TSTP Solution File: REL050+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL050+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 19:54:34 EDT 2022
% Result : Theorem 4.60s 4.85s
% Output : Refutation 4.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL050+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n018.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 08:03:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.48/1.03 ============================== Prover9 ===============================
% 0.48/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.48/1.03 Process 19131 was started by sandbox on n018.cluster.edu,
% 0.48/1.03 Fri Jul 8 08:03:26 2022
% 0.48/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18978_n018.cluster.edu".
% 0.48/1.03 ============================== end of head ===========================
% 0.48/1.03
% 0.48/1.03 ============================== INPUT =================================
% 0.48/1.03
% 0.48/1.03 % Reading from file /tmp/Prover9_18978_n018.cluster.edu
% 0.48/1.03
% 0.48/1.03 set(prolog_style_variables).
% 0.48/1.03 set(auto2).
% 0.48/1.03 % set(auto2) -> set(auto).
% 0.48/1.03 % set(auto) -> set(auto_inference).
% 0.48/1.03 % set(auto) -> set(auto_setup).
% 0.48/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.48/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/1.03 % set(auto) -> set(auto_limits).
% 0.48/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/1.03 % set(auto) -> set(auto_denials).
% 0.48/1.03 % set(auto) -> set(auto_process).
% 0.48/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.48/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.48/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.48/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.48/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.48/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.48/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.48/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.48/1.03 % set(auto2) -> assign(stats, some).
% 0.48/1.03 % set(auto2) -> clear(echo_input).
% 0.48/1.03 % set(auto2) -> set(quiet).
% 0.48/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.48/1.03 % set(auto2) -> clear(print_given).
% 0.48/1.03 assign(lrs_ticks,-1).
% 0.48/1.03 assign(sos_limit,10000).
% 0.48/1.03 assign(order,kbo).
% 0.48/1.03 set(lex_order_vars).
% 0.48/1.03 clear(print_given).
% 0.48/1.03
% 0.48/1.03 % formulas(sos). % not echoed (17 formulas)
% 0.48/1.03
% 0.48/1.03 ============================== end of input ==========================
% 0.48/1.03
% 0.48/1.03 % From the command line: assign(max_seconds, 300).
% 0.48/1.03
% 0.48/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/1.03
% 0.48/1.03 % Formulas that are not ordinary clauses:
% 0.48/1.03 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 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].
% 0.48/1.03 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].
% 0.48/1.03 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].
% 0.48/1.03 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].
% 0.48/1.03 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 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].
% 0.48/1.03 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 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].
% 0.48/1.03 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 4.60/4.85 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].
% 4.60/4.85 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].
% 4.60/4.85 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].
% 4.60/4.85 17 -(all X0 complement(composition(X0,top)) = composition(complement(composition(X0,top)),top)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.60/4.85
% 4.60/4.85 ============================== end of process non-clausal formulas ===
% 4.60/4.85
% 4.60/4.85 ============================== PROCESS INITIAL CLAUSES ===============
% 4.60/4.85
% 4.60/4.85 ============================== PREDICATE ELIMINATION =================
% 4.60/4.85
% 4.60/4.85 ============================== end predicate elimination =============
% 4.60/4.85
% 4.60/4.85 Auto_denials:
% 4.60/4.85 % copying label goals to answer in negative clause
% 4.60/4.85
% 4.60/4.85 Term ordering decisions:
% 4.60/4.85 Function symbol KB weights: one=1. top=1. zero=1. c1=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 4.60/4.85
% 4.60/4.85 ============================== end of process initial clauses ========
% 4.60/4.85
% 4.60/4.85 ============================== CLAUSES FOR SEARCH ====================
% 4.60/4.85
% 4.60/4.85 ============================== end of clauses for search =============
% 4.60/4.85
% 4.60/4.85 ============================== SEARCH ================================
% 4.60/4.85
% 4.60/4.85 % Starting search at 0.01 seconds.
