TSTP Solution File: REL006+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL006+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 19:53:29 EDT 2022
% Result : Theorem 4.31s 4.63s
% Output : Refutation 4.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL006+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 11:30:06 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.45/1.01 ============================== Prover9 ===============================
% 0.45/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.01 Process 18575 was started by sandbox on n014.cluster.edu,
% 0.45/1.01 Fri Jul 8 11:30:07 2022
% 0.45/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18124_n014.cluster.edu".
% 0.45/1.01 ============================== end of head ===========================
% 0.45/1.01
% 0.45/1.01 ============================== INPUT =================================
% 0.45/1.01
% 0.45/1.01 % Reading from file /tmp/Prover9_18124_n014.cluster.edu
% 0.45/1.01
% 0.45/1.01 set(prolog_style_variables).
% 0.45/1.01 set(auto2).
% 0.45/1.01 % set(auto2) -> set(auto).
% 0.45/1.01 % set(auto) -> set(auto_inference).
% 0.45/1.01 % set(auto) -> set(auto_setup).
% 0.45/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.01 % set(auto) -> set(auto_limits).
% 0.45/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.01 % set(auto) -> set(auto_denials).
% 0.45/1.01 % set(auto) -> set(auto_process).
% 0.45/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.01 % set(auto2) -> assign(stats, some).
% 0.45/1.01 % set(auto2) -> clear(echo_input).
% 0.45/1.01 % set(auto2) -> set(quiet).
% 0.45/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.01 % set(auto2) -> clear(print_given).
% 0.45/1.01 assign(lrs_ticks,-1).
% 0.45/1.01 assign(sos_limit,10000).
% 0.45/1.01 assign(order,kbo).
% 0.45/1.01 set(lex_order_vars).
% 0.45/1.01 clear(print_given).
% 0.45/1.01
% 0.45/1.01 % formulas(sos). % not echoed (14 formulas)
% 0.45/1.01
% 0.45/1.01 ============================== end of input ==========================
% 0.45/1.01
% 0.45/1.01 % From the command line: assign(max_seconds, 300).
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.01
% 0.45/1.01 % Formulas that are not ordinary clauses:
% 0.45/1.01 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 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].
% 0.45/1.01 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].
% 0.45/1.01 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].
% 0.45/1.01 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].
% 0.45/1.01 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 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].
% 0.45/1.01 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 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].
% 0.45/1.01 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 4.31/4.63 14 -(all X0 all X1 (meet(converse(X0),X1) = zero -> meet(X0,converse(X1)) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.31/4.63
% 4.31/4.63 ============================== end of process non-clausal formulas ===
% 4.31/4.63
% 4.31/4.63 ============================== PROCESS INITIAL CLAUSES ===============
% 4.31/4.63
% 4.31/4.63 ============================== PREDICATE ELIMINATION =================
% 4.31/4.63
% 4.31/4.63 ============================== end predicate elimination =============
% 4.31/4.63
% 4.31/4.63 Auto_denials:
% 4.31/4.63 % copying label goals to answer in negative clause
% 4.31/4.63
% 4.31/4.63 Term ordering decisions:
% 4.31/4.63 Function symbol KB weights: zero=1. one=1. top=1. c1=1. c2=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 4.31/4.63
% 4.31/4.63 ============================== end of process initial clauses ========
% 4.31/4.63
% 4.31/4.63 ============================== CLAUSES FOR SEARCH ====================
% 4.31/4.63
% 4.31/4.63 ============================== end of clauses for search =============
% 4.31/4.63
% 4.31/4.63 ============================== SEARCH ================================
% 4.31/4.63
% 4.31/4.63 % Starting search at 0.01 seconds.
