TSTP Solution File: REL026-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL026-4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 19:53:59 EDT 2022
% Result : Unsatisfiable 26.13s 26.46s
% Output : Refutation 26.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL026-4 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n011.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 13:46:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.23/3.58 ============================== Prover9 ===============================
% 3.23/3.58 Prover9 (32) version 2009-11A, November 2009.
% 3.23/3.58 Process 21687 was started by sandbox on n011.cluster.edu,
% 3.23/3.58 Fri Jul 8 13:46:25 2022
% 3.23/3.58 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21534_n011.cluster.edu".
% 3.23/3.58 ============================== end of head ===========================
% 3.23/3.58
% 3.23/3.58 ============================== INPUT =================================
% 3.23/3.58
% 3.23/3.58 % Reading from file /tmp/Prover9_21534_n011.cluster.edu
% 3.23/3.58
% 3.23/3.58 set(prolog_style_variables).
% 3.23/3.58 set(auto2).
% 3.23/3.58 % set(auto2) -> set(auto).
% 3.23/3.58 % set(auto) -> set(auto_inference).
% 3.23/3.58 % set(auto) -> set(auto_setup).
% 3.23/3.58 % set(auto_setup) -> set(predicate_elim).
% 3.23/3.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.23/3.58 % set(auto) -> set(auto_limits).
% 3.23/3.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.23/3.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.23/3.58 % set(auto) -> set(auto_denials).
% 3.23/3.58 % set(auto) -> set(auto_process).
% 3.23/3.58 % set(auto2) -> assign(new_constants, 1).
% 3.23/3.58 % set(auto2) -> assign(fold_denial_max, 3).
% 3.23/3.58 % set(auto2) -> assign(max_weight, "200.000").
% 3.23/3.58 % set(auto2) -> assign(max_hours, 1).
% 3.23/3.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.23/3.58 % set(auto2) -> assign(max_seconds, 0).
% 3.23/3.58 % set(auto2) -> assign(max_minutes, 5).
% 3.23/3.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.23/3.58 % set(auto2) -> set(sort_initial_sos).
% 3.23/3.58 % set(auto2) -> assign(sos_limit, -1).
% 3.23/3.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.23/3.58 % set(auto2) -> assign(max_megs, 400).
% 3.23/3.58 % set(auto2) -> assign(stats, some).
% 3.23/3.58 % set(auto2) -> clear(echo_input).
% 3.23/3.58 % set(auto2) -> set(quiet).
% 3.23/3.58 % set(auto2) -> clear(print_initial_clauses).
% 3.23/3.58 % set(auto2) -> clear(print_given).
% 3.23/3.58 assign(lrs_ticks,-1).
% 3.23/3.58 assign(sos_limit,10000).
% 3.23/3.58 assign(order,kbo).
% 3.23/3.58 set(lex_order_vars).
% 3.23/3.58 clear(print_given).
% 3.23/3.58
% 3.23/3.58 % formulas(sos). % not echoed (18 formulas)
% 3.23/3.58
% 3.23/3.58 ============================== end of input ==========================
% 3.23/3.58
% 3.23/3.58 % From the command line: assign(max_seconds, 300).
% 3.23/3.58
% 3.23/3.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.23/3.58
% 3.23/3.58 % Formulas that are not ordinary clauses:
% 3.23/3.58
% 3.23/3.58 ============================== end of process non-clausal formulas ===
% 3.23/3.58
% 3.23/3.58 ============================== PROCESS INITIAL CLAUSES ===============
% 3.23/3.58
% 3.23/3.58 ============================== PREDICATE ELIMINATION =================
% 3.23/3.58
% 3.23/3.58 ============================== end predicate elimination =============
% 3.23/3.58
% 3.23/3.58 Auto_denials:
% 3.23/3.58 % copying label goals_18 to answer in negative clause
% 3.23/3.58
% 3.23/3.58 Term ordering decisions:
% 3.23/3.58 Function symbol KB weights: one=1. sk1=1. top=1. zero=1. sk2=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 3.23/3.58
% 3.23/3.58 ============================== end of process initial clauses ========
% 3.23/3.58
% 3.23/3.58 ============================== CLAUSES FOR SEARCH ====================
% 3.23/3.58
% 3.23/3.58 ============================== end of clauses for search =============
% 3.23/3.58
% 3.23/3.58 ============================== SEARCH ================================
% 3.23/3.58
% 3.23/3.58 % Starting search at 0.01 seconds.
