TSTP Solution File: REL006-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL006-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:53:28 EDT 2022
% Result : Unsatisfiable 4.15s 4.43s
% Output : Refutation 4.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL006-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 09:59:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.15/4.43 ============================== Prover9 ===============================
% 4.15/4.43 Prover9 (32) version 2009-11A, November 2009.
% 4.15/4.43 Process 25038 was started by sandbox2 on n022.cluster.edu,
% 4.15/4.43 Fri Jul 8 09:59:11 2022
% 4.15/4.43 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24885_n022.cluster.edu".
% 4.15/4.43 ============================== end of head ===========================
% 4.15/4.43
% 4.15/4.43 ============================== INPUT =================================
% 4.15/4.43
% 4.15/4.43 % Reading from file /tmp/Prover9_24885_n022.cluster.edu
% 4.15/4.43
% 4.15/4.43 set(prolog_style_variables).
% 4.15/4.43 set(auto2).
% 4.15/4.43 % set(auto2) -> set(auto).
% 4.15/4.43 % set(auto) -> set(auto_inference).
% 4.15/4.43 % set(auto) -> set(auto_setup).
% 4.15/4.43 % set(auto_setup) -> set(predicate_elim).
% 4.15/4.43 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.15/4.43 % set(auto) -> set(auto_limits).
% 4.15/4.43 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.15/4.43 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.15/4.43 % set(auto) -> set(auto_denials).
% 4.15/4.43 % set(auto) -> set(auto_process).
% 4.15/4.43 % set(auto2) -> assign(new_constants, 1).
% 4.15/4.43 % set(auto2) -> assign(fold_denial_max, 3).
% 4.15/4.43 % set(auto2) -> assign(max_weight, "200.000").
% 4.15/4.43 % set(auto2) -> assign(max_hours, 1).
% 4.15/4.43 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.15/4.43 % set(auto2) -> assign(max_seconds, 0).
% 4.15/4.43 % set(auto2) -> assign(max_minutes, 5).
% 4.15/4.43 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.15/4.43 % set(auto2) -> set(sort_initial_sos).
% 4.15/4.43 % set(auto2) -> assign(sos_limit, -1).
% 4.15/4.43 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.15/4.43 % set(auto2) -> assign(max_megs, 400).
% 4.15/4.43 % set(auto2) -> assign(stats, some).
% 4.15/4.43 % set(auto2) -> clear(echo_input).
% 4.15/4.43 % set(auto2) -> set(quiet).
% 4.15/4.43 % set(auto2) -> clear(print_initial_clauses).
% 4.15/4.43 % set(auto2) -> clear(print_given).
% 4.15/4.43 assign(lrs_ticks,-1).
% 4.15/4.43 assign(sos_limit,10000).
% 4.15/4.43 assign(order,kbo).
% 4.15/4.43 set(lex_order_vars).
% 4.15/4.43 clear(print_given).
% 4.15/4.43
% 4.15/4.43 % formulas(sos). % not echoed (15 formulas)
% 4.15/4.43
% 4.15/4.43 ============================== end of input ==========================
% 4.15/4.43
% 4.15/4.43 % From the command line: assign(max_seconds, 300).
% 4.15/4.43
% 4.15/4.43 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.15/4.43
% 4.15/4.43 % Formulas that are not ordinary clauses:
% 4.15/4.43
% 4.15/4.43 ============================== end of process non-clausal formulas ===
% 4.15/4.43
% 4.15/4.43 ============================== PROCESS INITIAL CLAUSES ===============
% 4.15/4.43
% 4.15/4.43 ============================== PREDICATE ELIMINATION =================
% 4.15/4.43
% 4.15/4.43 ============================== end predicate elimination =============
% 4.15/4.43
% 4.15/4.43 Auto_denials:
% 4.15/4.43 % copying label goals_15 to answer in negative clause
% 4.15/4.43
% 4.15/4.43 Term ordering decisions:
% 4.15/4.43 Function symbol KB weights: zero=1. one=1. sk1=1. sk2=1. top=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 4.15/4.43
% 4.15/4.43 ============================== end of process initial clauses ========
% 4.15/4.43
% 4.15/4.43 ============================== CLAUSES FOR SEARCH ====================
% 4.15/4.43
% 4.15/4.43 ============================== end of clauses for search =============
% 4.15/4.43
% 4.15/4.43 ============================== SEARCH ================================
% 4.15/4.43
% 4.15/4.43 % Starting search at 0.01 seconds.
