TSTP Solution File: REL041-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL041-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 19:54:24 EDT 2022
% Result : Unsatisfiable 3.18s 3.47s
% Output : Refutation 3.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL041-2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.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 09:04:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.18/3.47 ============================== Prover9 ===============================
% 3.18/3.47 Prover9 (32) version 2009-11A, November 2009.
% 3.18/3.47 Process 24243 was started by sandbox on n018.cluster.edu,
% 3.18/3.47 Fri Jul 8 09:04:26 2022
% 3.18/3.47 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24090_n018.cluster.edu".
% 3.18/3.47 ============================== end of head ===========================
% 3.18/3.47
% 3.18/3.47 ============================== INPUT =================================
% 3.18/3.47
% 3.18/3.47 % Reading from file /tmp/Prover9_24090_n018.cluster.edu
% 3.18/3.47
% 3.18/3.47 set(prolog_style_variables).
% 3.18/3.47 set(auto2).
% 3.18/3.47 % set(auto2) -> set(auto).
% 3.18/3.47 % set(auto) -> set(auto_inference).
% 3.18/3.47 % set(auto) -> set(auto_setup).
% 3.18/3.47 % set(auto_setup) -> set(predicate_elim).
% 3.18/3.47 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.18/3.47 % set(auto) -> set(auto_limits).
% 3.18/3.47 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.18/3.47 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.18/3.47 % set(auto) -> set(auto_denials).
% 3.18/3.47 % set(auto) -> set(auto_process).
% 3.18/3.47 % set(auto2) -> assign(new_constants, 1).
% 3.18/3.47 % set(auto2) -> assign(fold_denial_max, 3).
% 3.18/3.47 % set(auto2) -> assign(max_weight, "200.000").
% 3.18/3.47 % set(auto2) -> assign(max_hours, 1).
% 3.18/3.47 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.18/3.47 % set(auto2) -> assign(max_seconds, 0).
% 3.18/3.47 % set(auto2) -> assign(max_minutes, 5).
% 3.18/3.47 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.18/3.47 % set(auto2) -> set(sort_initial_sos).
% 3.18/3.47 % set(auto2) -> assign(sos_limit, -1).
% 3.18/3.47 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.18/3.47 % set(auto2) -> assign(max_megs, 400).
% 3.18/3.47 % set(auto2) -> assign(stats, some).
% 3.18/3.47 % set(auto2) -> clear(echo_input).
% 3.18/3.47 % set(auto2) -> set(quiet).
% 3.18/3.47 % set(auto2) -> clear(print_initial_clauses).
% 3.18/3.47 % set(auto2) -> clear(print_given).
% 3.18/3.47 assign(lrs_ticks,-1).
% 3.18/3.47 assign(sos_limit,10000).
% 3.18/3.47 assign(order,kbo).
% 3.18/3.47 set(lex_order_vars).
% 3.18/3.47 clear(print_given).
% 3.18/3.47
% 3.18/3.47 % formulas(sos). % not echoed (18 formulas)
% 3.18/3.47
% 3.18/3.47 ============================== end of input ==========================
% 3.18/3.47
% 3.18/3.47 % From the command line: assign(max_seconds, 300).
% 3.18/3.47
% 3.18/3.47 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.18/3.47
% 3.18/3.47 % Formulas that are not ordinary clauses:
% 3.18/3.47
% 3.18/3.47 ============================== end of process non-clausal formulas ===
% 3.18/3.47
% 3.18/3.47 ============================== PROCESS INITIAL CLAUSES ===============
% 3.18/3.47
% 3.18/3.47 ============================== PREDICATE ELIMINATION =================
% 3.18/3.47
% 3.18/3.47 ============================== end predicate elimination =============
% 3.18/3.47
% 3.18/3.47 Auto_denials:
% 3.18/3.47 % copying label goals_18 to answer in negative clause
% 3.18/3.47
% 3.18/3.47 Term ordering decisions:
% 3.18/3.47 Function symbol KB weights: one=1. sk1=1. top=1. zero=1. sk2=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 3.18/3.47
% 3.18/3.47 ============================== end of process initial clauses ========
% 3.18/3.47
% 3.18/3.47 ============================== CLAUSES FOR SEARCH ====================
% 3.18/3.47
% 3.18/3.47 ============================== end of clauses for search =============
% 3.18/3.47
% 3.18/3.47 ============================== SEARCH ================================
% 3.18/3.47
% 3.18/3.47 % Starting search at 0.01 seconds.
