TSTP Solution File: REL025-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL025-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 19:53:56 EDT 2022
% Result : Unsatisfiable 3.66s 3.95s
% Output : Refutation 3.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL025-2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 8 08:19:41 EDT 2022
% 0.14/0.35 % CPUTime :
% 3.21/3.56 ============================== Prover9 ===============================
% 3.21/3.56 Prover9 (32) version 2009-11A, November 2009.
% 3.21/3.56 Process 18340 was started by sandbox2 on n023.cluster.edu,
% 3.21/3.56 Fri Jul 8 08:19:42 2022
% 3.21/3.56 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18186_n023.cluster.edu".
% 3.21/3.56 ============================== end of head ===========================
% 3.21/3.56
% 3.21/3.56 ============================== INPUT =================================
% 3.21/3.56
% 3.21/3.56 % Reading from file /tmp/Prover9_18186_n023.cluster.edu
% 3.21/3.56
% 3.21/3.56 set(prolog_style_variables).
% 3.21/3.56 set(auto2).
% 3.21/3.56 % set(auto2) -> set(auto).
% 3.21/3.56 % set(auto) -> set(auto_inference).
% 3.21/3.56 % set(auto) -> set(auto_setup).
% 3.21/3.56 % set(auto_setup) -> set(predicate_elim).
% 3.21/3.56 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.21/3.56 % set(auto) -> set(auto_limits).
% 3.21/3.56 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.21/3.56 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.21/3.56 % set(auto) -> set(auto_denials).
% 3.21/3.56 % set(auto) -> set(auto_process).
% 3.21/3.56 % set(auto2) -> assign(new_constants, 1).
% 3.21/3.56 % set(auto2) -> assign(fold_denial_max, 3).
% 3.21/3.56 % set(auto2) -> assign(max_weight, "200.000").
% 3.21/3.56 % set(auto2) -> assign(max_hours, 1).
% 3.21/3.56 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.21/3.56 % set(auto2) -> assign(max_seconds, 0).
% 3.21/3.56 % set(auto2) -> assign(max_minutes, 5).
% 3.21/3.56 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.21/3.56 % set(auto2) -> set(sort_initial_sos).
% 3.21/3.56 % set(auto2) -> assign(sos_limit, -1).
% 3.21/3.56 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.21/3.56 % set(auto2) -> assign(max_megs, 400).
% 3.21/3.56 % set(auto2) -> assign(stats, some).
% 3.21/3.56 % set(auto2) -> clear(echo_input).
% 3.21/3.56 % set(auto2) -> set(quiet).
% 3.21/3.56 % set(auto2) -> clear(print_initial_clauses).
% 3.21/3.56 % set(auto2) -> clear(print_given).
% 3.21/3.56 assign(lrs_ticks,-1).
% 3.21/3.56 assign(sos_limit,10000).
% 3.21/3.56 assign(order,kbo).
% 3.21/3.56 set(lex_order_vars).
% 3.21/3.56 clear(print_given).
% 3.21/3.56
% 3.21/3.56 % formulas(sos). % not echoed (15 formulas)
% 3.21/3.56
% 3.21/3.56 ============================== end of input ==========================
% 3.21/3.56
% 3.21/3.56 % From the command line: assign(max_seconds, 300).
% 3.21/3.56
% 3.21/3.56 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.21/3.56
% 3.21/3.56 % Formulas that are not ordinary clauses:
% 3.21/3.56
% 3.21/3.56 ============================== end of process non-clausal formulas ===
% 3.21/3.56
% 3.21/3.56 ============================== PROCESS INITIAL CLAUSES ===============
% 3.21/3.56
% 3.21/3.56 ============================== PREDICATE ELIMINATION =================
% 3.21/3.56
% 3.21/3.56 ============================== end predicate elimination =============
% 3.21/3.56
% 3.21/3.56 Auto_denials:
% 3.21/3.56 % copying label goals_17 to answer in negative clause
% 3.21/3.56
% 3.21/3.56 Term ordering decisions:
% 3.21/3.56 Function symbol KB weights: one=1. sk1=1. top=1. zero=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 3.21/3.56
% 3.21/3.56 ============================== end of process initial clauses ========
% 3.21/3.56
% 3.21/3.56 ============================== CLAUSES FOR SEARCH ====================
% 3.21/3.56
% 3.21/3.56 ============================== end of clauses for search =============
% 3.21/3.56
% 3.21/3.56 ============================== SEARCH ================================
% 3.21/3.56
% 3.21/3.56 % Starting search at 0.01 seconds.