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=33.000, iters=3341
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=31.000, iters=3394
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=30.000, iters=3346
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=29.000, iters=3344
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=28.000, iters=3382
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=27.000, iters=3385
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=26.000, iters=3350
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=25.000, iters=3377
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=24.000, iters=3337
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=23.000, iters=3367
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=22.000, iters=3334
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=21.000, iters=3335
% 4.15/4.43
% 4.15/4.43 Low Water (keep): wt=20.000, iters=3338
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=7072, wt=50.000
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=7343, wt=44.000
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=6944, wt=42.000
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=7071, wt=41.000
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=7488, wt=40.000
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=6764, wt=39.000
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=7334, wt=38.000
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=14043, wt=17.000
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=14303, wt=16.000
% 4.15/4.43
% 4.15/4.43 Low Water (displace): id=14389, wt=14.000
% 4.15/4.43
% 4.15/4.43 ============================== PROOF =================================
% 4.15/4.43 % SZS status Unsatisfiable
% 4.15/4.43 % SZS output start Refutation
% 4.15/4.43
% 4.15/4.43 % Proof 1 at 3.37 (+ 0.10) seconds: goals_15.
% 4.15/4.43 % Length of proof is 142.
% 4.15/4.43 % Level of proof is 45.
% 4.15/4.43 % Maximum clause weight is 33.000.
% 4.15/4.43 % Given clauses 952.
% 4.15/4.43
% 4.15/4.43 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 4.15/4.43 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 4.15/4.43 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 4.15/4.43 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 4.15/4.43 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 4.15/4.43 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 4.15/4.43 7 meet(converse(sk1),sk2) = zero # label(goals_14) # label(negated_conjecture). [assumption].
% 4.15/4.43 8 zero = meet(converse(sk1),sk2). [copy(7),flip(a)].
% 4.15/4.43 9 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 4.15/4.43 10 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 4.15/4.43 11 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 4.15/4.43 12 join(converse(A),converse(B)) = converse(join(A,B)). [copy(11),flip(a)].
% 4.15/4.43 13 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 4.15/4.43 14 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(13),flip(a)].
% 4.15/4.43 15 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 4.15/4.43 16 join(A,join(B,C)) = join(C,join(A,B)). [copy(15),rewrite([9(4)])].
% 4.15/4.43 17 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 4.15/4.43 18 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(17),flip(a)].
% 4.15/4.43 19 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 4.15/4.43 20 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(19),flip(a)].
% 4.15/4.43 21 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 4.15/4.43 22 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(21),rewrite([9(6)])].
% 4.15/4.43 23 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 4.15/4.43 24 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(23),rewrite([9(6),9(8)]),flip(a),rewrite([9(6)])].
% 4.15/4.43 25 meet(sk1,converse(sk2)) != zero # label(goals_15) # label(negated_conjecture) # answer(goals_15). [assumption].
% 4.15/4.43 26 complement(join(complement(sk2),complement(converse(sk1)))) != complement(join(complement(sk1),complement(converse(sk2)))) # answer(goals_15). [copy(25),rewrite([10(4),8(8),10(11),9(13)]),flip(a)].
% 4.15/4.43 27 complement(join(complement(sk2),complement(converse(sk1)))) = complement(top). [back_rewrite(6),rewrite([10(2),4(4),8(3),10(6),9(8)]),flip(a)].
% 4.15/4.43 29 complement(join(complement(sk1),complement(converse(sk2)))) != complement(top) # answer(goals_15). [back_rewrite(26),rewrite([27(7)]),flip(a)].
% 4.15/4.43 30 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),12(a,1,1)),rewrite([9(4)]),flip(a)].