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=86.000, iters=3353
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=80.000, iters=3358
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=77.000, iters=3340
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=75.000, iters=3342
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=74.000, iters=3350
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=73.000, iters=3417
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=72.000, iters=3386
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=70.000, iters=3390
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=66.000, iters=3345
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=65.000, iters=3339
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=64.000, iters=3338
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=61.000, iters=3425
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=59.000, iters=3406
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=58.000, iters=3407
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=57.000, iters=3380
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=55.000, iters=3440
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=54.000, iters=3360
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=53.000, iters=3356
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=49.000, iters=3401
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=48.000, iters=3365
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=46.000, iters=3425
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=45.000, iters=3416
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=43.000, iters=3355
% 3.18/3.47
% 3.18/3.47 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 28 (0.00 of 2.44 sec).
% 3.18/3.47
% 3.18/3.47 ============================== PROOF =================================
% 3.18/3.47 % SZS status Unsatisfiable
% 3.18/3.47 % SZS output start Refutation
% 3.18/3.47
% 3.18/3.47 % Proof 1 at 2.44 (+ 0.04) seconds: goals_18.
% 3.18/3.47 % Length of proof is 95.
% 3.18/3.47 % Level of proof is 26.
% 3.18/3.47 % Maximum clause weight is 48.000.
% 3.18/3.47 % Given clauses 501.
% 3.18/3.47
% 3.18/3.47 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 3.18/3.47 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 3.18/3.47 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 3.18/3.47 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 3.18/3.47 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 3.18/3.47 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 3.18/3.47 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 3.18/3.47 8 join(composition(converse(sk1),sk1),one) = one # label(goals_17) # label(negated_conjecture). [assumption].
% 3.18/3.47 9 join(one,composition(converse(sk1),sk1)) = one. [copy(8),rewrite([7(6)])].
% 3.18/3.47 10 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 3.18/3.47 11 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 3.18/3.47 12 join(converse(A),converse(B)) = converse(join(A,B)). [copy(11),flip(a)].
% 3.18/3.47 13 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 3.18/3.47 14 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(13),flip(a)].
% 3.18/3.47 15 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 3.18/3.47 16 join(A,join(B,C)) = join(C,join(A,B)). [copy(15),rewrite([7(4)])].
% 3.18/3.47 17 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 3.18/3.47 18 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(17),flip(a)].
% 3.18/3.47 19 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 3.18/3.47 20 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(19),flip(a)].
% 3.18/3.47 21 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 3.18/3.47 22 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(21),rewrite([7(6)])].
% 3.18/3.47 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].
% 3.18/3.47 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)])].
% 3.18/3.47 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].
% 3.18/3.47 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)])].
% 3.18/3.47 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].
% 3.18/3.47 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)])].
% 3.18/3.47 31 meet(composition(sk1,sk2),composition(sk1,complement(sk2))) != zero # label(goals_18) # label(negated_conjecture) # answer(goals_18). [assumption].
% 3.18/3.47 32 complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,complement(sk2))))) != zero # answer(goals_18). [copy(31),rewrite([10(8)])].
% 3.18/3.47 33 complement(top) = zero. [back_rewrite(6),rewrite([10(2),4(4)])].
% 3.18/3.47 34 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),12(a,1,1)),rewrite([7(4)]),flip(a)].
% 3.18/3.47 35 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),14(a,1,1)),flip(a)].
% 3.18/3.47 36 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),14(a,1,2)),flip(a)].
% 3.18/3.47 37 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),16(a,2,2)),rewrite([7(2)])].
% 3.18/3.47 38 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),18(a,1,1)),flip(a)].
% 3.18/3.47 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)])].
% 3.18/3.47 45 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),22(a,1,2,2,1))].
% 3.18/3.47 46 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(2(a,1),22(a,1,2,1))].
% 3.18/3.47 50 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),24(a,1,1,1)),rewrite([33(2)])].
% 3.18/3.47 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)])].
