TSTP Solution File: REL043-2 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : REL043-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n026.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 19:54:26 EDT 2022

% Result   : Unsatisfiable 3.34s 3.68s
% Output   : Refutation 3.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : REL043-2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n026.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  8 07:22:09 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 3.34/3.68  ============================== Prover9 ===============================
% 3.34/3.68  Prover9 (32) version 2009-11A, November 2009.
% 3.34/3.68  Process 27065 was started by sandbox2 on n026.cluster.edu,
% 3.34/3.68  Fri Jul  8 07:22:10 2022
% 3.34/3.68  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26912_n026.cluster.edu".
% 3.34/3.68  ============================== end of head ===========================
% 3.34/3.68  
% 3.34/3.68  ============================== INPUT =================================
% 3.34/3.68  
% 3.34/3.68  % Reading from file /tmp/Prover9_26912_n026.cluster.edu
% 3.34/3.68  
% 3.34/3.68  set(prolog_style_variables).
% 3.34/3.68  set(auto2).
% 3.34/3.68      % set(auto2) -> set(auto).
% 3.34/3.68      % set(auto) -> set(auto_inference).
% 3.34/3.68      % set(auto) -> set(auto_setup).
% 3.34/3.68      % set(auto_setup) -> set(predicate_elim).
% 3.34/3.68      % set(auto_setup) -> assign(eq_defs, unfold).
% 3.34/3.68      % set(auto) -> set(auto_limits).
% 3.34/3.68      % set(auto_limits) -> assign(max_weight, "100.000").
% 3.34/3.68      % set(auto_limits) -> assign(sos_limit, 20000).
% 3.34/3.68      % set(auto) -> set(auto_denials).
% 3.34/3.68      % set(auto) -> set(auto_process).
% 3.34/3.68      % set(auto2) -> assign(new_constants, 1).
% 3.34/3.68      % set(auto2) -> assign(fold_denial_max, 3).
% 3.34/3.68      % set(auto2) -> assign(max_weight, "200.000").
% 3.34/3.68      % set(auto2) -> assign(max_hours, 1).
% 3.34/3.68      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.34/3.68      % set(auto2) -> assign(max_seconds, 0).
% 3.34/3.68      % set(auto2) -> assign(max_minutes, 5).
% 3.34/3.68      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.34/3.68      % set(auto2) -> set(sort_initial_sos).
% 3.34/3.68      % set(auto2) -> assign(sos_limit, -1).
% 3.34/3.68      % set(auto2) -> assign(lrs_ticks, 3000).
% 3.34/3.68      % set(auto2) -> assign(max_megs, 400).
% 3.34/3.68      % set(auto2) -> assign(stats, some).
% 3.34/3.68      % set(auto2) -> clear(echo_input).
% 3.34/3.68      % set(auto2) -> set(quiet).
% 3.34/3.68      % set(auto2) -> clear(print_initial_clauses).
% 3.34/3.68      % set(auto2) -> clear(print_given).
% 3.34/3.68  assign(lrs_ticks,-1).
% 3.34/3.68  assign(sos_limit,10000).
% 3.34/3.68  assign(order,kbo).
% 3.34/3.68  set(lex_order_vars).
% 3.34/3.68  clear(print_given).
% 3.34/3.68  
% 3.34/3.68  % formulas(sos).  % not echoed (18 formulas)
% 3.34/3.68  
% 3.34/3.68  ============================== end of input ==========================
% 3.34/3.68  
% 3.34/3.68  % From the command line: assign(max_seconds, 300).
% 3.34/3.68  
% 3.34/3.68  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.34/3.68  
% 3.34/3.68  % Formulas that are not ordinary clauses:
% 3.34/3.68  
% 3.34/3.68  ============================== end of process non-clausal formulas ===
% 3.34/3.68  
% 3.34/3.68  ============================== PROCESS INITIAL CLAUSES ===============
% 3.34/3.68  
% 3.34/3.68  ============================== PREDICATE ELIMINATION =================
% 3.34/3.68  
% 3.34/3.68  ============================== end predicate elimination =============
% 3.34/3.68  
% 3.34/3.68  Auto_denials:
% 3.34/3.68    % copying label goals_18 to answer in negative clause
% 3.34/3.68  
% 3.34/3.68  Term ordering decisions:
% 3.34/3.68  Function symbol KB weights:  sk3=1. one=1. sk1=1. sk2=1. top=1. zero=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 3.34/3.68  
% 3.34/3.68  ============================== end of process initial clauses ========
% 3.34/3.68  
% 3.34/3.68  ============================== CLAUSES FOR SEARCH ====================
% 3.34/3.68  
% 3.34/3.68  ============================== end of clauses for search =============
% 3.34/3.68  
% 3.34/3.68  ============================== SEARCH ================================
% 3.34/3.68  
% 3.34/3.68  % Starting search at 0.01 seconds.