% 4.15/4.43 31 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),14(a,1,1)),flip(a)].
% 4.15/4.43 32 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),14(a,1,2)),flip(a)].
% 4.15/4.43 33 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),16(a,2,2)),rewrite([9(2)])].
% 4.15/4.43 34 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),18(a,1,1)),flip(a)].
% 4.15/4.43 36 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(14(a,1),20(a,1,1)),rewrite([9(7)])].
% 4.15/4.43 41 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(2(a,1),22(a,1,2,1))].
% 4.15/4.43 44 join(complement(A),composition(converse(composition(B,C)),complement(composition(B,composition(C,A))))) = complement(A). [para(18(a,1),22(a,1,2,2,1))].
% 4.15/4.43 45 join(complement(top),complement(join(complement(A),complement(A)))) = A. [para(4(a,1),24(a,1,1,1))].
% 4.15/4.43 46 join(complement(top),complement(join(A,complement(complement(A))))) = complement(A). [para(4(a,1),24(a,1,2,1)),rewrite([9(7)])].
% 4.15/4.43 47 join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B. [para(24(a,1),9(a,1)),rewrite([9(3),9(8)]),flip(a)].
% 4.15/4.43 48 join(complement(A),complement(join(complement(join(complement(A),complement(B))),complement(complement(join(B,complement(A))))))) = join(complement(A),complement(B)). [para(24(a,1),24(a,1,1,1)),rewrite([9(8),9(10),9(15)])].
% 4.15/4.43 49 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(24(a,1),24(a,1,2,1)),rewrite([9(10)])].
% 4.15/4.43 52 join(complement(sk2),complement(converse(sk1))) = top. [para(27(a,1),24(a,1,1,1,2)),rewrite([27(12),24(10)]),flip(a)].
% 4.15/4.43 55 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(30(a,1),12(a,1,1)),rewrite([9(7),16(7,R),9(6)]),flip(a)].
% 4.15/4.43 56 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(30(a,1),12(a,1,2)),rewrite([16(4,R),9(3),12(3),55(7)]),flip(a)].
% 4.15/4.43 60 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(30(a,1),30(a,2,2)),rewrite([56(4),30(4),16(6,R),9(5)])].
% 4.15/4.43 61 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(55),rewrite([60(8),12(7)])].
% 4.15/4.43 63 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(31(a,1),12(a,1,1)),rewrite([9(7)]),flip(a)].
% 4.15/4.43 67 composition(converse(one),A) = A. [para(1(a,1),32(a,1,1)),rewrite([2(2)]),flip(a)].
% 4.15/4.43 68 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(32(a,1),12(a,1,1)),rewrite([9(7)]),flip(a)].
% 4.15/4.43 73 join(top,converse(sk1)) = join(top,complement(sk2)). [para(52(a,1),33(a,1,2)),rewrite([9(4),9(8)])].
% 4.15/4.43 74 converse(one) = one. [para(67(a,1),1(a,1)),flip(a)].
% 4.15/4.43 76 composition(join(A,one),B) = join(B,composition(A,B)). [para(67(a,1),20(a,1,1)),rewrite([74(4),9(4)]),flip(a)].
% 4.15/4.43 78 join(complement(A),complement(composition(one,A))) = complement(A). [para(67(a,1),22(a,1,2))].
% 4.15/4.43 79 composition(one,A) = A. [para(67(a,1),34(a,2)),rewrite([74(2),34(4)])].
% 4.15/4.43 80 join(complement(A),complement(A)) = complement(A). [back_rewrite(78),rewrite([79(3)])].
% 4.15/4.43 81 join(complement(top),complement(complement(A))) = A. [back_rewrite(45),rewrite([80(5)])].
% 4.15/4.43 82 converse(join(A,one)) = join(one,converse(A)). [para(74(a,1),12(a,1,1)),rewrite([9(5)]),flip(a)].
% 4.15/4.43 83 join(top,complement(A)) = top. [para(80(a,1),33(a,1,2)),rewrite([4(2),9(4)]),flip(a)].
