TSTP Solution File: REL050-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL050-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 19:54:33 EDT 2022
% Result : Unsatisfiable 2.10s 2.35s
% Output : Refutation 2.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL050-2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n004.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 07:40:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.10/2.35 ============================== Prover9 ===============================
% 2.10/2.35 Prover9 (32) version 2009-11A, November 2009.
% 2.10/2.35 Process 4363 was started by sandbox on n004.cluster.edu,
% 2.10/2.35 Fri Jul 8 07:40:53 2022
% 2.10/2.35 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4210_n004.cluster.edu".
% 2.10/2.35 ============================== end of head ===========================
% 2.10/2.35
% 2.10/2.35 ============================== INPUT =================================
% 2.10/2.35
% 2.10/2.35 % Reading from file /tmp/Prover9_4210_n004.cluster.edu
% 2.10/2.35
% 2.10/2.35 set(prolog_style_variables).
% 2.10/2.35 set(auto2).
% 2.10/2.35 % set(auto2) -> set(auto).
% 2.10/2.35 % set(auto) -> set(auto_inference).
% 2.10/2.35 % set(auto) -> set(auto_setup).
% 2.10/2.35 % set(auto_setup) -> set(predicate_elim).
% 2.10/2.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.10/2.35 % set(auto) -> set(auto_limits).
% 2.10/2.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.10/2.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.10/2.35 % set(auto) -> set(auto_denials).
% 2.10/2.35 % set(auto) -> set(auto_process).
% 2.10/2.35 % set(auto2) -> assign(new_constants, 1).
% 2.10/2.35 % set(auto2) -> assign(fold_denial_max, 3).
% 2.10/2.35 % set(auto2) -> assign(max_weight, "200.000").
% 2.10/2.35 % set(auto2) -> assign(max_hours, 1).
% 2.10/2.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.10/2.35 % set(auto2) -> assign(max_seconds, 0).
% 2.10/2.35 % set(auto2) -> assign(max_minutes, 5).
% 2.10/2.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.10/2.35 % set(auto2) -> set(sort_initial_sos).
% 2.10/2.35 % set(auto2) -> assign(sos_limit, -1).
% 2.10/2.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.10/2.35 % set(auto2) -> assign(max_megs, 400).
% 2.10/2.35 % set(auto2) -> assign(stats, some).
% 2.10/2.35 % set(auto2) -> clear(echo_input).
% 2.10/2.35 % set(auto2) -> set(quiet).
% 2.10/2.35 % set(auto2) -> clear(print_initial_clauses).
% 2.10/2.35 % set(auto2) -> clear(print_given).
% 2.10/2.35 assign(lrs_ticks,-1).
% 2.10/2.35 assign(sos_limit,10000).
% 2.10/2.35 assign(order,kbo).
% 2.10/2.35 set(lex_order_vars).
% 2.10/2.35 clear(print_given).
% 2.10/2.35
% 2.10/2.35 % formulas(sos). % not echoed (14 formulas)
% 2.10/2.35
% 2.10/2.35 ============================== end of input ==========================
% 2.10/2.35
% 2.10/2.35 % From the command line: assign(max_seconds, 300).
% 2.10/2.35
% 2.10/2.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.10/2.35
% 2.10/2.35 % Formulas that are not ordinary clauses:
% 2.10/2.35
% 2.10/2.35 ============================== end of process non-clausal formulas ===
% 2.10/2.35
% 2.10/2.35 ============================== PROCESS INITIAL CLAUSES ===============
% 2.10/2.35
% 2.10/2.35 ============================== PREDICATE ELIMINATION =================
% 2.10/2.35
% 2.10/2.35 ============================== end predicate elimination =============
% 2.10/2.35
% 2.10/2.35 Auto_denials:
% 2.10/2.35 % copying label goals_14 to answer in negative clause
% 2.10/2.35
% 2.10/2.35 Term ordering decisions:
% 2.10/2.35 Function symbol KB weights: one=1. top=1. zero=1. sk1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 2.10/2.35
% 2.10/2.35 ============================== end of process initial clauses ========
% 2.10/2.35
% 2.10/2.35 ============================== CLAUSES FOR SEARCH ====================
% 2.10/2.35
% 2.10/2.35 ============================== end of clauses for search =============
% 2.10/2.35
% 2.10/2.35 ============================== SEARCH ================================
% 2.10/2.35
% 2.10/2.35 % Starting search at 0.01 seconds.