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=49.000, iters=3475
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=39.000, iters=3463
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=33.000, iters=3341
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=31.000, iters=3375
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=30.000, iters=3364
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=29.000, iters=3333
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=28.000, iters=3333
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=27.000, iters=3336
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=26.000, iters=3334
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=25.000, iters=3354
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=24.000, iters=3351
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=23.000, iters=3369
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=22.000, iters=3355
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=21.000, iters=3348
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=20.000, iters=3346
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=6454, wt=50.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=7293, wt=44.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=6911, wt=42.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=6453, wt=41.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=7409, wt=40.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=6749, wt=39.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=7289, wt=38.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=13944, wt=18.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=13945, wt=16.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=14094, wt=15.000
% 4.31/4.63
% 4.31/4.63 Low Water (displace): id=14098, wt=14.000
% 4.31/4.63
% 4.31/4.63 Low Water (keep): wt=19.000, iters=3435
% 4.31/4.63
% 4.31/4.63 ============================== PROOF =================================
% 4.31/4.63 % SZS status Theorem
% 4.31/4.63 % SZS output start Refutation
% 4.31/4.63
% 4.31/4.63 % Proof 1 at 3.50 (+ 0.12) seconds: goals.
% 4.31/4.63 % Length of proof is 174.
% 4.31/4.63 % Level of proof is 46.
% 4.31/4.63 % Maximum clause weight is 33.000.
% 4.31/4.63 % Given clauses 988.
% 4.31/4.63
% 4.31/4.63 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 4.31/4.63 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].
% 4.31/4.63 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].
% 4.31/4.63 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].
% 4.31/4.63 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].
% 4.31/4.63 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 4.31/4.63 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].
% 4.31/4.63 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 4.31/4.63 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 4.31/4.63 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 4.31/4.63 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].
% 4.31/4.63 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 4.31/4.63 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 4.31/4.63 14 -(all X0 all X1 (meet(converse(X0),X1) = zero -> meet(X0,converse(X1)) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.31/4.63 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 4.31/4.63 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 4.31/4.63 17 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 4.31/4.63 18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 4.31/4.63 19 meet(converse(c1),c2) = zero # label(goals) # label(negated_conjecture). [clausify(14)].
% 4.31/4.63 20 zero = meet(converse(c1),c2). [copy(19),flip(a)].
% 4.31/4.63 21 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 4.31/4.63 22 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 4.31/4.63 23 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 4.31/4.63 24 join(converse(A),converse(B)) = converse(join(A,B)). [copy(23),flip(a)].
% 4.31/4.63 25 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 4.31/4.63 26 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(25),flip(a)].
% 4.31/4.63 27 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 4.31/4.63 28 join(A,join(B,C)) = join(C,join(A,B)). [copy(27),rewrite([21(2)]),flip(a)].
% 4.31/4.63 29 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 4.31/4.63 30 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 4.31/4.63 31 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(30),flip(a)].
% 4.31/4.63 32 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 4.31/4.63 33 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(32),rewrite([21(7)]),flip(a)].
% 4.31/4.63 34 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 4.31/4.63 35 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(34),rewrite([21(6),21(8)]),rewrite([21(6)])].
% 4.31/4.63 36 meet(c1,converse(c2)) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 4.31/4.63 37 complement(join(complement(c2),complement(converse(c1)))) != complement(join(complement(c1),complement(converse(c2)))) # answer(goals). [copy(36),rewrite([22(4),20(8),22(11),21(13)]),flip(a)].
% 4.31/4.63 38 complement(join(complement(c2),complement(converse(c1)))) = complement(top). [back_rewrite(18),rewrite([22(2),17(4),20(3),22(6),21(8)]),flip(a)].
% 4.31/4.63 40 complement(join(complement(c1),complement(converse(c2)))) != complement(top) # answer(goals). [back_rewrite(37),rewrite([38(7)]),flip(a)].
% 4.31/4.63 41 converse(join(A,converse(B))) = join(B,converse(A)). [para(16(a,1),24(a,1,1)),rewrite([21(4)]),flip(a)].
% 4.31/4.63 42 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(16(a,1),26(a,1,1)),flip(a)].
% 4.31/4.63 43 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),26(a,1,2)),flip(a)].
