TSTP Solution File: REL027+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL027+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : 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 19:54:02 EDT 2022
% Result : Theorem 4.12s 4.43s
% Output : Refutation 4.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : REL027+4 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 09:05:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.40/1.00 ============================== Prover9 ===============================
% 0.40/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.40/1.00 Process 12035 was started by sandbox on n011.cluster.edu,
% 0.40/1.00 Fri Jul 8 09:05:25 2022
% 0.40/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11880_n011.cluster.edu".
% 0.40/1.00 ============================== end of head ===========================
% 0.40/1.00
% 0.40/1.00 ============================== INPUT =================================
% 0.40/1.00
% 0.40/1.00 % Reading from file /tmp/Prover9_11880_n011.cluster.edu
% 0.40/1.00
% 0.40/1.00 set(prolog_style_variables).
% 0.40/1.00 set(auto2).
% 0.40/1.00 % set(auto2) -> set(auto).
% 0.40/1.00 % set(auto) -> set(auto_inference).
% 0.40/1.00 % set(auto) -> set(auto_setup).
% 0.40/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.40/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/1.00 % set(auto) -> set(auto_limits).
% 0.40/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/1.00 % set(auto) -> set(auto_denials).
% 0.40/1.00 % set(auto) -> set(auto_process).
% 0.40/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.40/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.40/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.40/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.40/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.40/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.40/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.40/1.00 % set(auto2) -> assign(stats, some).
% 0.40/1.00 % set(auto2) -> clear(echo_input).
% 0.40/1.00 % set(auto2) -> set(quiet).
% 0.40/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.40/1.00 % set(auto2) -> clear(print_given).
% 0.40/1.00 assign(lrs_ticks,-1).
% 0.40/1.00 assign(sos_limit,10000).
% 0.40/1.00 assign(order,kbo).
% 0.40/1.00 set(lex_order_vars).
% 0.40/1.00 clear(print_given).
% 0.40/1.00
% 0.40/1.00 % formulas(sos). % not echoed (17 formulas)
% 0.40/1.00
% 0.40/1.00 ============================== end of input ==========================
% 0.40/1.00
% 0.40/1.00 % From the command line: assign(max_seconds, 300).
% 0.40/1.00
% 0.40/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/1.00
% 0.40/1.00 % Formulas that are not ordinary clauses:
% 0.40/1.00 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) # label(dedekind_law) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 15 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) # label(modular_law_1) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 16 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) # label(modular_law_2) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 17 -(all X0 (join(X0,one) = one -> join(meet(complement(composition(X0,top)),one),meet(complement(X0),one)) = meet(complement(X0),one) & join(meet(complement(X0),one),meet(complement(composition(X0,top)),one)) = meet(complement(composition(X0,top)),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.12/4.43
% 4.12/4.43 ============================== end of process non-clausal formulas ===
% 4.12/4.43
% 4.12/4.43 ============================== PROCESS INITIAL CLAUSES ===============
% 4.12/4.43
% 4.12/4.43 ============================== PREDICATE ELIMINATION =================
% 4.12/4.43
% 4.12/4.43 ============================== end predicate elimination =============
% 4.12/4.43
% 4.12/4.43 Auto_denials:
% 4.12/4.43 % copying label goals to answer in negative clause
% 4.12/4.43
% 4.12/4.43 Term ordering decisions:
% 4.12/4.43 Function symbol KB weights: one=1. top=1. zero=1. c1=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 4.12/4.43
% 4.12/4.43 ============================== end of process initial clauses ========
% 4.12/4.43
% 4.12/4.43 ============================== CLAUSES FOR SEARCH ====================
% 4.12/4.43
% 4.12/4.43 ============================== end of clauses for search =============
% 4.12/4.43
% 4.12/4.43 ============================== SEARCH ================================
% 4.12/4.43
% 4.12/4.43 % Starting search at 0.01 seconds.
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=128.000, iters=3388
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=104.000, iters=3375
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=76.000, iters=3394
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=74.000, iters=3375
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=72.000, iters=3337
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=71.000, iters=3382
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=69.000, iters=3345
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=67.000, iters=3383
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=66.000, iters=3405
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=65.000, iters=3358
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=64.000, iters=3376
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=62.000, iters=3353
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=61.000, iters=3335
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=60.000, iters=3355
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=59.000, iters=3352
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=58.000, iters=3356
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=57.000, iters=3400
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=56.000, iters=3339
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=55.000, iters=3415
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=54.000, iters=3335
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=53.000, iters=3333
% 4.12/4.43
% 4.12/4.43 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 2.31 sec).
