TSTP Solution File: REL025+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL025+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:53:56 EDT 2022
% Result : Theorem 3.35s 3.65s
% Output : Refutation 3.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : REL025+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n016.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 15:22:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/0.98 ============================== Prover9 ===============================
% 0.42/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.98 Process 15337 was started by sandbox on n016.cluster.edu,
% 0.42/0.98 Fri Jul 8 15:22:39 2022
% 0.42/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15183_n016.cluster.edu".
% 0.42/0.98 ============================== end of head ===========================
% 0.42/0.98
% 0.42/0.98 ============================== INPUT =================================
% 0.42/0.98
% 0.42/0.98 % Reading from file /tmp/Prover9_15183_n016.cluster.edu
% 0.42/0.98
% 0.42/0.98 set(prolog_style_variables).
% 0.42/0.98 set(auto2).
% 0.42/0.98 % set(auto2) -> set(auto).
% 0.42/0.98 % set(auto) -> set(auto_inference).
% 0.42/0.98 % set(auto) -> set(auto_setup).
% 0.42/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.98 % set(auto) -> set(auto_limits).
% 0.42/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.98 % set(auto) -> set(auto_denials).
% 0.42/0.98 % set(auto) -> set(auto_process).
% 0.42/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.98 % set(auto2) -> assign(stats, some).
% 0.42/0.98 % set(auto2) -> clear(echo_input).
% 0.42/0.98 % set(auto2) -> set(quiet).
% 0.42/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.98 % set(auto2) -> clear(print_given).
% 0.42/0.98 assign(lrs_ticks,-1).
% 0.42/0.98 assign(sos_limit,10000).
% 0.42/0.98 assign(order,kbo).
% 0.42/0.98 set(lex_order_vars).
% 0.42/0.98 clear(print_given).
% 0.42/0.98
% 0.42/0.98 % formulas(sos). % not echoed (14 formulas)
% 0.42/0.98
% 0.42/0.98 ============================== end of input ==========================
% 0.42/0.98
% 0.42/0.98 % From the command line: assign(max_seconds, 300).
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.98
% 0.42/0.98 % Formulas that are not ordinary clauses:
% 0.42/0.98 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 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].
% 0.42/0.98 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].
% 0.42/0.98 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].
% 0.42/0.98 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].
% 0.42/0.98 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 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].
% 0.42/0.98 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 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].
% 0.42/0.98 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 3.35/3.65 14 -(all X0 (join(X0,one) = one -> converse(X0) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.35/3.65
% 3.35/3.65 ============================== end of process non-clausal formulas ===
% 3.35/3.65
% 3.35/3.65 ============================== PROCESS INITIAL CLAUSES ===============
% 3.35/3.65
% 3.35/3.65 ============================== PREDICATE ELIMINATION =================
% 3.35/3.65
% 3.35/3.65 ============================== end predicate elimination =============
% 3.35/3.65
% 3.35/3.65 Auto_denials:
% 3.35/3.65 % copying label goals to answer in negative clause
% 3.35/3.65
% 3.35/3.65 Term ordering decisions:
% 3.35/3.65 Function symbol KB weights: one=1. top=1. zero=1. c1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 3.35/3.65
% 3.35/3.65 ============================== end of process initial clauses ========
% 3.35/3.65
% 3.35/3.65 ============================== CLAUSES FOR SEARCH ====================
% 3.35/3.65
% 3.35/3.65 ============================== end of clauses for search =============
% 3.35/3.65
% 3.35/3.65 ============================== SEARCH ================================
% 3.35/3.65
% 3.35/3.65 % Starting search at 0.01 seconds.
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=43.000, iters=3352
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=35.000, iters=3360
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=33.000, iters=3376
% 3.35/3.65
% 3.35/3.65 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 1.05 sec).
