TSTP Solution File: REL026+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL026+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 19:53:58 EDT 2022
% Result : Theorem 27.44s 27.72s
% Output : Refutation 27.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : REL026+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.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 07:15:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.97 ============================== Prover9 ===============================
% 0.41/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.97 Process 10641 was started by sandbox on n029.cluster.edu,
% 0.41/0.97 Fri Jul 8 07:15:45 2022
% 0.41/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10488_n029.cluster.edu".
% 0.41/0.97 ============================== end of head ===========================
% 0.41/0.97
% 0.41/0.97 ============================== INPUT =================================
% 0.41/0.97
% 0.41/0.97 % Reading from file /tmp/Prover9_10488_n029.cluster.edu
% 0.41/0.97
% 0.41/0.97 set(prolog_style_variables).
% 0.41/0.97 set(auto2).
% 0.41/0.97 % set(auto2) -> set(auto).
% 0.41/0.97 % set(auto) -> set(auto_inference).
% 0.41/0.97 % set(auto) -> set(auto_setup).
% 0.41/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.97 % set(auto) -> set(auto_limits).
% 0.41/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.97 % set(auto) -> set(auto_denials).
% 0.41/0.97 % set(auto) -> set(auto_process).
% 0.41/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.97 % set(auto2) -> assign(stats, some).
% 0.41/0.97 % set(auto2) -> clear(echo_input).
% 0.41/0.97 % set(auto2) -> set(quiet).
% 0.41/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.97 % set(auto2) -> clear(print_given).
% 0.41/0.97 assign(lrs_ticks,-1).
% 0.41/0.97 assign(sos_limit,10000).
% 0.41/0.97 assign(order,kbo).
% 0.41/0.97 set(lex_order_vars).
% 0.41/0.97 clear(print_given).
% 0.41/0.97
% 0.41/0.97 % formulas(sos). % not echoed (17 formulas)
% 0.41/0.97
% 0.41/0.97 ============================== end of input ==========================
% 0.41/0.97
% 0.41/0.97 % From the command line: assign(max_seconds, 300).
% 0.41/0.97
% 0.41/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.97
% 0.41/0.97 % Formulas that are not ordinary clauses:
% 0.41/0.97 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 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].
% 0.41/0.97 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].
% 0.41/0.97 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].
% 0.41/0.97 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].
% 0.41/0.97 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 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].
% 0.41/0.97 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 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].
% 0.41/0.97 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 6.69/7.03 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].
% 6.69/7.03 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].
% 6.69/7.03 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].
% 6.69/7.03 17 -(all X0 all X1 (join(X0,one) = one -> meet(composition(X0,top),X1) = composition(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.69/7.03
% 6.69/7.03 ============================== end of process non-clausal formulas ===
% 6.69/7.03
% 6.69/7.03 ============================== PROCESS INITIAL CLAUSES ===============
% 6.69/7.03
% 6.69/7.03 ============================== PREDICATE ELIMINATION =================
% 6.69/7.03
% 6.69/7.03 ============================== end predicate elimination =============
% 6.69/7.03
% 6.69/7.03 Auto_denials:
% 6.69/7.03 % copying label goals to answer in negative clause
% 6.69/7.03
% 6.69/7.03 Term ordering decisions:
% 6.69/7.03 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 6.69/7.03
% 6.69/7.03 ============================== end of process initial clauses ========
% 6.69/7.03
% 6.69/7.03 ============================== CLAUSES FOR SEARCH ====================
% 6.69/7.03
% 6.69/7.03 ============================== end of clauses for search =============
% 6.69/7.03
% 6.69/7.03 ============================== SEARCH ================================
% 6.69/7.03
% 6.69/7.03 % Starting search at 0.01 seconds.
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=128.000, iters=3388
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=104.000, iters=3375
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=76.000, iters=3394
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=74.000, iters=3375
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=72.000, iters=3337
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=71.000, iters=3382
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=69.000, iters=3345
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=67.000, iters=3383
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=66.000, iters=3405
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=65.000, iters=3358
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=64.000, iters=3376
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=62.000, iters=3353
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=61.000, iters=3335
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=60.000, iters=3355
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% 6.69/7.03 Low Water (keep): wt=59.000, iters=3352
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% 6.69/7.03 Low Water (keep): wt=58.000, iters=3356
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=57.000, iters=3400
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=56.000, iters=3339
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=55.000, iters=3415
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=54.000, iters=3335
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=53.000, iters=3333
% 6.69/7.03
% 6.69/7.03 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 2.27 sec).
