TSTP Solution File: REL027-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL027-4 : 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 19:54:01 EDT 2022
% Result : Unsatisfiable 4.04s 4.31s
% Output : Refutation 4.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL027-4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n026.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 11:54:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.16/3.45 ============================== Prover9 ===============================
% 3.16/3.45 Prover9 (32) version 2009-11A, November 2009.
% 3.16/3.45 Process 8107 was started by sandbox2 on n026.cluster.edu,
% 3.16/3.45 Fri Jul 8 11:54:55 2022
% 3.16/3.45 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7954_n026.cluster.edu".
% 3.16/3.45 ============================== end of head ===========================
% 3.16/3.45
% 3.16/3.45 ============================== INPUT =================================
% 3.16/3.45
% 3.16/3.45 % Reading from file /tmp/Prover9_7954_n026.cluster.edu
% 3.16/3.45
% 3.16/3.45 set(prolog_style_variables).
% 3.16/3.45 set(auto2).
% 3.16/3.45 % set(auto2) -> set(auto).
% 3.16/3.45 % set(auto) -> set(auto_inference).
% 3.16/3.45 % set(auto) -> set(auto_setup).
% 3.16/3.45 % set(auto_setup) -> set(predicate_elim).
% 3.16/3.45 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.16/3.45 % set(auto) -> set(auto_limits).
% 3.16/3.45 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.16/3.45 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.16/3.45 % set(auto) -> set(auto_denials).
% 3.16/3.45 % set(auto) -> set(auto_process).
% 3.16/3.45 % set(auto2) -> assign(new_constants, 1).
% 3.16/3.45 % set(auto2) -> assign(fold_denial_max, 3).
% 3.16/3.45 % set(auto2) -> assign(max_weight, "200.000").
% 3.16/3.45 % set(auto2) -> assign(max_hours, 1).
% 3.16/3.45 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.16/3.45 % set(auto2) -> assign(max_seconds, 0).
% 3.16/3.45 % set(auto2) -> assign(max_minutes, 5).
% 3.16/3.45 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.16/3.45 % set(auto2) -> set(sort_initial_sos).
% 3.16/3.45 % set(auto2) -> assign(sos_limit, -1).
% 3.16/3.45 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.16/3.45 % set(auto2) -> assign(max_megs, 400).
% 3.16/3.45 % set(auto2) -> assign(stats, some).
% 3.16/3.45 % set(auto2) -> clear(echo_input).
% 3.16/3.45 % set(auto2) -> set(quiet).
% 3.16/3.45 % set(auto2) -> clear(print_initial_clauses).
% 3.16/3.45 % set(auto2) -> clear(print_given).
% 3.16/3.45 assign(lrs_ticks,-1).
% 3.16/3.45 assign(sos_limit,10000).
% 3.16/3.45 assign(order,kbo).
% 3.16/3.45 set(lex_order_vars).
% 3.16/3.45 clear(print_given).
% 3.16/3.45
% 3.16/3.45 % formulas(sos). % not echoed (18 formulas)
% 3.16/3.45
% 3.16/3.45 ============================== end of input ==========================
% 3.16/3.45
% 3.16/3.45 % From the command line: assign(max_seconds, 300).
% 3.16/3.45
% 3.16/3.45 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.16/3.45
% 3.16/3.45 % Formulas that are not ordinary clauses:
% 3.16/3.45
% 3.16/3.45 ============================== end of process non-clausal formulas ===
% 3.16/3.45
% 3.16/3.45 ============================== PROCESS INITIAL CLAUSES ===============
% 3.16/3.45
% 3.16/3.45 ============================== PREDICATE ELIMINATION =================
% 3.16/3.45
% 3.16/3.45 ============================== end predicate elimination =============
% 3.16/3.45
% 3.16/3.45 Auto_denials:
% 3.16/3.45 % copying label goals_18 to answer in negative clause
% 3.16/3.45
% 3.16/3.45 Term ordering decisions:
% 3.16/3.45 Function symbol KB weights: one=1. sk1=1. top=1. zero=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 3.16/3.45
% 3.16/3.45 ============================== end of process initial clauses ========
% 3.16/3.45
% 3.16/3.45 ============================== CLAUSES FOR SEARCH ====================
% 3.16/3.45
% 3.16/3.45 ============================== end of clauses for search =============
% 3.16/3.45
% 3.16/3.45 ============================== SEARCH ================================
% 3.16/3.45
% 3.16/3.45 % Starting search at 0.01 seconds.