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=32.000, iters=3375
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=31.000, iters=3411
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=30.000, iters=3355
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=29.000, iters=3336
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=27.000, iters=3334
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=26.000, iters=3377
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=25.000, iters=3333
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=24.000, iters=3345
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=23.000, iters=3339
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=22.000, iters=3370
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=21.000, iters=3353
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=20.000, iters=3353
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=19.000, iters=3345
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=4398, wt=46.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=7094, wt=45.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=7269, wt=44.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=7435, wt=43.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=7260, wt=42.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=7242, wt=41.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=5065, wt=40.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=6762, wt=39.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=7270, wt=38.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=13467, wt=16.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=13473, wt=15.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=13504, wt=14.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=13680, wt=13.000
% 3.35/3.65
% 3.35/3.65 ============================== PROOF =================================
% 3.35/3.65 % SZS status Theorem
% 3.35/3.65 % SZS output start Refutation
% 3.35/3.65
% 3.35/3.65 % Proof 1 at 2.61 (+ 0.07) seconds: goals.
% 3.35/3.65 % Length of proof is 150.
% 3.35/3.65 % Level of proof is 35.
% 3.35/3.65 % Maximum clause weight is 21.000.
% 3.35/3.65 % Given clauses 889.
% 3.35/3.65
% 3.35/3.65 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 3.35/3.65 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].
% 3.35/3.65 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].
% 3.35/3.65 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].
% 3.35/3.65 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].
% 3.35/3.65 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 3.35/3.65 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].
% 3.35/3.65 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 3.35/3.65 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 3.35/3.65 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 3.35/3.65 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].
% 3.35/3.65 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 3.35/3.65 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 3.35/3.65 14 -(all X0 (join(X0,one) = one -> converse(X0) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.35/3.65 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 3.35/3.65 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 3.35/3.65 17 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(14)].
% 3.35/3.65 18 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 3.35/3.65 19 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 3.35/3.65 20 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 3.35/3.65 21 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 3.35/3.65 22 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 3.35/3.65 23 join(converse(A),converse(B)) = converse(join(A,B)). [copy(22),flip(a)].
% 3.35/3.65 24 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 3.35/3.65 25 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(24),flip(a)].
% 3.35/3.65 26 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 3.35/3.65 27 join(A,join(B,C)) = join(C,join(A,B)). [copy(26),rewrite([20(2)]),flip(a)].
% 3.35/3.65 28 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 3.35/3.65 29 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 3.35/3.65 30 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(29),flip(a)].
% 3.35/3.65 31 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 3.35/3.65 32 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(31),rewrite([20(7)]),flip(a)].
% 3.35/3.65 33 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 3.35/3.65 34 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(33),rewrite([20(6),20(8)]),rewrite([20(6)])].
% 3.35/3.65 35 converse(c1) != c1 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 3.35/3.65 36 join(one,c1) = one. [back_rewrite(17),rewrite([20(3)])].
% 3.35/3.65 37 complement(top) = zero. [back_rewrite(19),rewrite([21(2),18(4)])].
% 3.35/3.65 38 converse(join(A,converse(B))) = join(B,converse(A)). [para(16(a,1),23(a,1,1)),rewrite([20(4)]),flip(a)].
% 3.35/3.65 39 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(16(a,1),25(a,1,1)),flip(a)].
% 3.35/3.65 40 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),25(a,1,2)),flip(a)].
% 3.35/3.65 41 join(A,join(B,complement(A))) = join(B,top). [para(18(a,1),27(a,2,2)),rewrite([20(2)])].
% 3.35/3.65 42 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),28(a,1,1)),flip(a)].
% 3.35/3.65 44 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(25(a,1),30(a,1,1)),rewrite([20(7)])].
% 3.35/3.65 46 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(28(a,1),30(a,1,1)),rewrite([20(6)])].
% 3.35/3.65 48 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(15(a,1),32(a,1,2,2,1))].
% 3.35/3.65 51 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(25(a,1),32(a,1,2,2,1)),rewrite([16(4)])].
% 3.35/3.65 53 join(zero,complement(join(complement(A),complement(A)))) = A. [para(18(a,1),34(a,1,1,1)),rewrite([37(2)])].
% 3.35/3.65 57 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(34(a,1),34(a,1,2,1)),rewrite([20(10)])].
% 3.35/3.65 59 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(37(a,1),32(a,1,1)),rewrite([37(9)])].
% 3.35/3.65 61 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(37(a,1),34(a,1,2,1,1))].
% 3.35/3.65 62 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(38(a,1),23(a,1,1)),rewrite([20(7),27(7,R),20(6)]),flip(a)].
