TSTP Solution File: REL025-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL025-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 19:53:55 EDT 2022
% Result : Unsatisfiable 3.48s 3.79s
% Output : Refutation 3.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL025-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 07:23:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.15/3.46 ============================== Prover9 ===============================
% 3.15/3.46 Prover9 (32) version 2009-11A, November 2009.
% 3.15/3.46 Process 24702 was started by sandbox2 on n009.cluster.edu,
% 3.15/3.46 Fri Jul 8 07:23:07 2022
% 3.15/3.46 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24549_n009.cluster.edu".
% 3.15/3.46 ============================== end of head ===========================
% 3.15/3.46
% 3.15/3.46 ============================== INPUT =================================
% 3.15/3.46
% 3.15/3.46 % Reading from file /tmp/Prover9_24549_n009.cluster.edu
% 3.15/3.46
% 3.15/3.46 set(prolog_style_variables).
% 3.15/3.46 set(auto2).
% 3.15/3.46 % set(auto2) -> set(auto).
% 3.15/3.46 % set(auto) -> set(auto_inference).
% 3.15/3.46 % set(auto) -> set(auto_setup).
% 3.15/3.46 % set(auto_setup) -> set(predicate_elim).
% 3.15/3.46 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.15/3.46 % set(auto) -> set(auto_limits).
% 3.15/3.46 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.15/3.46 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.15/3.46 % set(auto) -> set(auto_denials).
% 3.15/3.46 % set(auto) -> set(auto_process).
% 3.15/3.46 % set(auto2) -> assign(new_constants, 1).
% 3.15/3.46 % set(auto2) -> assign(fold_denial_max, 3).
% 3.15/3.46 % set(auto2) -> assign(max_weight, "200.000").
% 3.15/3.46 % set(auto2) -> assign(max_hours, 1).
% 3.15/3.46 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.15/3.46 % set(auto2) -> assign(max_seconds, 0).
% 3.15/3.46 % set(auto2) -> assign(max_minutes, 5).
% 3.15/3.46 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.15/3.46 % set(auto2) -> set(sort_initial_sos).
% 3.15/3.46 % set(auto2) -> assign(sos_limit, -1).
% 3.15/3.46 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.15/3.46 % set(auto2) -> assign(max_megs, 400).
% 3.15/3.46 % set(auto2) -> assign(stats, some).
% 3.15/3.46 % set(auto2) -> clear(echo_input).
% 3.15/3.46 % set(auto2) -> set(quiet).
% 3.15/3.46 % set(auto2) -> clear(print_initial_clauses).
% 3.15/3.46 % set(auto2) -> clear(print_given).
% 3.15/3.46 assign(lrs_ticks,-1).
% 3.15/3.46 assign(sos_limit,10000).
% 3.15/3.46 assign(order,kbo).
% 3.15/3.46 set(lex_order_vars).
% 3.15/3.46 clear(print_given).
% 3.15/3.46
% 3.15/3.46 % formulas(sos). % not echoed (15 formulas)
% 3.15/3.46
% 3.15/3.46 ============================== end of input ==========================
% 3.15/3.46
% 3.15/3.46 % From the command line: assign(max_seconds, 300).
% 3.15/3.46
% 3.15/3.46 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.15/3.46
% 3.15/3.46 % Formulas that are not ordinary clauses:
% 3.15/3.46
% 3.15/3.46 ============================== end of process non-clausal formulas ===
% 3.15/3.46
% 3.15/3.46 ============================== PROCESS INITIAL CLAUSES ===============
% 3.15/3.46
% 3.15/3.46 ============================== PREDICATE ELIMINATION =================
% 3.15/3.46
% 3.15/3.46 ============================== end predicate elimination =============
% 3.15/3.46
% 3.15/3.46 Auto_denials:
% 3.15/3.46 % copying label goals_15 to answer in negative clause
% 3.15/3.46
% 3.15/3.46 Term ordering decisions:
% 3.15/3.46 Function symbol KB weights: one=1. sk1=1. top=1. zero=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 3.15/3.46
% 3.15/3.46 ============================== end of process initial clauses ========
% 3.15/3.46
% 3.15/3.46 ============================== CLAUSES FOR SEARCH ====================
% 3.15/3.46
% 3.15/3.46 ============================== end of clauses for search =============
% 3.15/3.46
% 3.15/3.46 ============================== SEARCH ================================
% 3.15/3.46
% 3.15/3.46 % Starting search at 0.01 seconds.