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=86.000, iters=3396
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=84.000, iters=3338
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=80.000, iters=3351
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=76.000, iters=3516
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=70.000, iters=3410
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=68.000, iters=3348
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=67.000, iters=3361
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=66.000, iters=3346
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=65.000, iters=3333
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=64.000, iters=3355
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=61.000, iters=3411
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=60.000, iters=3356
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=58.000, iters=3363
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=57.000, iters=3400
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=56.000, iters=3350
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=52.000, iters=3395
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=51.000, iters=3360
% 3.34/3.68  
% 3.34/3.68  Low Water (keep): wt=48.000, iters=3391
% 3.34/3.68  
% 3.34/3.68  ============================== PROOF =================================
% 3.34/3.68  % SZS status Unsatisfiable
% 3.34/3.68  % SZS output start Refutation
% 3.34/3.68  
% 3.34/3.68  % Proof 1 at 2.63 (+ 0.05) seconds: goals_18.
% 3.34/3.68  % Length of proof is 106.
% 3.34/3.68  % Level of proof is 30.
% 3.34/3.68  % Maximum clause weight is 48.000.
% 3.34/3.68  % Given clauses 486.
% 3.34/3.68  
% 3.34/3.68  1 composition(A,one) = A # label(composition_identity_6) # label(axiom).  [assumption].
% 3.34/3.68  2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom).  [assumption].
% 3.34/3.68  3 top = join(A,complement(A)) # label(def_top_12) # label(axiom).  [assumption].
% 3.34/3.68  4 join(A,complement(A)) = top.  [copy(3),flip(a)].
% 3.34/3.68  5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom).  [assumption].
% 3.34/3.68  6 meet(A,complement(A)) = zero.  [copy(5),flip(a)].
% 3.34/3.68  7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom).  [assumption].
% 3.34/3.68  8 join(composition(sk1,converse(sk2)),sk3) = sk3 # label(goals_17) # label(negated_conjecture).  [assumption].
% 3.34/3.68  9 join(sk3,composition(sk1,converse(sk2))) = sk3.  [copy(8),rewrite([7(6)])].
% 3.34/3.68  10 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom).  [assumption].
% 3.34/3.68  11 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom).  [assumption].
% 3.34/3.68  12 join(converse(A),converse(B)) = converse(join(A,B)).  [copy(11),flip(a)].
% 3.34/3.68  13 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom).  [assumption].
% 3.34/3.68  14 composition(converse(A),converse(B)) = converse(composition(B,A)).  [copy(13),flip(a)].
% 3.34/3.68  15 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom).  [assumption].
% 3.34/3.68  16 join(A,join(B,C)) = join(C,join(A,B)).  [copy(15),rewrite([7(4)])].
% 3.34/3.68  17 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom).  [assumption].
% 3.34/3.68  18 composition(composition(A,B),C) = composition(A,composition(B,C)).  [copy(17),flip(a)].
% 3.34/3.68  19 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom).  [assumption].
% 3.34/3.68  20 join(composition(A,B),composition(C,B)) = composition(join(A,C),B).  [copy(19),flip(a)].
% 3.34/3.68  21 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom).  [assumption].
% 3.34/3.68  22 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(21),rewrite([7(6)])].
% 3.34/3.68  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].
% 3.34/3.68  24 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(23),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 3.34/3.68  25 join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) = meet(composition(A,meet(B,composition(converse(A),C))),C) # label(modular_law_1_15) # label(axiom).  [assumption].
% 3.34/3.68  26 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A)))))))).  [copy(25),rewrite([10(2),7(4),10(8),10(13),7(15),10(20),10(25),7(27)])].
% 3.34/3.68  27 join(meet(composition(A,B),C),meet(composition(meet(A,composition(C,converse(B))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C) # label(modular_law_2_16) # label(axiom).  [assumption].
% 3.34/3.68  28 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(27),rewrite([10(2),7(4),10(8),10(13),7(15),10(20),10(25),7(27)])].
% 3.34/3.68  29 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_14) # label(axiom).  [assumption].
% 3.34/3.68  30 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(29),rewrite([10(2),7(4),10(8),10(14),10(22),10(28)])].