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=36.000, iters=3348
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=35.000, iters=3366
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=33.000, iters=3455
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=32.000, iters=3376
% 3.21/3.56
% 3.21/3.56 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 1.09 sec).
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=31.000, iters=3370
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=30.000, iters=3366
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=29.000, iters=3343
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=27.000, iters=3376
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=26.000, iters=3379
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=25.000, iters=3350
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=24.000, iters=3349
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=23.000, iters=3351
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=22.000, iters=3385
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=21.000, iters=3339
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=20.000, iters=3348
% 3.21/3.56
% 3.21/3.56 Low Water (keep): wt=19.000, iters=3354
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=3373, wt=46.000
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=7275, wt=45.000
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=7472, wt=44.000
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=7127, wt=43.000
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=7446, wt=42.000
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=7447, wt=41.000
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=6899, wt=40.000
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=7486, wt=39.000
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=7488, wt=38.000
% 3.21/3.56
% 3.21/3.56 Low Water (displace): id=13489, wt=15.000
% 3.66/3.95
% 3.66/3.95 Low Water (displace): id=13587, wt=14.000
% 3.66/3.95
% 3.66/3.95 Low Water (displace): id=13647, wt=13.000
% 3.66/3.95
% 3.66/3.95 ============================== PROOF =================================
% 3.66/3.95 % SZS status Unsatisfiable
% 3.66/3.95 % SZS output start Refutation
% 3.66/3.95
% 3.66/3.95 % Proof 1 at 2.83 (+ 0.08) seconds: goals_17.
% 3.66/3.95 % Length of proof is 138.
% 3.66/3.95 % Level of proof is 34.
% 3.66/3.95 % Maximum clause weight is 21.000.
% 3.66/3.95 % Given clauses 889.
% 3.66/3.95
% 3.66/3.95 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 3.66/3.95 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 3.66/3.95 3 join(sk1,one) = one # label(goals_14) # label(negated_conjecture). [assumption].
% 3.66/3.95 4 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 3.66/3.95 5 join(A,complement(A)) = top. [copy(4),flip(a)].
% 3.66/3.95 6 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 3.66/3.95 7 meet(A,complement(A)) = zero. [copy(6),flip(a)].
% 3.66/3.95 8 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 3.66/3.95 9 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 3.66/3.95 10 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 3.66/3.95 11 join(converse(A),converse(B)) = converse(join(A,B)). [copy(10),flip(a)].
% 3.66/3.95 12 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 3.66/3.95 13 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(12),flip(a)].
% 3.66/3.95 14 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 3.66/3.95 15 join(A,join(B,C)) = join(C,join(A,B)). [copy(14),rewrite([8(4)])].
% 3.66/3.95 16 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 3.66/3.95 17 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(16),flip(a)].
% 3.66/3.95 18 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 3.66/3.95 19 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(18),flip(a)].
% 3.66/3.95 20 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 3.66/3.95 21 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(20),rewrite([8(6)])].
% 3.66/3.95 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].
% 3.66/3.95 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)])].
% 3.66/3.95 24 join(sk1,converse(sk1)) != converse(sk1) | join(converse(sk1),sk1) != sk1 # label(goals_17) # label(negated_conjecture) # answer(goals_17). [assumption].
% 3.66/3.95 25 join(sk1,converse(sk1)) != converse(sk1) | join(sk1,converse(sk1)) != sk1 # answer(goals_17). [copy(24),rewrite([8(11)])].
% 3.66/3.95 26 join(one,sk1) = one. [back_rewrite(3),rewrite([8(3)])].
% 3.66/3.95 27 complement(top) = zero. [back_rewrite(7),rewrite([9(2),5(4)])].
% 3.66/3.95 28 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),11(a,1,1)),rewrite([8(4)]),flip(a)].
% 3.66/3.95 29 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),13(a,1,1)),flip(a)].
% 3.66/3.95 30 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),13(a,1,2)),flip(a)].
% 3.66/3.95 31 join(A,join(B,complement(A))) = join(B,top). [para(5(a,1),15(a,2,2)),rewrite([8(2)])].
% 3.66/3.95 32 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),17(a,1,1)),flip(a)].