% 4.31/4.63 44 join(A,join(B,complement(A))) = join(B,top). [para(17(a,1),28(a,2,2)),rewrite([21(2)])].
% 4.31/4.63 45 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),29(a,1,1)),flip(a)].
% 4.31/4.63 47 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(26(a,1),31(a,1,1)),rewrite([21(7)])].
% 4.31/4.63 52 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(16(a,1),33(a,1,2,1))].
% 4.31/4.63 55 join(complement(A),composition(converse(composition(B,C)),complement(composition(B,composition(C,A))))) = complement(A). [para(29(a,1),33(a,1,2,2,1))].
% 4.31/4.63 56 join(complement(top),complement(join(complement(A),complement(A)))) = A. [para(17(a,1),35(a,1,1,1))].
% 4.31/4.63 57 join(complement(top),complement(join(A,complement(complement(A))))) = complement(A). [para(17(a,1),35(a,1,2,1)),rewrite([21(7)])].
% 4.31/4.63 58 join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B. [para(35(a,1),21(a,1)),rewrite([21(3),21(8)]),flip(a)].
% 4.31/4.63 59 join(complement(A),complement(join(complement(join(complement(A),complement(B))),complement(complement(join(B,complement(A))))))) = join(complement(A),complement(B)). [para(35(a,1),35(a,1,1,1)),rewrite([21(8),21(10),21(15)])].
% 4.31/4.63 60 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(35(a,1),35(a,1,2,1)),rewrite([21(10)])].
% 4.31/4.63 63 join(complement(c2),complement(converse(c1))) = top. [para(38(a,1),35(a,1,1,1,2)),rewrite([38(12),35(10)]),flip(a)].
% 4.31/4.63 66 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(41(a,1),24(a,1,1)),rewrite([21(7),28(7,R),21(6)]),flip(a)].
% 4.31/4.63 67 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(41(a,1),24(a,1,2)),rewrite([28(4,R),21(3),24(3),66(7)]),flip(a)].
% 4.31/4.63 71 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(41(a,1),41(a,2,2)),rewrite([67(4),41(4),28(6,R),21(5)])].
% 4.31/4.63 72 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(66),rewrite([71(8),24(7)])].
% 4.31/4.63 74 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(42(a,1),24(a,1,1)),rewrite([21(7)]),flip(a)].
% 4.31/4.63 78 composition(converse(one),A) = A. [para(15(a,1),43(a,1,1)),rewrite([16(2)]),flip(a)].
% 4.31/4.63 79 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(43(a,1),24(a,1,1)),rewrite([21(7)]),flip(a)].
% 4.31/4.63 84 join(top,converse(c1)) = join(top,complement(c2)). [para(63(a,1),44(a,1,2)),rewrite([21(4),21(8)])].
% 4.31/4.63 85 converse(one) = one. [para(78(a,1),15(a,1)),flip(a)].
% 4.31/4.63 87 composition(join(A,one),B) = join(B,composition(A,B)). [para(78(a,1),31(a,1,1)),rewrite([85(4),21(4)]),flip(a)].
% 4.31/4.63 89 join(complement(A),complement(composition(one,A))) = complement(A). [para(78(a,1),33(a,1,2))].
% 4.31/4.63 90 composition(one,A) = A. [para(78(a,1),45(a,2)),rewrite([85(2),45(4)])].
% 4.31/4.63 91 join(complement(A),complement(A)) = complement(A). [back_rewrite(89),rewrite([90(3)])].
% 4.31/4.63 92 join(complement(top),complement(complement(A))) = A. [back_rewrite(56),rewrite([91(5)])].
% 4.31/4.63 93 converse(join(A,one)) = join(one,converse(A)). [para(85(a,1),24(a,1,1)),rewrite([21(5)]),flip(a)].
% 4.31/4.63 94 join(top,complement(A)) = top. [para(91(a,1),44(a,1,2)),rewrite([17(2),21(4)]),flip(a)].