% 3.34/3.68  31 join(composition(complement(sk3),sk2),complement(sk1)) != complement(sk1) # label(goals_18) # label(negated_conjecture) # answer(goals_18).  [assumption].
% 3.34/3.68  32 join(complement(sk1),composition(complement(sk3),sk2)) != complement(sk1) # answer(goals_18).  [copy(31),rewrite([7(7)])].
% 3.34/3.68  33 complement(top) = zero.  [back_rewrite(6),rewrite([10(2),4(4)])].
% 3.34/3.68  34 converse(join(A,converse(B))) = join(B,converse(A)).  [para(2(a,1),12(a,1,1)),rewrite([7(4)]),flip(a)].
% 3.34/3.68  35 converse(composition(A,converse(B))) = composition(B,converse(A)).  [para(2(a,1),14(a,1,1)),flip(a)].
% 3.34/3.68  36 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(2(a,1),14(a,1,2)),flip(a)].
% 3.34/3.68  37 join(A,join(B,complement(A))) = join(B,top).  [para(4(a,1),16(a,2,2)),rewrite([7(2)])].
% 3.34/3.68  38 composition(A,composition(one,B)) = composition(A,B).  [para(1(a,1),18(a,1,1)),flip(a)].
% 3.34/3.68  43 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C).  [para(18(a,1),20(a,1,1)),rewrite([7(6)])].
% 3.34/3.68  45 join(complement(one),composition(converse(A),complement(A))) = complement(one).  [para(1(a,1),22(a,1,2,2,1))].
% 3.34/3.68  46 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A).  [para(2(a,1),22(a,1,2,1))].
% 3.34/3.68  50 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(4(a,1),24(a,1,1,1)),rewrite([33(2)])].
% 3.34/3.68  51 join(zero,complement(join(A,complement(complement(A))))) = complement(A).  [para(4(a,1),24(a,1,2,1)),rewrite([33(6),7(6)])].
% 3.34/3.68  80 join(zero,composition(converse(A),complement(composition(A,top)))) = zero.  [para(33(a,1),22(a,1,1)),rewrite([33(9)])].
% 3.34/3.68  90 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)).  [para(34(a,1),12(a,1,1)),rewrite([7(7),16(7,R),7(6)]),flip(a)].
% 3.34/3.68  91 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))).  [para(34(a,1),12(a,1,2)),rewrite([16(4,R),7(3),12(3),90(7)]),flip(a)].
% 3.34/3.68  99 join(join(A,B),converse(C)) = join(A,join(B,converse(C))).  [para(34(a,1),34(a,2,2)),rewrite([91(4),34(4),16(6,R),7(5)])].
% 3.34/3.68  100 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))).  [back_rewrite(90),rewrite([99(8),12(7)])].
% 3.34/3.68  107 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)).  [para(35(a,1),12(a,1,1)),rewrite([7(7)]),flip(a)].
% 3.34/3.68  115 composition(converse(one),A) = A.  [para(1(a,1),36(a,1,1)),rewrite([2(2)]),flip(a)].
% 3.34/3.68  124 join(top,complement(join(A,complement(B)))) = join(top,complement(A)).  [para(24(a,1),37(a,1,2)),rewrite([7(4),37(4),7(3),7(8)]),flip(a)].
% 3.34/3.68  125 join(top,complement(complement(A))) = top.  [para(26(a,1),37(a,1,2)),rewrite([4(22),7(8),124(8)]),flip(a)].
% 3.34/3.68  126 converse(one) = one.  [para(115(a,1),1(a,1)),flip(a)].
% 3.34/3.68  128 composition(join(A,one),B) = join(B,composition(A,B)).  [para(115(a,1),20(a,1,1)),rewrite([126(4),7(4)]),flip(a)].
% 3.34/3.68  130 join(complement(A),complement(composition(one,A))) = complement(A).  [para(115(a,1),22(a,1,2))].
% 3.34/3.68  144 composition(one,A) = A.  [para(115(a,1),38(a,2)),rewrite([126(2),38(4)])].
% 3.34/3.68  150 join(complement(A),complement(A)) = complement(A).  [back_rewrite(130),rewrite([144(3)])].
% 3.34/3.68  151 join(zero,complement(complement(A))) = A.  [back_rewrite(50),rewrite([150(4)])].
% 3.34/3.68  152 converse(join(A,one)) = join(one,converse(A)).  [para(126(a,1),12(a,1,1)),rewrite([7(5)]),flip(a)].
% 3.34/3.68  153 join(zero,complement(A)) = complement(A).  [para(125(a,1),24(a,1,1,1)),rewrite([33(2),33(3),151(5)])].