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=128.000, iters=3476
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=104.000, iters=3463
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=76.000, iters=3406
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=74.000, iters=3335
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=72.000, iters=3399
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=70.000, iters=3340
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=66.000, iters=3358
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=64.000, iters=3350
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=63.000, iters=3334
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=62.000, iters=3350
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=61.000, iters=3386
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=60.000, iters=3351
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=58.000, iters=3381
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=57.000, iters=3362
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=55.000, iters=3440
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=54.000, iters=3465
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=53.000, iters=3417
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=52.000, iters=3360
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=51.000, iters=3336
% 3.16/3.45
% 3.16/3.45 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 32 (0.00 of 2.23 sec).
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=49.000, iters=3370
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=48.000, iters=3359
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=47.000, iters=3446
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=45.000, iters=3401
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=43.000, iters=3421
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=42.000, iters=3378
% 3.16/3.45
% 3.16/3.45 Low Water (keep): wt=41.000, iters=3353
% 4.04/4.31
% 4.04/4.31 Low Water (keep): wt=40.000, iters=3345
% 4.04/4.31
% 4.04/4.31 Low Water (keep): wt=39.000, iters=3353
% 4.04/4.31
% 4.04/4.31 Low Water (keep): wt=38.000, iters=3339
% 4.04/4.31
% 4.04/4.31 Low Water (keep): wt=37.000, iters=3375
% 4.04/4.31
% 4.04/4.31 Low Water (keep): wt=36.000, iters=3440
% 4.04/4.31
% 4.04/4.31 Low Water (keep): wt=35.000, iters=3357
% 4.04/4.31
% 4.04/4.31 Low Water (keep): wt=34.000, iters=3425
% 4.04/4.31
% 4.04/4.31 Low Water (keep): wt=33.000, iters=3438
% 4.04/4.31
% 4.04/4.31 Low Water (keep): wt=30.000, iters=3341
% 4.04/4.31
% 4.04/4.31 ============================== PROOF =================================
% 4.04/4.31 % SZS status Unsatisfiable
% 4.04/4.31 % SZS output start Refutation
% 4.04/4.31
% 4.04/4.31 % Proof 1 at 3.27 (+ 0.06) seconds: goals_18.
% 4.04/4.31 % Length of proof is 84.
% 4.04/4.31 % Level of proof is 20.
% 4.04/4.31 % Maximum clause weight is 52.000.
% 4.04/4.31 % Given clauses 607.
% 4.04/4.31
% 4.04/4.31 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 4.04/4.31 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 4.04/4.31 3 join(sk1,one) = one # label(goals_17) # label(negated_conjecture). [assumption].
% 4.04/4.31 4 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 4.04/4.31 5 join(A,complement(A)) = top. [copy(4),flip(a)].
% 4.04/4.31 6 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 4.04/4.31 7 meet(A,complement(A)) = zero. [copy(6),flip(a)].
% 4.04/4.31 8 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 4.04/4.31 9 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 4.04/4.31 10 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 4.04/4.31 11 join(converse(A),converse(B)) = converse(join(A,B)). [copy(10),flip(a)].
% 4.04/4.31 12 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 4.04/4.31 13 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(12),flip(a)].
% 4.04/4.31 14 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 4.04/4.31 15 join(A,join(B,C)) = join(C,join(A,B)). [copy(14),rewrite([8(4)])].
% 4.04/4.31 16 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 4.04/4.31 17 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(16),flip(a)].
% 4.04/4.31 18 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 4.04/4.31 19 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(18),flip(a)].
% 4.04/4.31 20 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 4.04/4.31 21 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(20),rewrite([8(6)])].
% 4.04/4.31 22 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 4.04/4.31 23 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(22),rewrite([8(6),8(8)]),flip(a),rewrite([8(6)])].
% 4.04/4.31 24 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].
% 4.04/4.31 25 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(24),rewrite([9(2),8(4),9(8),9(13),8(15),9(20),9(25),8(27)])].
% 4.04/4.31 28 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].
% 4.04/4.31 29 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(28),rewrite([9(2),8(4),9(8),9(14),9(22),9(28)])].
% 4.04/4.31 30 join(meet(complement(sk1),one),meet(complement(composition(sk1,top)),one)) != meet(complement(composition(sk1,top)),one) | join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one) # label(goals_18) # label(negated_conjecture) # answer(goals_18). [assumption].
% 4.04/4.31 31 join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) | join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1)))) # answer(goals_18). [copy(30),rewrite([9(4),8(6),9(13),8(15),9(23),8(25),9(33),8(35),9(40),8(42),8(44),9(48),8(50)])].
% 4.04/4.31 32 join(one,sk1) = one. [back_rewrite(3),rewrite([8(3)])].
% 4.04/4.31 33 complement(top) = zero. [back_rewrite(7),rewrite([9(2),5(4)])].
% 4.04/4.31 34 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),11(a,1,1)),rewrite([8(4)]),flip(a)].
