TSTP Solution File: REL010+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL010+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 19:53:35 EDT 2022
% Result : Theorem 2.63s 2.93s
% Output : Refutation 2.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL010+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 14:26:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.42/0.99 ============================== Prover9 ===============================
% 0.42/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.99 Process 5619 was started by sandbox2 on n008.cluster.edu,
% 0.42/0.99 Fri Jul 8 14:26:09 2022
% 0.42/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5466_n008.cluster.edu".
% 0.42/0.99 ============================== end of head ===========================
% 0.42/0.99
% 0.42/0.99 ============================== INPUT =================================
% 0.42/0.99
% 0.42/0.99 % Reading from file /tmp/Prover9_5466_n008.cluster.edu
% 0.42/0.99
% 0.42/0.99 set(prolog_style_variables).
% 0.42/0.99 set(auto2).
% 0.42/0.99 % set(auto2) -> set(auto).
% 0.42/0.99 % set(auto) -> set(auto_inference).
% 0.42/0.99 % set(auto) -> set(auto_setup).
% 0.42/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.99 % set(auto) -> set(auto_limits).
% 0.42/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.99 % set(auto) -> set(auto_denials).
% 0.42/0.99 % set(auto) -> set(auto_process).
% 0.42/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.99 % set(auto2) -> assign(stats, some).
% 0.42/0.99 % set(auto2) -> clear(echo_input).
% 0.42/0.99 % set(auto2) -> set(quiet).
% 0.42/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.99 % set(auto2) -> clear(print_given).
% 0.42/0.99 assign(lrs_ticks,-1).
% 0.42/0.99 assign(sos_limit,10000).
% 0.42/0.99 assign(order,kbo).
% 0.42/0.99 set(lex_order_vars).
% 0.42/0.99 clear(print_given).
% 0.42/0.99
% 0.42/0.99 % formulas(sos). % not echoed (17 formulas)
% 0.42/0.99
% 0.42/0.99 ============================== end of input ==========================
% 0.42/0.99
% 0.42/0.99 % From the command line: assign(max_seconds, 300).
% 0.42/0.99
% 0.42/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.99
% 0.42/0.99 % Formulas that are not ordinary clauses:
% 0.42/0.99 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 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].
% 0.42/0.99 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].
% 0.42/0.99 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].
% 0.42/0.99 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].
% 0.42/0.99 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 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].
% 0.42/0.99 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 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].
% 0.42/0.99 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.93 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].
% 2.63/2.93 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].
% 2.63/2.93 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].
% 2.63/2.93 17 -(all X0 all X1 all X2 (meet(composition(X0,X1),X2) = zero -> meet(X1,composition(converse(X0),X2)) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.63/2.93
% 2.63/2.93 ============================== end of process non-clausal formulas ===
% 2.63/2.93
% 2.63/2.93 ============================== PROCESS INITIAL CLAUSES ===============
% 2.63/2.93
% 2.63/2.93 ============================== PREDICATE ELIMINATION =================
% 2.63/2.93
% 2.63/2.93 ============================== end predicate elimination =============
% 2.63/2.93
% 2.63/2.93 Auto_denials:
% 2.63/2.93 % copying label goals to answer in negative clause
% 2.63/2.93
% 2.63/2.93 Term ordering decisions:
% 2.63/2.93 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.
% 2.63/2.93
% 2.63/2.93 ============================== end of process initial clauses ========
% 2.63/2.93
% 2.63/2.93 ============================== CLAUSES FOR SEARCH ====================
% 2.63/2.93
% 2.63/2.93 ============================== end of clauses for search =============
% 2.63/2.93
% 2.63/2.93 ============================== SEARCH ================================
% 2.63/2.93
% 2.63/2.93 % Starting search at 0.02 seconds.
% 2.63/2.93
% 2.63/2.93 ============================== PROOF =================================
% 2.63/2.93 % SZS status Theorem
% 2.63/2.93 % SZS output start Refutation
% 2.63/2.93
% 2.63/2.93 % Proof 1 at 1.94 (+ 0.03) seconds: goals.
% 2.63/2.93 % Length of proof is 165.
% 2.63/2.93 % Level of proof is 39.
% 2.63/2.93 % Maximum clause weight is 49.000.
% 2.63/2.93 % Given clauses 336.
% 2.63/2.93
% 2.63/2.93 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.93 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].