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=36.000, iters=3348
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=35.000, iters=3366
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=33.000, iters=3455
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=32.000, iters=3376
% 3.15/3.46
% 3.15/3.46 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 1.11 sec).
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=31.000, iters=3370
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=30.000, iters=3366
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=29.000, iters=3343
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=27.000, iters=3376
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=26.000, iters=3379
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=25.000, iters=3350
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=24.000, iters=3349
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=23.000, iters=3351
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=22.000, iters=3385
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=21.000, iters=3339
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=20.000, iters=3348
% 3.15/3.46
% 3.15/3.46 Low Water (keep): wt=19.000, iters=3354
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=3372, wt=46.000
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=7274, wt=45.000
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=7471, wt=44.000
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=7126, wt=43.000
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=7445, wt=42.000
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=7446, wt=41.000
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=6898, wt=40.000
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=7485, wt=39.000
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=7487, wt=38.000
% 3.15/3.46
% 3.15/3.46 Low Water (displace): id=13488, wt=15.000
% 3.48/3.79
% 3.48/3.79 Low Water (displace): id=13586, wt=14.000
% 3.48/3.79
% 3.48/3.79 Low Water (displace): id=13646, wt=13.000
% 3.48/3.79
% 3.48/3.79 ============================== PROOF =================================
% 3.48/3.79 % SZS status Unsatisfiable
% 3.48/3.79 % SZS output start Refutation
% 3.48/3.79
% 3.48/3.79 % Proof 1 at 2.74 (+ 0.10) seconds: goals_15.
% 3.48/3.79 % Length of proof is 137.
% 3.48/3.79 % Level of proof is 34.
% 3.48/3.79 % Maximum clause weight is 21.000.
% 3.48/3.79 % Given clauses 889.
% 3.48/3.79
% 3.48/3.79 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 3.48/3.79 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 3.48/3.79 3 join(sk1,one) = one # label(goals_14) # label(negated_conjecture). [assumption].
% 3.48/3.79 4 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 3.48/3.79 5 join(A,complement(A)) = top. [copy(4),flip(a)].
% 3.48/3.79 6 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 3.48/3.79 7 meet(A,complement(A)) = zero. [copy(6),flip(a)].
% 3.48/3.79 8 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 3.48/3.79 9 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 3.48/3.79 10 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 3.48/3.79 11 join(converse(A),converse(B)) = converse(join(A,B)). [copy(10),flip(a)].
% 3.48/3.79 12 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 3.48/3.79 13 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(12),flip(a)].
% 3.48/3.79 14 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 3.48/3.79 15 join(A,join(B,C)) = join(C,join(A,B)). [copy(14),rewrite([8(4)])].
% 3.48/3.79 16 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 3.48/3.79 17 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(16),flip(a)].
% 3.48/3.79 18 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 3.48/3.79 19 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(18),flip(a)].
% 3.48/3.79 20 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 3.48/3.79 21 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(20),rewrite([8(6)])].
% 3.48/3.79 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].
% 3.48/3.79 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)])].
% 3.48/3.79 24 converse(sk1) != sk1 # label(goals_15) # label(negated_conjecture) # answer(goals_15). [assumption].
% 3.48/3.79 25 join(one,sk1) = one. [back_rewrite(3),rewrite([8(3)])].
% 3.48/3.79 26 complement(top) = zero. [back_rewrite(7),rewrite([9(2),5(4)])].
% 3.48/3.79 27 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),11(a,1,1)),rewrite([8(4)]),flip(a)].
% 3.48/3.79 28 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),13(a,1,1)),flip(a)].
% 3.48/3.79 29 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),13(a,1,2)),flip(a)].
% 3.48/3.79 30 join(A,join(B,complement(A))) = join(B,top). [para(5(a,1),15(a,2,2)),rewrite([8(2)])].
% 3.48/3.79 31 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),17(a,1,1)),flip(a)].
% 3.48/3.79 33 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)])].
% 3.48/3.79 35 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)])].
% 3.48/3.79 37 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),21(a,1,2,2,1))].