% 3.34/3.68  155 join(top,complement(A)) = join(top,top).  [para(125(a,1),37(a,1,2)),rewrite([7(3)])].
% 3.34/3.68  156 complement(complement(A)) = A.  [back_rewrite(151),rewrite([153(4)])].
% 3.34/3.68  166 complement(join(A,A)) = complement(A).  [back_rewrite(51),rewrite([156(3),153(4)])].
% 3.34/3.68  168 join(A,top) = top.  [back_rewrite(125),rewrite([156(3),7(2)])].
% 3.34/3.68  174 join(top,complement(A)) = top.  [back_rewrite(155),rewrite([168(6)])].
% 3.34/3.68  184 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B).  [para(156(a,1),24(a,1,1,1,2)),rewrite([156(5),7(4)])].
% 3.34/3.68  188 join(complement(join(complement(A),complement(composition(complement(B),C)))),complement(join(complement(A),complement(composition(complement(join(B,complement(composition(A,converse(C))))),C))))) = complement(join(complement(A),complement(composition(complement(join(B,complement(composition(A,converse(C))))),C)))).  [para(156(a,1),28(a,1,2,1,2,1,1,1,1)),rewrite([156(20)])].
% 3.34/3.68  192 complement(zero) = top.  [para(33(a,1),156(a,1,1))].
% 3.34/3.68  207 join(A,A) = A.  [para(166(a,1),24(a,1,1,1,2)),rewrite([166(6),24(8)]),flip(a)].
% 3.34/3.68  214 join(A,join(A,B)) = join(A,B).  [para(207(a,1),16(a,1)),rewrite([7(3),16(4,R),7(3),16(3,R),207(2)]),flip(a)].
% 3.34/3.68  255 join(complement(one),composition(converse(complement(A)),A)) = complement(one).  [para(156(a,1),45(a,1,2,2))].
% 3.34/3.68  268 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero.  [para(152(a,1),80(a,1,2,1))].
% 3.34/3.68  304 join(complement(one),converse(complement(one))) = complement(one).  [para(1(a,1),255(a,1,2))].
% 3.34/3.68  308 converse(complement(one)) = complement(one).  [para(304(a,1),12(a,2,1)),rewrite([2(7),7(6),304(6)]),flip(a)].
% 3.34/3.68  317 converse(top) = top.  [para(308(a,1),152(a,2,2)),rewrite([7(4),4(4),4(6)])].
% 3.34/3.68  328 join(top,converse(A)) = top.  [para(317(a,1),12(a,1,1)),rewrite([7(5),168(5),317(5)])].
% 3.34/3.68  335 join(top,composition(A,converse(B))) = top.  [para(35(a,1),328(a,1,2))].
% 3.34/3.68  337 join(top,composition(A,B)) = top.  [para(2(a,1),335(a,1,2,2))].
% 3.34/3.68  338 composition(join(A,one),top) = top.  [para(317(a,1),335(a,1,2,2)),rewrite([128(4,R)])].
% 3.34/3.68  339 composition(join(one,converse(A)),zero) = zero.  [back_rewrite(268),rewrite([338(8),33(6),128(7,R),7(5),214(5)])].
% 3.34/3.68  366 composition(top,zero) = zero.  [para(308(a,1),339(a,1,1,2)),rewrite([4(4)])].
% 3.34/3.68  371 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)).  [para(366(a,1),30(a,1,1,1,2,1)),rewrite([192(3),7(3),174(3),33(2),33(3),153(7),156(6),192(6),317(7),174(9),33(6),18(6),33(9),153(13),156(12),192(12),317(13),174(15),33(12),18(12)])].
% 3.34/3.68  375 join(zero,composition(A,composition(B,zero))) = zero.  [para(366(a,1),43(a,1,2)),rewrite([7(5),337(8),366(8)])].
% 3.34/3.68  378 composition(A,composition(converse(zero),zero)) = zero.  [back_rewrite(371),rewrite([375(7)]),flip(a)].
% 3.34/3.68  457 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B).  [para(378(a,1),18(a,1,1)),rewrite([18(7)]),flip(a)].
% 3.34/3.68  458 composition(A,zero) = zero.  [para(378(a,1),18(a,1)),rewrite([378(6)]),flip(a)].
% 3.34/3.68  459 composition(converse(zero),A) = converse(zero).  [para(378(a,1),36(a,1,1)),rewrite([458(6)]),flip(a)].