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=86.000, iters=3414
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=84.000, iters=3355
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=76.000, iters=3491
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=70.000, iters=3384
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=69.000, iters=3385
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=68.000, iters=3407
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=67.000, iters=3383
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=66.000, iters=3339
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=65.000, iters=3396
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=61.000, iters=3390
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=60.000, iters=3336
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=58.000, iters=3372
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=57.000, iters=3340
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=56.000, iters=3334
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=55.000, iters=3356
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=53.000, iters=3399
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=51.000, iters=3357
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=50.000, iters=3335
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=49.000, iters=3359
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=48.000, iters=3370
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=45.000, iters=3383
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=40.000, iters=3436
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=38.000, iters=3562
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=33.000, iters=3377
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=31.000, iters=3341
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=30.000, iters=3340
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=29.000, iters=3359
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=28.000, iters=3432
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=27.000, iters=3349
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=26.000, iters=3394
% 4.60/4.85
% 4.60/4.85 Low Water (keep): wt=25.000, iters=3333
% 4.60/4.85
% 4.60/4.85 ============================== PROOF =================================
% 4.60/4.85 % SZS status Theorem
% 4.60/4.85 % SZS output start Refutation
% 4.60/4.85
% 4.60/4.85 % Proof 1 at 3.77 (+ 0.06) seconds: goals.
% 4.60/4.85 % Length of proof is 145.
% 4.60/4.85 % Level of proof is 37.
% 4.60/4.85 % Maximum clause weight is 48.000.
% 4.60/4.85 % Given clauses 614.
% 4.60/4.85
% 4.60/4.85 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 4.60/4.85 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].
% 4.60/4.85 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].
% 4.60/4.85 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].
% 4.60/4.85 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].
% 4.60/4.85 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 4.60/4.85 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].
% 4.60/4.85 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 4.60/4.85 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 4.60/4.85 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 4.60/4.85 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].
% 4.60/4.85 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 4.60/4.85 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 4.60/4.85 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].
% 4.60/4.85 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].
% 4.60/4.85 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].
% 4.60/4.85 17 -(all X0 complement(composition(X0,top)) = composition(complement(composition(X0,top)),top)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.60/4.85 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 4.60/4.85 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 4.60/4.85 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 4.60/4.85 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 4.60/4.85 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 4.60/4.85 23 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 4.60/4.85 24 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 4.60/4.85 25 join(converse(A),converse(B)) = converse(join(A,B)). [copy(24),flip(a)].
% 4.60/4.85 26 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 4.60/4.85 27 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(26),flip(a)].
% 4.60/4.85 28 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 4.60/4.85 29 join(A,join(B,C)) = join(C,join(A,B)). [copy(28),rewrite([22(2)]),flip(a)].
% 4.60/4.85 30 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 4.60/4.85 31 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 4.60/4.85 32 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(31),flip(a)].
% 4.60/4.85 33 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 4.60/4.85 34 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(33),rewrite([22(7)]),flip(a)].
% 4.60/4.85 35 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 4.60/4.85 36 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(35),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 4.60/4.85 37 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)].
% 4.60/4.85 38 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(37),rewrite([23(3),23(8),22(10),23(13),22(15),23(19),23(24),22(26)]),flip(a)].
% 4.60/4.85 39 meet(composition(meet(A,composition(B,converse(C))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)) # label(modular_law_2) # label(axiom). [clausify(16)].
% 4.60/4.85 40 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C))))) = complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C)))). [copy(39),rewrite([23(3),23(8),22(10),23(13),22(15),23(19),23(24),22(26)]),flip(a)].
% 4.60/4.85 41 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)].
% 4.60/4.85 42 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(41),rewrite([23(3),23(9),23(15),22(17),23(21),23(27)]),flip(a)].
% 4.60/4.85 43 composition(complement(composition(c1,top)),top) != complement(composition(c1,top)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 4.60/4.85 44 complement(top) = zero. [back_rewrite(21),rewrite([23(2),20(4)])].
% 4.60/4.85 45 converse(join(A,converse(B))) = join(B,converse(A)). [para(19(a,1),25(a,1,1)),rewrite([22(4)]),flip(a)].
