TSTP Solution File: REL011+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL011+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 19:53:37 EDT 2022
% Result : Theorem 2.28s 2.56s
% Output : Refutation 2.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL011+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 07:43:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.46/0.91 ============================== Prover9 ===============================
% 0.46/0.91 Prover9 (32) version 2009-11A, November 2009.
% 0.46/0.91 Process 6074 was started by sandbox on n009.cluster.edu,
% 0.46/0.91 Fri Jul 8 07:43:22 2022
% 0.46/0.91 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5920_n009.cluster.edu".
% 0.46/0.91 ============================== end of head ===========================
% 0.46/0.91
% 0.46/0.91 ============================== INPUT =================================
% 0.46/0.91
% 0.46/0.91 % Reading from file /tmp/Prover9_5920_n009.cluster.edu
% 0.46/0.91
% 0.46/0.91 set(prolog_style_variables).
% 0.46/0.91 set(auto2).
% 0.46/0.91 % set(auto2) -> set(auto).
% 0.46/0.91 % set(auto) -> set(auto_inference).
% 0.46/0.91 % set(auto) -> set(auto_setup).
% 0.46/0.91 % set(auto_setup) -> set(predicate_elim).
% 0.46/0.91 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/0.91 % set(auto) -> set(auto_limits).
% 0.46/0.91 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/0.91 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/0.91 % set(auto) -> set(auto_denials).
% 0.46/0.91 % set(auto) -> set(auto_process).
% 0.46/0.91 % set(auto2) -> assign(new_constants, 1).
% 0.46/0.91 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/0.91 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/0.91 % set(auto2) -> assign(max_hours, 1).
% 0.46/0.91 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/0.91 % set(auto2) -> assign(max_seconds, 0).
% 0.46/0.91 % set(auto2) -> assign(max_minutes, 5).
% 0.46/0.91 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/0.91 % set(auto2) -> set(sort_initial_sos).
% 0.46/0.91 % set(auto2) -> assign(sos_limit, -1).
% 0.46/0.91 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/0.91 % set(auto2) -> assign(max_megs, 400).
% 0.46/0.91 % set(auto2) -> assign(stats, some).
% 0.46/0.91 % set(auto2) -> clear(echo_input).
% 0.46/0.91 % set(auto2) -> set(quiet).
% 0.46/0.91 % set(auto2) -> clear(print_initial_clauses).
% 0.46/0.91 % set(auto2) -> clear(print_given).
% 0.46/0.91 assign(lrs_ticks,-1).
% 0.46/0.91 assign(sos_limit,10000).
% 0.46/0.91 assign(order,kbo).
% 0.46/0.91 set(lex_order_vars).
% 0.46/0.91 clear(print_given).
% 0.46/0.91
% 0.46/0.91 % formulas(sos). % not echoed (17 formulas)
% 0.46/0.91
% 0.46/0.91 ============================== end of input ==========================
% 0.46/0.91
% 0.46/0.91 % From the command line: assign(max_seconds, 300).
% 0.46/0.91
% 0.46/0.91 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/0.91
% 0.46/0.91 % Formulas that are not ordinary clauses:
% 0.46/0.91 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.91 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].
% 0.46/0.91 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].
% 0.46/0.91 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].
% 0.46/0.91 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].
% 0.46/0.91 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.91 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].
% 0.46/0.91 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.91 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.91 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.91 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].
% 0.46/0.91 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.91 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 2.28/2.56 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].
% 2.28/2.56 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].
% 2.28/2.56 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].
% 2.28/2.56 17 -(all X0 all X1 all X2 (meet(X0,composition(converse(X1),X2)) = zero -> meet(composition(X1,X0),X2) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.28/2.56
% 2.28/2.56 ============================== end of process non-clausal formulas ===
% 2.28/2.56
% 2.28/2.56 ============================== PROCESS INITIAL CLAUSES ===============
% 2.28/2.56
% 2.28/2.56 ============================== PREDICATE ELIMINATION =================
% 2.28/2.56
% 2.28/2.56 ============================== end predicate elimination =============
% 2.28/2.56
% 2.28/2.56 Auto_denials:
% 2.28/2.56 % copying label goals to answer in negative clause
% 2.28/2.56
% 2.28/2.56 Term ordering decisions:
% 2.28/2.56 Function symbol KB weights: zero=1. one=1. top=1. c1=1. c2=1. c3=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 2.28/2.56
% 2.28/2.56 ============================== end of process initial clauses ========
% 2.28/2.56
% 2.28/2.56 ============================== CLAUSES FOR SEARCH ====================
% 2.28/2.56
% 2.28/2.56 ============================== end of clauses for search =============
% 2.28/2.56
% 2.28/2.56 ============================== SEARCH ================================
% 2.28/2.56
% 2.28/2.56 % Starting search at 0.02 seconds.