% 4.15/4.43 84 join(top,converse(sk1)) = top. [back_rewrite(73),rewrite([83(8)])].
% 4.15/4.43 87 join(top,top) = join(A,top). [para(83(a,1),33(a,1,2)),flip(a)].
% 4.15/4.43 93 join(A,top) = join(B,top). [para(87(a,1),33(a,2)),rewrite([83(3)])].
% 4.15/4.43 94 join(A,top) = c_0. [new_symbol(93)].
% 4.15/4.43 97 join(A,join(B,complement(A))) = c_0. [back_rewrite(33),rewrite([94(5)])].
% 4.15/4.43 109 join(complement(A),complement(top)) = complement(A). [para(81(a,1),24(a,1,2,1)),rewrite([83(4),9(4)])].
% 4.15/4.43 110 c_0 = top. [para(52(a,1),97(a,1,2)),rewrite([9(4),84(4)]),flip(a)].
% 4.15/4.43 111 join(A,join(B,complement(A))) = top. [back_rewrite(97),rewrite([110(4)])].
% 4.15/4.43 113 join(A,top) = top. [back_rewrite(94),rewrite([110(3)])].
% 4.15/4.43 118 join(complement(complement(A)),complement(join(A,complement(top)))) = top. [para(109(a,1),24(a,1,2,1)),rewrite([9(7)])].
% 4.15/4.43 154 composition(join(one,one),A) = join(A,A). [para(79(a,1),76(a,2,2))].
% 4.15/4.43 176 composition(A,join(one,one)) = join(A,A). [para(154(a,2),30(a,1,1)),rewrite([31(6),82(4),74(3),2(6)])].
% 4.15/4.43 200 join(A,join(A,composition(B,join(one,one)))) = composition(join(B,A),join(one,one)). [para(176(a,1),20(a,1,2)),rewrite([16(6),9(5)])].
% 4.15/4.43 208 composition(top,join(one,one)) = top. [para(176(a,2),113(a,1))].
% 4.15/4.43 218 composition(join(one,one),A) = composition(A,join(one,one)). [para(176(a,2),154(a,2))].
% 4.15/4.43 234 composition(converse(top),join(one,one)) = converse(top). [para(208(a,1),14(a,2,1)),rewrite([82(4),74(3),218(6)])].
% 4.15/4.43 236 join(top,composition(A,join(one,one))) = top. [para(208(a,1),20(a,1,1)),rewrite([9(8),113(8),208(11)])].
% 4.15/4.43 264 join(top,converse(top)) = top. [para(234(a,1),236(a,1,2))].
% 4.15/4.43 273 converse(top) = top. [para(264(a,1),12(a,2,1)),rewrite([2(5),9(4),264(4)]),flip(a)].
% 4.15/4.43 276 join(top,converse(A)) = top. [para(273(a,1),12(a,1,1)),rewrite([9(5),113(5),273(5)])].
% 4.15/4.43 277 converse(composition(A,top)) = composition(top,converse(A)). [para(273(a,1),14(a,1,1)),flip(a)].
% 4.15/4.43 281 join(top,composition(A,converse(B))) = top. [para(31(a,1),276(a,1,2))].
% 4.15/4.43 283 join(top,composition(A,B)) = top. [para(2(a,1),281(a,1,2,2))].
% 4.15/4.43 299 composition(top,join(one,converse(A))) = top. [para(82(a,1),277(a,2,2)),rewrite([76(4),283(4),273(2)]),flip(a)].
% 4.15/4.43 313 composition(top,top) = top. [para(273(a,1),299(a,1,2,2)),rewrite([113(4)])].
% 4.15/4.43 315 composition(top,composition(top,A)) = composition(top,A). [para(313(a,1),18(a,1,1)),flip(a)].
% 4.15/4.43 364 join(A,complement(complement(A))) = A. [para(46(a,1),24(a,1,2,1)),rewrite([83(6),81(5)]),flip(a)].
% 4.15/4.43 365 complement(complement(top)) = top. [para(81(a,1),46(a,1,2,1)),rewrite([4(6)]),flip(a)].
