0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.29 % Computer : n018.cluster.edu 0.10/0.29 % Model : x86_64 x86_64 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.29 % Memory : 8042.1875MB 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.29 % CPULimit : 960 0.10/0.30 % WCLimit : 120 0.10/0.30 % DateTime : Tue Aug 9 03:38:00 EDT 2022 0.10/0.30 % CPUTime : 0.58/0.89 ============================== Prover9 =============================== 0.58/0.89 Prover9 (32) version 2009-11A, November 2009. 0.58/0.89 Process 8694 was started by sandbox2 on n018.cluster.edu, 0.58/0.89 Tue Aug 9 03:38:01 2022 0.58/0.89 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_8347_n018.cluster.edu". 0.58/0.89 ============================== end of head =========================== 0.58/0.89 0.58/0.89 ============================== INPUT ================================= 0.58/0.89 0.58/0.89 % Reading from file /tmp/Prover9_8347_n018.cluster.edu 0.58/0.89 0.58/0.89 set(prolog_style_variables). 0.58/0.89 set(auto2). 0.58/0.89 % set(auto2) -> set(auto). 0.58/0.89 % set(auto) -> set(auto_inference). 0.58/0.89 % set(auto) -> set(auto_setup). 0.58/0.89 % set(auto_setup) -> set(predicate_elim). 0.58/0.89 % set(auto_setup) -> assign(eq_defs, unfold). 0.58/0.89 % set(auto) -> set(auto_limits). 0.58/0.89 % set(auto_limits) -> assign(max_weight, "100.000"). 0.58/0.89 % set(auto_limits) -> assign(sos_limit, 20000). 0.58/0.89 % set(auto) -> set(auto_denials). 0.58/0.89 % set(auto) -> set(auto_process). 0.58/0.89 % set(auto2) -> assign(new_constants, 1). 0.58/0.89 % set(auto2) -> assign(fold_denial_max, 3). 0.58/0.89 % set(auto2) -> assign(max_weight, "200.000"). 0.58/0.89 % set(auto2) -> assign(max_hours, 1). 0.58/0.89 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.58/0.89 % set(auto2) -> assign(max_seconds, 0). 0.58/0.89 % set(auto2) -> assign(max_minutes, 5). 0.58/0.89 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.58/0.89 % set(auto2) -> set(sort_initial_sos). 0.58/0.89 % set(auto2) -> assign(sos_limit, -1). 0.58/0.89 % set(auto2) -> assign(lrs_ticks, 3000). 0.58/0.89 % set(auto2) -> assign(max_megs, 400). 0.58/0.89 % set(auto2) -> assign(stats, some). 0.58/0.89 % set(auto2) -> clear(echo_input). 0.58/0.89 % set(auto2) -> set(quiet). 0.58/0.89 % set(auto2) -> clear(print_initial_clauses). 0.58/0.89 % set(auto2) -> clear(print_given). 0.58/0.89 assign(lrs_ticks,-1). 0.58/0.89 assign(sos_limit,10000). 0.58/0.89 assign(order,kbo). 0.58/0.89 set(lex_order_vars). 0.58/0.89 clear(print_given). 0.58/0.89 0.58/0.89 % formulas(sos). % not echoed (14 formulas) 0.58/0.89 0.58/0.89 ============================== end of input ========================== 0.58/0.89 0.58/0.89 % From the command line: assign(max_seconds, 960). 0.58/0.89 0.58/0.89 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.58/0.89 0.58/0.89 % Formulas that are not ordinary clauses: 0.58/0.89 1 (all X0 all X1 join(converse(X0),converse(X1)) = converse(join(X0,X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption]. 0.58/0.89 2 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption]. 0.58/0.89 3 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.58/0.89 4 (all X0 meet(X0,complement(X0)) = zero) # label(def_zero) # label(axiom) # label(non_clause). [assumption]. 0.58/0.89 5 (all X0 all X1 join(X1,X0) = join(X0,X1)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.58/0.89 6 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption]. 0.58/0.89 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]. 0.58/0.89 8 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause). [assumption]. 0.58/0.89 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]. 0.58/0.89 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]. 