% 3.35/3.65 63 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(38(a,1),23(a,1,2)),rewrite([27(4,R),20(3),23(3),62(7)]),flip(a)].
% 3.35/3.65 67 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(38(a,1),38(a,2,2)),rewrite([63(4),38(4),27(6,R),20(5)])].
% 3.35/3.65 68 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(62),rewrite([67(8),23(7)])].
% 3.35/3.65 70 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(39(a,1),23(a,1,1)),rewrite([20(7)]),flip(a)].
% 3.35/3.65 74 composition(converse(one),A) = A. [para(15(a,1),40(a,1,1)),rewrite([16(2)]),flip(a)].
% 3.35/3.65 80 converse(one) = one. [para(74(a,1),15(a,1)),flip(a)].
% 3.35/3.65 82 composition(join(A,one),B) = join(B,composition(A,B)). [para(74(a,1),30(a,1,1)),rewrite([80(4),20(4)]),flip(a)].
% 3.35/3.65 84 join(complement(A),complement(composition(one,A))) = complement(A). [para(74(a,1),32(a,1,2))].
% 3.35/3.65 85 composition(one,A) = A. [para(74(a,1),42(a,2)),rewrite([80(2),42(4)])].
% 3.35/3.65 86 join(complement(A),complement(A)) = complement(A). [back_rewrite(84),rewrite([85(3)])].
% 3.35/3.65 87 join(zero,complement(complement(A))) = A. [back_rewrite(53),rewrite([86(4)])].
% 3.35/3.65 88 converse(join(A,one)) = join(one,converse(A)). [para(80(a,1),23(a,1,1)),rewrite([20(5)]),flip(a)].
% 3.35/3.65 92 join(top,complement(A)) = top. [para(86(a,1),41(a,1,2)),rewrite([18(2),20(4)]),flip(a)].
% 3.35/3.65 93 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(61),rewrite([92(3),37(2)])].
% 3.35/3.65 94 join(top,top) = join(A,top). [para(92(a,1),41(a,1,2)),flip(a)].
% 3.35/3.65 99 join(A,top) = join(B,top). [para(94(a,1),41(a,2)),rewrite([92(3)])].
% 3.35/3.65 100 join(A,top) = c_0. [new_symbol(99)].
% 3.35/3.65 103 join(A,join(B,complement(A))) = c_0. [back_rewrite(41),rewrite([100(5)])].
% 3.35/3.65 114 c_0 = top. [para(87(a,1),103(a,1,2)),rewrite([20(2),18(2)]),flip(a)].
% 3.35/3.65 115 join(A,join(B,complement(A))) = top. [back_rewrite(103),rewrite([114(4)])].
% 3.35/3.65 117 join(A,top) = top. [back_rewrite(100),rewrite([114(3)])].
% 3.35/3.65 127 converse(join(A,join(B,one))) = join(one,converse(join(A,B))). [para(88(a,1),23(a,1,1)),rewrite([67(5),23(4),20(7),27(7,R),20(6)]),flip(a)].
% 3.35/3.65 138 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(85(a,1),46(a,1,2)),rewrite([20(3)]),flip(a)].
% 3.35/3.65 142 join(zero,complement(A)) = complement(A). [para(87(a,1),93(a,1,2,1))].
% 3.35/3.65 143 complement(complement(A)) = A. [back_rewrite(93),rewrite([142(4),142(4)])].
% 3.35/3.65 144 join(A,zero) = A. [back_rewrite(87),rewrite([143(3),20(2)])].
% 3.35/3.65 149 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(143(a,1),34(a,1,1,1,2)),rewrite([143(5),20(4)])].
% 3.35/3.65 151 join(A,A) = A. [para(143(a,1),86(a,1,1)),rewrite([143(2),143(3)])].
% 3.35/3.65 155 join(A,join(A,B)) = join(A,B). [para(151(a,1),27(a,1)),rewrite([20(3),27(4,R),20(3),27(3,R),151(2)]),flip(a)].
% 3.35/3.65 156 join(A,complement(join(B,complement(A)))) = A. [para(34(a,1),155(a,1,2)),rewrite([20(4),34(12)])].
% 3.35/3.65 158 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(156(a,1),27(a,2,2)),rewrite([20(4),20(6)])].