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=38.000, iters=3354
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=35.000, iters=3378
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=32.000, iters=3358
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=31.000, iters=3407
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=30.000, iters=3370
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=29.000, iters=3336
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=28.000, iters=3339
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=27.000, iters=3406
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=26.000, iters=3336
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=25.000, iters=3366
% 2.10/2.35
% 2.10/2.35 Low Water (keep): wt=24.000, iters=3335
% 2.10/2.35
% 2.10/2.35 ============================== PROOF =================================
% 2.10/2.35 % SZS status Unsatisfiable
% 2.10/2.35 % SZS output start Refutation
% 2.10/2.35
% 2.10/2.35 % Proof 1 at 1.34 (+ 0.04) seconds: goals_14.
% 2.10/2.35 % Length of proof is 118.
% 2.10/2.35 % Level of proof is 31.
% 2.10/2.35 % Maximum clause weight is 34.000.
% 2.10/2.35 % Given clauses 514.
% 2.10/2.35
% 2.10/2.35 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 2.10/2.35 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 2.10/2.35 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 2.10/2.35 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 2.10/2.35 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 2.10/2.35 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 2.10/2.35 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 2.10/2.35 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 2.10/2.35 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 2.10/2.35 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 2.10/2.35 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 2.10/2.35 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 2.10/2.35 13 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 2.10/2.35 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([7(4)])].
% 2.10/2.35 15 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 2.10/2.35 16 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(15),flip(a)].
% 2.10/2.35 17 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 2.10/2.35 18 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(17),flip(a)].
% 2.10/2.35 19 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 2.10/2.35 20 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(19),rewrite([7(6)])].
% 2.10/2.35 21 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 2.10/2.35 22 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(21),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 2.10/2.35 23 join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) | join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top)) # label(goals_14) # label(negated_conjecture) # answer(goals_14). [assumption].
% 2.10/2.35 24 join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) | join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != complement(composition(sk1,top)) # answer(goals_14). [copy(23),rewrite([7(29)])].
% 2.10/2.35 25 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 2.10/2.35 27 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),12(a,1,1)),flip(a)].
% 2.10/2.35 28 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 2.10/2.35 29 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),14(a,2,2)),rewrite([7(2)])].
% 2.10/2.35 30 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),16(a,1,1)),flip(a)].
% 2.10/2.35 32 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(12(a,1),18(a,1,1)),rewrite([7(7)])].
% 2.10/2.35 34 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(16(a,1),18(a,1,1)),rewrite([7(6)])].
% 2.10/2.35 36 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),20(a,1,2,2,1))].
% 2.10/2.35 37 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(2(a,1),20(a,1,2,1))].
% 2.10/2.35 39 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(12(a,1),20(a,1,2,2,1)),rewrite([2(4)])].
% 2.10/2.35 40 join(complement(A),composition(converse(composition(B,C)),complement(composition(B,composition(C,A))))) = complement(A). [para(16(a,1),20(a,1,2,2,1))].
% 2.10/2.35 41 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),22(a,1,1,1)),rewrite([25(2)])].
% 2.10/2.35 45 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(22(a,1),22(a,1,2,1)),rewrite([7(10)])].
% 2.10/2.35 47 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(25(a,1),20(a,1,1)),rewrite([25(9)])].
% 2.10/2.35 49 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(25(a,1),22(a,1,2,1,1))].
% 2.10/2.35 58 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(27(a,1),10(a,1,1)),rewrite([7(7)]),flip(a)].
% 2.10/2.35 62 composition(converse(one),A) = A. [para(1(a,1),28(a,1,1)),rewrite([2(2)]),flip(a)].
% 2.10/2.35 68 converse(one) = one. [para(62(a,1),1(a,1)),flip(a)].