0.58/0.89 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]. 0.58/0.89 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]. 0.58/0.89 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]. 1.85/2.12 14 -(all X0 composition(complement(composition(X0,top)),top) = complement(composition(X0,top))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 1.85/2.12 1.85/2.12 ============================== end of process non-clausal formulas === 1.85/2.12 1.85/2.12 ============================== PROCESS INITIAL CLAUSES =============== 1.85/2.12 1.85/2.12 ============================== PREDICATE ELIMINATION ================= 1.85/2.12 1.85/2.12 ============================== end predicate elimination ============= 1.85/2.12 1.85/2.12 Auto_denials: 1.85/2.12 % copying label goals to answer in negative clause 1.85/2.12 1.85/2.12 Term ordering decisions: 1.85/2.12 Function symbol KB weights: one=1. top=1. zero=1. c1=1. join=1. composition=1. meet=1. complement=1. converse=1. 1.85/2.12 1.85/2.12 ============================== end of process initial clauses ======== 1.85/2.12 1.85/2.12 ============================== CLAUSES FOR SEARCH ==================== 1.85/2.12 1.85/2.12 ============================== end of clauses for search ============= 1.85/2.12 1.85/2.12 ============================== SEARCH ================================ 1.85/2.12 1.85/2.12 % Starting search at 0.01 seconds. 1.85/2.12 1.85/2.12 Low Water (keep): wt=38.000, iters=3353 1.85/2.12 1.85/2.12 Low Water (keep): wt=35.000, iters=3371 1.85/2.12 1.85/2.12 Low Water (keep): wt=32.000, iters=3360 1.85/2.12 1.85/2.12 Low Water (keep): wt=31.000, iters=3378 1.85/2.12 1.85/2.12 Low Water (keep): wt=29.000, iters=3340 1.85/2.12 1.85/2.12 Low Water (keep): wt=27.000, iters=3335 1.85/2.12 1.85/2.12 Low Water (keep): wt=26.000, iters=3361 1.85/2.12 1.85/2.12 Low Water (keep): wt=25.000, iters=3381 1.85/2.12 1.85/2.12 ============================== PROOF ================================= 1.85/2.12 % SZS status Theorem 1.85/2.12 % SZS output start Refutation 1.85/2.12 1.85/2.12 % Proof 1 at 1.19 (+ 0.05) seconds: goals. 1.85/2.12 % Length of proof is 118. 1.85/2.12 % Level of proof is 31. 1.85/2.12 % Maximum clause weight is 21.000. 1.85/2.12 % Given clauses 506. 1.85/2.12 1.85/2.12 1 (all X0 all X1 join(converse(X0),converse(X1)) = converse(join(X0,X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption]. 1.85/2.12 2 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption]. 1.85/2.12 3 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption]. 1.85/2.12 4 (all X0 meet(X0,complement(X0)) = zero) # label(def_zero) # label(axiom) # label(non_clause). [assumption]. 1.85/2.12 5 (all X0 all X1 join(X1,X0) = join(X0,X1)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption]. 1.85/2.12 6 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption]. 1.85/2.12 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]. 1.85/2.12 8 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause). [assumption]. 1.85/2.12 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]. 1.85/2.12 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]. 1.85/2.12 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]. 1.85/2.12 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]. 1.85/2.12 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]. 1.85/2.12 14 -(all X0 composition(complement(composition(X0,top)),top) = complement(composition(X0,top))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 1.85/2.12 15 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(3)]. 1.85/2.12 16 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(8)]. 1.85/2.12 17 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(4)]. 1.85/2.12 18 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(6)]. 