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=119.000, iters=3953
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=97.000, iters=3939
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=76.000, iters=3406
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=74.000, iters=3335
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=72.000, iters=3399
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=70.000, iters=3340
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=66.000, iters=3358
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=64.000, iters=3350
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=63.000, iters=3334
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=62.000, iters=3350
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=61.000, iters=3386
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=60.000, iters=3351
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=58.000, iters=3381
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=57.000, iters=3362
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=55.000, iters=3440
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=54.000, iters=3465
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=53.000, iters=3417
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=52.000, iters=3360
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=51.000, iters=3336
% 3.23/3.58
% 3.23/3.58 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 32 (0.00 of 2.35 sec).
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=49.000, iters=3370
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=48.000, iters=3359
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=47.000, iters=3446
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=45.000, iters=3401
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=43.000, iters=3421
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=42.000, iters=3378
% 3.23/3.58
% 3.23/3.58 Low Water (keep): wt=41.000, iters=3353
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=40.000, iters=3345
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=39.000, iters=3353
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=38.000, iters=3339
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=37.000, iters=3375
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=36.000, iters=3440
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=35.000, iters=3357
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=34.000, iters=3425
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=33.000, iters=3438
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=30.000, iters=3341
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=29.000, iters=3415
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=28.000, iters=3391
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=27.000, iters=3382
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=26.000, iters=3358
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=25.000, iters=3417
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=24.000, iters=3505
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=23.000, iters=3343
% 26.13/26.46
% 26.13/26.46 Low Water (displace): id=5409, wt=166.000
% 26.13/26.46
% 26.13/26.46 Low Water (displace): id=16834, wt=20.000
% 26.13/26.46
% 26.13/26.46 Low Water (displace): id=16839, wt=15.000
% 26.13/26.46
% 26.13/26.46 Low Water (displace): id=16844, wt=14.000
% 26.13/26.46
% 26.13/26.46 Low Water (displace): id=16886, wt=13.000
% 26.13/26.46
% 26.13/26.46 Low Water (displace): id=16910, wt=12.000
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=22.000, iters=3406
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=21.000, iters=3345
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=20.000, iters=3351
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=19.000, iters=3340
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=18.000, iters=3334
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=17.000, iters=3340
% 26.13/26.46
% 26.13/26.46 Low Water (keep): wt=16.000, iters=3379
% 26.13/26.46
% 26.13/26.46 ============================== PROOF =================================
% 26.13/26.46 % SZS status Unsatisfiable
% 26.13/26.46 % SZS output start Refutation
% 26.13/26.46
% 26.13/26.46 % Proof 1 at 24.88 (+ 0.58) seconds: goals_18.
% 26.13/26.46 % Length of proof is 138.
% 26.13/26.46 % Level of proof is 36.
% 26.13/26.46 % Maximum clause weight is 49.000.
% 26.13/26.46 % Given clauses 2057.
% 26.13/26.46
% 26.13/26.46 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 26.13/26.46 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 26.13/26.46 3 join(sk1,one) = one # label(goals_17) # label(negated_conjecture). [assumption].
% 26.13/26.46 4 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 26.13/26.46 5 join(A,complement(A)) = top. [copy(4),flip(a)].
% 26.13/26.46 6 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 26.13/26.46 7 meet(A,complement(A)) = zero. [copy(6),flip(a)].