% 4.15/4.43 367 join(A,join(B,complement(complement(A)))) = join(A,B). [para(364(a,1),16(a,2,2)),rewrite([9(3),9(5)])].
% 4.15/4.43 375 composition(top,complement(composition(top,A))) = complement(composition(top,A)). [para(315(a,1),22(a,1,2,2,1)),rewrite([273(5),76(9,R),9(3),113(3)])].
% 4.15/4.43 380 join(complement(A),complement(composition(top,A))) = complement(A). [para(315(a,1),44(a,1,2,2,1)),rewrite([313(4),273(3),375(6)])].
% 4.15/4.43 384 join(complement(top),complement(join(complement(sk2),converse(sk1)))) = sk2. [para(52(a,1),47(a,1,2,1)),rewrite([9(5),9(9)])].
% 4.15/4.43 437 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(A),complement(B)))))) = join(complement(A),complement(B)). [para(9(a,1),49(a,1,2,1,1)),rewrite([9(3),9(6),9(13)])].
% 4.15/4.43 443 join(complement(top),complement(join(A,complement(top)))) = complement(A). [para(109(a,1),49(a,1,2,1,2,1)),rewrite([9(8),16(8),9(7),364(7),9(5),109(11)])].
% 4.15/4.43 445 join(complement(A),complement(join(complement(join(complement(A),complement(B))),complement(complement(join(complement(A),join(join(B,complement(A)),complement(join(complement(A),complement(B)))))))))) = join(complement(A),complement(B)). [para(49(a,1),48(a,1,2,1,1,1)),rewrite([9(4),9(10),9(14),9(25),437(29)])].
% 4.15/4.43 534 join(complement(A),composition(top,A)) = top. [para(380(a,1),111(a,1,2)),rewrite([9(4)])].
% 4.15/4.43 572 join(complement(top),complement(join(complement(complement(complement(A))),complement(join(A,complement(top)))))) = join(A,complement(top)). [para(118(a,1),24(a,1,1,1))].
% 4.15/4.43 574 join(complement(complement(complement(A))),complement(join(A,complement(top)))) = complement(A). [para(118(a,1),48(a,1,2,1,2,1,1)),rewrite([9(12),365(16),9(15),83(15),9(7),443(7),9(9)]),flip(a)].
% 4.15/4.43 575 join(A,complement(top)) = A. [back_rewrite(572),rewrite([574(10),81(5)]),flip(a)].
% 4.15/4.43 673 join(A,join(complement(A),converse(B))) = top. [para(4(a,1),60(a,1,1)),rewrite([276(3)]),flip(a)].
% 4.15/4.43 675 join(complement(A),join(composition(converse(B),complement(composition(B,A))),converse(C))) = join(complement(A),converse(C)). [para(22(a,1),60(a,1,1)),flip(a)].
% 4.15/4.43 701 join(complement(A),join(composition(top,A),converse(B))) = top. [para(534(a,1),60(a,1,1)),rewrite([276(3)]),flip(a)].
% 4.15/4.43 708 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(31(a,1),673(a,1,2,2))].
% 4.15/4.43 938 join(A,A) = A. [para(81(a,1),367(a,1,2)),rewrite([575(4)])].
% 4.15/4.43 974 join(A,join(A,B)) = join(A,B). [back_rewrite(200),rewrite([938(3),1(2),9(3),938(6),1(5)])].
% 4.15/4.43 1003 join(A,complement(join(B,complement(A)))) = A. [para(24(a,1),974(a,1,2)),rewrite([9(4),24(12)])].
% 4.15/4.43 1013 join(complement(join(A,complement(complement(B)))),complement(join(B,join(complement(complement(B)),complement(join(A,complement(complement(B)))))))) = complement(B). [para(1003(a,1),49(a,1,2,1,2,1)),rewrite([9(12),16(12,R),9(11),1003(20)])].
% 4.15/4.43 1021 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(36(a,1),68(a,1,1)),rewrite([12(3),14(4),2(4),2(4),2(6)]),flip(a)].