% 4.04/4.31 35 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),13(a,1,1)),flip(a)].
% 4.04/4.31 36 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),13(a,1,2)),flip(a)].
% 4.04/4.31 37 join(A,join(B,complement(A))) = join(B,top). [para(5(a,1),15(a,2,2)),rewrite([8(2)])].
% 4.04/4.31 38 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),17(a,1,1)),flip(a)].
% 4.04/4.31 44 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),21(a,1,2,2,1))].
% 4.04/4.31 49 join(zero,complement(join(complement(A),complement(A)))) = A. [para(5(a,1),23(a,1,1,1)),rewrite([33(2)])].
% 4.04/4.31 50 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(5(a,1),23(a,1,2,1)),rewrite([33(6),8(6)])].
% 4.04/4.31 53 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(23(a,1),23(a,1,2,1)),rewrite([8(10)])].
% 4.04/4.31 70 join(complement(join(complement(A),complement(B))),composition(complement(join(complement(B),complement(composition(A,converse(one))))),complement(join(complement(one),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(one))))),complement(join(complement(one),complement(composition(converse(B),A))))). [para(1(a,1),29(a,1,1,1,2,1))].
% 4.04/4.31 89 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(34(a,1),11(a,1,1)),rewrite([8(7),15(7,R),8(6)]),flip(a)].
% 4.04/4.31 90 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(34(a,1),11(a,1,2)),rewrite([15(4,R),8(3),11(3),89(7)]),flip(a)].
% 4.04/4.31 98 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(34(a,1),34(a,2,2)),rewrite([90(4),34(4),15(6,R),8(5)])].
% 4.04/4.31 106 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(35(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 4.04/4.31 114 composition(converse(one),A) = A. [para(1(a,1),36(a,1,1)),rewrite([2(2)]),flip(a)].
% 4.04/4.31 123 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(23(a,1),37(a,1,2)),rewrite([8(4),37(4),8(3),8(8)]),flip(a)].
% 4.04/4.31 124 join(top,complement(complement(A))) = top. [para(25(a,1),37(a,1,2)),rewrite([5(22),8(8),123(8)]),flip(a)].
% 4.04/4.31 125 converse(one) = one. [para(114(a,1),1(a,1)),flip(a)].
% 4.04/4.31 127 composition(join(A,one),B) = join(B,composition(A,B)). [para(114(a,1),19(a,1,1)),rewrite([125(4),8(4)]),flip(a)].
% 4.04/4.31 129 join(complement(A),complement(composition(one,A))) = complement(A). [para(114(a,1),21(a,1,2))].
% 4.04/4.31 143 composition(one,A) = A. [para(114(a,1),38(a,2)),rewrite([125(2),38(4)])].
% 4.04/4.31 144 join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(B),A)))))) = composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(B),A))))). [back_rewrite(70),rewrite([125(7),1(7),8(7),125(20),1(20),8(20)])].
% 4.04/4.31 149 join(complement(A),complement(A)) = complement(A). [back_rewrite(129),rewrite([143(3)])].
% 4.04/4.31 150 join(zero,complement(complement(A))) = A. [back_rewrite(49),rewrite([149(4)])].
% 4.04/4.31 151 converse(join(A,one)) = join(one,converse(A)). [para(125(a,1),11(a,1,1)),rewrite([8(5)]),flip(a)].
% 4.04/4.31 152 join(zero,complement(A)) = complement(A). [para(124(a,1),23(a,1,1,1)),rewrite([33(2),33(3),150(5)])].
% 4.04/4.31 155 complement(complement(A)) = A. [back_rewrite(150),rewrite([152(4)])].
% 4.04/4.31 165 complement(join(A,A)) = complement(A). [back_rewrite(50),rewrite([155(3),152(4)])].
% 4.04/4.31 172 join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),composition(sk1,top))) | join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(sk1,complement(one))) # answer(goals_18). [back_rewrite(31),rewrite([155(5),8(4),155(12),155(20),155(26),8(25),155(33),155(39),8(38)])].
% 4.04/4.31 207 join(A,A) = A. [para(165(a,1),23(a,1,1,1,2)),rewrite([165(6),23(8)]),flip(a)].
% 4.04/4.31 214 join(A,join(A,B)) = join(A,B). [para(207(a,1),15(a,1)),rewrite([8(3),15(4,R),8(3),15(3,R),207(2)]),flip(a)].
% 4.04/4.31 232 join(A,complement(join(B,complement(A)))) = A. [para(23(a,1),214(a,1,2)),rewrite([8(4),23(12)])].
% 4.04/4.31 255 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(155(a,1),44(a,1,2,2))].
% 4.04/4.31 275 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(127(a,1),19(a,1,2)),rewrite([15(4,R),19(3),8(1)]),flip(a)].