% 26.13/26.46 8 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 26.13/26.46 9 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 26.13/26.46 10 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 26.13/26.46 11 join(converse(A),converse(B)) = converse(join(A,B)). [copy(10),flip(a)].
% 26.13/26.46 12 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 26.13/26.46 13 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(12),flip(a)].
% 26.13/26.46 14 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 26.13/26.46 15 join(A,join(B,C)) = join(C,join(A,B)). [copy(14),rewrite([8(4)])].
% 26.13/26.46 16 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 26.13/26.46 17 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(16),flip(a)].
% 26.13/26.46 18 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 26.13/26.46 19 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(18),flip(a)].
% 26.13/26.46 20 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 26.13/26.46 21 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(20),rewrite([8(6)])].
% 26.13/26.46 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].
% 26.13/26.46 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)])].
% 26.13/26.46 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].
% 26.13/26.46 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)])].
% 26.13/26.46 26 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].
% 26.13/26.46 27 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(26),rewrite([9(2),8(4),9(8),9(13),8(15),9(20),9(25),8(27)])].
% 26.13/26.46 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].
% 26.13/26.46 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)])].
% 26.13/26.46 30 join(composition(sk1,sk2),meet(composition(sk1,top),sk2)) != meet(composition(sk1,top),sk2) | join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2) # label(goals_18) # label(negated_conjecture) # answer(goals_18). [assumption].
% 26.13/26.46 31 join(composition(sk1,sk2),complement(join(complement(sk2),complement(composition(sk1,top))))) != complement(join(complement(sk2),complement(composition(sk1,top)))) | join(composition(sk1,sk2),complement(join(complement(sk2),complement(composition(sk1,top))))) != composition(sk1,sk2) # answer(goals_18). [copy(30),rewrite([9(8),8(10),9(17),8(19),9(26),8(28),8(33)])].
% 26.13/26.46 32 join(one,sk1) = one. [back_rewrite(3),rewrite([8(3)])].
% 26.13/26.46 33 complement(top) = zero. [back_rewrite(7),rewrite([9(2),5(4)])].
% 26.13/26.46 34 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),11(a,1,1)),rewrite([8(4)]),flip(a)].
% 26.13/26.46 35 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),13(a,1,1)),flip(a)].
% 26.13/26.46 36 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),13(a,1,2)),flip(a)].
% 26.13/26.46 37 join(A,join(B,complement(A))) = join(B,top). [para(5(a,1),15(a,2,2)),rewrite([8(2)])].
% 26.13/26.46 38 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),17(a,1,1)),flip(a)].
% 26.13/26.46 39 composition(converse(A),composition(converse(B),C)) = composition(converse(composition(B,A)),C). [para(13(a,1),17(a,1,1)),flip(a)].
% 26.13/26.46 40 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(13(a,1),19(a,1,1)),rewrite([8(7)])].
% 26.13/26.46 42 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(17(a,1),19(a,1,1)),rewrite([8(6)])].
% 26.13/26.46 43 join(composition(A,B),composition(C,composition(D,B))) = composition(join(A,composition(C,D)),B). [para(17(a,1),19(a,1,2))].
% 26.13/26.46 44 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),21(a,1,2,2,1))].
% 26.13/26.46 48 join(complement(A),composition(converse(composition(B,C)),complement(composition(B,composition(C,A))))) = complement(A). [para(17(a,1),21(a,1,2,2,1))].
% 26.13/26.46 49 join(zero,complement(join(complement(A),complement(A)))) = A. [para(5(a,1),23(a,1,1,1)),rewrite([33(2)])].
% 26.13/26.46 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)])].
% 26.13/26.46 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)])].
% 26.13/26.46 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))].
% 26.13/26.46 72 join(complement(join(complement(A),complement(composition(B,converse(C))))),composition(complement(join(complement(B),complement(composition(A,C)))),complement(join(complement(converse(C)),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,C)))),complement(join(complement(converse(C)),complement(composition(converse(B),A))))). [para(2(a,1),29(a,1,2,1,1,2,1,2)),rewrite([2(23)])].