% 2.28/2.56
% 2.28/2.56 ============================== PROOF =================================
% 2.28/2.56 % SZS status Theorem
% 2.28/2.56 % SZS output start Refutation
% 2.28/2.56
% 2.28/2.56 % Proof 1 at 1.63 (+ 0.03) seconds: goals.
% 2.28/2.56 % Length of proof is 164.
% 2.28/2.56 % Level of proof is 38.
% 2.28/2.56 % Maximum clause weight is 49.000.
% 2.28/2.56 % Given clauses 320.
% 2.28/2.56
% 2.28/2.56 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.28/2.56 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].
% 2.28/2.56 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].
% 2.28/2.56 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].
% 2.28/2.56 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].
% 2.28/2.56 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 2.28/2.56 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].
% 2.28/2.56 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.28/2.56 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 2.28/2.56 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 2.28/2.56 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].
% 2.28/2.56 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 2.28/2.56 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 2.28/2.56 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].
% 2.28/2.56 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].
% 2.28/2.56 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].
% 2.28/2.56 17 -(all X0 all X1 all X2 (meet(X0,composition(converse(X1),X2)) = zero -> meet(composition(X1,X0),X2) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.28/2.56 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 2.28/2.56 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 2.28/2.56 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 2.28/2.56 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 2.28/2.56 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 2.28/2.56 23 meet(c1,composition(converse(c2),c3)) = zero # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.28/2.56 24 zero = meet(c1,composition(converse(c2),c3)). [copy(23),flip(a)].
% 2.28/2.56 25 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 2.28/2.56 26 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 2.28/2.56 27 join(converse(A),converse(B)) = converse(join(A,B)). [copy(26),flip(a)].
% 2.28/2.56 28 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 2.28/2.56 29 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(28),flip(a)].
% 2.28/2.56 30 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 2.28/2.56 31 join(A,join(B,C)) = join(C,join(A,B)). [copy(30),rewrite([22(2)]),flip(a)].
% 2.28/2.56 32 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 2.28/2.56 33 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 2.28/2.56 34 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(33),flip(a)].
% 2.28/2.56 35 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 2.28/2.56 36 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(35),rewrite([22(7)]),flip(a)].
% 2.28/2.56 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)].
% 2.28/2.56 38 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(37),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 2.28/2.56 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)].
% 2.28/2.56 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)].
% 2.28/2.56 41 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)].
% 2.28/2.56 42 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(41),rewrite([25(3),25(8),22(10),25(13),22(15),25(19),25(24),22(26)]),flip(a)].
% 2.28/2.56 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)].
% 2.28/2.56 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)].
% 2.28/2.56 45 meet(composition(c2,c1),c3) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 2.28/2.56 46 complement(join(complement(c1),complement(composition(converse(c2),c3)))) != complement(join(complement(c3),complement(composition(c2,c1)))) # answer(goals). [copy(45),rewrite([25(5),22(7),24(9),25(14)]),flip(a)].
% 2.28/2.56 47 complement(join(complement(c1),complement(composition(converse(c2),c3)))) = complement(top). [back_rewrite(21),rewrite([25(2),20(4),24(3),25(8)]),flip(a)].
% 2.28/2.56 49 complement(join(complement(c3),complement(composition(c2,c1)))) != complement(top) # answer(goals). [back_rewrite(46),rewrite([47(9)]),flip(a)].
% 2.28/2.56 50 converse(join(A,converse(B))) = join(B,converse(A)). [para(19(a,1),27(a,1,1)),rewrite([22(4)]),flip(a)].
% 2.28/2.56 51 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),29(a,1,1)),flip(a)].
% 2.28/2.56 52 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),29(a,1,2)),flip(a)].
