TSTP Solution File: REL041+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL041+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 19:54:24 EDT 2022
% Result : Theorem 3.62s 3.88s
% Output : Refutation 3.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : REL041+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Fri Jul 8 12:50:15 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.50/1.06 ============================== Prover9 ===============================
% 0.50/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.50/1.06 Process 30502 was started by sandbox on n007.cluster.edu,
% 0.50/1.06 Fri Jul 8 12:50:16 2022
% 0.50/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30348_n007.cluster.edu".
% 0.50/1.06 ============================== end of head ===========================
% 0.50/1.06
% 0.50/1.06 ============================== INPUT =================================
% 0.50/1.06
% 0.50/1.06 % Reading from file /tmp/Prover9_30348_n007.cluster.edu
% 0.50/1.06
% 0.50/1.06 set(prolog_style_variables).
% 0.50/1.06 set(auto2).
% 0.50/1.06 % set(auto2) -> set(auto).
% 0.50/1.06 % set(auto) -> set(auto_inference).
% 0.50/1.06 % set(auto) -> set(auto_setup).
% 0.50/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.50/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.50/1.06 % set(auto) -> set(auto_limits).
% 0.50/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.50/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.50/1.06 % set(auto) -> set(auto_denials).
% 0.50/1.06 % set(auto) -> set(auto_process).
% 0.50/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.50/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.50/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.50/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.50/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.50/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.50/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.50/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.50/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.50/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.50/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.50/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.50/1.06 % set(auto2) -> assign(stats, some).
% 0.50/1.06 % set(auto2) -> clear(echo_input).
% 0.50/1.06 % set(auto2) -> set(quiet).
% 0.50/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.50/1.06 % set(auto2) -> clear(print_given).
% 0.50/1.06 assign(lrs_ticks,-1).
% 0.50/1.06 assign(sos_limit,10000).
% 0.50/1.06 assign(order,kbo).
% 0.50/1.06 set(lex_order_vars).
% 0.50/1.06 clear(print_given).
% 0.50/1.06
% 0.50/1.06 % formulas(sos). % not echoed (17 formulas)
% 0.50/1.06
% 0.50/1.06 ============================== end of input ==========================
% 0.50/1.06
% 0.50/1.06 % From the command line: assign(max_seconds, 300).
% 0.50/1.06
% 0.50/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.50/1.06
% 0.50/1.06 % Formulas that are not ordinary clauses:
% 0.50/1.06 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 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].
% 0.50/1.06 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].
% 0.50/1.06 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].
% 0.50/1.06 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].
% 0.50/1.06 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 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].
% 0.50/1.06 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 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].
% 0.50/1.06 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.88 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].
% 3.62/3.88 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].
% 3.62/3.88 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].
% 3.62/3.88 17 -(all X0 (join(composition(converse(X0),X0),one) = one -> (all X1 meet(composition(X0,X1),composition(X0,complement(X1))) = zero))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.62/3.88
% 3.62/3.88 ============================== end of process non-clausal formulas ===
% 3.62/3.88
% 3.62/3.88 ============================== PROCESS INITIAL CLAUSES ===============
% 3.62/3.88
% 3.62/3.88 ============================== PREDICATE ELIMINATION =================
% 3.62/3.88
% 3.62/3.88 ============================== end predicate elimination =============
% 3.62/3.88
% 3.62/3.88 Auto_denials:
% 3.62/3.88 % copying label goals to answer in negative clause
% 3.62/3.88
% 3.62/3.88 Term ordering decisions:
% 3.62/3.88 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 3.62/3.88
% 3.62/3.88 ============================== end of process initial clauses ========
% 3.62/3.88
% 3.62/3.88 ============================== CLAUSES FOR SEARCH ====================
% 3.62/3.88
% 3.62/3.88 ============================== end of clauses for search =============
% 3.62/3.88
% 3.62/3.88 ============================== SEARCH ================================
% 3.62/3.88
% 3.62/3.88 % Starting search at 0.01 seconds.