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=51.000, iters=3361
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=49.000, iters=3370
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=48.000, iters=3421
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=46.000, iters=3348
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=45.000, iters=3362
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=44.000, iters=3365
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=43.000, iters=3371
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=41.000, iters=3335
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=40.000, iters=3340
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=39.000, iters=3366
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=38.000, iters=3346
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=37.000, iters=3420
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=35.000, iters=3355
% 4.12/4.43
% 4.12/4.43 Low Water (keep): wt=33.000, iters=3357
% 4.12/4.43
% 4.12/4.43 ============================== PROOF =================================
% 4.12/4.43 % SZS status Theorem
% 4.12/4.43 % SZS output start Refutation
% 4.12/4.43
% 4.12/4.43 % Proof 1 at 3.39 (+ 0.05) seconds: goals.
% 4.12/4.43 % Length of proof is 97.
% 4.12/4.43 % Level of proof is 21.
% 4.12/4.43 % Maximum clause weight is 52.000.
% 4.12/4.43 % Given clauses 607.
% 4.12/4.43
% 4.12/4.43 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) # label(dedekind_law) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 15 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) # label(modular_law_1) # label(axiom) # label(non_clause). [assumption].
% 4.12/4.43 17 -(all X0 (join(X0,one) = one -> join(meet(complement(composition(X0,top)),one),meet(complement(X0),one)) = meet(complement(X0),one) & join(meet(complement(X0),one),meet(complement(composition(X0,top)),one)) = meet(complement(composition(X0,top)),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.12/4.43 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 4.12/4.43 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 4.12/4.43 20 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(17)].
% 4.12/4.43 21 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 4.12/4.43 22 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 4.12/4.43 23 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 4.12/4.43 24 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 4.12/4.43 25 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 4.12/4.43 26 join(converse(A),converse(B)) = converse(join(A,B)). [copy(25),flip(a)].
% 4.12/4.43 27 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 4.12/4.43 28 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(27),flip(a)].
% 4.12/4.43 29 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 4.12/4.43 30 join(A,join(B,C)) = join(C,join(A,B)). [copy(29),rewrite([23(2)]),flip(a)].
% 4.12/4.43 31 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 4.12/4.43 32 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 4.12/4.43 33 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(32),flip(a)].
% 4.12/4.43 34 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 4.12/4.43 35 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(34),rewrite([23(7)]),flip(a)].
% 4.12/4.43 36 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 4.12/4.43 37 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(36),rewrite([23(6),23(8)]),rewrite([23(6)])].
% 4.12/4.43 38 meet(composition(A,meet(B,composition(converse(A),C))),C) = join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) # label(modular_law_1) # label(axiom). [clausify(15)].
% 4.12/4.43 39 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(38),rewrite([24(3),24(8),23(10),24(13),23(15),24(19),24(24),23(26)]),flip(a)].
% 4.12/4.43 42 composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))) # label(dedekind_law) # label(axiom). [clausify(14)].
% 4.12/4.43 43 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(42),rewrite([24(3),24(9),24(15),23(17),24(21),24(27)]),flip(a)].
% 4.12/4.43 44 meet(complement(c1),one) != join(meet(complement(composition(c1,top)),one),meet(complement(c1),one)) | meet(complement(composition(c1,top)),one) != join(meet(complement(c1),one),meet(complement(composition(c1,top)),one)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 4.12/4.43 45 join(complement(join(complement(one),complement(complement(c1)))),complement(join(complement(one),complement(complement(composition(c1,top)))))) != complement(join(complement(one),complement(complement(c1)))) | join(complement(join(complement(one),complement(complement(c1)))),complement(join(complement(one),complement(complement(composition(c1,top)))))) != complement(join(complement(one),complement(complement(composition(c1,top))))) # answer(goals). [copy(44),rewrite([24(4),23(6),24(13),23(15),24(20),23(22),23(24),24(31),23(33),24(38),23(40),24(47),23(49)]),flip(a),flip(b)].
% 4.12/4.43 46 join(one,c1) = one. [back_rewrite(20),rewrite([23(3)])].
% 4.12/4.43 47 complement(top) = zero. [back_rewrite(22),rewrite([24(2),21(4)])].
% 4.12/4.43 48 converse(join(A,converse(B))) = join(B,converse(A)). [para(19(a,1),26(a,1,1)),rewrite([23(4)]),flip(a)].
% 4.12/4.43 49 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),28(a,1,1)),flip(a)].
% 4.12/4.43 50 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),28(a,1,2)),flip(a)].
% 4.12/4.43 51 join(A,join(B,complement(A))) = join(B,top). [para(21(a,1),30(a,2,2)),rewrite([23(2)])].