% 2.28/2.56 53 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),31(a,2,2)),rewrite([22(2)])].
% 2.28/2.56 54 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),32(a,1,1)),flip(a)].
% 2.28/2.56 56 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(29(a,1),34(a,1,1)),rewrite([22(7)])].
% 2.28/2.56 57 join(composition(A,converse(B)),converse(composition(B,C))) = composition(join(A,converse(C)),converse(B)). [para(29(a,1),34(a,1,2))].
% 2.28/2.56 62 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(36(a,1),27(a,2,1)),rewrite([52(7)])].
% 2.28/2.56 63 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(29(a,1),36(a,1,2,2,1)),rewrite([19(4)])].
% 2.28/2.56 65 join(complement(top),complement(join(complement(A),complement(A)))) = A. [para(20(a,1),38(a,1,1,1))].
% 2.28/2.56 66 join(complement(top),complement(join(A,complement(complement(A))))) = complement(A). [para(20(a,1),38(a,1,2,1)),rewrite([22(7)])].
% 2.28/2.56 67 join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B. [para(38(a,1),22(a,1)),rewrite([22(3),22(8)]),flip(a)].
% 2.28/2.56 68 join(complement(A),complement(join(complement(join(complement(A),complement(B))),complement(complement(join(B,complement(A))))))) = join(complement(A),complement(B)). [para(38(a,1),38(a,1,1,1)),rewrite([22(8),22(10),22(15)])].
% 2.28/2.56 69 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(38(a,1),38(a,1,2,1)),rewrite([22(10)])].
% 2.28/2.56 79 join(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,C)))),converse(C)))))) = complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,C)))),converse(C))))). [para(19(a,1),42(a,1,2,1,2,1,1,1,2,1,2)),rewrite([19(22)])].
% 2.28/2.56 89 join(complement(join(complement(A),complement(composition(converse(B),C)))),composition(complement(join(complement(converse(B)),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(B,A)))))) = composition(complement(join(complement(converse(B)),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(B,A))))). [para(19(a,1),44(a,1,2,2,1,2,1,1)),rewrite([19(30)])].
% 2.28/2.56 96 join(complement(c1),complement(composition(converse(c2),c3))) = top. [para(47(a,1),38(a,1,1,1,2)),rewrite([47(14),38(10)]),flip(a)].
% 2.28/2.56 100 join(complement(join(complement(c3),complement(composition(c2,c1)))),complement(join(complement(c3),complement(composition(c2,complement(top)))))) = complement(join(complement(c3),complement(composition(c2,complement(top))))). [para(47(a,1),40(a,1,2,1,2,1,2)),rewrite([96(29)])].
% 2.28/2.56 104 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(50(a,1),27(a,1,1)),rewrite([22(7),31(7,R),22(6)]),flip(a)].
% 2.28/2.56 105 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(50(a,1),27(a,1,2)),rewrite([31(4,R),22(3),27(3),104(7)]),flip(a)].
% 2.28/2.56 113 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(50(a,1),50(a,2,2)),rewrite([105(4),50(4),31(6,R),22(5)])].
% 2.28/2.56 121 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(51(a,1),27(a,1,1)),rewrite([22(7)]),flip(a)].
% 2.28/2.56 129 composition(converse(one),A) = A. [para(18(a,1),52(a,1,1)),rewrite([19(2)]),flip(a)].
% 2.28/2.56 130 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(52(a,1),27(a,1,1)),rewrite([22(7)]),flip(a)].
% 2.28/2.56 137 converse(one) = one. [para(129(a,1),18(a,1)),flip(a)].
% 2.28/2.56 139 composition(join(A,one),B) = join(B,composition(A,B)). [para(129(a,1),34(a,1,1)),rewrite([137(4),22(4)]),flip(a)].
% 2.28/2.56 140 composition(join(one,one),complement(A)) = complement(A). [para(129(a,1),36(a,1,2,2,1)),rewrite([137(3),137(3),139(5,R)])].
% 2.28/2.56 141 join(complement(A),complement(composition(one,A))) = complement(A). [para(129(a,1),36(a,1,2))].
% 2.28/2.56 155 composition(one,A) = A. [para(129(a,1),54(a,2)),rewrite([137(2),54(4)])].