% 2.63/2.93 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].
% 2.63/2.93 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].
% 2.63/2.93 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].
% 2.63/2.93 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.93 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].
% 2.63/2.93 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.93 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.93 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.93 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].
% 2.63/2.93 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.93 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.93 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].
% 2.63/2.93 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].
% 2.63/2.93 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].
% 2.63/2.93 17 -(all X0 all X1 all X2 (meet(composition(X0,X1),X2) = zero -> meet(X1,composition(converse(X0),X2)) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.63/2.93 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 2.63/2.93 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 2.63/2.93 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 2.63/2.93 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 2.63/2.93 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 2.63/2.93 23 meet(composition(c1,c2),c3) = zero # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.63/2.93 24 zero = meet(composition(c1,c2),c3). [copy(23),flip(a)].
% 2.63/2.93 25 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 2.63/2.93 26 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 2.63/2.93 27 join(converse(A),converse(B)) = converse(join(A,B)). [copy(26),flip(a)].
% 2.63/2.93 28 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 2.63/2.93 29 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(28),flip(a)].
% 2.63/2.93 30 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 2.63/2.93 31 join(A,join(B,C)) = join(C,join(A,B)). [copy(30),rewrite([22(2)]),flip(a)].
% 2.63/2.93 32 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 2.63/2.93 33 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 2.63/2.93 34 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(33),flip(a)].
% 2.63/2.93 35 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 2.63/2.93 36 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(35),rewrite([22(7)]),flip(a)].
% 2.63/2.93 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)].
% 2.63/2.93 38 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(37),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 2.63/2.93 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)].
% 2.63/2.93 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)].
% 2.63/2.93 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)].
% 2.63/2.93 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)].
% 2.63/2.93 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)].
% 2.63/2.93 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)].
% 2.63/2.93 45 meet(c2,composition(converse(c1),c3)) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 2.63/2.93 46 complement(join(complement(c2),complement(composition(converse(c1),c3)))) != complement(join(complement(c3),complement(composition(c1,c2)))) # answer(goals). [copy(45),rewrite([25(6),24(10),25(14),22(16)])].
% 2.63/2.93 47 complement(join(complement(c3),complement(composition(c1,c2)))) = complement(top). [back_rewrite(21),rewrite([25(2),20(4),24(3),25(7),22(9)]),flip(a)].
% 2.63/2.93 49 complement(join(complement(c2),complement(composition(converse(c1),c3)))) != complement(top) # answer(goals). [back_rewrite(46),rewrite([47(17)])].
% 2.63/2.93 50 converse(join(A,converse(B))) = join(B,converse(A)). [para(19(a,1),27(a,1,1)),rewrite([22(4)]),flip(a)].
% 2.63/2.93 51 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),29(a,1,1)),flip(a)].
% 2.63/2.93 52 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),29(a,1,2)),flip(a)].
% 2.63/2.93 53 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),31(a,2,2)),rewrite([22(2)])].
% 2.63/2.93 54 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),32(a,1,1)),flip(a)].
% 2.63/2.93 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)])].
% 2.63/2.93 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))].
% 2.63/2.93 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)])].
% 2.63/2.93 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)])].
% 2.63/2.93 65 join(complement(top),complement(join(complement(A),complement(A)))) = A. [para(20(a,1),38(a,1,1,1))].
% 2.63/2.93 66 join(complement(top),complement(join(A,complement(complement(A))))) = complement(A). [para(20(a,1),38(a,1,2,1)),rewrite([22(7)])].
% 2.63/2.93 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)])].
% 2.63/2.93 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)])].
% 2.63/2.93 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)])].
% 2.63/2.93 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)])].
% 2.63/2.93 96 join(complement(c3),complement(composition(c1,c2))) = top. [para(47(a,1),38(a,1,1,1,2)),rewrite([47(13),38(10)]),flip(a)].
% 2.63/2.93 102 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)].
% 2.63/2.93 103 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),102(7)]),flip(a)].
% 2.63/2.93 111 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(50(a,1),50(a,2,2)),rewrite([103(4),50(4),31(6,R),22(5)])].
% 2.63/2.93 119 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)].
% 2.63/2.93 127 composition(converse(one),A) = A. [para(18(a,1),52(a,1,1)),rewrite([19(2)]),flip(a)].
% 2.63/2.93 128 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)].