% 4.31/4.63 95 join(top,converse(c1)) = top. [back_rewrite(84),rewrite([94(8)])].
% 4.31/4.63 98 join(top,top) = join(A,top). [para(94(a,1),44(a,1,2)),flip(a)].
% 4.31/4.63 104 join(A,top) = join(B,top). [para(98(a,1),44(a,2)),rewrite([94(3)])].
% 4.31/4.63 105 join(A,top) = c_0. [new_symbol(104)].
% 4.31/4.63 108 join(A,join(B,complement(A))) = c_0. [back_rewrite(44),rewrite([105(5)])].
% 4.31/4.63 120 join(complement(A),complement(top)) = complement(A). [para(92(a,1),35(a,1,2,1)),rewrite([94(4),21(4)])].
% 4.31/4.63 121 c_0 = top. [para(63(a,1),108(a,1,2)),rewrite([21(4),95(4)]),flip(a)].
% 4.31/4.63 122 join(A,join(B,complement(A))) = top. [back_rewrite(108),rewrite([121(4)])].
% 4.31/4.63 124 join(A,top) = top. [back_rewrite(105),rewrite([121(3)])].
% 4.31/4.63 129 join(complement(complement(A)),complement(join(A,complement(top)))) = top. [para(120(a,1),35(a,1,2,1)),rewrite([21(7)])].
% 4.31/4.63 165 composition(join(one,one),A) = join(A,A). [para(90(a,1),87(a,2,2))].
% 4.31/4.63 187 composition(A,join(one,one)) = join(A,A). [para(165(a,2),41(a,1,1)),rewrite([42(6),93(4),85(3),16(6)])].
% 4.31/4.63 211 join(A,join(A,composition(B,join(one,one)))) = composition(join(B,A),join(one,one)). [para(187(a,1),31(a,1,2)),rewrite([28(6),21(5)])].
% 4.31/4.63 219 composition(top,join(one,one)) = top. [para(187(a,2),124(a,1))].
% 4.31/4.63 229 composition(join(one,one),A) = composition(A,join(one,one)). [para(187(a,2),165(a,2))].
% 4.31/4.63 241 composition(converse(top),join(one,one)) = converse(top). [para(219(a,1),26(a,2,1)),rewrite([93(4),85(3),229(6)])].
% 4.31/4.63 242 composition(top,composition(A,join(one,one))) = composition(top,A). [para(219(a,1),29(a,1,1)),rewrite([229(7)]),flip(a)].
% 4.31/4.63 243 join(top,composition(A,join(one,one))) = top. [para(219(a,1),31(a,1,1)),rewrite([21(8),124(8),219(11)])].
% 4.31/4.63 275 join(top,converse(top)) = top. [para(241(a,1),243(a,1,2))].
% 4.31/4.63 277 converse(top) = top. [para(275(a,1),24(a,2,1)),rewrite([16(5),21(4),275(4)]),flip(a)].
% 4.31/4.63 288 join(top,converse(A)) = top. [para(277(a,1),24(a,1,1)),rewrite([21(5),124(5),277(5)])].
% 4.31/4.63 289 converse(composition(A,top)) = composition(top,converse(A)). [para(277(a,1),26(a,1,1)),flip(a)].
% 4.31/4.63 293 join(top,composition(A,converse(B))) = top. [para(42(a,1),288(a,1,2))].
% 4.31/4.63 295 join(top,composition(A,B)) = top. [para(16(a,1),293(a,1,2,2))].
% 4.31/4.63 311 composition(top,join(one,converse(A))) = top. [para(93(a,1),289(a,2,2)),rewrite([87(4),295(4),277(2)]),flip(a)].
% 4.31/4.63 325 composition(top,top) = top. [para(277(a,1),311(a,1,2,2)),rewrite([124(4)])].
% 4.31/4.63 327 composition(top,composition(top,A)) = composition(top,A). [para(325(a,1),29(a,1,1)),flip(a)].