% 2.28/2.56 161 join(complement(A),complement(A)) = complement(A). [back_rewrite(141),rewrite([155(3)])].
% 2.28/2.56 162 join(complement(top),complement(complement(A))) = A. [back_rewrite(65),rewrite([161(5)])].
% 2.28/2.56 164 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(38(a,1),53(a,1,2)),rewrite([22(4),53(4),22(3),22(8)]),flip(a)].
% 2.28/2.56 165 join(top,complement(complement(A))) = top. [para(40(a,1),53(a,1,2)),rewrite([20(22),22(8),164(8)]),flip(a)].
% 2.28/2.56 166 converse(join(A,one)) = join(one,converse(A)). [para(137(a,1),27(a,1,1)),rewrite([22(5)]),flip(a)].
% 2.28/2.56 167 join(complement(A),complement(top)) = complement(A). [para(165(a,1),38(a,1,1,1)),rewrite([162(7),22(4)])].
% 2.28/2.56 168 join(top,complement(A)) = join(top,top). [para(165(a,1),53(a,1,2)),rewrite([22(3)])].
% 2.28/2.56 169 join(top,top) = top. [back_rewrite(165),rewrite([168(4)])].
% 2.28/2.56 170 join(top,complement(A)) = top. [back_rewrite(168),rewrite([169(6)])].
% 2.28/2.56 171 join(A,top) = top. [para(169(a,1),53(a,2)),rewrite([170(3)])].
% 2.28/2.56 194 join(complement(complement(A)),complement(join(A,complement(top)))) = top. [para(167(a,1),38(a,1,2,1)),rewrite([22(7)])].
% 2.28/2.56 197 composition(join(A,join(one,one)),complement(B)) = composition(join(A,one),complement(B)). [para(140(a,1),34(a,1,1)),rewrite([139(4,R),22(8)]),flip(a)].
% 2.28/2.56 247 composition(join(one,one),A) = join(A,A). [para(155(a,1),139(a,2,2))].
% 2.28/2.56 273 composition(A,join(one,one)) = join(A,A). [para(247(a,2),50(a,1,1)),rewrite([51(6),166(4),137(3),19(6)])].
% 2.28/2.56 276 composition(join(one,one),top) = top. [para(247(a,2),171(a,1))].
% 2.28/2.56 287 composition(converse(top),join(one,one)) = converse(top). [para(276(a,1),29(a,2,1)),rewrite([166(6),137(5)])].
% 2.28/2.56 312 join(A,join(A,composition(B,join(one,one)))) = composition(join(B,A),join(one,one)). [para(273(a,1),34(a,1,2)),rewrite([31(6),22(5)])].
% 2.28/2.56 324 composition(top,join(one,one)) = top. [para(273(a,2),171(a,1))].
% 2.28/2.56 335 composition(join(one,one),A) = composition(A,join(one,one)). [para(273(a,2),247(a,2))].
% 2.28/2.56 357 composition(top,composition(A,join(one,one))) = composition(top,A). [para(324(a,1),32(a,1,1)),rewrite([335(7)]),flip(a)].
% 2.28/2.56 358 join(top,composition(A,join(one,one))) = top. [para(324(a,1),34(a,1,1)),rewrite([22(8),171(8),324(11)])].
% 2.28/2.56 400 join(top,converse(top)) = top. [para(287(a,1),358(a,1,2))].
% 2.28/2.56 402 converse(top) = top. [para(400(a,1),27(a,2,1)),rewrite([19(5),22(4),400(4)]),flip(a)].
% 2.28/2.56 412 join(top,converse(A)) = top. [para(402(a,1),27(a,1,1)),rewrite([22(5),171(5),402(5)])].
% 2.28/2.56 413 converse(composition(A,top)) = composition(top,converse(A)). [para(402(a,1),29(a,1,1)),flip(a)].
% 2.28/2.56 421 join(top,composition(A,converse(B))) = top. [para(51(a,1),412(a,1,2))].
% 2.28/2.56 431 composition(join(A,one),top) = top. [para(402(a,1),421(a,1,2,2)),rewrite([139(4,R)])].
% 2.28/2.56 434 composition(top,join(one,converse(A))) = top. [para(431(a,1),29(a,2,1)),rewrite([402(2),166(4),402(7)])].