% 2.10/2.35 70 composition(join(A,one),B) = join(B,composition(A,B)). [para(62(a,1),18(a,1,1)),rewrite([68(4),7(4)]),flip(a)].
% 2.10/2.35 72 join(complement(A),complement(composition(one,A))) = complement(A). [para(62(a,1),20(a,1,2))].
% 2.10/2.35 73 composition(one,A) = A. [para(62(a,1),30(a,2)),rewrite([68(2),30(4)])].
% 2.10/2.35 74 join(complement(A),complement(A)) = complement(A). [back_rewrite(72),rewrite([73(3)])].
% 2.10/2.35 75 join(zero,complement(complement(A))) = A. [back_rewrite(41),rewrite([74(4)])].
% 2.10/2.35 76 converse(join(A,one)) = join(one,converse(A)). [para(68(a,1),10(a,1,1)),rewrite([7(5)]),flip(a)].
% 2.10/2.35 80 join(top,complement(A)) = top. [para(74(a,1),29(a,1,2)),rewrite([4(2),7(4)]),flip(a)].
% 2.10/2.35 81 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(49),rewrite([80(3),25(2)])].
% 2.10/2.35 82 join(top,top) = join(A,top). [para(80(a,1),29(a,1,2)),flip(a)].
% 2.10/2.35 87 join(A,top) = join(B,top). [para(82(a,1),29(a,2)),rewrite([80(3)])].
% 2.10/2.35 88 join(A,top) = c_0. [new_symbol(87)].
% 2.10/2.35 91 join(A,join(B,complement(A))) = c_0. [back_rewrite(29),rewrite([88(5)])].
% 2.10/2.35 97 converse(join(A,composition(A,B))) = composition(join(one,converse(B)),converse(A)). [para(73(a,1),32(a,1,2)),rewrite([7(4),10(4)])].
% 2.10/2.35 102 c_0 = top. [para(75(a,1),91(a,1,2)),rewrite([7(2),4(2)]),flip(a)].
% 2.10/2.35 103 join(A,join(B,complement(A))) = top. [back_rewrite(91),rewrite([102(4)])].
% 2.10/2.35 105 join(A,top) = top. [back_rewrite(88),rewrite([102(3)])].
% 2.10/2.35 116 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(76(a,1),12(a,1,1))].
% 2.10/2.35 123 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(97),rewrite([116(8)]),flip(a)].
% 2.10/2.35 130 join(zero,complement(A)) = complement(A). [para(75(a,1),81(a,1,2,1))].
% 2.10/2.35 131 complement(complement(A)) = A. [back_rewrite(81),rewrite([130(4),130(4)])].
% 2.10/2.35 132 join(A,zero) = A. [back_rewrite(75),rewrite([131(3),7(2)])].
% 2.10/2.35 137 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(131(a,1),22(a,1,1,1,2)),rewrite([131(5),7(4)])].
% 2.10/2.35 138 complement(zero) = top. [para(25(a,1),131(a,1,1))].
% 2.10/2.35 139 join(A,A) = A. [para(131(a,1),74(a,1,1)),rewrite([131(2),131(3)])].
% 2.10/2.35 143 join(A,join(A,B)) = join(A,B). [para(139(a,1),14(a,1)),rewrite([7(3),14(4,R),7(3),14(3,R),139(2)]),flip(a)].
% 2.10/2.35 144 join(A,complement(join(B,complement(A)))) = A. [para(22(a,1),143(a,1,2)),rewrite([7(4),22(12)])].
% 2.10/2.35 146 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(144(a,1),14(a,2,2)),rewrite([7(4),7(6)])].
% 2.10/2.35 149 join(complement(A),complement(join(A,B))) = complement(A). [para(131(a,1),144(a,1,2,1,2)),rewrite([7(2)])].
% 2.10/2.35 157 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(131(a,1),36(a,1,2,2))].
% 2.10/2.35 160 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(10(a,1),149(a,1,2,1))].
% 2.10/2.35 171 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(47(a,1),10(a,2,1)),rewrite([28(8)])].
% 2.10/2.35 211 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),157(a,1,2))].