% 3.66/3.95 34 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)])].
% 3.66/3.95 36 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)])].
% 3.66/3.95 38 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),21(a,1,2,2,1))].
% 3.66/3.95 41 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)])].
% 3.66/3.95 43 join(zero,complement(join(complement(A),complement(A)))) = A. [para(5(a,1),23(a,1,1,1)),rewrite([27(2)])].
% 3.66/3.95 47 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)])].
% 3.66/3.95 49 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(27(a,1),21(a,1,1)),rewrite([27(9)])].
% 3.66/3.95 51 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(27(a,1),23(a,1,2,1,1))].
% 3.66/3.95 52 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(28(a,1),11(a,1,1)),rewrite([8(7),15(7,R),8(6)]),flip(a)].
% 3.66/3.95 53 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(28(a,1),11(a,1,2)),rewrite([15(4,R),8(3),11(3),52(7)]),flip(a)].
% 3.66/3.95 57 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(28(a,1),28(a,2,2)),rewrite([53(4),28(4),15(6,R),8(5)])].
% 3.66/3.95 58 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(52),rewrite([57(8),11(7)])].
% 3.66/3.95 60 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(29(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 3.66/3.95 64 composition(converse(one),A) = A. [para(1(a,1),30(a,1,1)),rewrite([2(2)]),flip(a)].
% 3.66/3.95 70 converse(one) = one. [para(64(a,1),1(a,1)),flip(a)].
% 3.66/3.95 72 composition(join(A,one),B) = join(B,composition(A,B)). [para(64(a,1),19(a,1,1)),rewrite([70(4),8(4)]),flip(a)].
% 3.66/3.95 74 join(complement(A),complement(composition(one,A))) = complement(A). [para(64(a,1),21(a,1,2))].
% 3.66/3.95 75 composition(one,A) = A. [para(64(a,1),32(a,2)),rewrite([70(2),32(4)])].
% 3.66/3.95 76 join(complement(A),complement(A)) = complement(A). [back_rewrite(74),rewrite([75(3)])].
% 3.66/3.95 77 join(zero,complement(complement(A))) = A. [back_rewrite(43),rewrite([76(4)])].
% 3.66/3.95 78 converse(join(A,one)) = join(one,converse(A)). [para(70(a,1),11(a,1,1)),rewrite([8(5)]),flip(a)].
% 3.66/3.95 82 join(top,complement(A)) = top. [para(76(a,1),31(a,1,2)),rewrite([5(2),8(4)]),flip(a)].
% 3.66/3.95 83 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(51),rewrite([82(3),27(2)])].
% 3.66/3.95 84 join(top,top) = join(A,top). [para(82(a,1),31(a,1,2)),flip(a)].
% 3.66/3.95 89 join(A,top) = join(B,top). [para(84(a,1),31(a,2)),rewrite([82(3)])].
% 3.66/3.95 90 join(A,top) = c_0. [new_symbol(89)].
% 3.66/3.95 93 join(A,join(B,complement(A))) = c_0. [back_rewrite(31),rewrite([90(5)])].
% 3.66/3.95 104 c_0 = top. [para(77(a,1),93(a,1,2)),rewrite([8(2),5(2)]),flip(a)].
% 3.66/3.95 105 join(A,join(B,complement(A))) = top. [back_rewrite(93),rewrite([104(4)])].
% 3.66/3.95 107 join(A,top) = top. [back_rewrite(90),rewrite([104(3)])].
% 3.66/3.95 128 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(75(a,1),36(a,1,2)),rewrite([8(3)]),flip(a)].
% 3.66/3.95 132 join(zero,complement(A)) = complement(A). [para(77(a,1),83(a,1,2,1))].
% 3.66/3.95 133 complement(complement(A)) = A. [back_rewrite(83),rewrite([132(4),132(4)])].
% 3.66/3.95 134 join(A,zero) = A. [back_rewrite(77),rewrite([133(3),8(2)])].
% 3.66/3.95 139 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(133(a,1),23(a,1,1,1,2)),rewrite([133(5),8(4)])].
% 3.66/3.95 141 join(A,A) = A. [para(133(a,1),76(a,1,1)),rewrite([133(2),133(3)])].
% 3.66/3.95 145 join(A,join(A,B)) = join(A,B). [para(141(a,1),15(a,1)),rewrite([8(3),15(4,R),8(3),15(3,R),141(2)]),flip(a)].