% 2.28/2.56 445 composition(top,join(A,one)) = top. [para(19(a,1),434(a,1,2,2)),rewrite([22(3)])].
% 2.28/2.56 455 composition(top,top) = top. [para(402(a,1),434(a,1,2,2)),rewrite([171(4)])].
% 2.28/2.56 464 composition(top,composition(top,A)) = composition(top,A). [para(455(a,1),32(a,1,1)),flip(a)].
% 2.28/2.56 465 composition(top,complement(top)) = complement(top). [para(455(a,1),36(a,1,2,2,1)),rewrite([402(4),139(7,R),22(3),171(3)])].
% 2.28/2.56 474 composition(top,composition(join(A,one),B)) = composition(top,B). [para(445(a,1),32(a,1,1)),flip(a)].
% 2.28/2.56 484 composition(join(A,one),complement(top)) = complement(top). [para(445(a,1),63(a,1,2,2,1,1)),rewrite([402(2),402(6),139(8,R),22(4),31(4,R),197(7),402(7)])].
% 2.28/2.56 485 composition(converse(complement(top)),top) = converse(complement(top)). [para(465(a,1),29(a,2,1)),rewrite([402(5)])].
% 2.28/2.56 486 composition(top,composition(complement(top),A)) = composition(complement(top),A). [para(465(a,1),32(a,1,1)),flip(a)].
% 2.28/2.56 493 join(composition(A,top),converse(complement(top))) = composition(join(A,converse(complement(top))),top). [para(465(a,1),57(a,1,2,1)),rewrite([402(2),402(12)])].
% 2.28/2.56 554 composition(top,complement(composition(top,A))) = complement(composition(top,A)). [para(464(a,1),36(a,1,2,2,1)),rewrite([402(5),139(9,R),22(3),171(3)])].
% 2.28/2.56 566 join(A,complement(complement(A))) = A. [para(66(a,1),38(a,1,2,1)),rewrite([170(6),162(5)]),flip(a)].
% 2.28/2.56 567 complement(complement(top)) = top. [para(162(a,1),66(a,1,2,1)),rewrite([20(6)]),flip(a)].
% 2.28/2.56 574 join(A,join(B,complement(complement(A)))) = join(A,B). [para(566(a,1),31(a,2,2)),rewrite([22(3),22(5)])].
% 2.28/2.56 682 join(complement(top),complement(join(A,complement(top)))) = complement(A). [para(167(a,1),69(a,1,2,1,2,1)),rewrite([22(8),31(8),22(7),566(7),22(5),167(11)])].
% 2.28/2.56 944 join(complement(top),complement(join(complement(complement(complement(A))),complement(join(A,complement(top)))))) = join(A,complement(top)). [para(194(a,1),38(a,1,1,1))].
% 2.28/2.56 946 join(complement(complement(complement(A))),complement(join(A,complement(top)))) = complement(A). [para(194(a,1),68(a,1,2,1,2,1,1)),rewrite([22(12),567(16),22(15),170(15),22(7),682(7),22(9)]),flip(a)].
% 2.28/2.56 947 join(A,complement(top)) = A. [back_rewrite(944),rewrite([946(10),162(5)]),flip(a)].
% 2.28/2.56 1219 composition(top,join(A,A)) = composition(top,A). [para(273(a,1),357(a,1,2))].
% 2.28/2.56 1239 join(join(A,A),composition(top,A)) = composition(top,A). [para(1219(a,1),139(a,2,2)),rewrite([22(3),171(3),1219(3)]),flip(a)].
% 2.28/2.56 1540 join(complement(join(complement(top),complement(composition(A,top)))),complement(join(complement(top),complement(composition(complement(complement(A)),top))))) = complement(join(complement(top),complement(composition(complement(complement(A)),top)))). [para(455(a,1),79(a,1,2,1,2,1,1,1,2,1)),rewrite([402(4),947(13),402(13),455(23),947(23),402(23)])].
% 2.28/2.56 1619 composition(top,join(A,composition(B,A))) = composition(top,A). [para(139(a,1),474(a,1,2))].
% 2.28/2.56 1775 join(A,A) = A. [para(162(a,1),574(a,1,2)),rewrite([947(4)])].
% 2.28/2.56 1813 join(A,composition(top,A)) = composition(top,A). [back_rewrite(1239),rewrite([1775(1)])].