% 3.35/3.65 161 join(complement(A),complement(join(A,B))) = complement(A). [para(143(a,1),156(a,1,2,1,2)),rewrite([20(2)])].
% 3.35/3.65 169 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(143(a,1),48(a,1,2,2))].
% 3.35/3.65 172 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(23(a,1),161(a,1,2,1))].
% 3.35/3.65 183 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(59(a,1),23(a,2,1)),rewrite([40(8)])].
% 3.35/3.65 196 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(82(a,1),30(a,1,2)),rewrite([27(4,R),30(3),20(1)]),flip(a)].
% 3.35/3.65 223 join(complement(one),converse(complement(one))) = complement(one). [para(15(a,1),169(a,1,2))].
% 3.35/3.65 227 converse(complement(one)) = complement(one). [para(223(a,1),23(a,2,1)),rewrite([16(7),20(6),223(6)]),flip(a)].
% 3.35/3.65 228 converse(join(A,complement(one))) = join(complement(one),converse(A)). [para(227(a,1),23(a,1,1)),rewrite([20(7)]),flip(a)].
% 3.35/3.65 232 converse(top) = top. [para(227(a,1),88(a,2,2)),rewrite([20(4),18(4),18(6)])].
% 3.35/3.65 236 join(top,converse(A)) = top. [para(232(a,1),23(a,1,1)),rewrite([20(5),117(5),232(5)])].
% 3.35/3.65 237 converse(composition(A,top)) = composition(top,converse(A)). [para(232(a,1),25(a,1,1)),flip(a)].
% 3.35/3.65 245 join(top,composition(A,converse(B))) = top. [para(39(a,1),236(a,1,2))].
% 3.35/3.65 247 join(top,composition(A,B)) = top. [para(16(a,1),245(a,1,2,2))].
% 3.35/3.65 258 converse(composition(A,composition(B,top))) = composition(top,converse(composition(A,B))). [para(237(a,1),25(a,1,1)),rewrite([28(5),25(4)]),flip(a)].
% 3.35/3.65 263 composition(top,join(one,converse(A))) = top. [para(88(a,1),237(a,2,2)),rewrite([82(4),247(4),232(2)]),flip(a)].
% 3.35/3.65 268 composition(top,join(A,one)) = top. [para(16(a,1),263(a,1,2,2)),rewrite([20(3)])].
% 3.35/3.65 292 join(zero,composition(A,zero)) = zero. [para(268(a,1),51(a,1,2,2,1,1)),rewrite([232(2),37(2),232(5),37(5),82(5),155(6),232(6),37(6)])].
% 3.35/3.65 301 join(complement(A),complement(join(B,A))) = complement(A). [para(156(a,1),57(a,2)),rewrite([143(2),143(4),143(8),57(13)])].
% 3.35/3.65 302 join(A,complement(join(complement(A),complement(B)))) = A. [para(57(a,1),161(a,1,2,1)),rewrite([143(2),20(3),143(7)])].
% 3.35/3.65 307 join(A,composition(B,zero)) = A. [para(292(a,1),27(a,1,2)),rewrite([144(2),144(4),20(3)]),flip(a)].
% 3.35/3.65 311 composition(join(A,B),zero) = composition(A,zero). [para(307(a,1),30(a,1)),flip(a)].
% 3.35/3.65 313 composition(A,zero) = zero. [para(307(a,1),82(a,2)),rewrite([311(4)])].
% 3.35/3.65 315 composition(converse(zero),A) = converse(zero). [para(313(a,1),40(a,1,1)),flip(a)].
% 3.35/3.65 324 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(315(a,1),46(a,1,1,2)),flip(a)].
% 3.35/3.65 328 converse(zero) = zero. [para(315(a,1),313(a,1))].
% 3.35/3.65 331 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(324),rewrite([328(2),313(2),144(2),328(3),313(3)]),flip(a)].
% 3.35/3.65 334 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(183),rewrite([328(2),331(7),328(7)])].
% 3.35/3.65 358 join(zero,converse(A)) = converse(A). [para(328(a,1),23(a,1,1)),rewrite([20(5),144(5)])].
% 3.35/3.65 427 converse(composition(A,join(B,complement(composition(converse(A),top))))) = converse(composition(A,B)). [para(334(a,1),44(a,1,2)),rewrite([20(4),358(4),20(9),23(9),25(10)]),flip(a)].