% 4.31/4.63 328 composition(top,complement(top)) = complement(top). [para(325(a,1),33(a,1,2,2,1)),rewrite([277(4),87(7,R),21(3),124(3)])].
% 4.31/4.63 376 join(A,complement(complement(A))) = A. [para(57(a,1),35(a,1,2,1)),rewrite([94(6),92(5)]),flip(a)].
% 4.31/4.63 377 complement(complement(top)) = top. [para(92(a,1),57(a,1,2,1)),rewrite([17(6)]),flip(a)].
% 4.31/4.63 379 join(A,join(B,complement(complement(A)))) = join(A,B). [para(376(a,1),28(a,2,2)),rewrite([21(3),21(5)])].
% 4.31/4.63 387 composition(top,complement(composition(top,A))) = complement(composition(top,A)). [para(327(a,1),33(a,1,2,2,1)),rewrite([277(5),87(9,R),21(3),124(3)])].
% 4.31/4.63 392 join(complement(A),complement(composition(top,A))) = complement(A). [para(327(a,1),55(a,1,2,2,1)),rewrite([325(4),277(3),387(6)])].
% 4.31/4.63 395 join(complement(A),complement(join(join(complement(B),complement(A)),complement(join(B,complement(A)))))) = join(B,complement(A)). [para(35(a,1),58(a,1,2,1)),rewrite([21(10)])].
% 4.31/4.63 396 join(complement(top),complement(join(complement(c2),converse(c1)))) = c2. [para(63(a,1),58(a,1,2,1)),rewrite([21(5),21(9)])].
% 4.31/4.63 397 join(A,join(complement(A),complement(B))) = top. [para(58(a,1),122(a,1,2)),rewrite([21(4)])].
% 4.31/4.63 411 join(top,c2) = top. [para(63(a,1),397(a,1,2)),rewrite([21(3)])].
% 4.31/4.63 448 join(complement(top),complement(join(A,complement(top)))) = complement(A). [para(120(a,1),60(a,1,2,1,2,1)),rewrite([21(8),28(8),21(7),376(7),21(5),120(11)])].
% 4.31/4.63 547 join(complement(A),composition(top,A)) = top. [para(392(a,1),122(a,1,2)),rewrite([21(4)])].
% 4.31/4.63 585 join(complement(top),complement(join(complement(complement(complement(A))),complement(join(A,complement(top)))))) = join(A,complement(top)). [para(129(a,1),35(a,1,1,1))].
% 4.31/4.63 587 join(complement(complement(complement(A))),complement(join(A,complement(top)))) = complement(A). [para(129(a,1),59(a,1,2,1,2,1,1)),rewrite([21(12),377(16),21(15),94(15),21(7),448(7),21(9)]),flip(a)].
% 4.31/4.63 588 join(A,complement(top)) = A. [back_rewrite(585),rewrite([587(10),92(5)]),flip(a)].
% 4.31/4.63 658 join(A,join(complement(A),converse(B))) = top. [para(17(a,1),71(a,1,1)),rewrite([288(3)]),flip(a)].
% 4.31/4.63 660 join(complement(A),join(composition(converse(B),complement(composition(B,A))),converse(C))) = join(complement(A),converse(C)). [para(33(a,1),71(a,1,1)),flip(a)].
% 4.31/4.63 689 join(complement(A),join(composition(top,A),converse(B))) = top. [para(547(a,1),71(a,1,1)),rewrite([288(3)]),flip(a)].
% 4.31/4.63 699 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(42(a,1),658(a,1,2,2))].
% 4.31/4.63 882 composition(top,join(A,A)) = composition(top,A). [para(187(a,1),242(a,1,2))].
% 4.31/4.63 896 join(join(A,A),composition(top,A)) = composition(top,A). [para(882(a,1),87(a,2,2)),rewrite([21(3),124(3),882(3)]),flip(a)].
% 4.31/4.63 987 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(47(a,1),79(a,1,1)),rewrite([24(3),26(4),16(4),16(4),16(6)]),flip(a)].