% 2.63/2.93 136 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)].
% 2.63/2.93 137 join(top,complement(complement(A))) = top. [para(40(a,1),53(a,1,2)),rewrite([20(22),22(8),136(8)]),flip(a)].
% 2.63/2.93 139 converse(one) = one. [para(127(a,1),18(a,1)),flip(a)].
% 2.63/2.93 141 composition(join(A,one),B) = join(B,composition(A,B)). [para(127(a,1),34(a,1,1)),rewrite([139(4),22(4)]),flip(a)].
% 2.63/2.93 142 composition(join(one,one),complement(A)) = complement(A). [para(127(a,1),36(a,1,2,2,1)),rewrite([139(3),139(3),141(5,R)])].
% 2.63/2.93 143 join(complement(A),complement(composition(one,A))) = complement(A). [para(127(a,1),36(a,1,2))].
% 2.63/2.93 157 composition(one,A) = A. [para(127(a,1),54(a,2)),rewrite([139(2),54(4)])].
% 2.63/2.93 163 join(complement(A),complement(A)) = complement(A). [back_rewrite(143),rewrite([157(3)])].
% 2.63/2.93 164 join(complement(top),complement(complement(A))) = A. [back_rewrite(65),rewrite([163(5)])].
% 2.63/2.93 165 converse(join(A,one)) = join(one,converse(A)). [para(139(a,1),27(a,1,1)),rewrite([22(5)]),flip(a)].
% 2.63/2.93 166 join(complement(A),complement(top)) = complement(A). [para(137(a,1),38(a,1,1,1)),rewrite([164(7),22(4)])].
% 2.63/2.93 167 join(top,complement(A)) = join(top,top). [para(137(a,1),53(a,1,2)),rewrite([22(3)])].
% 2.63/2.93 169 join(top,top) = top. [back_rewrite(137),rewrite([167(4)])].
% 2.63/2.93 171 join(top,complement(A)) = top. [back_rewrite(167),rewrite([169(6)])].
% 2.63/2.93 178 join(A,top) = top. [para(169(a,1),53(a,2)),rewrite([171(3)])].
% 2.63/2.93 195 join(complement(complement(A)),complement(join(A,complement(top)))) = top. [para(166(a,1),38(a,1,2,1)),rewrite([22(7)])].
% 2.63/2.93 202 composition(join(A,join(one,one)),complement(B)) = composition(join(A,one),complement(B)). [para(142(a,1),34(a,1,1)),rewrite([141(4,R),22(8)]),flip(a)].
% 2.63/2.93 246 composition(join(one,one),A) = join(A,A). [para(157(a,1),141(a,2,2))].
% 2.63/2.93 272 composition(A,join(one,one)) = join(A,A). [para(246(a,2),50(a,1,1)),rewrite([51(6),165(4),139(3),19(6)])].
% 2.63/2.93 275 composition(join(one,one),top) = top. [para(246(a,2),178(a,1))].
% 2.63/2.93 286 composition(converse(top),join(one,one)) = converse(top). [para(275(a,1),29(a,2,1)),rewrite([165(6),139(5)])].
% 2.63/2.93 304 join(A,join(A,composition(B,join(one,one)))) = composition(join(B,A),join(one,one)). [para(272(a,1),34(a,1,2)),rewrite([31(6),22(5)])].
% 2.63/2.93 316 composition(top,join(one,one)) = top. [para(272(a,2),178(a,1))].
% 2.63/2.93 327 composition(join(one,one),A) = composition(A,join(one,one)). [para(272(a,2),246(a,2))].
% 2.63/2.93 353 composition(top,composition(A,join(one,one))) = composition(top,A). [para(316(a,1),32(a,1,1)),rewrite([327(7)]),flip(a)].
% 2.63/2.93 354 join(top,composition(A,join(one,one))) = top. [para(316(a,1),34(a,1,1)),rewrite([22(8),178(8),316(11)])].
% 2.63/2.93 392 join(top,converse(top)) = top. [para(286(a,1),354(a,1,2))].
% 2.63/2.93 398 converse(top) = top. [para(392(a,1),27(a,2,1)),rewrite([19(5),22(4),392(4)]),flip(a)].
% 2.63/2.93 407 join(top,converse(A)) = top. [para(398(a,1),27(a,1,1)),rewrite([22(5),178(5),398(5)])].