% 4.15/4.43 1134 join(A,complement(join(complement(sk2),converse(sk1)))) = join(A,sk2). [para(384(a,1),16(a,1,2)),rewrite([575(11),9(9)]),flip(a)].
% 4.15/4.43 1135 join(complement(sk2),converse(sk1)) = complement(sk2). [para(384(a,1),24(a,1,1,1)),rewrite([365(5),1134(10),9(5),113(5),575(5)]),flip(a)].
% 4.15/4.43 1137 join(sk1,converse(complement(sk2))) = converse(complement(sk2)). [para(1135(a,1),12(a,2,1)),rewrite([2(6),9(5)])].
% 4.15/4.43 1437 join(complement(A),composition(top,join(A,converse(B)))) = top. [para(277(a,1),701(a,1,2,2)),rewrite([1021(7)])].
% 4.15/4.43 1498 join(A,join(complement(A),composition(B,C))) = top. [para(2(a,1),708(a,1,2,2,2))].
% 4.15/4.43 1500 join(A,composition(join(B,one),complement(A))) = top. [para(76(a,2),1498(a,1,2))].
% 4.15/4.43 1566 join(A,join(B,composition(join(C,one),complement(A)))) = top. [para(1500(a,1),16(a,2,2)),rewrite([9(5),113(8)])].
% 4.15/4.43 2595 join(complement(A),composition(top,join(A,B))) = top. [para(2(a,1),1437(a,1,2,2,2))].
% 4.15/4.43 2621 join(composition(top,A),complement(complement(join(B,complement(A))))) = top. [para(24(a,1),2595(a,1,2,2)),rewrite([9(7)])].
% 4.15/4.43 5245 join(complement(A),composition(join(one,converse(B)),A)) = top. [para(41(a,1),1566(a,1,2)),rewrite([82(3),9(6)])].
% 4.15/4.43 5258 join(converse(complement(converse(A))),composition(A,join(B,one))) = top. [para(5245(a,1),63(a,1,1)),rewrite([273(2),30(5),74(3),9(8)]),flip(a)].
% 4.15/4.43 6995 join(composition(top,A),complement(complement(complement(A)))) = top. [para(380(a,1),2621(a,1,2,1,1)),rewrite([315(4)])].
% 4.15/4.43 6998 join(complement(top),complement(join(A,complement(B)))) = complement(join(A,complement(B))). [para(2621(a,1),1003(a,1,2,1)),rewrite([9(6)])].
% 4.15/4.43 7044 complement(join(complement(composition(top,A)),complement(complement(complement(A))))) = complement(complement(A)). [para(6995(a,1),24(a,1,1,1)),rewrite([6998(11)])].
% 4.15/4.43 7045 complement(complement(A)) = A. [para(6995(a,1),47(a,1,1,1)),rewrite([9(9),7044(10),81(5)]),flip(a)].
% 4.15/4.43 7065 join(complement(join(A,B)),complement(join(B,complement(join(A,B))))) = complement(B). [back_rewrite(1013),rewrite([7045(2),7045(4),7045(4),974(6)])].
% 4.15/4.43 7073 join(complement(A),complement(join(complement(A),join(join(B,complement(A)),complement(join(complement(A),complement(B))))))) = join(complement(A),complement(B)). [back_rewrite(445),rewrite([7045(16),16(15,R),9(14),16(14,R),938(13)])].
% 4.15/4.43 7082 join(A,complement(join(join(A,B),complement(join(A,complement(B)))))) = join(A,complement(B)). [para(7045(a,1),49(a,1,1)),rewrite([7045(2),9(1),7045(4),9(3),7045(10),9(9)])].
% 4.15/4.43 7086 join(complement(A),complement(join(A,B))) = complement(A). [para(7045(a,1),1003(a,1,2,1,2)),rewrite([9(2)])].
% 4.15/4.43 7135 join(complement(sk1),complement(converse(complement(sk2)))) = complement(sk1). [para(1137(a,1),7086(a,1,2,1))].