% 3.35/3.65 559 join(complement(one),complement(c1)) = complement(c1). [para(36(a,1),301(a,1,2,1)),rewrite([20(5)])].
% 3.35/3.65 573 join(A,join(complement(A),complement(B))) = top. [para(302(a,1),115(a,1,2)),rewrite([20(4)])].
% 3.35/3.65 591 join(one,complement(c1)) = top. [para(559(a,1),573(a,1,2))].
% 3.35/3.65 594 join(zero,c1) = c1. [para(591(a,1),34(a,1,1,1)),rewrite([37(2),559(6),143(4)])].
% 3.35/3.65 997 join(one,converse(c1)) = one. [para(594(a,1),127(a,2,2,1)),rewrite([20(4),36(4),20(3),144(3),80(2)]),flip(a)].
% 3.35/3.65 1010 join(A,composition(converse(c1),A)) = A. [para(997(a,1),30(a,2,1)),rewrite([85(2),85(6)])].
% 3.35/3.65 1016 join(A,composition(A,c1)) = A. [para(1010(a,1),70(a,1,1)),rewrite([16(2),16(3),16(4),20(3)]),flip(a)].
% 3.35/3.65 1018 join(A,join(B,composition(A,c1))) = join(A,B). [para(1016(a,1),27(a,2,2)),rewrite([20(3),20(5)])].
% 3.35/3.65 1769 join(A,composition(c1,A)) = A. [para(1016(a,1),138(a,1,1)),rewrite([85(2),85(4)]),flip(a)].
% 3.35/3.65 1796 join(A,join(B,composition(c1,A))) = join(A,B). [para(1769(a,1),27(a,2,2)),rewrite([20(3),20(5)])].
% 3.35/3.65 2072 join(A,complement(join(A,B))) = join(A,complement(B)). [para(149(a,1),158(a,1,2)),flip(a)].
% 3.35/3.65 2434 join(complement(converse(A)),converse(join(A,B))) = top. [para(172(a,1),115(a,1,2)),rewrite([20(5)])].
% 3.35/3.65 2465 join(A,join(B,converse(complement(converse(A))))) = top. [para(2434(a,1),23(a,2,1)),rewrite([16(6),27(5),20(4),27(5,R),20(4),232(7)])].
% 3.35/3.65 2557 join(A,converse(complement(converse(A)))) = top. [para(151(a,1),2465(a,1,2))].
% 3.35/3.65 2579 join(complement(converse(A)),converse(join(B,A))) = top. [para(2557(a,1),68(a,1,1,2)),rewrite([117(2),232(2)]),flip(a)].
% 3.35/3.65 2685 join(converse(A),complement(composition(converse(A),c1))) = top. [para(1010(a,1),2579(a,1,2,1)),rewrite([40(4),20(6)])].
% 3.35/3.65 2715 join(A,converse(complement(composition(converse(A),c1)))) = top. [para(2685(a,1),23(a,2,1)),rewrite([16(2),232(8)])].
% 3.35/3.65 2887 join(complement(composition(converse(A),c1)),converse(join(B,A))) = top. [para(2715(a,1),68(a,1,1,2)),rewrite([117(2),232(2)]),flip(a)].
% 3.35/3.65 3615 join(A,composition(complement(one),A)) = composition(top,A). [para(48(a,1),196(a,2,2,1)),rewrite([20(7),27(8,R),20(7),48(7),18(4)]),flip(a)].
% 3.35/3.65 3744 join(A,composition(A,complement(one))) = composition(A,top). [para(3615(a,1),70(a,1,1)),rewrite([39(4),232(2),227(5),16(7),20(6)]),flip(a)].
% 3.35/3.65 3748 join(complement(one),composition(top,c1)) = join(c1,complement(one)). [para(3615(a,1),1018(a,1,2)),rewrite([20(10)])].
% 3.35/3.65 4576 join(complement(one),composition(c1,top)) = join(c1,complement(one)). [para(3744(a,1),1796(a,1,2)),rewrite([20(10)])].
% 3.35/3.65 5122 complement(join(complement(A),complement(join(B,complement(A))))) = complement(join(complement(A),complement(B))). [para(2072(a,1),21(a,2,1)),rewrite([20(2),21(3)])].