% 3.66/3.95 146 join(A,complement(join(B,complement(A)))) = A. [para(23(a,1),145(a,1,2)),rewrite([8(4),23(12)])].
% 3.66/3.95 148 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(146(a,1),15(a,2,2)),rewrite([8(4),8(6)])].
% 3.66/3.95 151 join(complement(A),complement(join(A,B))) = complement(A). [para(133(a,1),146(a,1,2,1,2)),rewrite([8(2)])].
% 3.66/3.95 159 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(133(a,1),38(a,1,2,2))].
% 3.66/3.95 162 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(11(a,1),151(a,1,2,1))].
% 3.66/3.95 173 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(49(a,1),11(a,2,1)),rewrite([30(8)])].
% 3.66/3.95 186 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(72(a,1),19(a,1,2)),rewrite([15(4,R),19(3),8(1)]),flip(a)].
% 3.66/3.95 213 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),159(a,1,2))].
% 3.66/3.95 217 converse(complement(one)) = complement(one). [para(213(a,1),11(a,2,1)),rewrite([2(7),8(6),213(6)]),flip(a)].
% 3.66/3.95 218 converse(join(A,complement(one))) = join(complement(one),converse(A)). [para(217(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 3.66/3.95 222 converse(top) = top. [para(217(a,1),78(a,2,2)),rewrite([8(4),5(4),5(6)])].
% 3.66/3.95 226 join(top,converse(A)) = top. [para(222(a,1),11(a,1,1)),rewrite([8(5),107(5),222(5)])].
% 3.66/3.95 227 converse(composition(A,top)) = composition(top,converse(A)). [para(222(a,1),13(a,1,1)),flip(a)].
% 3.66/3.95 235 join(top,composition(A,converse(B))) = top. [para(29(a,1),226(a,1,2))].
% 3.66/3.95 237 join(top,composition(A,B)) = top. [para(2(a,1),235(a,1,2,2))].
% 3.66/3.95 248 converse(composition(A,composition(B,top))) = composition(top,converse(composition(A,B))). [para(227(a,1),13(a,1,1)),rewrite([17(5),13(4)]),flip(a)].
% 3.66/3.95 253 composition(top,join(one,converse(A))) = top. [para(78(a,1),227(a,2,2)),rewrite([72(4),237(4),222(2)]),flip(a)].
% 3.66/3.95 258 composition(top,join(A,one)) = top. [para(2(a,1),253(a,1,2,2)),rewrite([8(3)])].
% 3.66/3.95 282 join(zero,composition(A,zero)) = zero. [para(258(a,1),41(a,1,2,2,1,1)),rewrite([222(2),27(2),222(5),27(5),72(5),145(6),222(6),27(6)])].
% 3.66/3.95 291 join(complement(A),complement(join(B,A))) = complement(A). [para(146(a,1),47(a,2)),rewrite([133(2),133(4),133(8),47(13)])].
% 3.66/3.95 292 join(A,complement(join(complement(A),complement(B)))) = A. [para(47(a,1),151(a,1,2,1)),rewrite([133(2),8(3),133(7)])].
% 3.66/3.95 297 join(A,composition(B,zero)) = A. [para(282(a,1),15(a,1,2)),rewrite([134(2),134(4),8(3)]),flip(a)].
% 3.66/3.95 301 composition(join(A,B),zero) = composition(A,zero). [para(297(a,1),19(a,1)),flip(a)].
% 3.66/3.95 303 composition(A,zero) = zero. [para(297(a,1),72(a,2)),rewrite([301(4)])].
% 3.66/3.95 305 composition(converse(zero),A) = converse(zero). [para(303(a,1),30(a,1,1)),flip(a)].
% 3.66/3.95 314 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(305(a,1),36(a,1,1,2)),flip(a)].
% 3.66/3.95 318 converse(zero) = zero. [para(305(a,1),303(a,1))].
% 3.66/3.95 321 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(314),rewrite([318(2),303(2),134(2),318(3),303(3)]),flip(a)].
% 3.66/3.95 324 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(173),rewrite([318(2),321(7),318(7)])].
% 3.66/3.95 348 join(zero,converse(A)) = converse(A). [para(318(a,1),11(a,1,1)),rewrite([8(5),134(5)])].
