34(a,1),264(a,1,2,1)),rewrite([20(5)])]. 4.68/4.98 567 join(A,join(complement(A),complement(B))) = top. [para(265(a,1),113(a,1,2)),rewrite([20(4)])]. 4.68/4.98 571 join(one,complement(c1)) = top. [para(539(a,1),567(a,1,2))]. 4.68/4.98 574 join(zero,c1) = c1. [para(571(a,1),32(a,1,1,1)),rewrite([35(2),539(6),141(4)])]. 4.68/4.98 943 join(one,converse(c1)) = one. [para(574(a,1),125(a,2,2,1)),rewrite([20(4),34(4),20(3),142(3),78(2)]),flip(a)]. 4.68/4.98 956 join(A,composition(converse(c1),A)) = A. [para(943(a,1),28(a,2,1)),rewrite([83(2),83(6)])]. 4.68/4.98 962 join(A,composition(A,c1)) = A. [para(956(a,1),68(a,1,1)),rewrite([15(2),15(3),15(4),20(3)]),flip(a)]. 4.68/4.98 964 join(A,join(B,composition(A,c1))) = join(A,B). [para(962(a,1),25(a,2,2)),rewrite([20(3),20(5)])]. 4.68/4.98 1679 join(A,composition(c1,A)) = A. [para(962(a,1),136(a,1,1)),rewrite([83(2),83(4)]),flip(a)]. 4.68/4.98 1706 join(A,join(B,composition(c1,A))) = join(A,B). [para(1679(a,1),25(a,2,2)),rewrite([20(3),20(5)])]. 4.68/4.98 2016 join(A,complement(join(A,B))) = join(A,complement(B)). [para(147(a,1),156(a,1,2)),flip(a)]. 4.68/4.98 2238 join(complement(converse(A)),converse(join(A,B))) = top. [para(167(a,1),113(a,1,2)),rewrite([20(5)])]. 4.68/4.98 2268 join(A,join(B,converse(complement(converse(A))))) = top. [para(2238(a,1),21(a,2,1)),rewrite([15(6),25(5),20(4),25(5,R),20(4),246(7)])]. 4.68/4.98 2358 join(A,converse(complement(converse(A)))) = top. [para(149(a,1),2268(a,1,2))]. 4.68/4.98 2380 join(complement(converse(A)),converse(join(B,A))) = top. [para(2358(a,1),66(a,1,1,2)),rewrite([115(2),246(2)]),flip(a)]. 4.68/4.98 2483 join(converse(A),complement(composition(converse(A),c1))) = top. [para(956(a,1),2380(a,1,2,1)),rewrite([38(4),20(6)])]. 4.68/4.98 2510 join(A,converse(complement(composition(converse(A),c1)))) = top. [para(2483(a,1),21(a,2,1)),rewrite([15(2),246(8)])]. 4.68/4.98 2669 join(complement(composition(converse(A),c1)),converse(join(B,A))) = top. [para(2510(a,1),66(a,1,1,2)),rewrite([115(2),246(2)]),flip(a)]. 4.68/4.98 3776 join(A,composition(complement(one),A)) = composition(top,A). [para(47(a,1),198(a,2,2,1)),rewrite([20(7),25(8,R),20(7),47(7),19(4)]),flip(a)]. 4.68/4.98 3848 join(A,composition(A,complement(one))) = composition(A,top). [para(3776(a,1),68(a,1,1)),rewrite([37(4),246(2),241(5),15(7),20(6)]),flip(a)]. 4.68/4.98 3854 join(complement(one),composition(top,c1)) = join(c1,complement(one)). [para(3776(a,1),964(a,1,2)),rewrite([20(10)])]. 4.68/4.98 4592 join(complement(one),composition(c1,top)) = join(c1,complement(one)). [para(3848(a,1),1706(a,1,2)),rewrite([20(10)])]. 4.68/4.98 5096 complement(join(complement(A),complement(join(B,complement(A))))) = complement(join(complement(A),complement(B))). [para(2016(a,1),23(a,2,1)),rewrite([20(2),23(3)])]. 4.68/4.98 5108 join(complement(A),complement(join(B,complement(A)))) = join(complement(A),complement(B)). [para(2016(a,1),55(a,2)),rewrite([20(2),20(5),154(7),20(6),5096(9),265(8),20(5)])]. 