1.85/2.12 19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(5)]. 1.85/2.12 20 join(converse(A),converse(B)) = converse(join(A,B)) # label(converse_additivity) # label(axiom). [clausify(1)]. 1.85/2.12 21 composition(converse(A),converse(B)) = converse(composition(B,A)) # label(converse_multiplicativity) # label(axiom). [clausify(2)]. 1.85/2.12 22 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(9)]. 1.85/2.12 23 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(7)]. 1.85/2.12 24 join(A,join(B,C)) = join(C,join(A,B)). [copy(23),rewrite([19(2)]),flip(a)]. 1.85/2.12 25 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(10)]. 1.85/2.12 26 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(12)]. 1.85/2.12 27 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(26),flip(a)]. 1.85/2.12 28 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(13)]. 1.85/2.12 29 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(28),rewrite([19(7)]),flip(a)]. 1.85/2.12 30 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(11)]. 1.85/2.12 31 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(30),rewrite([19(6),19(8)]),rewrite([19(6)])]. 1.85/2.12 32 complement(composition(c1,top)) != composition(complement(composition(c1,top)),top) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)]. 1.85/2.12 33 composition(complement(composition(c1,top)),top) != complement(composition(c1,top)) # answer(goals). [copy(32),flip(a)]. 1.85/2.12 34 complement(top) = zero. [back_rewrite(17),rewrite([22(2),18(4)])]. 1.85/2.12 36 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(15(a,1),21(a,1,1)),flip(a)]. 1.85/2.12 37 converse(composition(converse(A),B)) = composition(converse(B),A). [para(15(a,1),21(a,1,2)),flip(a)]. 1.85/2.12 38 join(A,join(B,complement(A))) = join(B,top). [para(18(a,1),24(a,2,2)),rewrite([19(2)])]. 1.85/2.12 39 composition(A,composition(one,B)) = composition(A,B). [para(16(a,1),25(a,1,1)),flip(a)]. 1.85/2.12 41 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(21(a,1),27(a,1,1)),rewrite([19(7)])]. 1.85/2.12 43 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(25(a,1),27(a,1,1)),rewrite([19(6)])]. 1.85/2.12 45 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(15(a,1),29(a,1,2,1))]. 1.85/2.12 46 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(16(a,1),29(a,1,2,2,1))]. 1.85/2.12 47 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(29(a,1),20(a,2,1)),rewrite([37(7)])]. 1.85/2.12 48 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(21(a,1),29(a,1,2,2,1)),rewrite([15(4)])]. 1.85/2.12 50 join(zero,complement(join(complement(A),complement(A)))) = A. [para(18(a,1),31(a,1,1,1)),rewrite([34(2)])]. 1.85/2.12 54 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(31(a,1),31(a,1,2,1)),rewrite([19(10)])]. 1.85/2.12 58 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(34(a,1),31(a,1,2,1,1))]. 1.85/2.12 71 composition(converse(one),A) = A. [para(16(a,1),37(a,1,1)),rewrite([15(2)]),flip(a)]. 1.85/2.12 77 converse(one) = one. [para(71(a,1),16(a,1)),flip(a)]. 1.85/2.12 79 composition(join(A,one),B) = join(B,composition(A,B)). [para(71(a,1),27(a,1,1)),rewrite([77(4),19(4)]),flip(a)]. 1.85/2.12 81 join(complement(A),complement(composition(one,A))) = complement(A). [para(71(a,1),29(a,1,2))]. 1.85/2.12 82 composition(one,A) = A. [para(71(a,1),39(a,2)),rewrite([77(2),39(4)])]. 1.85/2.12 83 join(complement(A),complement(A)) = complement(A). [back_rewrite(81),rewrite([82(3)])]. 1.85/2.12 84 join(zero,complement(complement(A))) = A. [back_rewrite(50),rewrite([83(4)])]. 1.85/2.12 85 converse(join(A,one)) = join(one,converse(A)). [para(77(a,1),20(a,1,1)),rewrite([19(5)]),flip(a)]. 1.85/2.12 89 join(top,complement(A)) = top. [para(83(a,1),38(a,1,2)),rewrite([18(2),19(4)]),flip(a)]. 