% 3.35/3.65 5136 join(complement(A),complement(join(B,complement(A)))) = join(complement(A),complement(B)). [para(2072(a,1),57(a,2)),rewrite([20(2),20(5),156(7),20(6),5122(9),302(8),20(5)])].
% 3.35/3.65 5217 join(A,complement(converse(complement(converse(A))))) = A. [para(2557(a,1),2072(a,1,2,1)),rewrite([37(2),144(2)]),flip(a)].
% 3.35/3.65 5301 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(16(a,1),5217(a,1,2,1,1,1))].
% 3.35/3.65 5304 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(5217(a,1),34(a,1,2,1)),rewrite([143(9),20(8),2072(8),143(6)])].
% 3.35/3.65 5488 converse(complement(converse(complement(A)))) = A. [para(5301(a,1),23(a,2,1)),rewrite([16(2),5304(5),16(6)])].
% 3.35/3.65 5516 complement(converse(complement(A))) = converse(A). [para(5488(a,1),16(a,1,1)),flip(a)].
% 3.35/3.65 5627 converse(complement(A)) = complement(converse(A)). [para(5516(a,1),143(a,1,1)),flip(a)].
% 3.35/3.65 7631 join(complement(one),complement(composition(top,c1))) = complement(c1). [para(3748(a,1),2072(a,1,2,1)),rewrite([5136(8),559(5)]),flip(a)].
% 3.35/3.65 13237 join(join(complement(one),converse(c1)),complement(composition(top,composition(converse(c1),c1)))) = top. [para(4576(a,1),2887(a,1,2,1)),rewrite([237(4),28(6),228(12),20(13)])].
% 3.35/3.65 14071 composition(top,composition(A,converse(A))) = composition(top,converse(A)). [para(18(a,1),427(a,1,1,2)),rewrite([237(3),258(8),39(7)]),flip(a)].
% 3.35/3.65 14083 composition(top,composition(converse(A),A)) = composition(top,A). [para(16(a,1),14071(a,1,2,2)),rewrite([16(7)])].
% 3.35/3.65 14122 join(complement(c1),converse(c1)) = top. [back_rewrite(13237),rewrite([14083(11),20(10),27(10),20(9),7631(9),20(5)])].
% 3.35/3.65 14178 join(c1,complement(converse(c1))) = top. [para(14122(a,1),23(a,2,1)),rewrite([5627(3),16(6),20(5),232(7)])].
% 3.35/3.65 14184 join(complement(c1),complement(converse(c1))) = complement(c1). [para(14122(a,1),2072(a,1,2,1)),rewrite([37(4),20(4),142(4)]),flip(a)].
% 3.35/3.65 14189 converse(c1) = c1. [para(14178(a,1),34(a,1,1,1)),rewrite([37(2),14184(7),143(4),594(3)]),flip(a)].
% 3.35/3.65 14190 $F # answer(goals). [resolve(14189,a,35,a)].
% 3.35/3.65
% 3.35/3.65 % SZS output end Refutation
% 3.35/3.65 ============================== end of proof ==========================
% 3.35/3.65
% 3.35/3.65 ============================== STATISTICS ============================
% 3.35/3.65
% 3.35/3.65 Given=889. Generated=140996. Kept=14169. proofs=1.
% 3.35/3.65 Usable=725. Sos=9982. Demods=10258. Limbo=0, Disabled=3476. Hints=0.
% 3.35/3.65 Megabytes=15.53.
% 3.35/3.65 User_CPU=2.61, System_CPU=0.07, Wall_clock=2.
% 3.35/3.65
% 3.35/3.65 ============================== end of statistics =====================
% 3.35/3.65
% 3.35/3.65 ============================== end of search =========================
% 3.35/3.65
% 3.35/3.65 THEOREM PROVED
% 3.35/3.65 % SZS status Theorem
% 3.35/3.65
% 3.35/3.65 Exiting with 1 proof.
% 3.35/3.65
% 3.35/3.65 Process 15337 exit (max_proofs) Fri Jul 8 15:22:41 2022
% 3.35/3.65 Prover9 interrupted
%------------------------------------------------------------------------------