% 3.48/3.79 40 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(13(a,1),21(a,1,2,2,1)),rewrite([2(4)])].
% 3.48/3.79 42 join(zero,complement(join(complement(A),complement(A)))) = A. [para(5(a,1),23(a,1,1,1)),rewrite([26(2)])].
% 3.48/3.79 46 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)])].
% 3.48/3.79 48 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(26(a,1),21(a,1,1)),rewrite([26(9)])].
% 3.48/3.79 50 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(26(a,1),23(a,1,2,1,1))].
% 3.48/3.79 51 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(27(a,1),11(a,1,1)),rewrite([8(7),15(7,R),8(6)]),flip(a)].
% 3.48/3.79 52 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(27(a,1),11(a,1,2)),rewrite([15(4,R),8(3),11(3),51(7)]),flip(a)].
% 3.48/3.79 56 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(27(a,1),27(a,2,2)),rewrite([52(4),27(4),15(6,R),8(5)])].
% 3.48/3.79 57 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(51),rewrite([56(8),11(7)])].
% 3.48/3.79 59 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(28(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 3.48/3.79 63 composition(converse(one),A) = A. [para(1(a,1),29(a,1,1)),rewrite([2(2)]),flip(a)].
% 3.48/3.79 69 converse(one) = one. [para(63(a,1),1(a,1)),flip(a)].
% 3.48/3.79 71 composition(join(A,one),B) = join(B,composition(A,B)). [para(63(a,1),19(a,1,1)),rewrite([69(4),8(4)]),flip(a)].
% 3.48/3.79 73 join(complement(A),complement(composition(one,A))) = complement(A). [para(63(a,1),21(a,1,2))].
% 3.48/3.79 74 composition(one,A) = A. [para(63(a,1),31(a,2)),rewrite([69(2),31(4)])].
% 3.48/3.79 75 join(complement(A),complement(A)) = complement(A). [back_rewrite(73),rewrite([74(3)])].
% 3.48/3.79 76 join(zero,complement(complement(A))) = A. [back_rewrite(42),rewrite([75(4)])].
% 3.48/3.79 77 converse(join(A,one)) = join(one,converse(A)). [para(69(a,1),11(a,1,1)),rewrite([8(5)]),flip(a)].
% 3.48/3.79 81 join(top,complement(A)) = top. [para(75(a,1),30(a,1,2)),rewrite([5(2),8(4)]),flip(a)].
% 3.48/3.79 82 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(50),rewrite([81(3),26(2)])].
% 3.48/3.79 83 join(top,top) = join(A,top). [para(81(a,1),30(a,1,2)),flip(a)].
% 3.48/3.79 88 join(A,top) = join(B,top). [para(83(a,1),30(a,2)),rewrite([81(3)])].
% 3.48/3.79 89 join(A,top) = c_0. [new_symbol(88)].
% 3.48/3.79 92 join(A,join(B,complement(A))) = c_0. [back_rewrite(30),rewrite([89(5)])].
% 3.48/3.79 103 c_0 = top. [para(76(a,1),92(a,1,2)),rewrite([8(2),5(2)]),flip(a)].
% 3.48/3.79 104 join(A,join(B,complement(A))) = top. [back_rewrite(92),rewrite([103(4)])].
% 3.48/3.79 106 join(A,top) = top. [back_rewrite(89),rewrite([103(3)])].
% 3.48/3.79 127 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(74(a,1),35(a,1,2)),rewrite([8(3)]),flip(a)].
% 3.48/3.79 131 join(zero,complement(A)) = complement(A). [para(76(a,1),82(a,1,2,1))].
% 3.48/3.79 132 complement(complement(A)) = A. [back_rewrite(82),rewrite([131(4),131(4)])].
% 3.48/3.79 133 join(A,zero) = A. [back_rewrite(76),rewrite([132(3),8(2)])].
% 3.48/3.79 138 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(132(a,1),23(a,1,1,1,2)),rewrite([132(5),8(4)])].
% 3.48/3.79 140 join(A,A) = A. [para(132(a,1),75(a,1,1)),rewrite([132(2),132(3)])].
% 3.48/3.79 144 join(A,join(A,B)) = join(A,B). [para(140(a,1),15(a,1)),rewrite([8(3),15(4,R),8(3),15(3,R),140(2)]),flip(a)].