% 4.31/4.63 1039 join(A,A) = A. [para(92(a,1),379(a,1,2)),rewrite([588(4)])].
% 4.31/4.63 1064 join(A,composition(top,A)) = composition(top,A). [back_rewrite(896),rewrite([1039(1)])].
% 4.31/4.63 1078 join(A,join(A,B)) = join(A,B). [back_rewrite(211),rewrite([1039(3),15(2),21(3),1039(6),15(5)])].
% 4.31/4.63 1134 join(A,composition(A,top)) = composition(A,top). [para(1064(a,1),74(a,1,1)),rewrite([42(4),277(2),277(4),16(6),21(5)]),flip(a)].
% 4.31/4.63 1135 join(A,complement(join(B,complement(A)))) = A. [para(35(a,1),1078(a,1,2)),rewrite([21(4),35(12)])].
% 4.31/4.63 1170 join(complement(join(A,complement(complement(B)))),complement(join(B,join(complement(complement(B)),complement(join(A,complement(complement(B)))))))) = complement(B). [para(1135(a,1),60(a,1,2,1,2,1)),rewrite([21(12),28(12,R),21(11),1135(20)])].
% 4.31/4.63 1236 join(A,complement(join(complement(c2),converse(c1)))) = join(A,c2). [para(396(a,1),28(a,1,2)),rewrite([588(11),21(9)]),flip(a)].
% 4.31/4.63 1237 join(complement(c2),converse(c1)) = join(complement(top),complement(c2)). [para(396(a,1),35(a,1,1,1)),rewrite([377(5),1236(10),411(5),21(5)]),flip(a)].
% 4.31/4.63 1346 join(complement(A),composition(top,join(A,converse(B)))) = top. [para(289(a,1),689(a,1,2,2)),rewrite([987(7)])].
% 4.31/4.63 1350 join(A,join(complement(A),composition(B,C))) = top. [para(16(a,1),699(a,1,2,2,2))].
% 4.31/4.63 1364 join(A,composition(join(B,one),complement(A))) = top. [para(87(a,2),1350(a,1,2))].
% 4.31/4.63 1367 join(A,composition(complement(A),top)) = top. [para(1134(a,1),1350(a,1,2))].
% 4.31/4.63 1370 join(A,join(B,composition(complement(A),top))) = top. [para(1367(a,1),28(a,2,2)),rewrite([21(4),124(7)])].
% 4.31/4.63 1374 join(A,join(B,composition(join(C,one),complement(A)))) = top. [para(1364(a,1),28(a,2,2)),rewrite([21(5),124(8)])].
% 4.31/4.63 1386 join(A,composition(join(B,complement(A)),top)) = top. [para(31(a,1),1370(a,1,2))].
% 4.31/4.63 1405 join(complement(A),composition(A,top)) = top. [para(92(a,1),1386(a,1,2,1))].
% 4.31/4.63 1460 join(composition(top,A),converse(complement(converse(A)))) = top. [para(1405(a,1),79(a,1,1)),rewrite([277(2),277(3)]),flip(a)].
% 4.31/4.63 1470 join(complement(top),converse(complement(converse(complement(top))))) = top. [para(328(a,1),1460(a,1,1))].
% 4.31/4.63 1484 join(A,converse(complement(converse(complement(top))))) = top. [para(1470(a,1),28(a,1,2)),rewrite([124(2),588(9),21(7)]),flip(a)].
% 4.31/4.63 1531 converse(complement(converse(complement(top)))) = top. [para(1484(a,1),1039(a,1)),flip(a)].
% 4.31/4.63 1532 complement(converse(complement(top))) = top. [para(1531(a,1),16(a,1,1)),rewrite([277(2)]),flip(a)].
% 4.31/4.63 1537 converse(complement(top)) = complement(top). [para(1532(a,1),35(a,1,1,1,2)),rewrite([124(2),1532(7),21(5),94(5),1039(5)]),flip(a)].