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=51.000, iters=3361
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=49.000, iters=3370
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=48.000, iters=3421
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=46.000, iters=3348
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=45.000, iters=3362
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% 6.69/7.03 Low Water (keep): wt=44.000, iters=3365
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% 6.69/7.03 Low Water (keep): wt=43.000, iters=3371
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% 6.69/7.03 Low Water (keep): wt=41.000, iters=3335
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% 6.69/7.03 Low Water (keep): wt=40.000, iters=3340
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% 6.69/7.03 Low Water (keep): wt=39.000, iters=3366
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% 6.69/7.03 Low Water (keep): wt=38.000, iters=3346
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% 6.69/7.03 Low Water (keep): wt=37.000, iters=3420
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% 6.69/7.03 Low Water (keep): wt=35.000, iters=3355
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% 6.69/7.03 Low Water (keep): wt=33.000, iters=3357
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=30.000, iters=3346
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=29.000, iters=3387
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=28.000, iters=3373
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=27.000, iters=3384
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=26.000, iters=3376
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% 6.69/7.03 Low Water (keep): wt=25.000, iters=3333
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=24.000, iters=3384
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=23.000, iters=3368
% 6.69/7.03
% 6.69/7.03 Low Water (displace): id=5255, wt=166.000
% 6.69/7.03
% 6.69/7.03 Low Water (displace): id=4126, wt=157.000
% 6.69/7.03
% 6.69/7.03 Low Water (displace): id=16746, wt=20.000
% 6.69/7.03
% 6.69/7.03 Low Water (displace): id=16747, wt=15.000
% 6.69/7.03
% 6.69/7.03 Low Water (displace): id=16778, wt=13.000
% 6.69/7.03
% 6.69/7.03 Low Water (displace): id=16848, wt=12.000
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=22.000, iters=3363
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=21.000, iters=3333
% 6.69/7.03
% 6.69/7.03 Low Water (keep): wt=20.000, iters=3342
% 27.44/27.72
% 27.44/27.72 Low Water (keep): wt=19.000, iters=3333
% 27.44/27.72
% 27.44/27.72 Low Water (keep): wt=18.000, iters=3337
% 27.44/27.72
% 27.44/27.72 Low Water (keep): wt=17.000, iters=3355
% 27.44/27.72
% 27.44/27.72 Low Water (keep): wt=16.000, iters=3355
% 27.44/27.72
% 27.44/27.72 ============================== PROOF =================================
% 27.44/27.72 % SZS status Theorem
% 27.44/27.72 % SZS output start Refutation
% 27.44/27.72
% 27.44/27.72 % Proof 1 at 26.20 (+ 0.56) seconds: goals.
% 27.44/27.72 % Length of proof is 95.
% 27.44/27.72 % Level of proof is 22.
% 27.44/27.72 % Maximum clause weight is 48.000.
% 27.44/27.72 % Given clauses 2077.
% 27.44/27.72
% 27.44/27.72 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 27.44/27.72 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].
% 27.44/27.72 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].
% 27.44/27.72 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].
% 27.44/27.72 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].
% 27.44/27.72 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 27.44/27.72 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].
% 27.44/27.72 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 27.44/27.72 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 27.44/27.72 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 27.44/27.72 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].
% 27.44/27.72 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 27.44/27.72 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 27.44/27.72 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].
% 27.44/27.72 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].
% 27.44/27.72 17 -(all X0 all X1 (join(X0,one) = one -> meet(composition(X0,top),X1) = composition(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 27.44/27.72 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 27.44/27.72 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 27.44/27.72 20 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(17)].
% 27.44/27.72 21 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 27.44/27.72 22 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 27.44/27.72 23 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 27.44/27.72 24 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 27.44/27.72 25 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 27.44/27.72 26 join(converse(A),converse(B)) = converse(join(A,B)). [copy(25),flip(a)].
% 27.44/27.72 27 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 27.44/27.72 28 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(27),flip(a)].
% 27.44/27.72 29 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 27.44/27.72 30 join(A,join(B,C)) = join(C,join(A,B)). [copy(29),rewrite([23(2)]),flip(a)].
% 27.44/27.72 31 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 27.44/27.72 32 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 27.44/27.72 33 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(32),flip(a)].
% 27.44/27.72 34 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 27.44/27.72 35 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(34),rewrite([23(7)]),flip(a)].
% 27.44/27.72 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)].