% 2.28/2.56 1835 join(A,join(A,B)) = join(A,B). [back_rewrite(312),rewrite([1775(3),18(2),22(3),1775(6),18(5)])].
% 2.28/2.56 1907 join(A,complement(join(B,complement(A)))) = A. [para(38(a,1),1835(a,1,2)),rewrite([22(4),38(12)])].
% 2.28/2.56 2505 join(complement(join(complement(top),complement(composition(top,A)))),composition(complement(join(complement(top),complement(composition(top,converse(A))))),complement(complement(A)))) = composition(complement(join(complement(top),complement(composition(top,converse(A))))),complement(complement(A))). [para(455(a,1),89(a,1,2,2,1,2,1)),rewrite([402(4),402(9),947(19),402(21),455(31),947(31)])].
% 2.28/2.56 3435 join(complement(complement(join(complement(c3),complement(composition(c2,complement(top)))))),complement(join(join(complement(c3),complement(composition(c2,complement(top)))),complement(join(complement(c3),complement(composition(c2,c1))))))) = join(complement(c3),complement(composition(c2,c1))). [para(100(a,1),67(a,1,2,1)),rewrite([22(29)])].
% 2.28/2.56 4363 join(A,join(complement(A),converse(B))) = top. [para(20(a,1),113(a,1,1)),rewrite([412(3)]),flip(a)].
% 2.28/2.56 4483 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(51(a,1),4363(a,1,2,2))].
% 2.28/2.56 4551 join(A,join(complement(A),composition(B,C))) = top. [para(19(a,1),4483(a,1,2,2,2))].
% 2.28/2.56 4591 join(A,composition(A,top)) = composition(A,top). [para(1813(a,1),121(a,1,1)),rewrite([51(4),402(2),402(4),19(6),22(5)]),flip(a)].
% 2.28/2.56 4630 join(A,composition(complement(A),top)) = top. [para(4591(a,1),4551(a,1,2))].
% 2.28/2.56 4669 join(A,join(B,composition(complement(A),top))) = top. [para(4630(a,1),31(a,2,2)),rewrite([22(4),171(7)])].
% 2.28/2.56 4855 join(A,composition(join(B,complement(A)),top)) = top. [para(34(a,1),4669(a,1,2))].
% 2.28/2.56 4946 join(complement(A),composition(A,top)) = top. [para(162(a,1),4855(a,1,2,1))].
% 2.28/2.56 4953 join(complement(A),join(composition(A,top),converse(B))) = top. [para(4946(a,1),113(a,1,1)),rewrite([412(3)]),flip(a)].
% 2.28/2.56 5423 join(complement(converse(complement(top))),converse(A)) = top. [para(485(a,1),4953(a,1,2,1)),rewrite([22(9),27(9),947(7)])].
% 2.28/2.56 5425 join(A,complement(converse(complement(top)))) = top. [para(19(a,1),5423(a,1,2)),rewrite([22(5)])].
% 2.28/2.56 5491 converse(complement(top)) = complement(top). [para(5425(a,1),38(a,1,1,1)),rewrite([5425(8),1775(5)]),flip(a)].
% 2.28/2.56 5677 join(complement(top),composition(A,top)) = composition(A,top). [back_rewrite(493),rewrite([5491(5),22(5),5491(8),947(8)])].
% 2.28/2.56 5684 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(56(a,1),130(a,1,1)),rewrite([27(3),29(4),19(4),19(4),19(6)]),flip(a)].
% 2.28/2.56 5759 join(complement(top),converse(A)) = converse(A). [para(5491(a,1),27(a,1,1)),rewrite([22(7),947(7)])].
% 2.28/2.56 5765 join(complement(top),composition(converse(complement(composition(A,top))),A)) = complement(top). [para(5491(a,1),62(a,1,1)),rewrite([5491(11)])].
% 2.28/2.56 5815 join(complement(top),composition(converse(A),B)) = composition(converse(A),B). [para(52(a,1),5759(a,1,2)),rewrite([52(8)])].
% 2.28/2.56 5818 composition(converse(complement(composition(A,top))),A) = complement(top). [back_rewrite(5765),rewrite([5815(8)])].