% 26.13/26.46 79 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(33(a,1),21(a,1,1)),rewrite([33(9)])].
% 26.13/26.46 81 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(33(a,1),23(a,1,2,1,1))].
% 26.13/26.46 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)].
% 26.13/26.46 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)].
% 26.13/26.46 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)])].
% 26.13/26.46 106 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)].
% 26.13/26.46 114 composition(converse(one),A) = A. [para(1(a,1),36(a,1,1)),rewrite([2(2)]),flip(a)].
% 26.13/26.46 115 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(36(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 26.13/26.46 123 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)].
% 26.13/26.46 124 join(top,complement(complement(A))) = top. [para(25(a,1),37(a,1,2)),rewrite([5(22),8(8),123(8)]),flip(a)].
% 26.13/26.46 125 converse(one) = one. [para(114(a,1),1(a,1)),flip(a)].
% 26.13/26.46 127 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)].
% 26.13/26.46 129 join(complement(A),complement(composition(one,A))) = complement(A). [para(114(a,1),21(a,1,2))].
% 26.13/26.46 135 join(complement(join(complement(A),complement(B))),complement(join(complement(A),complement(composition(complement(join(complement(one),complement(composition(A,converse(B))))),B))))) = complement(join(complement(A),complement(composition(complement(join(complement(one),complement(composition(A,converse(B))))),B)))). [para(114(a,1),27(a,1,1,1,2,1)),rewrite([125(7),125(20)])].
% 26.13/26.46 143 composition(one,A) = A. [para(114(a,1),38(a,2)),rewrite([125(2),38(4)])].
% 26.13/26.46 144 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)])].
% 26.13/26.46 149 join(complement(A),complement(A)) = complement(A). [back_rewrite(129),rewrite([143(3)])].
% 26.13/26.46 150 join(zero,complement(complement(A))) = A. [back_rewrite(49),rewrite([149(4)])].
% 26.13/26.46 151 converse(join(A,one)) = join(one,converse(A)). [para(125(a,1),11(a,1,1)),rewrite([8(5)]),flip(a)].
% 26.13/26.46 152 join(zero,complement(A)) = complement(A). [para(124(a,1),23(a,1,1,1)),rewrite([33(2),33(3),150(5)])].
% 26.13/26.46 154 join(top,complement(A)) = join(top,top). [para(124(a,1),37(a,1,2)),rewrite([8(3)])].
% 26.13/26.46 155 complement(complement(A)) = A. [back_rewrite(150),rewrite([152(4)])].
% 26.13/26.46 163 join(A,complement(join(top,top))) = A. [back_rewrite(81),rewrite([154(3),152(7),155(6),8(5)])].
% 26.13/26.46 165 complement(join(A,A)) = complement(A). [back_rewrite(50),rewrite([155(3),152(4)])].
% 26.13/26.46 167 join(A,top) = top. [back_rewrite(124),rewrite([155(3),8(2)])].
% 26.13/26.46 172 join(A,zero) = A. [back_rewrite(163),rewrite([167(3),33(2)])].
% 26.13/26.46 173 join(top,complement(A)) = top. [back_rewrite(154),rewrite([167(6)])].
% 26.13/26.46 183 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(155(a,1),23(a,1,1,1,2)),rewrite([155(5),8(4)])].
% 26.13/26.46 191 complement(zero) = top. [para(33(a,1),155(a,1,1))].
% 26.13/26.46 206 join(A,A) = A. [para(165(a,1),23(a,1,1,1,2)),rewrite([165(6),23(8)]),flip(a)].
% 26.13/26.46 213 join(A,join(A,B)) = join(A,B). [para(206(a,1),15(a,1)),rewrite([8(3),15(4,R),8(3),15(3,R),206(2)]),flip(a)].
% 26.13/26.46 231 join(A,complement(join(B,complement(A)))) = A. [para(23(a,1),213(a,1,2)),rewrite([8(4),23(12)])].