% 2.63/2.93 408 converse(composition(A,top)) = composition(top,converse(A)). [para(398(a,1),29(a,1,1)),flip(a)].
% 2.63/2.93 416 join(top,composition(A,converse(B))) = top. [para(51(a,1),407(a,1,2))].
% 2.63/2.93 419 composition(join(A,one),top) = top. [para(398(a,1),416(a,1,2,2)),rewrite([141(4,R)])].
% 2.63/2.93 429 composition(top,join(one,converse(A))) = top. [para(419(a,1),29(a,2,1)),rewrite([398(2),165(4),398(7)])].
% 2.63/2.93 440 composition(top,join(A,one)) = top. [para(19(a,1),429(a,1,2,2)),rewrite([22(3)])].
% 2.63/2.93 450 composition(top,top) = top. [para(398(a,1),429(a,1,2,2)),rewrite([178(4)])].
% 2.63/2.93 452 composition(top,composition(top,A)) = composition(top,A). [para(450(a,1),32(a,1,1)),flip(a)].
% 2.63/2.93 453 composition(top,complement(top)) = complement(top). [para(450(a,1),36(a,1,2,2,1)),rewrite([398(4),141(7,R),22(3),178(3)])].
% 2.63/2.93 469 composition(top,composition(join(A,one),B)) = composition(top,B). [para(440(a,1),32(a,1,1)),flip(a)].
% 2.63/2.94 479 composition(join(A,one),complement(top)) = complement(top). [para(440(a,1),63(a,1,2,2,1,1)),rewrite([398(2),398(6),141(8,R),22(4),31(4,R),202(7),398(7)])].
% 2.63/2.94 480 composition(converse(complement(top)),top) = converse(complement(top)). [para(453(a,1),29(a,2,1)),rewrite([398(5)])].
% 2.63/2.94 481 composition(top,composition(complement(top),A)) = composition(complement(top),A). [para(453(a,1),32(a,1,1)),flip(a)].
% 2.63/2.94 488 join(composition(A,top),converse(complement(top))) = composition(join(A,converse(complement(top))),top). [para(453(a,1),57(a,1,2,1)),rewrite([398(2),398(12)])].
% 2.63/2.94 549 composition(top,complement(composition(top,A))) = complement(composition(top,A)). [para(452(a,1),36(a,1,2,2,1)),rewrite([398(5),141(9,R),22(3),178(3)])].
% 2.63/2.94 573 join(A,complement(complement(A))) = A. [para(66(a,1),38(a,1,2,1)),rewrite([171(6),164(5)]),flip(a)].
% 2.63/2.94 574 complement(complement(top)) = top. [para(164(a,1),66(a,1,2,1)),rewrite([20(6)]),flip(a)].
% 2.63/2.94 583 join(A,join(B,complement(complement(A)))) = join(A,B). [para(573(a,1),31(a,2,2)),rewrite([22(3),22(5)])].
% 2.63/2.94 696 join(complement(top),complement(join(A,complement(top)))) = complement(A). [para(166(a,1),69(a,1,2,1,2,1)),rewrite([22(8),31(8),22(7),573(7),22(5),166(11)])].
% 2.63/2.94 946 join(complement(top),complement(join(complement(complement(complement(A))),complement(join(A,complement(top)))))) = join(A,complement(top)). [para(195(a,1),38(a,1,1,1))].
% 2.63/2.94 948 join(complement(complement(complement(A))),complement(join(A,complement(top)))) = complement(A). [para(195(a,1),68(a,1,2,1,2,1,1)),rewrite([22(12),574(16),22(15),171(15),22(7),696(7),22(9)]),flip(a)].
% 2.63/2.94 949 join(A,complement(top)) = A. [back_rewrite(946),rewrite([948(10),164(5)]),flip(a)].
% 2.63/2.94 1219 composition(top,join(A,A)) = composition(top,A). [para(272(a,1),353(a,1,2))].
% 2.63/2.94 1241 join(join(A,A),composition(top,A)) = composition(top,A). [para(1219(a,1),141(a,2,2)),rewrite([22(3),178(3),1219(3)]),flip(a)].
% 2.63/2.94 1563 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(450(a,1),79(a,1,2,1,2,1,1,1,2,1)),rewrite([398(4),949(13),398(13),450(23),949(23),398(23)])].