% 4.31/4.63 1569 join(complement(top),converse(A)) = converse(A). [para(1537(a,1),24(a,1,1)),rewrite([21(7),588(7)])].
% 4.31/4.63 2097 converse(join(complement(top),complement(c2))) = join(c1,converse(complement(c2))). [para(1237(a,1),24(a,2,1)),rewrite([16(6),21(5)]),flip(a)].
% 4.31/4.63 2249 join(complement(A),composition(top,join(A,B))) = top. [para(16(a,1),1346(a,1,2,2,2))].
% 4.31/4.63 2261 join(composition(top,A),complement(complement(join(B,complement(A))))) = top. [para(35(a,1),2249(a,1,2,2)),rewrite([21(7)])].
% 4.31/4.63 4637 join(complement(A),composition(join(one,converse(B)),A)) = top. [para(52(a,1),1374(a,1,2)),rewrite([93(3),21(6)])].
% 4.31/4.63 4648 join(converse(complement(converse(A))),composition(A,join(B,one))) = top. [para(4637(a,1),74(a,1,1)),rewrite([277(2),41(5),85(3),21(8)]),flip(a)].
% 4.31/4.63 5417 join(c1,converse(complement(c2))) = converse(complement(c2)). [para(2097(a,1),24(a,2)),rewrite([1537(3),1569(6)]),flip(a)].
% 4.31/4.63 5464 join(complement(top),complement(c2)) = complement(c2). [para(5417(a,1),24(a,2,1)),rewrite([16(6),21(5),1237(5),16(9)])].
% 4.31/4.63 6409 join(composition(top,A),complement(complement(complement(A)))) = top. [para(392(a,1),2261(a,1,2,1,1)),rewrite([327(4)])].
% 4.31/4.63 6412 join(complement(top),complement(join(A,complement(B)))) = complement(join(A,complement(B))). [para(2261(a,1),1135(a,1,2,1)),rewrite([21(6)])].
% 4.31/4.63 6425 complement(join(complement(composition(top,A)),complement(complement(complement(A))))) = complement(complement(A)). [para(6409(a,1),35(a,1,1,1)),rewrite([6412(11)])].
% 4.31/4.63 6426 complement(complement(A)) = A. [para(6409(a,1),58(a,1,1,1)),rewrite([21(9),6425(10),92(5)]),flip(a)].
% 4.31/4.63 6447 join(complement(join(A,B)),complement(join(B,complement(join(A,B))))) = complement(B). [back_rewrite(1170),rewrite([6426(2),6426(4),6426(4),1078(6)])].
% 4.31/4.63 6464 join(A,complement(join(join(A,B),complement(join(A,complement(B)))))) = join(A,complement(B)). [para(6426(a,1),60(a,1,1)),rewrite([6426(2),21(1),6426(4),21(3),6426(10),21(9)])].
% 4.31/4.63 6469 join(complement(A),complement(join(A,B))) = complement(A). [para(6426(a,1),1135(a,1,2,1,2)),rewrite([21(2)])].
% 4.31/4.63 6530 join(A,complement(join(complement(A),complement(B)))) = A. [para(60(a,1),6469(a,1,2,1)),rewrite([6426(2),21(3),6426(7)])].
% 4.31/4.63 6547 join(complement(c1),complement(converse(complement(c2)))) = complement(c1). [para(5417(a,1),6469(a,1,2,1))].
% 4.31/4.63 6779 join(complement(c1),converse(complement(c2))) = top. [para(6547(a,1),122(a,1,2)),rewrite([21(6)])].
% 4.31/4.63 6784 join(complement(c2),converse(complement(c1))) = top. [para(6779(a,1),24(a,2,1)),rewrite([16(7),21(6),277(8)])].
% 4.31/4.63 7963 join(complement(join(A,complement(B))),complement(join(B,complement(join(join(complement(B),complement(A)),complement(join(A,complement(B)))))))) = join(join(complement(B),complement(A)),complement(join(A,complement(B)))). [para(395(a,1),35(a,1,2,1)),rewrite([21(3),21(14),21(17)])].