% 2.10/2.35 215 converse(complement(one)) = complement(one). [para(211(a,1),10(a,2,1)),rewrite([2(7),7(6),211(6)]),flip(a)].
% 2.10/2.35 220 converse(top) = top. [para(215(a,1),76(a,2,2)),rewrite([7(4),4(4),4(6)])].
% 2.10/2.35 224 join(top,converse(A)) = top. [para(220(a,1),10(a,1,1)),rewrite([7(5),105(5),220(5)])].
% 2.10/2.35 225 converse(composition(A,top)) = composition(top,converse(A)). [para(220(a,1),12(a,1,1)),flip(a)].
% 2.10/2.35 233 join(top,composition(A,converse(B))) = top. [para(27(a,1),224(a,1,2))].
% 2.10/2.35 235 join(top,composition(A,B)) = top. [para(2(a,1),233(a,1,2,2))].
% 2.10/2.35 251 composition(top,join(one,converse(A))) = top. [para(76(a,1),225(a,2,2)),rewrite([70(4),235(4),220(2)]),flip(a)].
% 2.10/2.35 256 composition(top,join(A,one)) = top. [para(2(a,1),251(a,1,2,2)),rewrite([7(3)])].
% 2.10/2.35 266 composition(top,top) = top. [para(215(a,1),251(a,1,2,2)),rewrite([4(5)])].
% 2.10/2.35 268 composition(top,composition(top,A)) = composition(top,A). [para(266(a,1),16(a,1,1)),flip(a)].
% 2.10/2.35 280 join(zero,composition(A,zero)) = zero. [para(256(a,1),39(a,1,2,2,1,1)),rewrite([220(2),25(2),220(5),25(5),70(5),143(6),220(6),25(6)])].
% 2.10/2.35 289 join(complement(A),complement(join(B,A))) = complement(A). [para(144(a,1),45(a,2)),rewrite([131(2),131(4),131(8),45(13)])].
% 2.10/2.35 295 join(A,composition(B,zero)) = A. [para(280(a,1),14(a,1,2)),rewrite([132(2),132(4),7(3)]),flip(a)].
% 2.10/2.35 299 composition(join(A,B),zero) = composition(A,zero). [para(295(a,1),18(a,1)),flip(a)].
% 2.10/2.35 301 composition(A,zero) = zero. [para(295(a,1),70(a,2)),rewrite([299(4)])].
% 2.10/2.35 303 composition(converse(zero),A) = converse(zero). [para(301(a,1),28(a,1,1)),flip(a)].
% 2.10/2.35 312 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(303(a,1),34(a,1,1,2)),flip(a)].
% 2.10/2.35 316 converse(zero) = zero. [para(303(a,1),301(a,1))].
% 2.10/2.35 319 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(312),rewrite([316(2),301(2),132(2),316(3),301(3)]),flip(a)].
% 2.10/2.35 321 composition(zero,A) = zero. [back_rewrite(303),rewrite([316(2),316(4)])].
% 2.10/2.35 322 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(171),rewrite([316(2),319(7),316(7)])].
% 2.10/2.35 380 composition(top,complement(composition(top,A))) = complement(composition(top,A)). [para(268(a,1),20(a,1,2,2,1)),rewrite([220(5),70(9,R),7(3),105(3)])].
% 2.10/2.35 384 join(complement(A),complement(composition(top,A))) = complement(A). [para(268(a,1),40(a,1,2,2,1)),rewrite([266(4),220(3),380(6)])].
% 2.10/2.35 407 composition(converse(complement(composition(A,top))),composition(A,B)) = zero. [para(322(a,1),16(a,1,1)),rewrite([321(2)]),flip(a)].
% 2.10/2.35 550 join(one,complement(composition(converse(complement(A)),A))) = complement(composition(converse(complement(A)),A)). [para(157(a,1),289(a,1,2,1)),rewrite([131(7),7(6)])].
% 2.10/2.35 587 join(A,composition(top,A)) = composition(top,A). [para(384(a,1),144(a,1,2,1)),rewrite([131(4),7(3)])].
% 2.10/2.35 618 join(A,composition(A,top)) = composition(A,top). [para(587(a,1),58(a,1,1)),rewrite([27(4),220(2),220(4),2(6),7(5)]),flip(a)].