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=125.000, iters=3436
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=105.000, iters=3426
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=104.000, iters=3517
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=75.000, iters=3360
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=74.000, iters=3343
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=72.000, iters=3371
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=71.000, iters=3345
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=70.000, iters=3368
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=68.000, iters=3340
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=67.000, iters=3345
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=66.000, iters=3360
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=65.000, iters=3390
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=64.000, iters=3382
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=63.000, iters=3360
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=62.000, iters=3350
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=61.000, iters=3357
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=60.000, iters=3348
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=58.000, iters=3346
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=57.000, iters=3356
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=56.000, iters=3355
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=54.000, iters=3355
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=53.000, iters=3339
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=51.000, iters=3365
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=50.000, iters=3371
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=49.000, iters=3363
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=47.000, iters=3406
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=45.000, iters=3425
% 3.62/3.88
% 3.62/3.88 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 2.70 sec).
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=44.000, iters=3511
% 3.62/3.88
% 3.62/3.88 Low Water (keep): wt=40.000, iters=3480
% 3.62/3.88
% 3.62/3.88 ============================== PROOF =================================
% 3.62/3.88 % SZS status Theorem
% 3.62/3.88 % SZS output start Refutation
% 3.62/3.88
% 3.62/3.88 % Proof 1 at 2.78 (+ 0.06) seconds: goals.
% 3.62/3.88 % Length of proof is 95.
% 3.62/3.88 % Level of proof is 24.
% 3.62/3.88 % Maximum clause weight is 48.000.
% 3.62/3.88 % Given clauses 508.
% 3.62/3.88
% 3.62/3.88 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.88 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].
% 3.62/3.88 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].
% 3.62/3.88 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].
% 3.62/3.88 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].
% 3.62/3.88 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.88 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].
% 3.62/3.88 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.88 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.88 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.88 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].
% 3.62/3.88 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.88 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.88 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].
% 3.62/3.88 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].
% 3.62/3.88 17 -(all X0 (join(composition(converse(X0),X0),one) = one -> (all X1 meet(composition(X0,X1),composition(X0,complement(X1))) = zero))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.62/3.88 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 3.62/3.88 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 3.62/3.88 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 3.62/3.88 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 3.62/3.88 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 3.62/3.88 23 join(composition(converse(c1),c1),one) = one # label(goals) # label(negated_conjecture). [clausify(17)].
% 3.62/3.88 24 join(one,composition(converse(c1),c1)) = one. [copy(23),rewrite([22(6)])].
% 3.62/3.88 25 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 3.62/3.88 26 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 3.62/3.88 27 join(converse(A),converse(B)) = converse(join(A,B)). [copy(26),flip(a)].
% 3.62/3.88 28 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 3.62/3.88 29 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(28),flip(a)].
% 3.62/3.88 30 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 3.62/3.88 31 join(A,join(B,C)) = join(C,join(A,B)). [copy(30),rewrite([22(2)]),flip(a)].
% 3.62/3.88 32 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 3.62/3.88 33 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 3.62/3.88 34 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(33),flip(a)].
% 3.62/3.88 35 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 3.62/3.88 36 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(35),rewrite([22(7)]),flip(a)].
% 3.62/3.88 37 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 3.62/3.88 38 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(37),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 3.62/3.88 39 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)].
% 3.62/3.88 40 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(39),rewrite([25(3),25(8),22(10),25(13),22(15),25(19),25(24),22(26)]),flip(a)].
% 3.62/3.88 43 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)].
% 3.62/3.88 44 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(43),rewrite([25(3),25(9),25(15),22(17),25(21),25(27)]),flip(a)].
% 3.62/3.88 45 meet(composition(c1,c2),composition(c1,complement(c2))) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 3.62/3.88 46 complement(join(complement(composition(c1,c2)),complement(composition(c1,complement(c2))))) != zero # answer(goals). [copy(45),rewrite([25(8)])].
% 3.62/3.88 47 complement(top) = zero. [back_rewrite(21),rewrite([25(2),20(4)])].
% 3.62/3.88 49 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),29(a,1,1)),flip(a)].
% 3.62/3.88 50 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),29(a,1,2)),flip(a)].
% 3.62/3.88 51 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),31(a,2,2)),rewrite([22(2)])].
% 3.62/3.88 52 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),32(a,1,1)),flip(a)].