% 4.12/4.43 52 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),31(a,1,1)),flip(a)].
% 4.12/4.43 58 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(18(a,1),35(a,1,2,2,1))].
% 4.12/4.43 63 join(zero,complement(join(complement(A),complement(A)))) = A. [para(21(a,1),37(a,1,1,1)),rewrite([47(2)])].
% 4.12/4.43 64 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(21(a,1),37(a,1,2,1)),rewrite([47(6),23(6)])].
% 4.12/4.43 67 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(37(a,1),37(a,1,2,1)),rewrite([23(10)])].
% 4.12/4.43 84 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(18(a,1),43(a,1,1,1,2,1))].
% 4.12/4.43 103 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(48(a,1),26(a,1,1)),rewrite([23(7),30(7,R),23(6)]),flip(a)].
% 4.12/4.43 104 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(48(a,1),26(a,1,2)),rewrite([30(4,R),23(3),26(3),103(7)]),flip(a)].
% 4.12/4.43 112 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(48(a,1),48(a,2,2)),rewrite([104(4),48(4),30(6,R),23(5)])].
% 4.12/4.43 120 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(49(a,1),26(a,1,1)),rewrite([23(7)]),flip(a)].
% 4.12/4.43 128 composition(converse(one),A) = A. [para(18(a,1),50(a,1,1)),rewrite([19(2)]),flip(a)].
% 4.12/4.43 137 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(37(a,1),51(a,1,2)),rewrite([23(4),51(4),23(3),23(8)]),flip(a)].
% 4.12/4.43 138 join(top,complement(complement(A))) = top. [para(39(a,1),51(a,1,2)),rewrite([21(22),23(8),137(8)]),flip(a)].
% 4.12/4.43 139 converse(one) = one. [para(128(a,1),18(a,1)),flip(a)].
% 4.12/4.43 141 composition(join(A,one),B) = join(B,composition(A,B)). [para(128(a,1),33(a,1,1)),rewrite([139(4),23(4)]),flip(a)].
% 4.12/4.43 143 join(complement(A),complement(composition(one,A))) = complement(A). [para(128(a,1),35(a,1,2))].
% 4.12/4.43 157 composition(one,A) = A. [para(128(a,1),52(a,2)),rewrite([139(2),52(4)])].
% 4.12/4.43 158 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(84),rewrite([139(7),18(7),23(7),139(20),18(20),23(20)])].
% 4.12/4.43 163 join(complement(A),complement(A)) = complement(A). [back_rewrite(143),rewrite([157(3)])].
% 4.12/4.43 164 join(zero,complement(complement(A))) = A. [back_rewrite(63),rewrite([163(4)])].
% 4.12/4.43 165 converse(join(A,one)) = join(one,converse(A)). [para(139(a,1),26(a,1,1)),rewrite([23(5)]),flip(a)].
% 4.12/4.43 166 join(zero,complement(A)) = complement(A). [para(138(a,1),37(a,1,1,1)),rewrite([47(2),47(3),164(5)])].
% 4.12/4.43 169 complement(complement(A)) = A. [back_rewrite(164),rewrite([166(4)])].
% 4.12/4.43 179 complement(join(A,A)) = complement(A). [back_rewrite(64),rewrite([169(3),166(4)])].
% 4.12/4.43 186 join(complement(join(c1,complement(one))),complement(join(complement(one),composition(c1,top)))) != complement(join(c1,complement(one))) | join(complement(join(c1,complement(one))),complement(join(complement(one),composition(c1,top)))) != complement(join(complement(one),composition(c1,top))) # answer(goals). [back_rewrite(45),rewrite([169(5),23(4),169(12),169(18),23(17),169(24),23(23),169(31),169(39)])].
% 4.12/4.43 221 join(A,A) = A. [para(179(a,1),37(a,1,1,1,2)),rewrite([179(6),37(8)]),flip(a)].
% 4.12/4.43 228 join(A,join(A,B)) = join(A,B). [para(221(a,1),30(a,1)),rewrite([23(3),30(4,R),23(3),30(3,R),221(2)]),flip(a)].
% 4.12/4.43 246 join(A,complement(join(B,complement(A)))) = A. [para(37(a,1),228(a,1,2)),rewrite([23(4),37(12)])].
% 4.12/4.43 269 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(169(a,1),58(a,1,2,2))].
% 4.12/4.43 289 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(141(a,1),33(a,1,2)),rewrite([30(4,R),33(3),23(1)]),flip(a)].
% 4.12/4.43 318 join(complement(one),converse(complement(one))) = complement(one). [para(18(a,1),269(a,1,2))].