% 3.18/3.47 80 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(33(a,1),22(a,1,1)),rewrite([33(9)])].
% 3.18/3.47 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)].
% 3.18/3.47 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)].
% 3.18/3.47 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)])].
% 3.18/3.47 100 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(90),rewrite([99(8),12(7)])].
% 3.18/3.47 107 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)].
% 3.18/3.47 115 composition(converse(one),A) = A. [para(1(a,1),36(a,1,1)),rewrite([2(2)]),flip(a)].
% 3.18/3.47 124 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)].
% 3.18/3.47 125 join(top,complement(complement(A))) = top. [para(26(a,1),37(a,1,2)),rewrite([4(22),7(8),124(8)]),flip(a)].
% 3.18/3.47 126 converse(one) = one. [para(115(a,1),1(a,1)),flip(a)].
% 3.18/3.47 128 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)].
% 3.18/3.47 130 join(complement(A),complement(composition(one,A))) = complement(A). [para(115(a,1),22(a,1,2))].
% 3.18/3.47 144 composition(one,A) = A. [para(115(a,1),38(a,2)),rewrite([126(2),38(4)])].
% 3.18/3.47 150 join(complement(A),complement(A)) = complement(A). [back_rewrite(130),rewrite([144(3)])].
% 3.18/3.47 151 join(zero,complement(complement(A))) = A. [back_rewrite(50),rewrite([150(4)])].
% 3.18/3.47 152 converse(join(A,one)) = join(one,converse(A)). [para(126(a,1),12(a,1,1)),rewrite([7(5)]),flip(a)].
% 3.18/3.47 153 join(zero,complement(A)) = complement(A). [para(125(a,1),24(a,1,1,1)),rewrite([33(2),33(3),151(5)])].
% 3.18/3.47 155 join(top,complement(A)) = join(top,top). [para(125(a,1),37(a,1,2)),rewrite([7(3)])].
% 3.18/3.47 156 complement(complement(A)) = A. [back_rewrite(151),rewrite([153(4)])].
% 3.18/3.47 166 complement(join(A,A)) = complement(A). [back_rewrite(51),rewrite([156(3),153(4)])].
% 3.18/3.47 168 join(A,top) = top. [back_rewrite(125),rewrite([156(3),7(2)])].
% 3.18/3.47 174 join(top,complement(A)) = top. [back_rewrite(155),rewrite([168(6)])].
% 3.18/3.47 192 complement(zero) = top. [para(33(a,1),156(a,1,1))].
% 3.18/3.47 207 join(A,A) = A. [para(166(a,1),24(a,1,1,1,2)),rewrite([166(6),24(8)]),flip(a)].
% 3.18/3.47 214 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)].
% 3.18/3.47 238 join(A,composition(converse(sk1),composition(sk1,A))) = A. [para(9(a,1),43(a,2,1)),rewrite([144(7),7(6),144(8)])].
% 3.18/3.47 250 join(converse(A),composition(converse(composition(sk1,A)),sk1)) = converse(A). [para(238(a,1),12(a,2,1)),rewrite([36(7)])].
% 3.18/3.47 258 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(156(a,1),45(a,1,2,2))].
% 3.18/3.47 271 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(152(a,1),80(a,1,2,1))].
% 3.18/3.47 307 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),258(a,1,2))].
% 3.18/3.47 311 converse(complement(one)) = complement(one). [para(307(a,1),12(a,2,1)),rewrite([2(7),7(6),307(6)]),flip(a)].
% 3.18/3.47 325 converse(top) = top. [para(311(a,1),152(a,2,2)),rewrite([7(4),4(4),4(6)])].
% 3.18/3.47 331 join(top,converse(A)) = top. [para(325(a,1),12(a,1,1)),rewrite([7(5),168(5),325(5)])].
% 3.18/3.47 338 join(top,composition(A,converse(B))) = top. [para(35(a,1),331(a,1,2))].
% 3.18/3.47 340 join(top,composition(A,B)) = top. [para(2(a,1),338(a,1,2,2))].
% 3.18/3.47 341 composition(join(A,one),top) = top. [para(325(a,1),338(a,1,2,2)),rewrite([128(4,R)])].