% 2.10/2.35 619 composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)) # answer(goals_14). [back_rewrite(24),rewrite([618(11),618(24)]),xx(a)].
% 2.10/2.35 1499 composition(A,join(B,one)) = join(A,composition(A,B)). [para(123(a,1),2(a,1,1)),rewrite([2(4)]),flip(a)].
% 2.10/2.35 1959 composition(complement(A),complement(composition(converse(complement(A)),A))) = complement(A). [para(1499(a,2),37(a,1)),rewrite([7(7),550(7)])].
% 2.10/2.35 2502 join(A,complement(join(A,B))) = join(A,complement(B)). [para(137(a,1),146(a,1,2)),flip(a)].
% 2.10/2.35 2930 join(complement(converse(A)),converse(join(A,B))) = top. [para(160(a,1),103(a,1,2)),rewrite([7(5)])].
% 2.10/2.35 2956 join(A,join(B,converse(complement(converse(A))))) = top. [para(2930(a,1),10(a,2,1)),rewrite([2(6),14(5),7(4),14(5,R),7(4),220(7)])].
% 2.10/2.35 2987 join(A,converse(complement(converse(A)))) = top. [para(139(a,1),2956(a,1,2))].
% 2.10/2.35 3024 join(A,complement(converse(complement(converse(A))))) = A. [para(2987(a,1),2502(a,1,2,1)),rewrite([25(2),132(2)]),flip(a)].
% 2.10/2.35 3025 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(2(a,1),3024(a,1,2,1,1,1))].
% 2.10/2.35 3028 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(3024(a,1),22(a,1,2,1)),rewrite([131(9),7(8),2502(8),131(6)])].
% 2.10/2.35 3147 converse(complement(converse(complement(A)))) = A. [para(3025(a,1),10(a,2,1)),rewrite([2(2),3028(5),2(6)])].
% 2.10/2.35 3170 complement(converse(complement(A))) = converse(A). [para(3147(a,1),2(a,1,1)),flip(a)].
% 2.10/2.35 3239 converse(complement(A)) = complement(converse(A)). [para(3170(a,1),131(a,1,1)),flip(a)].
% 2.10/2.35 3347 composition(complement(A),complement(composition(complement(converse(A)),A))) = complement(A). [back_rewrite(1959),rewrite([3239(3)])].
% 2.10/2.35 3417 composition(complement(composition(top,converse(A))),composition(A,B)) = zero. [back_rewrite(407),rewrite([3239(4),225(3)])].
% 2.10/2.35 9371 composition(complement(composition(A,top)),top) = complement(composition(A,top)). [para(225(a,1),3347(a,1,2,1,1,1)),rewrite([3417(10),138(5)])].
% 2.10/2.35 9372 $F # answer(goals_14). [resolve(9371,a,619,a)].
% 2.10/2.35
% 2.10/2.35 % SZS output end Refutation
% 2.10/2.35 ============================== end of proof ==========================
% 2.10/2.35
% 2.10/2.35 ============================== STATISTICS ============================
% 2.10/2.35
% 2.10/2.35 Given=514. Generated=69510. Kept=9361. proofs=1.
% 2.10/2.35 Usable=417. Sos=7403. Demods=7392. Limbo=9, Disabled=1545. Hints=0.
% 2.10/2.35 Megabytes=11.77.
% 2.10/2.35 User_CPU=1.34, System_CPU=0.04, Wall_clock=1.
% 2.10/2.35
% 2.10/2.35 ============================== end of statistics =====================
% 2.10/2.35
% 2.10/2.35 ============================== end of search =========================
% 2.10/2.35
% 2.10/2.35 THEOREM PROVED
% 2.10/2.35 % SZS status Unsatisfiable
% 2.10/2.35
% 2.10/2.35 Exiting with 1 proof.
% 2.10/2.35
% 2.10/2.35 Process 4363 exit (max_proofs) Fri Jul 8 07:40:54 2022
% 2.10/2.35 Prover9 interrupted
%------------------------------------------------------------------------------