% 4.12/4.43 322 converse(complement(one)) = complement(one). [para(318(a,1),26(a,2,1)),rewrite([19(7),23(6),318(6)]),flip(a)].
% 4.12/4.43 331 converse(top) = top. [para(322(a,1),165(a,2,2)),rewrite([23(4),21(4),21(6)])].
% 4.12/4.43 451 join(complement(A),complement(join(B,A))) = complement(A). [para(246(a,1),67(a,2)),rewrite([169(2),169(4),169(8),67(13)])].
% 4.12/4.43 771 join(complement(one),complement(c1)) = complement(c1). [para(46(a,1),451(a,1,2,1)),rewrite([23(5)])].
% 4.12/4.43 2365 join(one,join(c1,converse(A))) = join(one,converse(A)). [para(46(a,1),112(a,1,1)),flip(a)].
% 4.12/4.43 3737 join(A,join(one,converse(c1))) = join(A,one). [para(2365(a,1),26(a,2,1)),rewrite([139(2),48(5),30(5,R),23(4),48(9),139(7)])].
% 4.12/4.43 3745 join(one,converse(c1)) = one. [para(221(a,1),3737(a,2)),rewrite([228(6)])].
% 4.12/4.43 3746 join(A,composition(converse(c1),A)) = A. [para(3745(a,1),33(a,2,1)),rewrite([157(2),157(6)])].
% 4.12/4.43 3748 join(complement(one),complement(converse(c1))) = complement(converse(c1)). [para(3745(a,1),451(a,1,2,1)),rewrite([23(6)])].
% 4.12/4.43 3752 join(A,join(B,composition(converse(c1),A))) = join(A,B). [para(3746(a,1),30(a,2,2)),rewrite([23(4),23(6)])].
% 4.12/4.43 3757 join(A,composition(A,c1)) = A. [para(3746(a,1),120(a,1,1)),rewrite([19(2),19(3),19(4),23(3)]),flip(a)].
% 4.12/4.43 4241 composition(converse(c1),c1) = converse(c1). [para(3748(a,1),158(a,1,1,1)),rewrite([169(4),3748(8),169(6),19(9),18(9),771(9),169(7),3757(7),3748(8),169(6),19(9),18(9),771(9),169(7)]),flip(a)].
% 4.12/4.43 4274 converse(c1) = c1. [para(4241(a,1),28(a,2,1)),rewrite([19(5),4241(4),19(5)])].
% 4.12/4.43 4342 join(A,join(B,composition(c1,A))) = join(A,B). [back_rewrite(3752),rewrite([4274(2)])].
% 4.12/4.43 14276 join(A,composition(complement(one),A)) = composition(top,A). [para(58(a,1),289(a,2,2,1)),rewrite([23(7),30(8,R),23(7),58(7),21(4)]),flip(a)].
% 4.12/4.43 14336 join(A,composition(A,complement(one))) = composition(A,top). [para(14276(a,1),120(a,1,1)),rewrite([49(4),331(2),322(5),19(7),23(6)]),flip(a)].
% 4.12/4.43 14346 join(complement(one),composition(c1,top)) = join(c1,complement(one)). [para(14336(a,1),4342(a,1,2)),rewrite([23(10)])].
% 4.12/4.43 14354 $F # answer(goals). [back_rewrite(186),rewrite([14346(11),221(11),14346(22),221(22),14346(22)]),xx(a),xx(b)].
% 4.12/4.43
% 4.12/4.43 % SZS output end Refutation
% 4.12/4.43 ============================== end of proof ==========================
% 4.12/4.43
% 4.12/4.43 ============================== STATISTICS ============================
% 4.12/4.43
% 4.12/4.43 Given=607. Generated=87668. Kept=14326. proofs=1.
% 4.12/4.43 Usable=399. Sos=8204. Demods=8311. Limbo=8, Disabled=5733. Hints=0.
% 4.12/4.43 Megabytes=24.86.
% 4.12/4.43 User_CPU=3.39, System_CPU=0.05, Wall_clock=3.
% 4.12/4.43
% 4.12/4.43 ============================== end of statistics =====================
% 4.12/4.43
% 4.12/4.43 ============================== end of search =========================
% 4.12/4.43
% 4.12/4.43 THEOREM PROVED
% 4.12/4.43 % SZS status Theorem
% 4.12/4.43
% 4.12/4.43 Exiting with 1 proof.
% 4.12/4.43
% 4.12/4.43 Process 12035 exit (max_proofs) Fri Jul 8 09:05:28 2022
% 4.12/4.43 Prover9 interrupted
%------------------------------------------------------------------------------