% 3.48/3.79 145 join(A,complement(join(B,complement(A)))) = A. [para(23(a,1),144(a,1,2)),rewrite([8(4),23(12)])].
% 3.48/3.79 147 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(145(a,1),15(a,2,2)),rewrite([8(4),8(6)])].
% 3.48/3.79 150 join(complement(A),complement(join(A,B))) = complement(A). [para(132(a,1),145(a,1,2,1,2)),rewrite([8(2)])].
% 3.48/3.79 158 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(132(a,1),37(a,1,2,2))].
% 3.48/3.79 161 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(11(a,1),150(a,1,2,1))].
% 3.48/3.79 172 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(48(a,1),11(a,2,1)),rewrite([29(8)])].
% 3.48/3.79 185 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(71(a,1),19(a,1,2)),rewrite([15(4,R),19(3),8(1)]),flip(a)].
% 3.48/3.79 212 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),158(a,1,2))].
% 3.48/3.79 216 converse(complement(one)) = complement(one). [para(212(a,1),11(a,2,1)),rewrite([2(7),8(6),212(6)]),flip(a)].
% 3.48/3.79 217 converse(join(A,complement(one))) = join(complement(one),converse(A)). [para(216(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 3.48/3.79 221 converse(top) = top. [para(216(a,1),77(a,2,2)),rewrite([8(4),5(4),5(6)])].
% 3.48/3.79 225 join(top,converse(A)) = top. [para(221(a,1),11(a,1,1)),rewrite([8(5),106(5),221(5)])].
% 3.48/3.79 226 converse(composition(A,top)) = composition(top,converse(A)). [para(221(a,1),13(a,1,1)),flip(a)].
% 3.48/3.79 234 join(top,composition(A,converse(B))) = top. [para(28(a,1),225(a,1,2))].
% 3.48/3.79 236 join(top,composition(A,B)) = top. [para(2(a,1),234(a,1,2,2))].
% 3.48/3.79 247 converse(composition(A,composition(B,top))) = composition(top,converse(composition(A,B))). [para(226(a,1),13(a,1,1)),rewrite([17(5),13(4)]),flip(a)].
% 3.48/3.79 252 composition(top,join(one,converse(A))) = top. [para(77(a,1),226(a,2,2)),rewrite([71(4),236(4),221(2)]),flip(a)].
% 3.48/3.79 257 composition(top,join(A,one)) = top. [para(2(a,1),252(a,1,2,2)),rewrite([8(3)])].
% 3.48/3.79 281 join(zero,composition(A,zero)) = zero. [para(257(a,1),40(a,1,2,2,1,1)),rewrite([221(2),26(2),221(5),26(5),71(5),144(6),221(6),26(6)])].
% 3.48/3.79 290 join(complement(A),complement(join(B,A))) = complement(A). [para(145(a,1),46(a,2)),rewrite([132(2),132(4),132(8),46(13)])].
% 3.48/3.79 291 join(A,complement(join(complement(A),complement(B)))) = A. [para(46(a,1),150(a,1,2,1)),rewrite([132(2),8(3),132(7)])].
% 3.48/3.79 296 join(A,composition(B,zero)) = A. [para(281(a,1),15(a,1,2)),rewrite([133(2),133(4),8(3)]),flip(a)].
% 3.48/3.79 300 composition(join(A,B),zero) = composition(A,zero). [para(296(a,1),19(a,1)),flip(a)].
% 3.48/3.79 302 composition(A,zero) = zero. [para(296(a,1),71(a,2)),rewrite([300(4)])].
% 3.48/3.79 304 composition(converse(zero),A) = converse(zero). [para(302(a,1),29(a,1,1)),flip(a)].
% 3.48/3.79 313 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(304(a,1),35(a,1,1,2)),flip(a)].
% 3.48/3.79 317 converse(zero) = zero. [para(304(a,1),302(a,1))].
% 3.48/3.79 320 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(313),rewrite([317(2),302(2),133(2),317(3),302(3)]),flip(a)].
% 3.48/3.79 323 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(172),rewrite([317(2),320(7),317(7)])].
% 3.48/3.79 347 join(zero,converse(A)) = converse(A). [para(317(a,1),11(a,1,1)),rewrite([8(5),133(5)])].