% 3.18/3.47 342 composition(join(one,converse(A)),zero) = zero. [back_rewrite(271),rewrite([341(8),33(6),128(7,R),7(5),214(5)])].
% 3.18/3.47 369 composition(top,zero) = zero. [para(311(a,1),342(a,1,1,2)),rewrite([4(4)])].
% 3.18/3.47 374 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(369(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),325(7),174(9),33(6),18(6),33(9),153(13),156(12),192(12),325(13),174(15),33(12),18(12)])].
% 3.18/3.47 378 join(zero,composition(A,composition(B,zero))) = zero. [para(369(a,1),43(a,1,2)),rewrite([7(5),340(8),369(8)])].
% 3.18/3.47 381 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(374),rewrite([378(7)]),flip(a)].
% 3.18/3.47 459 composition(A,zero) = zero. [para(381(a,1),18(a,1)),rewrite([381(6)]),flip(a)].
% 3.18/3.47 2505 join(A,join(complement(A),converse(B))) = top. [para(4(a,1),99(a,1,1)),rewrite([331(3)]),flip(a)].
% 3.18/3.47 2589 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(35(a,1),2505(a,1,2,2))].
% 3.18/3.47 3290 join(A,join(complement(A),composition(B,C))) = top. [para(2(a,1),2589(a,1,2,2,2))].
% 3.18/3.47 3293 join(A,composition(join(B,one),complement(A))) = top. [para(128(a,2),3290(a,1,2))].
% 3.18/3.47 3303 join(A,join(B,composition(join(C,one),complement(A)))) = top. [para(3293(a,1),16(a,2,2)),rewrite([7(5),168(8)])].
% 3.18/3.47 7941 join(complement(A),composition(join(one,converse(B)),A)) = top. [para(46(a,1),3303(a,1,2)),rewrite([152(3),7(6)])].
% 3.18/3.47 7951 join(converse(complement(converse(A))),composition(A,join(B,one))) = top. [para(7941(a,1),107(a,1,1)),rewrite([325(2),34(5),126(3),7(8)]),flip(a)].
% 3.18/3.47 9689 join(A,converse(complement(converse(A)))) = top. [para(207(a,1),7951(a,1,2,2)),rewrite([1(5),7(4)])].
% 3.18/3.47 9717 join(complement(converse(A)),converse(join(B,A))) = top. [para(9689(a,1),100(a,1,1,2)),rewrite([168(2),325(2)]),flip(a)].
% 3.18/3.47 9797 join(A,complement(composition(converse(sk1),composition(sk1,A)))) = top. [para(250(a,1),9717(a,1,2,1)),rewrite([36(6),2(8),7(7)])].
% 3.18/3.47 10826 complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = zero. [para(9797(a,1),26(a,1,2,1,2,1,2,1)),rewrite([7(8),33(16),459(16),192(15),7(15),174(15),33(11),7(11),153(11),9797(23),33(16),459(16),192(15),7(15),174(15),33(11)])].
% 3.18/3.47 10827 $F # answer(goals_18). [resolve(10826,a,32,a)].
% 3.18/3.47
% 3.18/3.47 % SZS output end Refutation
% 3.18/3.47 ============================== end of proof ==========================
% 3.18/3.47
% 3.18/3.47 ============================== STATISTICS ============================
% 3.18/3.47
% 3.18/3.47 Given=501. Generated=72649. Kept=10812. proofs=1.
% 3.18/3.47 Usable=432. Sos=8915. Demods=9230. Limbo=2, Disabled=1480. Hints=0.
% 3.18/3.47 Megabytes=22.75.
% 3.18/3.47 User_CPU=2.44, System_CPU=0.04, Wall_clock=2.
% 3.18/3.47
% 3.18/3.47 ============================== end of statistics =====================
% 3.18/3.47
% 3.18/3.47 ============================== end of search =========================
% 3.18/3.47
% 3.18/3.47 THEOREM PROVED
% 3.18/3.47 % SZS status Unsatisfiable
% 3.18/3.47
% 3.18/3.47 Exiting with 1 proof.
% 3.18/3.47
% 3.18/3.47 Process 24243 exit (max_proofs) Fri Jul 8 09:04:28 2022
% 3.18/3.47 Prover9 interrupted
%------------------------------------------------------------------------------