1.85/2.12 90 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(58),rewrite([89(3),34(2)])]. 1.85/2.12 91 join(top,top) = join(A,top). [para(89(a,1),38(a,1,2)),flip(a)]. 1.85/2.12 96 join(A,top) = join(B,top). [para(91(a,1),38(a,2)),rewrite([89(3)])]. 1.85/2.12 97 join(A,top) = c_0. [new_symbol(96)]. 1.85/2.12 100 join(A,join(B,complement(A))) = c_0. [back_rewrite(38),rewrite([97(5)])]. 1.85/2.12 106 composition(join(one,converse(A)),converse(B)) = converse(join(B,composition(B,A))). [para(82(a,1),41(a,1,2)),rewrite([19(4),20(4)]),flip(a)]. 1.85/2.12 111 c_0 = top. [para(84(a,1),100(a,1,2)),rewrite([19(2),18(2)]),flip(a)]. 1.85/2.12 112 join(A,join(B,complement(A))) = top. [back_rewrite(100),rewrite([111(4)])]. 1.85/2.12 114 join(A,top) = top. [back_rewrite(97),rewrite([111(3)])]. 1.85/2.12 125 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(85(a,1),21(a,1,1))]. 1.85/2.12 132 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(106),rewrite([125(5)])]. 1.85/2.12 139 join(zero,complement(A)) = complement(A). [para(84(a,1),90(a,1,2,1))]. 1.85/2.12 140 complement(complement(A)) = A. [back_rewrite(90),rewrite([139(4),139(4)])]. 1.85/2.12 141 join(A,zero) = A. [back_rewrite(84),rewrite([140(3),19(2)])]. 1.85/2.12 146 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(140(a,1),31(a,1,1,1,2)),rewrite([140(5),19(4)])]. 1.85/2.12 147 complement(zero) = top. [para(34(a,1),140(a,1,1))]. 1.85/2.12 148 join(A,A) = A. [para(140(a,1),83(a,1,1)),rewrite([140(2),140(3)])]. 1.85/2.12 152 join(A,join(A,B)) = join(A,B). [para(148(a,1),24(a,1)),rewrite([19(3),24(4,R),19(3),24(3,R),148(2)]),flip(a)]. 1.85/2.12 153 join(A,complement(join(B,complement(A)))) = A. [para(31(a,1),152(a,1,2)),rewrite([19(4),31(12)])]. 1.85/2.12 155 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(153(a,1),24(a,2,2)),rewrite([19(4),19(6)])]. 1.85/2.12 158 join(complement(A),complement(join(A,B))) = complement(A). [para(140(a,1),153(a,1,2,1,2)),rewrite([19(2)])]. 1.85/2.12 166 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(20(a,1),158(a,1,2,1))]. 1.85/2.12 176 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(140(a,1),46(a,1,2,2))]. 1.85/2.12 180 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(34(a,1),47(a,1,1,1)),rewrite([34(10)])]. 1.85/2.12 229 join(complement(one),converse(complement(one))) = complement(one). [para(16(a,1),176(a,1,2))]. 1.85/2.12 240 converse(complement(one)) = complement(one). [para(229(a,1),20(a,2,1)),rewrite([15(7),19(6),229(6)]),flip(a)]. 1.85/2.12 245 converse(top) = top. [para(240(a,1),85(a,2,2)),rewrite([19(4),18(4),18(6)])]. 1.85/2.12 249 join(top,converse(A)) = top. [para(245(a,1),20(a,1,1)),rewrite([19(5),114(5),245(5)])]. 1.85/2.12 250 converse(composition(A,top)) = composition(top,converse(A)). [para(245(a,1),21(a,1,1)),flip(a)]. 1.85/2.12 254 join(top,composition(A,converse(B))) = top. [para(36(a,1),249(a,1,2))]. 1.85/2.12 263 join(complement(A),complement(join(B,A))) = complement(A). [para(153(a,1),54(a,2)),rewrite([140(2),140(4),140(8),54(13)])]. 1.85/2.12 269 join(top,composition(A,B)) = top. [para(15(a,1),254(a,1,2,2))]. 1.85/2.12 278 composition(top,join(one,converse(A))) = top. [para(85(a,1),250(a,2,2)),rewrite([79(4),269(4),245(2)]),flip(a)]. 1.85/2.12 300 composition(top,join(A,one)) = top. [para(15(a,1),278(a,1,2,2)),rewrite([19(3)])]. 1.85/2.12 324 join(zero,composition(A,zero)) = zero. [para(300(a,1),48(a,1,2,2,1,1)),rewrite([245(2),34(2),245(5),34(5),79(5),152(6),245(6),34(6)])]. 1.85/2.12 326 join(A,composition(B,zero)) = A. [para(324(a,1),24(a,1,2)),rewrite([141(2),141(4),19(3)]),flip(a)]. 1.85/2.12 345 composition(join(A,B),zero) = composition(A,zero). [para(326(a,1),27(a,1)),flip(a)]. 1.85/2.12 347 composition(A,zero) = zero. [para(326(a,1),79(a,2)),rewrite([345(4)])]. 