% 4.31/4.63 9463 join(A,converse(complement(converse(A)))) = top. [para(1039(a,1),4648(a,1,2,2)),rewrite([15(5),21(4)])].
% 4.31/4.63 9493 join(complement(converse(A)),converse(join(B,A))) = top. [para(9463(a,1),72(a,1,1,2)),rewrite([124(2),277(2)]),flip(a)].
% 4.31/4.63 9617 join(converse(A),complement(converse(complement(join(B,complement(A)))))) = top. [para(1135(a,1),9493(a,1,2,1)),rewrite([21(7)])].
% 4.31/4.63 12892 join(A,complement(join(complement(A),converse(B)))) = A. [para(660(a,1),6469(a,1,2,1)),rewrite([6426(2),6426(7)])].
% 4.31/4.63 12908 join(A,complement(join(B,join(converse(C),complement(A))))) = A. [para(41(a,1),12892(a,1,2,1,2)),rewrite([28(4,R)])].
% 4.31/4.63 14130 join(A,complement(join(B,join(C,complement(A))))) = A. [para(16(a,1),12908(a,1,2,1,2,1))].
% 4.31/4.63 14164 join(join(complement(A),complement(B)),complement(join(A,C))) = join(complement(A),complement(B)). [para(6530(a,1),14130(a,1,2,1,2)),rewrite([21(4)])].
% 4.31/4.63 14185 join(complement(A),complement(join(B,complement(A)))) = join(complement(B),complement(A)). [back_rewrite(7963),rewrite([21(6),14164(10),1135(8),21(5),21(8),14164(12)])].
% 4.31/4.63 14191 join(complement(A),complement(join(B,A))) = complement(A). [back_rewrite(6447),rewrite([14185(7)])].
% 4.31/4.63 14208 join(join(A,B),complement(join(C,complement(B)))) = join(A,B). [para(14191(a,1),14130(a,1,2,1,2))].
% 4.31/4.63 14209 join(A,complement(join(A,B))) = join(A,complement(B)). [back_rewrite(6464),rewrite([14208(5)])].
% 4.31/4.63 14377 join(complement(c2),complement(converse(complement(c1)))) = complement(c2). [para(6784(a,1),14209(a,1,2,1)),rewrite([21(5),5464(5)]),flip(a)].
% 4.31/4.63 14677 join(complement(c1),complement(converse(c2))) = top. [para(14377(a,1),9617(a,1,2,1,1,1)),rewrite([16(4),6426(5)])].
% 4.31/4.63 14680 $F # answer(goals). [back_rewrite(40),rewrite([14677(6)]),xx(a)].
% 4.31/4.63
% 4.31/4.63 % SZS output end Refutation
% 4.31/4.63 ============================== end of proof ==========================
% 4.31/4.63
% 4.31/4.63 ============================== STATISTICS ============================
% 4.31/4.63
% 4.31/4.63 Given=988. Generated=181297. Kept=14657. proofs=1.
% 4.31/4.63 Usable=771. Sos=10000. Demods=10286. Limbo=3, Disabled=3898. Hints=0.
% 4.31/4.63 Megabytes=16.82.
% 4.31/4.63 User_CPU=3.51, System_CPU=0.12, Wall_clock=3.
% 4.31/4.63
% 4.31/4.63 ============================== end of statistics =====================
% 4.31/4.63
% 4.31/4.63 ============================== end of search =========================
% 4.31/4.63
% 4.31/4.63 THEOREM PROVED
% 4.31/4.63 % SZS status Theorem
% 4.31/4.63
% 4.31/4.63 Exiting with 1 proof.
% 4.31/4.63
% 4.31/4.63 Process 18575 exit (max_proofs) Fri Jul 8 11:30:10 2022
% 4.31/4.63 Prover9 interrupted
%------------------------------------------------------------------------------