% 3.62/3.88 57 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(32(a,1),34(a,1,1)),rewrite([22(6)])].
% 3.62/3.88 59 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(18(a,1),36(a,1,2,2,1))].
% 3.62/3.88 64 join(zero,complement(join(complement(A),complement(A)))) = A. [para(20(a,1),38(a,1,1,1)),rewrite([47(2)])].
% 3.62/3.88 65 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(20(a,1),38(a,1,2,1)),rewrite([47(6),22(6)])].
% 3.62/3.88 94 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(47(a,1),36(a,1,1)),rewrite([47(9)])].
% 3.62/3.88 129 composition(converse(one),A) = A. [para(18(a,1),50(a,1,1)),rewrite([19(2)]),flip(a)].
% 3.62/3.88 138 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(38(a,1),51(a,1,2)),rewrite([22(4),51(4),22(3),22(8)]),flip(a)].
% 3.62/3.88 139 join(top,complement(complement(A))) = top. [para(40(a,1),51(a,1,2)),rewrite([20(22),22(8),138(8)]),flip(a)].
% 3.62/3.88 140 converse(one) = one. [para(129(a,1),18(a,1)),flip(a)].
% 3.62/3.88 142 composition(join(A,one),B) = join(B,composition(A,B)). [para(129(a,1),34(a,1,1)),rewrite([140(4),22(4)]),flip(a)].
% 3.62/3.88 144 join(complement(A),complement(composition(one,A))) = complement(A). [para(129(a,1),36(a,1,2))].
% 3.62/3.88 158 composition(one,A) = A. [para(129(a,1),52(a,2)),rewrite([140(2),52(4)])].
% 3.62/3.88 164 join(complement(A),complement(A)) = complement(A). [back_rewrite(144),rewrite([158(3)])].
% 3.62/3.88 165 join(zero,complement(complement(A))) = A. [back_rewrite(64),rewrite([164(4)])].
% 3.62/3.88 166 converse(join(A,one)) = join(one,converse(A)). [para(140(a,1),27(a,1,1)),rewrite([22(5)]),flip(a)].
% 3.62/3.88 167 join(zero,complement(A)) = complement(A). [para(139(a,1),38(a,1,1,1)),rewrite([47(2),47(3),165(5)])].
% 3.62/3.88 169 join(top,complement(A)) = join(top,top). [para(139(a,1),51(a,1,2)),rewrite([22(3)])].
% 3.62/3.88 170 complement(complement(A)) = A. [back_rewrite(165),rewrite([167(4)])].
% 3.62/3.88 180 complement(join(A,A)) = complement(A). [back_rewrite(65),rewrite([170(3),167(4)])].
% 3.62/3.88 182 join(A,top) = top. [back_rewrite(139),rewrite([170(3),22(2)])].
% 3.62/3.88 188 join(top,complement(A)) = top. [back_rewrite(169),rewrite([182(6)])].
% 3.62/3.88 198 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(170(a,1),38(a,1,1,1,2)),rewrite([170(5),22(4)])].
% 3.62/3.88 206 complement(zero) = top. [para(47(a,1),170(a,1,1))].
% 3.62/3.88 221 join(A,A) = A. [para(180(a,1),38(a,1,1,1,2)),rewrite([180(6),38(8)]),flip(a)].
% 3.62/3.88 228 join(A,join(A,B)) = join(A,B). [para(221(a,1),31(a,1)),rewrite([22(3),31(4,R),22(3),31(3,R),221(2)]),flip(a)].
% 3.62/3.88 246 join(A,complement(join(B,complement(A)))) = A. [para(38(a,1),228(a,1,2)),rewrite([22(4),38(12)])].
% 3.62/3.88 248 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(246(a,1),31(a,2,2)),rewrite([22(4),22(6)])].
% 3.62/3.88 252 join(A,composition(converse(c1),composition(c1,A))) = A. [para(24(a,1),57(a,2,1)),rewrite([158(7),22(6),158(8)])].
% 3.62/3.88 272 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(170(a,1),59(a,1,2,2))].
% 3.62/3.88 285 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(166(a,1),94(a,1,2,1))].