% 2.63/2.94 1620 composition(top,join(A,composition(B,A))) = composition(top,A). [para(141(a,1),469(a,1,2))].
% 2.63/2.94 1784 join(A,A) = A. [para(164(a,1),583(a,1,2)),rewrite([949(4)])].
% 2.63/2.94 1821 join(A,composition(top,A)) = composition(top,A). [back_rewrite(1241),rewrite([1784(1)])].
% 2.63/2.94 1843 join(A,join(A,B)) = join(A,B). [back_rewrite(304),rewrite([1784(3),18(2),22(3),1784(6),18(5)])].
% 2.63/2.94 1917 join(A,complement(join(B,complement(A)))) = A. [para(38(a,1),1843(a,1,2)),rewrite([22(4),38(12)])].
% 2.63/2.94 2498 join(complement(join(complement(c2),complement(composition(converse(c1),c3)))),composition(complement(join(complement(converse(c1)),complement(composition(c2,converse(c3))))),complement(top))) = composition(complement(join(complement(converse(c1)),complement(composition(c2,converse(c3))))),complement(top)). [para(96(a,1),89(a,1,2,2,1)),rewrite([96(40)])].
% 2.63/2.94 2507 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(450(a,1),89(a,1,2,2,1,2,1)),rewrite([398(4),398(9),949(19),398(21),450(31),949(31)])].
% 2.63/2.94 4378 join(A,join(complement(A),converse(B))) = top. [para(20(a,1),111(a,1,1)),rewrite([407(3)]),flip(a)].
% 2.63/2.94 4454 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(51(a,1),4378(a,1,2,2))].
% 2.63/2.94 4708 join(A,composition(A,top)) = composition(A,top). [para(1821(a,1),119(a,1,1)),rewrite([51(4),398(2),398(4),19(6),22(5)]),flip(a)].
% 2.63/2.94 4825 join(A,join(complement(A),composition(B,C))) = top. [para(19(a,1),4454(a,1,2,2,2))].
% 2.63/2.94 4839 join(A,composition(complement(A),top)) = top. [para(4708(a,1),4825(a,1,2))].
% 2.63/2.94 4896 join(A,join(B,composition(complement(A),top))) = top. [para(4839(a,1),31(a,2,2)),rewrite([22(4),178(7)])].
% 2.63/2.94 4924 join(A,composition(join(B,complement(A)),top)) = top. [para(34(a,1),4896(a,1,2))].
% 2.63/2.94 4971 join(complement(A),composition(A,top)) = top. [para(164(a,1),4924(a,1,2,1))].
% 2.63/2.94 4979 join(complement(A),join(composition(A,top),converse(B))) = top. [para(4971(a,1),111(a,1,1)),rewrite([407(3)]),flip(a)].
% 2.63/2.94 5410 join(complement(converse(complement(top))),converse(A)) = top. [para(480(a,1),4979(a,1,2,1)),rewrite([22(9),27(9),949(7)])].
% 2.63/2.94 5412 join(A,complement(converse(complement(top)))) = top. [para(19(a,1),5410(a,1,2)),rewrite([22(5)])].
% 2.63/2.94 5488 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(56(a,1),128(a,1,1)),rewrite([27(3),29(4),19(4),19(4),19(6)]),flip(a)].
% 2.63/2.94 5589 converse(complement(top)) = complement(top). [para(5412(a,1),38(a,1,1,1)),rewrite([5412(8),1784(5)]),flip(a)].
% 2.63/2.94 5775 join(complement(top),composition(A,top)) = composition(A,top). [back_rewrite(488),rewrite([5589(5),22(5),5589(8),949(8)])].
% 2.63/2.94 5777 join(complement(top),converse(A)) = converse(A). [para(5589(a,1),27(a,1,1)),rewrite([22(7),949(7)])].
% 2.63/2.94 5783 join(complement(top),composition(converse(complement(composition(A,top))),A)) = complement(top). [para(5589(a,1),62(a,1,1)),rewrite([5589(11)])].
% 2.63/2.94 5833 join(complement(top),composition(converse(A),B)) = composition(converse(A),B). [para(52(a,1),5777(a,1,2)),rewrite([52(8)])].
% 2.63/2.94 5836 composition(converse(complement(composition(A,top))),A) = complement(top). [back_rewrite(5783),rewrite([5833(8)])].