% 26.13/26.46 233 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(231(a,1),15(a,2,2)),rewrite([8(4),8(6)])].
% 26.13/26.46 254 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(155(a,1),44(a,1,2,2))].
% 26.13/26.46 261 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(79(a,1),11(a,2,1)),rewrite([36(8)])].
% 26.13/26.46 267 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(151(a,1),79(a,1,2,1))].
% 26.13/26.46 303 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),254(a,1,2))].
% 26.13/26.46 307 converse(complement(one)) = complement(one). [para(303(a,1),11(a,2,1)),rewrite([2(7),8(6),303(6)]),flip(a)].
% 26.13/26.46 316 converse(top) = top. [para(307(a,1),151(a,2,2)),rewrite([8(4),5(4),5(6)])].
% 26.13/26.46 327 join(top,converse(A)) = top. [para(316(a,1),11(a,1,1)),rewrite([8(5),167(5),316(5)])].
% 26.13/26.46 334 join(top,composition(A,converse(B))) = top. [para(35(a,1),327(a,1,2))].
% 26.13/26.46 336 join(top,composition(A,B)) = top. [para(2(a,1),334(a,1,2,2))].
% 26.13/26.46 337 composition(join(A,one),top) = top. [para(316(a,1),334(a,1,2,2)),rewrite([127(4,R)])].
% 26.13/26.46 338 composition(join(one,converse(A)),zero) = zero. [back_rewrite(267),rewrite([337(8),33(6),127(7,R),8(5),213(5)])].
% 26.13/26.46 365 composition(top,zero) = zero. [para(307(a,1),338(a,1,1,2)),rewrite([5(4)])].
% 26.13/26.46 369 composition(top,top) = top. [para(365(a,1),21(a,1,2,2,1)),rewrite([191(2),316(3),191(4),127(5,R),8(3),167(3),191(5)])].
% 26.13/26.46 370 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(365(a,1),29(a,1,1,1,2,1)),rewrite([191(3),8(3),173(3),33(2),33(3),152(7),155(6),191(6),316(7),173(9),33(6),17(6),33(9),152(13),155(12),191(12),316(13),173(15),33(12),17(12)])].
% 26.13/26.46 374 join(zero,composition(A,composition(B,zero))) = zero. [para(365(a,1),42(a,1,2)),rewrite([8(5),336(8),365(8)])].
% 26.13/26.46 377 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(370),rewrite([374(7)]),flip(a)].
% 26.13/26.46 436 join(complement(A),complement(join(B,A))) = complement(A). [para(231(a,1),53(a,2)),rewrite([155(2),155(4),155(8),53(13)])].
% 26.13/26.46 456 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(377(a,1),17(a,1,1)),rewrite([17(7)]),flip(a)].
% 26.13/26.46 457 composition(A,zero) = zero. [para(377(a,1),17(a,1)),rewrite([377(6)]),flip(a)].
% 26.13/26.46 458 composition(converse(zero),A) = converse(zero). [para(377(a,1),36(a,1,1)),rewrite([457(6)]),flip(a)].
% 26.13/26.46 463 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(456),rewrite([458(5)]),flip(a)].
% 26.13/26.46 465 composition(zero,A) = c_0. [new_symbol(463)].
% 26.13/26.46 466 composition(A,converse(zero)) = c_0. [back_rewrite(463),rewrite([465(2)]),flip(a)].
% 26.13/26.46 481 c_0 = zero. [para(465(a,1),1(a,1))].
% 26.13/26.46 482 converse(zero) = zero. [para(465(a,1),13(a,2,1)),rewrite([466(4),481(1),481(2)]),flip(a)].
% 26.13/26.46 483 join(zero,composition(A,B)) = composition(A,B). [para(465(a,1),19(a,1,1)),rewrite([481(1),8(5),172(5)])].
% 26.13/26.46 486 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(261),rewrite([482(2),483(7),482(7)])].