% 27.44/27.72 37 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(36),rewrite([23(6),23(8)]),rewrite([23(6)])].
% 27.44/27.72 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)].
% 27.44/27.72 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)].
% 27.44/27.72 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)].
% 27.44/27.72 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)].
% 27.44/27.72 44 composition(c1,c2) != meet(composition(c1,top),c2) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 27.44/27.72 45 complement(join(complement(c2),complement(composition(c1,top)))) != composition(c1,c2) # answer(goals). [copy(44),rewrite([24(8),23(10)]),flip(a)].
% 27.44/27.72 46 join(one,c1) = one. [back_rewrite(20),rewrite([23(3)])].
% 27.44/27.72 47 complement(top) = zero. [back_rewrite(22),rewrite([24(2),21(4)])].
% 27.44/27.72 48 converse(join(A,converse(B))) = join(B,converse(A)). [para(19(a,1),26(a,1,1)),rewrite([23(4)]),flip(a)].
% 27.44/27.72 49 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),28(a,1,1)),flip(a)].
% 27.44/27.72 50 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),28(a,1,2)),flip(a)].
% 27.44/27.72 51 join(A,join(B,complement(A))) = join(B,top). [para(21(a,1),30(a,2,2)),rewrite([23(2)])].
% 27.44/27.72 52 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),31(a,1,1)),flip(a)].
% 27.44/27.72 54 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(28(a,1),33(a,1,1)),rewrite([23(7)])].
% 27.44/27.72 63 join(zero,complement(join(complement(A),complement(A)))) = A. [para(21(a,1),37(a,1,1,1)),rewrite([47(2)])].
% 27.44/27.72 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)])].
% 27.44/27.72 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)])].
% 27.44/27.72 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))].
% 27.44/27.72 103 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)].
% 27.44/27.72 104 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)].
% 27.44/27.72 112 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)])].
% 27.44/27.72 120 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)].
% 27.44/27.72 128 composition(converse(one),A) = A. [para(18(a,1),50(a,1,1)),rewrite([19(2)]),flip(a)].
% 27.44/27.72 129 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(50(a,1),26(a,1,1)),rewrite([23(7)]),flip(a)].
% 27.44/27.72 137 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)].
% 27.44/27.72 138 join(top,complement(complement(A))) = top. [para(39(a,1),51(a,1,2)),rewrite([21(22),23(8),137(8)]),flip(a)].
% 27.44/27.72 139 converse(one) = one. [para(128(a,1),18(a,1)),flip(a)].
% 27.44/27.72 143 join(complement(A),complement(composition(one,A))) = complement(A). [para(128(a,1),35(a,1,2))].
% 27.44/27.72 157 composition(one,A) = A. [para(128(a,1),52(a,2)),rewrite([139(2),52(4)])].
% 27.44/27.72 158 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)])].
% 27.44/27.72 163 join(complement(A),complement(A)) = complement(A). [back_rewrite(143),rewrite([157(3)])].
% 27.44/27.72 164 join(zero,complement(complement(A))) = A. [back_rewrite(63),rewrite([163(4)])].
% 27.44/27.72 166 join(zero,complement(A)) = complement(A). [para(138(a,1),37(a,1,1,1)),rewrite([47(2),47(3),164(5)])].
% 27.44/27.72 169 complement(complement(A)) = A. [back_rewrite(164),rewrite([166(4)])].
% 27.44/27.72 179 complement(join(A,A)) = complement(A). [back_rewrite(64),rewrite([169(3),166(4)])].
% 27.44/27.72 197 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(169(a,1),37(a,1,1,1,2)),rewrite([169(5),23(4)])].
% 27.44/27.72 220 join(A,A) = A. [para(179(a,1),37(a,1,1,1,2)),rewrite([179(6),37(8)]),flip(a)].
% 27.44/27.72 227 join(A,join(A,B)) = join(A,B). [para(220(a,1),30(a,1)),rewrite([23(3),30(4,R),23(3),30(3,R),220(2)]),flip(a)].
% 27.44/27.72 245 join(A,complement(join(B,complement(A)))) = A. [para(37(a,1),227(a,1,2)),rewrite([23(4),37(12)])].
% 27.44/27.72 247 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(245(a,1),30(a,2,2)),rewrite([23(4),23(6)])].
% 27.44/27.72 450 join(complement(A),complement(join(B,A))) = complement(A). [para(245(a,1),67(a,2)),rewrite([169(2),169(4),169(8),67(13)])].