% 3.48/3.79 416 converse(composition(A,join(B,complement(composition(converse(A),top))))) = converse(composition(A,B)). [para(323(a,1),33(a,1,2)),rewrite([8(4),347(4),8(9),11(9),13(10)]),flip(a)].
% 3.48/3.79 452 join(one,join(sk1,converse(A))) = join(one,converse(A)). [para(25(a,1),56(a,1,1)),flip(a)].
% 3.48/3.79 548 join(complement(one),complement(sk1)) = complement(sk1). [para(25(a,1),290(a,1,2,1)),rewrite([8(5)])].
% 3.48/3.79 1347 join(A,join(one,converse(sk1))) = join(A,one). [para(452(a,1),11(a,2,1)),rewrite([69(2),27(5),15(5,R),8(4),27(9),69(7)])].
% 3.48/3.79 1375 join(one,converse(sk1)) = one. [para(140(a,1),1347(a,2)),rewrite([144(6)])].
% 3.48/3.79 1376 join(A,composition(converse(sk1),A)) = A. [para(1375(a,1),19(a,2,1)),rewrite([74(2),74(6)])].
% 3.48/3.79 1383 join(A,composition(A,sk1)) = A. [para(1376(a,1),59(a,1,1)),rewrite([2(2),2(3),2(4),8(3)]),flip(a)].
% 3.48/3.79 1387 join(A,join(B,composition(A,sk1))) = join(A,B). [para(1383(a,1),15(a,2,2)),rewrite([8(3),8(5)])].
% 3.48/3.79 1765 join(A,composition(sk1,A)) = A. [para(1383(a,1),127(a,1,1)),rewrite([74(2),74(4)]),flip(a)].
% 3.48/3.79 1783 join(A,join(B,composition(sk1,A))) = join(A,B). [para(1765(a,1),15(a,2,2)),rewrite([8(3),8(5)])].
% 3.48/3.79 2091 join(A,complement(join(A,B))) = join(A,complement(B)). [para(138(a,1),147(a,1,2)),flip(a)].
% 3.48/3.79 2564 join(complement(converse(A)),converse(join(A,B))) = top. [para(161(a,1),104(a,1,2)),rewrite([8(5)])].
% 3.48/3.79 2606 join(A,join(B,converse(complement(converse(A))))) = top. [para(2564(a,1),11(a,2,1)),rewrite([2(6),15(5),8(4),15(5,R),8(4),221(7)])].
% 3.48/3.79 2698 join(A,converse(complement(converse(A)))) = top. [para(140(a,1),2606(a,1,2))].
% 3.48/3.79 2771 join(complement(converse(A)),converse(join(B,A))) = top. [para(2698(a,1),57(a,1,1,2)),rewrite([106(2),221(2)]),flip(a)].
% 3.48/3.80 2828 join(converse(A),complement(composition(converse(A),sk1))) = top. [para(1376(a,1),2771(a,1,2,1)),rewrite([29(4),8(6)])].
% 3.48/3.80 2915 join(A,converse(complement(composition(converse(A),sk1)))) = top. [para(2828(a,1),11(a,2,1)),rewrite([2(2),221(8)])].
% 3.48/3.80 3037 join(complement(composition(converse(A),sk1)),converse(join(B,A))) = top. [para(2915(a,1),57(a,1,1,2)),rewrite([106(2),221(2)]),flip(a)].
% 3.48/3.80 3830 join(A,composition(complement(one),A)) = composition(top,A). [para(37(a,1),185(a,2,2,1)),rewrite([8(7),15(8,R),8(7),37(7),5(4)]),flip(a)].
% 3.48/3.80 3974 join(A,composition(A,complement(one))) = composition(A,top). [para(3830(a,1),59(a,1,1)),rewrite([28(4),221(2),216(5),2(7),8(6)]),flip(a)].
% 3.48/3.80 3978 join(complement(one),composition(top,sk1)) = join(sk1,complement(one)). [para(3830(a,1),1387(a,1,2)),rewrite([8(10)])].
% 3.48/3.80 4367 join(complement(one),composition(sk1,top)) = join(sk1,complement(one)). [para(3974(a,1),1783(a,1,2)),rewrite([8(10)])].
% 3.48/3.80 5237 complement(join(complement(A),complement(join(B,complement(A))))) = complement(join(complement(A),complement(B))). [para(2091(a,1),9(a,2,1)),rewrite([8(2),9(3)])].