% 4.04/4.31 304 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),255(a,1,2))].
% 4.04/4.31 308 converse(complement(one)) = complement(one). [para(304(a,1),11(a,2,1)),rewrite([2(7),8(6),304(6)]),flip(a)].
% 4.04/4.31 317 converse(top) = top. [para(308(a,1),151(a,2,2)),rewrite([8(4),5(4),5(6)])].
% 4.04/4.31 437 join(complement(A),complement(join(B,A))) = complement(A). [para(232(a,1),53(a,2)),rewrite([155(2),155(4),155(8),53(13)])].
% 4.04/4.31 757 join(complement(one),complement(sk1)) = complement(sk1). [para(32(a,1),437(a,1,2,1)),rewrite([8(5)])].
% 4.04/4.31 2354 join(one,join(sk1,converse(A))) = join(one,converse(A)). [para(32(a,1),98(a,1,1)),flip(a)].
% 4.04/4.31 3584 join(A,join(one,converse(sk1))) = join(A,one). [para(2354(a,1),11(a,2,1)),rewrite([125(2),34(5),15(5,R),8(4),34(9),125(7)])].
% 4.04/4.31 3592 join(one,converse(sk1)) = one. [para(207(a,1),3584(a,2)),rewrite([214(6)])].
% 4.04/4.31 3640 join(A,composition(converse(sk1),A)) = A. [para(3592(a,1),19(a,2,1)),rewrite([143(2),143(6)])].
% 4.04/4.31 3642 join(complement(one),complement(converse(sk1))) = complement(converse(sk1)). [para(3592(a,1),437(a,1,2,1)),rewrite([8(6)])].
% 4.04/4.31 3646 join(A,join(B,composition(converse(sk1),A))) = join(A,B). [para(3640(a,1),15(a,2,2)),rewrite([8(4),8(6)])].
% 4.04/4.31 3651 join(A,composition(A,sk1)) = A. [para(3640(a,1),106(a,1,1)),rewrite([2(2),2(3),2(4),8(3)]),flip(a)].
% 4.04/4.31 4287 composition(converse(sk1),sk1) = converse(sk1). [para(3642(a,1),144(a,1,1,1)),rewrite([155(4),3642(8),155(6),2(9),1(9),757(9),155(7),3651(7),3642(8),155(6),2(9),1(9),757(9),155(7)]),flip(a)].
% 4.04/4.31 4322 converse(sk1) = sk1. [para(4287(a,1),13(a,2,1)),rewrite([2(5),4287(4),2(5)])].
% 4.04/4.31 4391 join(A,join(B,composition(sk1,A))) = join(A,B). [back_rewrite(3646),rewrite([4322(2)])].
% 4.04/4.31 14364 join(A,composition(complement(one),A)) = composition(top,A). [para(44(a,1),275(a,2,2,1)),rewrite([8(7),15(8,R),8(7),44(7),5(4)]),flip(a)].
% 4.04/4.31 14423 join(A,composition(A,complement(one))) = composition(A,top). [para(14364(a,1),106(a,1,1)),rewrite([35(4),317(2),308(5),2(7),8(6)]),flip(a)].
% 4.04/4.31 14437 join(complement(one),composition(sk1,top)) = join(sk1,complement(one)). [para(14423(a,1),4391(a,1,2)),rewrite([8(10)])].
% 4.04/4.31 14443 $F # answer(goals_18). [back_rewrite(172),rewrite([14437(11),207(11),14437(11),14437(22),207(22)]),xx(a),xx(b)].
% 4.04/4.31
% 4.04/4.31 % SZS output end Refutation
% 4.04/4.31 ============================== end of proof ==========================
% 4.04/4.31
% 4.04/4.31 ============================== STATISTICS ============================
% 4.04/4.31
% 4.04/4.31 Given=607. Generated=89887. Kept=14429. proofs=1.
% 4.04/4.31 Usable=402. Sos=8240. Demods=8364. Limbo=6, Disabled=5799. Hints=0.
% 4.04/4.31 Megabytes=24.96.
% 4.04/4.31 User_CPU=3.27, System_CPU=0.06, Wall_clock=3.
% 4.04/4.31
% 4.04/4.31 ============================== end of statistics =====================
% 4.04/4.31
% 4.04/4.31 ============================== end of search =========================
% 4.04/4.31
% 4.04/4.31 THEOREM PROVED
% 4.04/4.31 % SZS status Unsatisfiable
% 4.04/4.31
% 4.04/4.31 Exiting with 1 proof.
% 4.04/4.31
% 4.04/4.31 Process 8107 exit (max_proofs) Fri Jul 8 11:54:58 2022
% 4.04/4.31 Prover9 interrupted
%------------------------------------------------------------------------------