% 4.60/4.85 46 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),27(a,1,1)),flip(a)].
% 4.60/4.85 47 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),27(a,1,2)),flip(a)].
% 4.60/4.85 48 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),29(a,2,2)),rewrite([22(2)])].
% 4.60/4.85 49 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),30(a,1,1)),flip(a)].
% 4.60/4.85 51 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(27(a,1),32(a,1,1)),rewrite([22(7)])].
% 4.60/4.85 53 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(30(a,1),32(a,1,1)),rewrite([22(6)])].
% 4.60/4.85 55 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(18(a,1),34(a,1,2,2,1))].
% 4.60/4.85 56 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(19(a,1),34(a,1,2,1))].
% 4.60/4.85 60 join(zero,complement(join(complement(A),complement(A)))) = A. [para(20(a,1),36(a,1,1,1)),rewrite([44(2)])].
% 4.60/4.85 61 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(20(a,1),36(a,1,2,1)),rewrite([44(6),22(6)])].
% 4.60/4.85 64 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(36(a,1),36(a,1,2,1)),rewrite([22(10)])].
% 4.60/4.85 90 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(44(a,1),34(a,1,1)),rewrite([44(9)])].
% 4.60/4.85 92 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(44(a,1),36(a,1,2,1,1))].
% 4.60/4.85 100 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(45(a,1),25(a,1,1)),rewrite([22(7),29(7,R),22(6)]),flip(a)].
% 4.60/4.85 101 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(45(a,1),25(a,1,2)),rewrite([29(4,R),22(3),25(3),100(7)]),flip(a)].
% 4.60/4.85 109 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(45(a,1),45(a,2,2)),rewrite([101(4),45(4),29(6,R),22(5)])].
% 4.60/4.85 110 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(100),rewrite([109(8),25(7)])].
% 4.60/4.85 117 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(46(a,1),25(a,1,1)),rewrite([22(7)]),flip(a)].
% 4.60/4.85 125 composition(converse(one),A) = A. [para(18(a,1),47(a,1,1)),rewrite([19(2)]),flip(a)].
% 4.60/4.85 134 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(36(a,1),48(a,1,2)),rewrite([22(4),48(4),22(3),22(8)]),flip(a)].
% 4.60/4.85 135 join(top,complement(complement(A))) = top. [para(38(a,1),48(a,1,2)),rewrite([20(22),22(8),134(8)]),flip(a)].
% 4.60/4.85 136 converse(one) = one. [para(125(a,1),18(a,1)),flip(a)].
% 4.60/4.85 138 composition(join(A,one),B) = join(B,composition(A,B)). [para(125(a,1),32(a,1,1)),rewrite([136(4),22(4)]),flip(a)].
% 4.60/4.85 140 join(complement(A),complement(composition(one,A))) = complement(A). [para(125(a,1),34(a,1,2))].
% 4.60/4.85 154 composition(one,A) = A. [para(125(a,1),49(a,2)),rewrite([136(2),49(4)])].
% 4.60/4.85 160 join(complement(A),complement(A)) = complement(A). [back_rewrite(140),rewrite([154(3)])].
% 4.60/4.85 161 join(zero,complement(complement(A))) = A. [back_rewrite(60),rewrite([160(4)])].
% 4.60/4.85 162 converse(join(A,one)) = join(one,converse(A)). [para(136(a,1),25(a,1,1)),rewrite([22(5)]),flip(a)].
% 4.60/4.85 163 join(zero,complement(A)) = complement(A). [para(135(a,1),36(a,1,1,1)),rewrite([44(2),44(3),161(5)])].
% 4.60/4.85 165 join(top,complement(A)) = join(top,top). [para(135(a,1),48(a,1,2)),rewrite([22(3)])].
% 4.60/4.85 166 complement(complement(A)) = A. [back_rewrite(161),rewrite([163(4)])].
% 4.60/4.85 174 join(A,complement(join(top,top))) = A. [back_rewrite(92),rewrite([165(3),163(7),166(6),22(5)])].