% 3.48/3.80 5251 join(complement(A),complement(join(B,complement(A)))) = join(complement(A),complement(B)). [para(2091(a,1),46(a,2)),rewrite([8(2),8(5),145(7),8(6),5237(9),291(8),8(5)])].
% 3.48/3.80 5338 join(A,complement(converse(complement(converse(A))))) = A. [para(2698(a,1),2091(a,1,2,1)),rewrite([26(2),133(2)]),flip(a)].
% 3.48/3.80 5413 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(2(a,1),5338(a,1,2,1,1,1))].
% 3.48/3.80 5416 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(5338(a,1),23(a,1,2,1)),rewrite([132(9),8(8),2091(8),132(6)])].
% 3.48/3.80 5681 converse(complement(converse(complement(A)))) = A. [para(5413(a,1),11(a,2,1)),rewrite([2(2),5416(5),2(6)])].
% 3.48/3.80 5709 complement(converse(complement(A))) = converse(A). [para(5681(a,1),2(a,1,1)),flip(a)].
% 3.48/3.80 5763 converse(complement(A)) = complement(converse(A)). [para(5709(a,1),132(a,1,1)),flip(a)].
% 3.48/3.80 7728 join(complement(one),complement(composition(top,sk1))) = complement(sk1). [para(3978(a,1),2091(a,1,2,1)),rewrite([5251(8),548(5)]),flip(a)].
% 3.48/3.80 13282 join(join(complement(one),converse(sk1)),complement(composition(top,composition(converse(sk1),sk1)))) = top. [para(4367(a,1),3037(a,1,2,1)),rewrite([226(4),17(6),217(12),8(13)])].
% 3.48/3.80 14157 composition(top,composition(A,converse(A))) = composition(top,converse(A)). [para(5(a,1),416(a,1,1,2)),rewrite([226(3),247(8),28(7)]),flip(a)].
% 3.48/3.80 14170 composition(top,composition(converse(A),A)) = composition(top,A). [para(2(a,1),14157(a,1,2,2)),rewrite([2(7)])].
% 3.48/3.80 14209 join(complement(sk1),converse(sk1)) = top. [back_rewrite(13282),rewrite([14170(11),8(10),15(10),8(9),7728(9),8(5)])].
% 3.48/3.80 14265 join(sk1,complement(converse(sk1))) = top. [para(14209(a,1),11(a,2,1)),rewrite([5763(3),2(6),8(5),221(7)])].
% 3.48/3.80 14271 join(complement(sk1),complement(converse(sk1))) = complement(sk1). [para(14209(a,1),2091(a,1,2,1)),rewrite([26(4),8(4),131(4)]),flip(a)].
% 3.48/3.80 14276 converse(sk1) = sk1. [para(14265(a,1),23(a,1,1,1)),rewrite([26(2),14271(7),132(4),8(3),133(3)]),flip(a)].
% 3.48/3.80 14277 $F # answer(goals_15). [resolve(14276,a,24,a)].
% 3.48/3.80
% 3.48/3.80 % SZS output end Refutation
% 3.48/3.80 ============================== end of proof ==========================
% 3.48/3.80
% 3.48/3.80 ============================== STATISTICS ============================
% 3.48/3.80
% 3.48/3.80 Given=889. Generated=143454. Kept=14267. proofs=1.
% 3.48/3.80 Usable=726. Sos=9982. Demods=10258. Limbo=0, Disabled=3573. Hints=0.
% 3.48/3.80 Megabytes=15.56.
% 3.48/3.80 User_CPU=2.74, System_CPU=0.10, Wall_clock=3.
% 3.48/3.80
% 3.48/3.80 ============================== end of statistics =====================
% 3.48/3.80
% 3.48/3.80 ============================== end of search =========================
% 3.48/3.80
% 3.48/3.80 THEOREM PROVED
% 3.48/3.80 % SZS status Unsatisfiable
% 3.48/3.80
% 3.48/3.80 Exiting with 1 proof.
% 3.48/3.80
% 3.48/3.80 Process 24702 exit (max_proofs) Fri Jul 8 07:23:10 2022
% 3.48/3.80 Prover9 interrupted
%------------------------------------------------------------------------------