4.68/4.98 5177 join(A,complement(converse(complement(converse(A))))) = A. [para(2358(a,1),2016(a,1,2,1)),rewrite([35(2),142(2)]),flip(a)]. 4.68/4.98 5255 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(15(a,1),5177(a,1,2,1,1,1))]. 4.68/4.98 5258 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(5177(a,1),32(a,1,2,1)),rewrite([141(9),20(8),2016(8),141(6)])]. 4.68/4.98 5511 converse(complement(converse(complement(A)))) = A. [para(5255(a,1),21(a,2,1)),rewrite([15(2),5258(5),15(6)])]. 4.68/4.98 5546 complement(converse(complement(A))) = converse(A). [para(5511(a,1),15(a,1,1)),flip(a)]. 4.68/4.98 5602 converse(complement(A)) = complement(converse(A)). [para(5546(a,1),141(a,1,1)),flip(a)]. 4.68/4.98 7679 join(complement(one),complement(composition(top,c1))) = complement(c1). [para(3854(a,1),2016(a,1,2,1)),rewrite([5108(8),539(5)]),flip(a)]. 4.68/4.98 13337 join(join(complement(one),converse(c1)),complement(composition(top,composition(converse(c1),c1)))) = top. [para(4592(a,1),2669(a,1,2,1)),rewrite([251(4),26(6),242(12),20(13)])]. 4.68/4.98 15821 composition(top,composition(A,converse(A))) = composition(top,converse(A)). [para(19(a,1),462(a,1,1,2)),rewrite([251(3),274(8),37(7)]),flip(a)]. 4.68/4.98 15832 composition(top,composition(converse(A),A)) = composition(top,A). [para(15(a,1),15821(a,1,2,2)),rewrite([15(7)])]. 4.68/4.98 15862 join(complement(c1),converse(c1)) = top. [back_rewrite(13337),rewrite([15832(11),20(10),25(10),20(9),7679(9),20(5)])]. 4.68/4.98 15904 join(c1,complement(converse(c1))) = top. [para(15862(a,1),21(a,2,1)),rewrite([5602(3),15(6),20(5),246(7)])]. 4.68/4.98 15910 join(complement(c1),complement(converse(c1))) = complement(c1). [para(15862(a,1),2016(a,1,2,1)),rewrite([35(4),20(4),140(4)]),flip(a)]. 4.68/4.98 15918 converse(c1) = c1. [para(15904(a,1),32(a,1,1,1)),rewrite([35(2),15910(7),141(4),574(3)]),flip(a)]. 4.68/4.98 15919 $F # answer(goals). [resolve(15918,a,33,a)]. 4.68/4.98 4.68/4.98 % SZS output end Refutation 4.68/4.98 ============================== end of proof ========================== 4.68/4.98 4.68/4.98 ============================== STATISTICS ============================ 4.68/4.98 4.68/4.98 Given=989. Generated=169364. Kept=15900. proofs=1. 4.68/4.98 Usable=787. Sos=9963. Demods=10290. Limbo=0, Disabled=5164. Hints=0. 4.68/4.98 Megabytes=16.49. 4.68/4.98 User_CPU=3.88, System_CPU=0.11, Wall_clock=4. 4.68/4.98 4.68/4.98 ============================== end of statistics ===================== 4.68/4.98 4.68/4.98 ============================== end of search ========================= 4.68/4.98 4.68/4.98 THEOREM PROVED 4.68/4.98 % SZS status Theorem 4.68/4.98 4.68/4.98 Exiting with 1 proof. 4.68/4.98 4.68/4.98 Process 1154 exit (max_proofs) Tue Aug 9 04:43:54 2022 4.68/4.98 Prover9 interrupted 4.68/4.98 EOF