% 4.60/4.85 176 complement(join(A,A)) = complement(A). [back_rewrite(61),rewrite([166(3),163(4)])].
% 4.60/4.85 178 join(A,top) = top. [back_rewrite(135),rewrite([166(3),22(2)])].
% 4.60/4.85 183 join(A,zero) = A. [back_rewrite(174),rewrite([178(3),44(2)])].
% 4.60/4.85 184 join(top,complement(A)) = top. [back_rewrite(165),rewrite([178(6)])].
% 4.60/4.85 193 join(A,composition(converse(B),complement(composition(B,complement(A))))) = A. [para(166(a,1),34(a,1,1)),rewrite([166(8)])].
% 4.60/4.85 194 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(166(a,1),36(a,1,1,1,2)),rewrite([166(5),22(4)])].
% 4.60/4.85 202 complement(zero) = top. [para(44(a,1),166(a,1,1))].
% 4.60/4.85 212 converse(join(A,composition(A,B))) = composition(join(one,converse(B)),converse(A)). [para(154(a,1),51(a,1,2)),rewrite([22(4),25(4)])].
% 4.60/4.85 217 join(A,A) = A. [para(176(a,1),36(a,1,1,1,2)),rewrite([176(6),36(8)]),flip(a)].
% 4.60/4.85 224 join(A,join(A,B)) = join(A,B). [para(217(a,1),29(a,1)),rewrite([22(3),29(4,R),22(3),29(3,R),217(2)]),flip(a)].
% 4.60/4.85 230 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(162(a,1),27(a,1,1))].
% 4.60/4.85 241 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(212),rewrite([230(8)]),flip(a)].
% 4.60/4.85 242 join(A,complement(join(B,complement(A)))) = A. [para(36(a,1),224(a,1,2)),rewrite([22(4),36(12)])].
% 4.60/4.85 259 join(complement(one),composition(A,complement(converse(A)))) = complement(one). [para(19(a,1),55(a,1,2,1))].
% 4.60/4.85 265 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(166(a,1),55(a,1,2,2))].
% 4.60/4.85 272 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(90(a,1),25(a,2,1)),rewrite([47(8)])].
% 4.60/4.85 278 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(162(a,1),90(a,1,2,1))].
% 4.60/4.85 314 join(complement(one),converse(complement(one))) = complement(one). [para(18(a,1),265(a,1,2))].
% 4.60/4.85 318 converse(complement(one)) = complement(one). [para(314(a,1),25(a,2,1)),rewrite([19(7),22(6),314(6)]),flip(a)].
% 4.60/4.85 327 converse(top) = top. [para(318(a,1),162(a,2,2)),rewrite([22(4),20(4),20(6)])].
% 4.60/4.85 338 join(top,converse(A)) = top. [para(327(a,1),25(a,1,1)),rewrite([22(5),178(5),327(5)])].
% 4.60/4.85 345 join(top,composition(A,converse(B))) = top. [para(46(a,1),338(a,1,2))].
% 4.60/4.85 347 join(top,composition(A,B)) = top. [para(19(a,1),345(a,1,2,2))].
% 4.60/4.85 348 composition(join(A,one),top) = top. [para(327(a,1),345(a,1,2,2)),rewrite([138(4,R)])].
% 4.60/4.85 349 composition(join(one,converse(A)),zero) = zero. [back_rewrite(278),rewrite([348(8),44(6),138(7,R),22(5),224(5)])].
% 4.60/4.85 376 composition(top,zero) = zero. [para(318(a,1),349(a,1,1,2)),rewrite([20(4)])].
% 4.60/4.85 381 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(376(a,1),42(a,1,1,1,2,1)),rewrite([202(3),22(3),184(3),44(2),44(3),163(7),166(6),202(6),327(7),184(9),44(6),30(6),44(9),163(13),166(12),202(12),327(13),184(15),44(12),30(12)])].
% 4.60/4.85 385 join(zero,composition(A,composition(B,zero))) = zero. [para(376(a,1),53(a,1,2)),rewrite([22(5),347(8),376(8)])].