% 3.66/3.95 417 converse(composition(A,join(B,complement(composition(converse(A),top))))) = converse(composition(A,B)). [para(324(a,1),34(a,1,2)),rewrite([8(4),348(4),8(9),11(9),13(10)]),flip(a)].
% 3.66/3.95 453 join(one,join(sk1,converse(A))) = join(one,converse(A)). [para(26(a,1),57(a,1,1)),flip(a)].
% 3.66/3.95 549 join(complement(one),complement(sk1)) = complement(sk1). [para(26(a,1),291(a,1,2,1)),rewrite([8(5)])].
% 3.66/3.95 1348 join(A,join(one,converse(sk1))) = join(A,one). [para(453(a,1),11(a,2,1)),rewrite([70(2),28(5),15(5,R),8(4),28(9),70(7)])].
% 3.66/3.95 1376 join(one,converse(sk1)) = one. [para(141(a,1),1348(a,2)),rewrite([145(6)])].
% 3.66/3.95 1377 join(A,composition(converse(sk1),A)) = A. [para(1376(a,1),19(a,2,1)),rewrite([75(2),75(6)])].
% 3.66/3.95 1384 join(A,composition(A,sk1)) = A. [para(1377(a,1),60(a,1,1)),rewrite([2(2),2(3),2(4),8(3)]),flip(a)].
% 3.66/3.95 1388 join(A,join(B,composition(A,sk1))) = join(A,B). [para(1384(a,1),15(a,2,2)),rewrite([8(3),8(5)])].
% 3.66/3.95 1766 join(A,composition(sk1,A)) = A. [para(1384(a,1),128(a,1,1)),rewrite([75(2),75(4)]),flip(a)].
% 3.66/3.95 1784 join(A,join(B,composition(sk1,A))) = join(A,B). [para(1766(a,1),15(a,2,2)),rewrite([8(3),8(5)])].
% 3.66/3.95 2092 join(A,complement(join(A,B))) = join(A,complement(B)). [para(139(a,1),148(a,1,2)),flip(a)].
% 3.66/3.95 2565 join(complement(converse(A)),converse(join(A,B))) = top. [para(162(a,1),105(a,1,2)),rewrite([8(5)])].
% 3.66/3.95 2607 join(A,join(B,converse(complement(converse(A))))) = top. [para(2565(a,1),11(a,2,1)),rewrite([2(6),15(5),8(4),15(5,R),8(4),222(7)])].
% 3.66/3.95 2699 join(A,converse(complement(converse(A)))) = top. [para(141(a,1),2607(a,1,2))].
% 3.66/3.95 2772 join(complement(converse(A)),converse(join(B,A))) = top. [para(2699(a,1),58(a,1,1,2)),rewrite([107(2),222(2)]),flip(a)].
% 3.66/3.95 2829 join(converse(A),complement(composition(converse(A),sk1))) = top. [para(1377(a,1),2772(a,1,2,1)),rewrite([30(4),8(6)])].
% 3.66/3.95 2916 join(A,converse(complement(composition(converse(A),sk1)))) = top. [para(2829(a,1),11(a,2,1)),rewrite([2(2),222(8)])].
% 3.66/3.95 3038 join(complement(composition(converse(A),sk1)),converse(join(B,A))) = top. [para(2916(a,1),58(a,1,1,2)),rewrite([107(2),222(2)]),flip(a)].
% 3.66/3.95 3831 join(A,composition(complement(one),A)) = composition(top,A). [para(38(a,1),186(a,2,2,1)),rewrite([8(7),15(8,R),8(7),38(7),5(4)]),flip(a)].
% 3.66/3.95 3975 join(A,composition(A,complement(one))) = composition(A,top). [para(3831(a,1),60(a,1,1)),rewrite([29(4),222(2),217(5),2(7),8(6)]),flip(a)].
% 3.66/3.95 3979 join(complement(one),composition(top,sk1)) = join(sk1,complement(one)). [para(3831(a,1),1388(a,1,2)),rewrite([8(10)])].
% 3.66/3.95 4368 join(complement(one),composition(sk1,top)) = join(sk1,complement(one)). [para(3975(a,1),1784(a,1,2)),rewrite([8(10)])].
% 3.66/3.95 5238 complement(join(complement(A),complement(join(B,complement(A))))) = complement(join(complement(A),complement(B))). [para(2092(a,1),9(a,2,1)),rewrite([8(2),9(3)])].