% 3.34/3.68  464 composition(zero,A) = composition(B,converse(zero)).  [back_rewrite(457),rewrite([459(5)]),flip(a)].
% 3.34/3.68  466 composition(zero,A) = c_0.  [new_symbol(464)].
% 3.34/3.68  482 c_0 = zero.  [para(466(a,1),1(a,1))].
% 3.34/3.68  486 composition(zero,A) = zero.  [back_rewrite(466),rewrite([482(3)])].
% 3.34/3.68  2477 join(A,join(complement(A),converse(B))) = top.  [para(4(a,1),99(a,1,1)),rewrite([328(3)]),flip(a)].
% 3.34/3.68  2562 join(A,join(complement(A),composition(B,converse(C)))) = top.  [para(35(a,1),2477(a,1,2,2))].
% 3.34/3.68  2626 join(converse(sk3),composition(sk2,converse(sk1))) = converse(sk3).  [para(9(a,1),107(a,1,1)),rewrite([7(9)]),flip(a)].
% 3.34/3.68  3162 join(A,join(complement(A),composition(B,C))) = top.  [para(2(a,1),2562(a,1,2,2,2))].
% 3.34/3.68  3209 join(A,composition(join(B,one),complement(A))) = top.  [para(128(a,2),3162(a,1,2))].
% 3.34/3.68  3219 join(A,join(B,composition(join(C,one),complement(A)))) = top.  [para(3209(a,1),16(a,2,2)),rewrite([7(5),168(8)])].
% 3.34/3.68  7392 join(complement(A),composition(join(one,converse(B)),A)) = top.  [para(46(a,1),3219(a,1,2)),rewrite([152(3),7(6)])].
% 3.34/3.68  7402 join(converse(complement(converse(A))),composition(A,join(B,one))) = top.  [para(7392(a,1),107(a,1,1)),rewrite([317(2),34(5),126(3),7(8)]),flip(a)].
% 3.34/3.68  9392 join(A,converse(complement(converse(A)))) = top.  [para(207(a,1),7402(a,1,2,2)),rewrite([1(5),7(4)])].
% 3.34/3.68  9420 join(complement(converse(A)),converse(join(B,A))) = top.  [para(9392(a,1),100(a,1,1,2)),rewrite([168(2),317(2)]),flip(a)].
% 3.34/3.68  9503 join(sk3,complement(composition(sk1,converse(sk2)))) = top.  [para(2626(a,1),9420(a,1,2,1)),rewrite([35(5),2(8),7(7)])].
% 3.34/3.68  9517 complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = zero.  [para(9503(a,1),188(a,1,2,1,2,1,1,1)),rewrite([33(13),486(14),192(13),7(13),174(13),33(11),7(11),153(11),9503(18),33(13),486(14),192(13),7(13),174(13),33(11)])].
% 3.34/3.68  9677 complement(join(complement(sk1),composition(complement(sk3),sk2))) = sk1.  [para(9517(a,1),184(a,1,2)),rewrite([7(7),7(10),153(10),156(11)])].
% 3.34/3.68  10047 join(complement(sk1),composition(complement(sk3),sk2)) = complement(sk1).  [para(9677(a,1),24(a,1,1,1,2)),rewrite([9677(12),7(6),184(8)]),flip(a)].
% 3.34/3.68  10048 $F # answer(goals_18).  [resolve(10047,a,32,a)].
% 3.34/3.68  
% 3.34/3.68  % SZS output end Refutation
% 3.34/3.68  ============================== end of proof ==========================
% 3.34/3.68  
% 3.34/3.68  ============================== STATISTICS ============================
% 3.34/3.68  
% 3.34/3.68  Given=486. Generated=66434. Kept=10033. proofs=1.
% 3.34/3.68  Usable=409. Sos=8084. Demods=8374. Limbo=1, Disabled=1556. Hints=0.
% 3.34/3.68  Megabytes=21.48.
% 3.34/3.68  User_CPU=2.63, System_CPU=0.05, Wall_clock=3.
% 3.34/3.68  
% 3.34/3.68  ============================== end of statistics =====================
% 3.34/3.68  
% 3.34/3.68  ============================== end of search =========================
% 3.34/3.68  
% 3.34/3.68  THEOREM PROVED
% 3.34/3.68  % SZS status Unsatisfiable
% 3.34/3.68  
% 3.34/3.68  Exiting with 1 proof.
% 3.34/3.68  
% 3.34/3.68  Process 27065 exit (max_proofs) Fri Jul  8 07:22:13 2022
% 3.34/3.68  Prover9 interrupted
%------------------------------------------------------------------------------