% 3.62/3.88 321 join(complement(one),converse(complement(one))) = complement(one). [para(18(a,1),272(a,1,2))].
% 3.62/3.88 325 converse(complement(one)) = complement(one). [para(321(a,1),27(a,2,1)),rewrite([19(7),22(6),321(6)]),flip(a)].
% 3.62/3.88 339 converse(top) = top. [para(325(a,1),166(a,2,2)),rewrite([22(4),20(4),20(6)])].
% 3.62/3.88 345 join(top,converse(A)) = top. [para(339(a,1),27(a,1,1)),rewrite([22(5),182(5),339(5)])].
% 3.62/3.88 352 join(top,composition(A,converse(B))) = top. [para(49(a,1),345(a,1,2))].
% 3.62/3.88 354 join(top,composition(A,B)) = top. [para(19(a,1),352(a,1,2,2))].
% 3.62/3.88 355 composition(join(A,one),top) = top. [para(339(a,1),352(a,1,2,2)),rewrite([142(4,R)])].
% 3.62/3.88 356 composition(join(one,converse(A)),zero) = zero. [back_rewrite(285),rewrite([355(8),47(6),142(7,R),22(5),228(5)])].
% 3.62/3.88 383 composition(top,zero) = zero. [para(325(a,1),356(a,1,1,2)),rewrite([20(4)])].
% 3.62/3.88 388 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(383(a,1),44(a,1,1,1,2,1)),rewrite([206(3),22(3),188(3),47(2),47(3),167(7),170(6),206(6),339(7),188(9),47(6),32(6),47(9),167(13),170(12),206(12),339(13),188(15),47(12),32(12)])].
% 3.62/3.88 392 join(zero,composition(A,composition(B,zero))) = zero. [para(383(a,1),57(a,1,2)),rewrite([22(5),354(8),383(8)])].
% 3.62/3.88 395 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(388),rewrite([392(7)]),flip(a)].
% 3.62/3.88 473 composition(A,zero) = zero. [para(395(a,1),32(a,1)),rewrite([395(6)]),flip(a)].
% 3.62/3.88 10345 join(A,complement(join(A,B))) = join(A,complement(B)). [para(198(a,1),248(a,1,2)),flip(a)].
% 3.62/3.88 10790 join(A,complement(composition(converse(c1),composition(c1,A)))) = top. [para(252(a,1),10345(a,1,2,1)),rewrite([20(2)]),flip(a)].
% 3.62/3.88 11429 complement(join(complement(composition(c1,A)),complement(composition(c1,complement(A))))) = zero. [para(10790(a,1),40(a,1,2,1,2,1,2,1)),rewrite([22(8),47(16),473(16),206(15),22(15),188(15),47(11),22(11),167(11),10790(23),47(16),473(16),206(15),22(15),188(15),47(11)])].
% 3.62/3.88 11430 $F # answer(goals). [resolve(11429,a,46,a)].
% 3.62/3.88
% 3.62/3.88 % SZS output end Refutation
% 3.62/3.88 ============================== end of proof ==========================
% 3.62/3.88
% 3.62/3.88 ============================== STATISTICS ============================
% 3.62/3.88
% 3.62/3.88 Given=508. Generated=73590. Kept=11401. proofs=1.
% 3.62/3.88 Usable=409. Sos=8900. Demods=9121. Limbo=2, Disabled=2107. Hints=0.
% 3.62/3.88 Megabytes=23.47.
% 3.62/3.88 User_CPU=2.78, System_CPU=0.06, Wall_clock=2.
% 3.62/3.88
% 3.62/3.88 ============================== end of statistics =====================
% 3.62/3.88
% 3.62/3.88 ============================== end of search =========================
% 3.62/3.88
% 3.62/3.88 THEOREM PROVED
% 3.62/3.88 % SZS status Theorem
% 3.62/3.88
% 3.62/3.88 Exiting with 1 proof.
% 3.62/3.88
% 3.62/3.88 Process 30502 exit (max_proofs) Fri Jul 8 12:50:18 2022
% 3.62/3.88 Prover9 interrupted
%------------------------------------------------------------------------------