% 4.15/4.43 7195 join(complement(sk1),converse(complement(sk2))) = top. [para(7135(a,1),111(a,1,2)),rewrite([9(6)])].
% 4.15/4.43 7202 join(complement(sk2),converse(complement(sk1))) = top. [para(7195(a,1),12(a,2,1)),rewrite([2(7),9(6),273(8)])].
% 4.15/4.43 9535 join(A,converse(complement(converse(A)))) = top. [para(938(a,1),5258(a,1,2,2)),rewrite([1(5),9(4)])].
% 4.15/4.43 9566 join(complement(converse(A)),converse(join(B,A))) = top. [para(9535(a,1),61(a,1,1,2)),rewrite([113(2),273(2)]),flip(a)].
% 4.15/4.43 9662 join(converse(A),complement(converse(complement(join(B,complement(A)))))) = top. [para(1003(a,1),9566(a,1,2,1)),rewrite([9(7)])].
% 4.15/4.43 13111 join(A,complement(join(complement(A),converse(B)))) = A. [para(675(a,1),7086(a,1,2,1)),rewrite([7045(2),7045(7)])].
% 4.15/4.43 13133 join(A,complement(join(B,join(converse(C),complement(A))))) = A. [para(30(a,1),13111(a,1,2,1,2)),rewrite([16(4,R)])].
% 4.15/4.43 14031 join(A,complement(join(B,join(C,complement(A))))) = A. [para(2(a,1),13133(a,1,2,1,2,1))].
% 4.15/4.43 14062 join(join(A,B),complement(join(C,complement(A)))) = join(A,B). [para(7086(a,1),14031(a,1,2,1,2))].
% 4.15/4.43 14083 join(complement(A),complement(join(B,complement(A)))) = join(complement(A),complement(B)). [back_rewrite(7073),rewrite([14062(9),16(5,R),938(4)])].
% 4.15/4.43 14087 join(complement(A),complement(join(B,A))) = complement(A). [back_rewrite(7065),rewrite([14083(7),9(4)])].
% 4.15/4.43 14103 join(join(A,B),complement(join(C,complement(B)))) = join(A,B). [para(14087(a,1),14031(a,1,2,1,2))].
% 4.15/4.43 14104 join(A,complement(join(A,B))) = join(A,complement(B)). [back_rewrite(7082),rewrite([14103(5)])].
% 4.15/4.43 14230 join(complement(sk2),complement(converse(complement(sk1)))) = complement(sk2). [para(7202(a,1),14104(a,1,2,1)),rewrite([575(5)]),flip(a)].
% 4.15/4.43 14499 join(complement(sk1),complement(converse(sk2))) = top. [para(14230(a,1),9662(a,1,2,1,1,1)),rewrite([2(4),7045(5)])].
% 4.15/4.43 14502 $F # answer(goals_15). [back_rewrite(29),rewrite([14499(6)]),xx(a)].
% 4.15/4.43
% 4.15/4.43 % SZS output end Refutation
% 4.15/4.43 ============================== end of proof ==========================
% 4.15/4.43
% 4.15/4.43 ============================== STATISTICS ============================
% 4.15/4.43
% 4.15/4.43 Given=952. Generated=169777. Kept=14490. proofs=1.
% 4.15/4.43 Usable=724. Sos=10000. Demods=10240. Limbo=3, Disabled=3778. Hints=0.
% 4.15/4.43 Megabytes=16.78.
% 4.15/4.43 User_CPU=3.37, System_CPU=0.10, Wall_clock=4.
% 4.15/4.43
% 4.15/4.43 ============================== end of statistics =====================
% 4.15/4.43
% 4.15/4.43 ============================== end of search =========================
% 4.15/4.43
% 4.15/4.43 THEOREM PROVED
% 4.15/4.43 % SZS status Unsatisfiable
% 4.15/4.43
% 4.15/4.43 Exiting with 1 proof.
% 4.15/4.43
% 4.15/4.43 Process 25038 exit (max_proofs) Fri Jul 8 09:59:15 2022
% 4.15/4.43 Prover9 interrupted
%------------------------------------------------------------------------------