% 26.13/26.46 604 composition(converse(A),complement(composition(A,top))) = zero. [para(486(a,1),13(a,2,1)),rewrite([2(6),482(7)])].
% 26.13/26.46 653 composition(join(A,composition(A,converse(B))),top) = composition(A,top). [para(604(a,1),48(a,1,2,2,1,2)),rewrite([155(4),35(5),457(6),191(6),17(6),43(7),155(9)])].
% 26.13/26.46 756 join(complement(one),complement(sk1)) = complement(sk1). [para(32(a,1),436(a,1,2,1)),rewrite([8(5)])].
% 26.13/26.46 1041 composition(A,composition(converse(A),top)) = composition(A,top). [para(369(a,1),72(a,1,2,1,1,2,1)),rewrite([33(2),316(3),152(5),155(4),33(5),8(5),152(5),155(4),316(4),33(4),152(8),155(7),43(7),653(5),369(6),33(5),8(5),152(5),155(4),316(4),33(4),152(8),155(7)]),flip(a)].
% 26.13/26.46 2353 join(one,join(sk1,converse(A))) = join(one,converse(A)). [para(32(a,1),98(a,1,1)),flip(a)].
% 26.13/26.46 3441 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(40(a,1),115(a,1,1)),rewrite([11(3),13(4),2(4),2(4),2(6)]),flip(a)].
% 26.13/26.46 3583 join(A,join(one,converse(sk1))) = join(A,one). [para(2353(a,1),11(a,2,1)),rewrite([125(2),34(5),15(5,R),8(4),34(9),125(7)])].
% 26.13/26.46 3591 join(one,converse(sk1)) = one. [para(206(a,1),3583(a,2)),rewrite([213(6)])].
% 26.13/26.46 3639 join(A,composition(converse(sk1),A)) = A. [para(3591(a,1),19(a,2,1)),rewrite([143(2),143(6)])].
% 26.13/26.46 3641 join(complement(one),complement(converse(sk1))) = complement(converse(sk1)). [para(3591(a,1),436(a,1,2,1)),rewrite([8(6)])].
% 26.13/26.46 3645 join(A,join(B,composition(converse(sk1),A))) = join(A,B). [para(3639(a,1),15(a,2,2)),rewrite([8(4),8(6)])].
% 26.13/26.46 3646 join(complement(A),complement(composition(converse(sk1),A))) = complement(composition(converse(sk1),A)). [para(3639(a,1),436(a,1,2,1)),rewrite([8(6)])].
% 26.13/26.46 3647 composition(join(sk1,converse(sk1)),top) = composition(sk1,top). [para(1041(a,1),3639(a,1,2)),rewrite([2(3),19(8),2(9)])].
% 26.13/26.46 3650 join(A,composition(A,sk1)) = A. [para(3639(a,1),106(a,1,1)),rewrite([2(2),2(3),2(4),8(3)]),flip(a)].
% 26.13/26.46 3765 join(complement(join(complement(A),complement(composition(sk1,top)))),complement(join(complement(A),complement(composition(join(sk1,converse(sk1)),composition(join(sk1,converse(sk1)),A)))))) = complement(join(complement(A),complement(composition(join(sk1,converse(sk1)),composition(join(sk1,converse(sk1)),A))))). [para(3647(a,1),25(a,1,1,1,2,1)),rewrite([33(14),34(18),152(20),155(19),33(29),34(33),152(35),155(34)])].
% 26.13/26.46 4169 join(sk1,complement(join(complement(one),complement(composition(converse(sk1),sk1))))) = complement(join(complement(one),complement(composition(converse(sk1),sk1)))). [para(756(a,1),135(a,1,1,1)),rewrite([155(3),143(9),3641(9),155(7),143(19),3641(19),155(17)])].
% 26.13/26.46 4286 composition(converse(sk1),sk1) = converse(sk1). [para(3641(a,1),144(a,1,1,1)),rewrite([155(4),3641(8),155(6),2(9),1(9),756(9),155(7),3650(7),3641(8),155(6),2(9),1(9),756(9),155(7)]),flip(a)].