% 2.63/2.94 6179 join(complement(top),composition(top,A)) = composition(top,A). [para(5775(a,1),128(a,1,1)),rewrite([408(4),19(3),398(4),5589(7),22(7)]),flip(a)].
% 2.63/2.94 6203 complement(complement(composition(A,top))) = composition(A,top). [para(5836(a,1),63(a,1,2,2,1,1)),rewrite([19(5),5589(7),574(7),22(7),573(7),19(7)]),flip(a)].
% 2.63/2.94 6308 join(complement(top),complement(composition(A,top))) = complement(composition(A,top)). [para(6203(a,1),164(a,1,2,1))].
% 2.63/2.94 6392 composition(complement(complement(A)),top) = composition(A,top). [back_rewrite(1563),rewrite([6308(6),6203(4),6308(10),6203(8),34(7),573(3),6308(10),6203(8)]),flip(a)].
% 2.63/2.94 6437 join(composition(A,top),complement(complement(complement(A)))) = top. [para(6392(a,1),4971(a,1,2)),rewrite([22(6)])].
% 2.63/2.94 6497 join(complement(top),complement(composition(top,A))) = complement(composition(top,A)). [para(549(a,1),6179(a,1,2)),rewrite([549(11)])].
% 2.63/2.94 6510 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(2507),rewrite([6497(6),6497(11),6497(20)])].
% 2.63/2.94 6716 complement(complement(A)) = A. [para(6437(a,1),1917(a,1,2,1)),rewrite([22(5),164(5)]),flip(a)].
% 2.63/2.94 6759 composition(top,composition(converse(A),A)) = composition(top,A). [back_rewrite(6510),rewrite([6716(4),6716(7),6716(7),32(6),5488(7),1620(5),6716(7),6716(7),32(6)]),flip(a)].
% 2.63/2.94 7622 join(complement(A),complement(join(A,B))) = complement(A). [para(6716(a,1),1917(a,1,2,1,2)),rewrite([22(2)])].
% 2.63/2.94 7774 composition(complement(top),complement(top)) = complement(top). [para(453(a,1),6759(a,2)),rewrite([5589(4),481(7)])].
% 2.63/2.94 7915 composition(A,complement(top)) = complement(top). [para(7774(a,1),34(a,1,1)),rewrite([141(6,R),479(5),22(5),949(5)]),flip(a)].
% 2.63/2.94 7975 join(complement(top),complement(join(complement(c2),complement(composition(converse(c1),c3))))) = complement(top). [back_rewrite(2498),rewrite([7915(22),22(12),7915(25)])].
% 2.63/2.94 8289 join(join(A,B),composition(complement(A),top)) = top. [para(7622(a,1),4924(a,1,2,1))].
% 2.63/2.94 9302 join(complement(top),complement(join(A,B))) = complement(join(A,B)). [para(8289(a,1),7622(a,1,2,1)),rewrite([22(5)])].
% 2.63/2.94 9320 complement(join(complement(c2),complement(composition(converse(c1),c3)))) = complement(top). [back_rewrite(7975),rewrite([9302(12)])].
% 2.63/2.94 9321 $F # answer(goals). [resolve(9320,a,49,a)].
% 2.63/2.94
% 2.63/2.94 % SZS output end Refutation
% 2.63/2.94 ============================== end of proof ==========================
% 2.63/2.94
% 2.63/2.94 ============================== STATISTICS ============================
% 2.63/2.94
% 2.63/2.94 Given=336. Generated=36000. Kept=9292. proofs=1.
% 2.63/2.94 Usable=237. Sos=3967. Demods=4185. Limbo=18, Disabled=5087. Hints=0.
% 2.63/2.94 Megabytes=19.62.
% 2.63/2.94 User_CPU=1.94, System_CPU=0.03, Wall_clock=2.
% 2.63/2.94
% 2.63/2.94 ============================== end of statistics =====================
% 2.63/2.94
% 2.63/2.94 ============================== end of search =========================
% 2.63/2.94
% 2.63/2.94 THEOREM PROVED
% 2.63/2.94 % SZS status Theorem
% 2.63/2.94
% 2.63/2.94 Exiting with 1 proof.
% 2.63/2.94
% 2.63/2.94 Process 5619 exit (max_proofs) Fri Jul 8 14:26:11 2022
% 2.63/2.94 Prover9 interrupted
%------------------------------------------------------------------------------