% 4.60/4.85 388 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(381),rewrite([385(7)]),flip(a)].
% 4.60/4.85 447 join(complement(A),complement(join(B,A))) = complement(A). [para(242(a,1),64(a,2)),rewrite([166(2),166(4),166(8),64(13)])].
% 4.60/4.85 467 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(388(a,1),30(a,1,1)),rewrite([30(7)]),flip(a)].
% 4.60/4.85 468 composition(A,zero) = zero. [para(388(a,1),30(a,1)),rewrite([388(6)]),flip(a)].
% 4.60/4.85 469 composition(converse(zero),A) = converse(zero). [para(388(a,1),47(a,1,1)),rewrite([468(6)]),flip(a)].
% 4.60/4.85 474 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(467),rewrite([469(5)]),flip(a)].
% 4.60/4.85 476 composition(zero,A) = c_0. [new_symbol(474)].
% 4.60/4.85 477 composition(A,converse(zero)) = c_0. [back_rewrite(474),rewrite([476(2)]),flip(a)].
% 4.60/4.85 492 c_0 = zero. [para(476(a,1),18(a,1))].
% 4.60/4.85 493 converse(zero) = zero. [para(476(a,1),27(a,2,1)),rewrite([477(4),492(1),492(2)]),flip(a)].
% 4.60/4.85 494 join(zero,composition(A,B)) = composition(A,B). [para(476(a,1),32(a,1,1)),rewrite([492(1),22(5),183(5)])].
% 4.60/4.85 496 composition(zero,A) = zero. [back_rewrite(476),rewrite([492(3)])].
% 4.60/4.85 497 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(272),rewrite([493(2),494(7),493(7)])].
% 4.60/4.85 616 composition(converse(complement(composition(A,top))),composition(A,B)) = zero. [para(497(a,1),30(a,1,1)),rewrite([496(2)]),flip(a)].
% 4.60/4.85 769 join(one,complement(composition(A,complement(converse(A))))) = complement(composition(A,complement(converse(A)))). [para(259(a,1),447(a,1,2,1)),rewrite([166(7),22(6)])].
% 4.60/4.85 2486 join(A,join(complement(A),converse(B))) = top. [para(20(a,1),109(a,1,1)),rewrite([338(3)]),flip(a)].
% 4.60/4.85 2570 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(46(a,1),2486(a,1,2,2))].
% 4.60/4.85 3166 join(A,join(complement(A),composition(B,C))) = top. [para(19(a,1),2570(a,1,2,2,2))].
% 4.60/4.85 3169 join(A,composition(join(B,one),complement(A))) = top. [para(138(a,2),3166(a,1,2))].
% 4.60/4.85 3223 join(A,join(B,composition(join(C,one),complement(A)))) = top. [para(3169(a,1),29(a,2,2)),rewrite([22(5),178(8)])].
% 4.60/4.85 7342 join(complement(A),composition(join(one,converse(B)),A)) = top. [para(56(a,1),3223(a,1,2)),rewrite([162(3),22(6)])].
% 4.60/4.85 7403 join(converse(complement(converse(A))),composition(A,join(B,one))) = top. [para(7342(a,1),117(a,1,1)),rewrite([327(2),45(5),136(3),22(8)]),flip(a)].
% 4.60/4.85 9348 join(A,converse(complement(converse(A)))) = top. [para(217(a,1),7403(a,1,2,2)),rewrite([18(5),22(4)])].
% 4.60/4.85 9387 join(complement(converse(A)),converse(join(B,A))) = top. [para(9348(a,1),110(a,1,1,2)),rewrite([178(2),327(2)]),flip(a)].
% 4.60/4.85 9393 complement(join(complement(A),converse(complement(converse(A))))) = complement(converse(complement(converse(A)))). [para(9348(a,1),194(a,1,1,1)),rewrite([44(2),22(6),163(8)])].
% 4.60/4.85 9428 join(complement(one),complement(composition(converse(complement(A)),A))) = top. [para(55(a,1),9387(a,1,2,1)),rewrite([47(4),318(7),22(7)])].