% 26.13/26.46 4289 join(sk1,converse(sk1)) = converse(sk1). [back_rewrite(4169),rewrite([4286(7),3641(7),155(5),4286(10),3641(10),155(8)])].
% 26.13/26.46 4318 join(complement(join(complement(A),complement(composition(sk1,top)))),complement(join(complement(A),complement(composition(converse(composition(sk1,sk1)),A))))) = complement(join(complement(A),complement(composition(converse(composition(sk1,sk1)),A)))). [back_rewrite(3765),rewrite([4289(12),4289(14),39(14),4289(22),4289(24),39(24)])].
% 26.13/26.46 4321 converse(sk1) = sk1. [para(4286(a,1),13(a,2,1)),rewrite([2(5),4286(4),2(5)])].
% 26.13/26.46 4332 composition(sk1,sk1) = sk1. [para(4286(a,1),36(a,1,1)),rewrite([4321(2),4321(2),4321(3)]),flip(a)].
% 26.13/26.46 4389 join(complement(A),complement(composition(sk1,A))) = complement(composition(sk1,A)). [back_rewrite(3646),rewrite([4321(3),4321(7)])].
% 26.13/26.46 4390 join(A,join(B,composition(sk1,A))) = join(A,B). [back_rewrite(3645),rewrite([4321(2)])].
% 26.13/26.46 4396 join(composition(sk1,A),complement(join(complement(A),complement(composition(sk1,top))))) = composition(sk1,A). [back_rewrite(4318),rewrite([4332(11),4321(10),4389(12),155(11),8(10),4332(14),4321(13),4389(15),155(14)])].
% 26.13/26.46 4402 complement(join(complement(sk2),complement(composition(sk1,top)))) != composition(sk1,sk2) # answer(goals_18). [back_rewrite(31),rewrite([4396(12),4396(24)]),flip(a),xx(b)].
% 26.13/26.46 9943 join(A,complement(join(A,B))) = join(A,complement(B)). [para(183(a,1),233(a,1,2)),flip(a)].
% 26.13/26.46 10913 join(A,complement(join(B,composition(sk1,A)))) = join(A,complement(B)). [para(4390(a,1),9943(a,1,2,1)),rewrite([9943(3)]),flip(a)].
% 26.13/26.46 40165 join(complement(A),complement(composition(sk1,top))) = complement(composition(sk1,A)). [para(4389(a,1),10913(a,2)),rewrite([3441(7),5(4)])].
% 26.13/26.46 40172 $F # answer(goals_18). [back_rewrite(4402),rewrite([40165(7),155(5)]),xx(a)].
% 26.13/26.46
% 26.13/26.46 % SZS output end Refutation
% 26.13/26.46 ============================== end of proof ==========================
% 26.13/26.46
% 26.13/26.46 ============================== STATISTICS ============================
% 26.13/26.46
% 26.13/26.46 Given=2057. Generated=989330. Kept=40158. proofs=1.
% 26.13/26.46 Usable=1609. Sos=9958. Demods=11286. Limbo=7, Disabled=28602. Hints=0.
% 26.13/26.46 Megabytes=38.47.
% 26.13/26.46 User_CPU=24.88, System_CPU=0.58, Wall_clock=26.
% 26.13/26.46
% 26.13/26.46 ============================== end of statistics =====================
% 26.13/26.46
% 26.13/26.46 ============================== end of search =========================
% 26.13/26.46
% 26.13/26.46 THEOREM PROVED
% 26.13/26.46 % SZS status Unsatisfiable
% 26.13/26.46
% 26.13/26.46 Exiting with 1 proof.
% 26.13/26.46
% 26.13/26.46 Process 21687 exit (max_proofs) Fri Jul 8 13:46:51 2022
% 26.13/26.46 Prover9 interrupted
%------------------------------------------------------------------------------