1.85/2.12 349 composition(converse(zero),A) = converse(zero). [para(347(a,1),37(a,1,1)),flip(a)]. 1.85/2.12 358 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(349(a,1),43(a,1,1,2)),flip(a)]. 1.85/2.12 362 converse(zero) = zero. [para(349(a,1),347(a,1))]. 1.85/2.12 365 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(358),rewrite([362(2),347(2),141(2),362(3),347(3)]),flip(a)]. 1.85/2.12 367 composition(zero,A) = zero. [back_rewrite(349),rewrite([362(2),362(4)])]. 1.85/2.12 368 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(180),rewrite([362(2),365(7),362(7)])]. 1.85/2.12 451 composition(converse(complement(composition(A,top))),composition(A,B)) = zero. [para(368(a,1),25(a,1,1)),rewrite([367(2)]),flip(a)]. 1.85/2.12 542 join(one,complement(composition(converse(complement(A)),A))) = complement(composition(converse(complement(A)),A)). [para(176(a,1),263(a,1,2,1)),rewrite([140(7),19(6)])]. 1.85/2.12 1424 composition(A,join(B,one)) = join(A,composition(A,B)). [para(132(a,1),15(a,1,1)),rewrite([15(4)]),flip(a)]. 1.85/2.12 1981 composition(complement(A),complement(composition(converse(complement(A)),A))) = complement(A). [para(1424(a,2),45(a,1)),rewrite([19(7),542(7)])]. 1.85/2.12 2466 join(A,complement(join(A,B))) = join(A,complement(B)). [para(146(a,1),155(a,1,2)),flip(a)]. 1.85/2.12 2791 join(complement(converse(A)),converse(join(A,B))) = top. [para(166(a,1),112(a,1,2)),rewrite([19(5)])]. 1.85/2.12 2816 join(A,join(B,converse(complement(converse(A))))) = top. [para(2791(a,1),20(a,2,1)),rewrite([15(6),24(5),19(4),24(5,R),19(4),245(7)])]. 1.85/2.12 2847 join(A,converse(complement(converse(A)))) = top. [para(148(a,1),2816(a,1,2))]. 1.85/2.12 2884 join(A,complement(converse(complement(converse(A))))) = A. [para(2847(a,1),2466(a,1,2,1)),rewrite([34(2),141(2)]),flip(a)]. 1.85/2.12 2885 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(15(a,1),2884(a,1,2,1,1,1))]. 1.85/2.12 2888 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(2884(a,1),31(a,1,2,1)),rewrite([140(9),19(8),2466(8),140(6)])]. 1.85/2.12 3004 converse(complement(converse(complement(A)))) = A. [para(2885(a,1),20(a,2,1)),rewrite([15(2),2888(5),15(6)])]. 1.85/2.12 3026 complement(converse(complement(A))) = converse(A). [para(3004(a,1),15(a,1,1)),flip(a)]. 1.85/2.12 3093 converse(complement(A)) = complement(converse(A)). [para(3026(a,1),140(a,1,1)),flip(a)]. 1.85/2.12 3190 composition(complement(A),complement(composition(complement(converse(A)),A))) = complement(A). [back_rewrite(1981),rewrite([3093(3)])]. 1.85/2.12 3261 composition(complement(composition(top,converse(A))),composition(A,B)) = zero. [back_rewrite(451),rewrite([3093(4),250(3)])]. 1.85/2.12 9083 composition(complement(composition(A,top)),top) = complement(composition(A,top)). [para(250(a,1),3190(a,1,2,1,1,1)),rewrite([3261(10),147(5)])]. 1.85/2.12 9084 $F # answer(goals). [resolve(9083,a,33,a)]. 1.85/2.12 1.85/2.12 % SZS output end Refutation 1.85/2.12 ============================== end of proof ========================== 1.85/2.12 1.85/2.12 ============================== STATISTICS ============================ 1.85/2.12 1.85/2.12 Given=506. Generated=67512. Kept=9064. proofs=1. 1.85/2.12 Usable=410. Sos=7163. Demods=7146. Limbo=9, Disabled=1495. Hints=0. 1.85/2.12 Megabytes=11.35. 1.85/2.12 User_CPU=1.19, System_CPU=0.05, Wall_clock=1. 1.85/2.12 1.85/2.12 ============================== end of statistics ===================== 1.85/2.12 1.85/2.12 ============================== end of search ========================= 1.85/2.12 1.85/2.12 THEOREM PROVED 1.85/2.12 % SZS status Theorem 1.85/2.12 1.85/2.12 Exiting with 1 proof. 1.85/2.12 1.85/2.12 Process 8694 exit (max_proofs) Tue Aug 9 03:38:02 2022 1.85/2.12 Prover9 interrupted 1.85/2.12 EOF