% 4.60/4.85 9431 join(complement(one),complement(converse(composition(A,complement(converse(A)))))) = top. [para(259(a,1),9387(a,1,2,1)),rewrite([318(8),22(8)])].
% 4.60/4.85 9539 complement(join(complement(A),complement(converse(complement(converse(A)))))) = zero. [para(9428(a,1),40(a,1,2,1,2,1,1,1)),rewrite([154(6),22(6),44(13),496(13),202(13),22(13),184(13),44(9),22(9),163(9),27(18),9431(19),44(13),496(13),202(13),22(13),184(13),44(9)])].
% 4.60/4.85 9614 complement(join(A,complement(converse(complement(converse(A)))))) = converse(complement(converse(A))). [para(9539(a,1),36(a,1,1)),rewrite([166(3),163(8)])].
% 4.60/4.85 9627 complement(converse(complement(converse(A)))) = A. [para(9539(a,1),194(a,1,2)),rewrite([22(5),9393(6),22(6),163(6),166(6)])].
% 4.60/4.85 9630 converse(complement(converse(A))) = complement(A). [back_rewrite(9614),rewrite([9627(4),217(1)]),flip(a)].
% 4.60/4.85 9660 complement(converse(A)) = converse(complement(A)). [para(9630(a,1),19(a,1,1)),flip(a)].
% 4.60/4.85 9664 converse(complement(composition(A,converse(B)))) = complement(composition(B,converse(A))). [para(46(a,1),9630(a,1,1,1))].
% 4.60/4.85 9665 converse(complement(composition(converse(A),B))) = complement(composition(converse(B),A)). [para(47(a,1),9630(a,1,1,1))].
% 4.60/4.85 10546 join(one,complement(composition(A,converse(complement(A))))) = complement(composition(A,converse(complement(A)))). [back_rewrite(769),rewrite([9660(3),9660(8)])].
% 4.60/4.85 11781 composition(complement(composition(complement(A),converse(A))),A) = A. [para(193(a,1),241(a,2,1)),rewrite([9660(3),22(7),10546(7),47(7),9664(5),19(7)])].
% 4.60/4.85 11942 composition(A,complement(composition(converse(A),complement(A)))) = A. [para(11781(a,1),46(a,1,1)),rewrite([19(2),9660(2),19(4),9665(5)]),flip(a)].
% 4.60/4.85 12025 composition(complement(A),complement(composition(converse(complement(A)),A))) = complement(A). [para(166(a,1),11942(a,1,2,1,2))].
% 4.60/4.85 15896 composition(complement(composition(A,top)),top) = complement(composition(A,top)). [para(616(a,1),12025(a,1,2,1)),rewrite([202(5)])].
% 4.60/4.85 15897 $F # answer(goals). [resolve(15896,a,43,a)].
% 4.60/4.85
% 4.60/4.85 % SZS output end Refutation
% 4.60/4.85 ============================== end of proof ==========================
% 4.60/4.85
% 4.60/4.85 ============================== STATISTICS ============================
% 4.60/4.85
% 4.60/4.85 Given=614. Generated=107885. Kept=15870. proofs=1.
% 4.60/4.85 Usable=446. Sos=9510. Demods=9566. Limbo=3, Disabled=5927. Hints=0.
% 4.60/4.85 Megabytes=26.36.
% 4.60/4.85 User_CPU=3.78, System_CPU=0.06, Wall_clock=3.
% 4.60/4.85
% 4.60/4.85 ============================== end of statistics =====================
% 4.60/4.85
% 4.60/4.85 ============================== end of search =========================
% 4.60/4.85
% 4.60/4.85 THEOREM PROVED
% 4.60/4.85 % SZS status Theorem
% 4.60/4.85
% 4.60/4.85 Exiting with 1 proof.
% 4.60/4.85
% 4.60/4.85 Process 19131 exit (max_proofs) Fri Jul 8 08:03:29 2022
% 4.60/4.85 Prover9 interrupted
%------------------------------------------------------------------------------