% 3.66/3.95 5252 join(complement(A),complement(join(B,complement(A)))) = join(complement(A),complement(B)). [para(2092(a,1),47(a,2)),rewrite([8(2),8(5),146(7),8(6),5238(9),292(8),8(5)])].
% 3.66/3.95 5339 join(A,complement(converse(complement(converse(A))))) = A. [para(2699(a,1),2092(a,1,2,1)),rewrite([27(2),134(2)]),flip(a)].
% 3.66/3.95 5414 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(2(a,1),5339(a,1,2,1,1,1))].
% 3.66/3.95 5417 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(5339(a,1),23(a,1,2,1)),rewrite([133(9),8(8),2092(8),133(6)])].
% 3.66/3.95 5682 converse(complement(converse(complement(A)))) = A. [para(5414(a,1),11(a,2,1)),rewrite([2(2),5417(5),2(6)])].
% 3.66/3.95 5710 complement(converse(complement(A))) = converse(A). [para(5682(a,1),2(a,1,1)),flip(a)].
% 3.66/3.95 5764 converse(complement(A)) = complement(converse(A)). [para(5710(a,1),133(a,1,1)),flip(a)].
% 3.66/3.95 7729 join(complement(one),complement(composition(top,sk1))) = complement(sk1). [para(3979(a,1),2092(a,1,2,1)),rewrite([5252(8),549(5)]),flip(a)].
% 3.66/3.95 13283 join(join(complement(one),converse(sk1)),complement(composition(top,composition(converse(sk1),sk1)))) = top. [para(4368(a,1),3038(a,1,2,1)),rewrite([227(4),17(6),218(12),8(13)])].
% 3.66/3.95 14158 composition(top,composition(A,converse(A))) = composition(top,converse(A)). [para(5(a,1),417(a,1,1,2)),rewrite([227(3),248(8),29(7)]),flip(a)].
% 3.66/3.95 14171 composition(top,composition(converse(A),A)) = composition(top,A). [para(2(a,1),14158(a,1,2,2)),rewrite([2(7)])].
% 3.66/3.95 14210 join(complement(sk1),converse(sk1)) = top. [back_rewrite(13283),rewrite([14171(11),8(10),15(10),8(9),7729(9),8(5)])].
% 3.66/3.95 14266 join(sk1,complement(converse(sk1))) = top. [para(14210(a,1),11(a,2,1)),rewrite([5764(3),2(6),8(5),222(7)])].
% 3.66/3.95 14272 join(complement(sk1),complement(converse(sk1))) = complement(sk1). [para(14210(a,1),2092(a,1,2,1)),rewrite([27(4),8(4),132(4)]),flip(a)].
% 3.66/3.95 14277 converse(sk1) = sk1. [para(14266(a,1),23(a,1,1,1)),rewrite([27(2),14272(7),133(4),8(3),134(3)]),flip(a)].
% 3.66/3.95 14345 $F # answer(goals_17). [back_rewrite(25),rewrite([14277(3),141(3),14277(3),14277(6),141(6)]),xx(a),xx(b)].
% 3.66/3.95
% 3.66/3.95 % SZS output end Refutation
% 3.66/3.95 ============================== end of proof ==========================
% 3.66/3.95
% 3.66/3.95 ============================== STATISTICS ============================
% 3.66/3.95
% 3.66/3.95 Given=889. Generated=144823. Kept=14334. proofs=1.
% 3.66/3.95 Usable=631. Sos=8793. Demods=9044. Limbo=68, Disabled=4857. Hints=0.
% 3.66/3.95 Megabytes=15.71.
% 3.66/3.95 User_CPU=2.84, System_CPU=0.08, Wall_clock=2.
% 3.66/3.95
% 3.66/3.95 ============================== end of statistics =====================
% 3.66/3.95
% 3.66/3.95 ============================== end of search =========================
% 3.66/3.95
% 3.66/3.95 THEOREM PROVED
% 3.66/3.95 % SZS status Unsatisfiable
% 3.66/3.95
% 3.66/3.95 Exiting with 1 proof.
% 3.66/3.95
% 3.66/3.95 Process 18340 exit (max_proofs) Fri Jul 8 08:19:44 2022
% 3.66/3.95 Prover9 interrupted
%------------------------------------------------------------------------------