% 2.28/2.56 5930 join(complement(top),composition(top,A)) = composition(top,A). [para(5677(a,1),130(a,1,1)),rewrite([413(4),19(3),402(4),5491(7),22(7)]),flip(a)].
% 2.28/2.56 5974 complement(complement(composition(A,top))) = composition(A,top). [para(5818(a,1),63(a,1,2,2,1,1)),rewrite([19(5),5491(7),567(7),22(7),566(7),19(7)]),flip(a)].
% 2.28/2.56 6094 join(complement(top),complement(composition(A,top))) = complement(composition(A,top)). [para(5974(a,1),162(a,1,2,1))].
% 2.28/2.56 6173 composition(complement(complement(A)),top) = composition(A,top). [back_rewrite(1540),rewrite([6094(6),5974(4),6094(10),5974(8),34(7),566(3),6094(10),5974(8)]),flip(a)].
% 2.28/2.56 6410 join(composition(A,top),complement(complement(complement(A)))) = top. [para(6173(a,1),4946(a,1,2)),rewrite([22(6)])].
% 2.28/2.56 6420 join(complement(top),complement(composition(top,A))) = complement(composition(top,A)). [para(554(a,1),5930(a,1,2)),rewrite([554(11)])].
% 2.28/2.56 6433 join(complement(complement(composition(top,A))),composition(complement(complement(composition(top,converse(A)))),complement(complement(A)))) = composition(complement(complement(composition(top,converse(A)))),complement(complement(A))). [back_rewrite(2505),rewrite([6420(6),6420(11),6420(20)])].
% 2.28/2.56 6691 complement(complement(A)) = A. [para(6410(a,1),1907(a,1,2,1)),rewrite([22(5),162(5)]),flip(a)].
% 2.28/2.56 6741 composition(top,composition(converse(A),A)) = composition(top,A). [back_rewrite(6433),rewrite([6691(4),6691(7),6691(7),32(6),5684(7),1619(5),6691(7),6691(7),32(6)]),flip(a)].
% 2.28/2.56 6990 join(join(complement(c3),complement(composition(c2,complement(top)))),complement(join(join(complement(c3),complement(composition(c2,complement(top)))),complement(join(complement(c3),complement(composition(c2,c1))))))) = join(complement(c3),complement(composition(c2,c1))). [back_rewrite(3435),rewrite([6691(10)])].
% 2.28/2.56 7711 composition(complement(top),complement(top)) = complement(top). [para(465(a,1),6741(a,2)),rewrite([5491(4),486(7)])].
% 2.28/2.56 7847 composition(A,complement(top)) = complement(top). [para(7711(a,1),34(a,1,1)),rewrite([139(6,R),484(5),22(5),947(5)]),flip(a)].
% 2.28/2.56 7858 join(complement(c3),complement(composition(c2,c1))) = top. [back_rewrite(6990),rewrite([7847(6),6691(5),22(4),170(4),7847(7),6691(6),22(5),170(5),170(11),20(4)]),flip(a)].
% 2.28/2.56 7907 $F # answer(goals). [back_rewrite(49),rewrite([7858(7)]),xx(a)].
% 2.28/2.56
% 2.28/2.56 % SZS output end Refutation
% 2.28/2.56 ============================== end of proof ==========================
% 2.28/2.56
% 2.28/2.56 ============================== STATISTICS ============================
% 2.28/2.56
% 2.28/2.56 Given=320. Generated=33475. Kept=7878. proofs=1.
% 2.28/2.56 Usable=226. Sos=4036. Demods=4271. Limbo=49, Disabled=3585. Hints=0.
% 2.28/2.56 Megabytes=18.38.
% 2.28/2.56 User_CPU=1.64, System_CPU=0.03, Wall_clock=2.
% 2.28/2.56
% 2.28/2.56 ============================== end of statistics =====================
% 2.28/2.56
% 2.28/2.56 ============================== end of search =========================
% 2.28/2.56
% 2.28/2.56 THEOREM PROVED
% 2.28/2.56 % SZS status Theorem
% 2.28/2.56
% 2.28/2.56 Exiting with 1 proof.
% 2.28/2.56
% 2.28/2.56 Process 6074 exit (max_proofs) Fri Jul 8 07:43:24 2022
% 2.28/2.56 Prover9 interrupted
%------------------------------------------------------------------------------