% 27.44/27.72 770 join(complement(one),complement(c1)) = complement(c1). [para(46(a,1),450(a,1,2,1)),rewrite([23(5)])].
% 27.44/27.72 2364 join(one,join(c1,converse(A))) = join(one,converse(A)). [para(46(a,1),112(a,1,1)),flip(a)].
% 27.44/27.72 3333 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(54(a,1),129(a,1,1)),rewrite([26(3),28(4),19(4),19(4),19(6)]),flip(a)].
% 27.44/27.72 3736 join(A,join(one,converse(c1))) = join(A,one). [para(2364(a,1),26(a,2,1)),rewrite([139(2),48(5),30(5,R),23(4),48(9),139(7)])].
% 27.44/27.72 3744 join(one,converse(c1)) = one. [para(220(a,1),3736(a,2)),rewrite([227(6)])].
% 27.44/27.72 3745 join(A,composition(converse(c1),A)) = A. [para(3744(a,1),33(a,2,1)),rewrite([157(2),157(6)])].
% 27.44/27.72 3747 join(complement(one),complement(converse(c1))) = complement(converse(c1)). [para(3744(a,1),450(a,1,2,1)),rewrite([23(6)])].
% 27.44/27.72 3751 join(A,join(B,composition(converse(c1),A))) = join(A,B). [para(3745(a,1),30(a,2,2)),rewrite([23(4),23(6)])].
% 27.44/27.72 3752 join(complement(A),complement(composition(converse(c1),A))) = complement(composition(converse(c1),A)). [para(3745(a,1),450(a,1,2,1)),rewrite([23(6)])].
% 27.44/27.72 3756 join(A,composition(A,c1)) = A. [para(3745(a,1),120(a,1,1)),rewrite([19(2),19(3),19(4),23(3)]),flip(a)].
% 27.44/27.72 4240 composition(converse(c1),c1) = converse(c1). [para(3747(a,1),158(a,1,1,1)),rewrite([169(4),3747(8),169(6),19(9),18(9),770(9),169(7),3756(7),3747(8),169(6),19(9),18(9),770(9),169(7)]),flip(a)].
% 27.44/27.72 4273 converse(c1) = c1. [para(4240(a,1),28(a,2,1)),rewrite([19(5),4240(4),19(5)])].
% 27.44/27.72 4340 join(complement(A),complement(composition(c1,A))) = complement(composition(c1,A)). [back_rewrite(3752),rewrite([4273(3),4273(7)])].
% 27.44/27.72 4341 join(A,join(B,composition(c1,A))) = join(A,B). [back_rewrite(3751),rewrite([4273(2)])].
% 27.44/27.72 9694 join(A,complement(join(A,B))) = join(A,complement(B)). [para(197(a,1),247(a,1,2)),flip(a)].
% 27.44/27.72 10651 join(A,complement(join(B,composition(c1,A)))) = join(A,complement(B)). [para(4341(a,1),9694(a,1,2,1)),rewrite([9694(3)]),flip(a)].
% 27.44/27.72 41479 join(complement(A),complement(composition(c1,top))) = complement(composition(c1,A)). [para(4340(a,1),10651(a,2)),rewrite([3333(7),21(4)])].
% 27.44/27.72 41485 $F # answer(goals). [back_rewrite(45),rewrite([41479(7),169(5)]),xx(a)].
% 27.44/27.72
% 27.44/27.72 % SZS output end Refutation
% 27.44/27.72 ============================== end of proof ==========================
% 27.44/27.72
% 27.44/27.72 ============================== STATISTICS ============================
% 27.44/27.72
% 27.44/27.72 Given=2077. Generated=1005644. Kept=41457. proofs=1.
% 27.44/27.72 Usable=1614. Sos=9960. Demods=11294. Limbo=6, Disabled=29895. Hints=0.
% 27.44/27.72 Megabytes=39.03.
% 27.44/27.72 User_CPU=26.20, System_CPU=0.56, Wall_clock=27.
% 27.44/27.72
% 27.44/27.72 ============================== end of statistics =====================
% 27.44/27.72
% 27.44/27.72 ============================== end of search =========================
% 27.44/27.72
% 27.44/27.72 THEOREM PROVED
% 27.44/27.72 % SZS status Theorem
% 27.44/27.72
% 27.44/27.72 Exiting with 1 proof.
% 27.44/27.72
% 27.44/27.72 Process 10641 exit (max_proofs) Fri Jul 8 07:16:12 2022
% 27.44/27.73 Prover9 interrupted
%------------------------------------------------------------------------------