TSTP Solution File: REL026+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL026+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 19:53:57 EDT 2022
% Result : Theorem 13.56s 13.86s
% Output : Refutation 13.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL026+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 8 09:06:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.01 ============================== Prover9 ===============================
% 0.46/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.01 Process 10071 was started by sandbox on n003.cluster.edu,
% 0.46/1.01 Fri Jul 8 09:06:28 2022
% 0.46/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9918_n003.cluster.edu".
% 0.46/1.01 ============================== end of head ===========================
% 0.46/1.01
% 0.46/1.01 ============================== INPUT =================================
% 0.46/1.01
% 0.46/1.01 % Reading from file /tmp/Prover9_9918_n003.cluster.edu
% 0.46/1.01
% 0.46/1.01 set(prolog_style_variables).
% 0.46/1.01 set(auto2).
% 0.46/1.01 % set(auto2) -> set(auto).
% 0.46/1.01 % set(auto) -> set(auto_inference).
% 0.46/1.01 % set(auto) -> set(auto_setup).
% 0.46/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.01 % set(auto) -> set(auto_limits).
% 0.46/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.01 % set(auto) -> set(auto_denials).
% 0.46/1.01 % set(auto) -> set(auto_process).
% 0.46/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.01 % set(auto2) -> assign(stats, some).
% 0.46/1.01 % set(auto2) -> clear(echo_input).
% 0.46/1.01 % set(auto2) -> set(quiet).
% 0.46/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.01 % set(auto2) -> clear(print_given).
% 0.46/1.01 assign(lrs_ticks,-1).
% 0.46/1.01 assign(sos_limit,10000).
% 0.46/1.01 assign(order,kbo).
% 0.46/1.01 set(lex_order_vars).
% 0.46/1.01 clear(print_given).
% 0.46/1.01
% 0.46/1.01 % formulas(sos). % not echoed (14 formulas)
% 0.46/1.01
% 0.46/1.01 ============================== end of input ==========================
% 0.46/1.01
% 0.46/1.01 % From the command line: assign(max_seconds, 300).
% 0.46/1.01
% 0.46/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.01
% 0.46/1.01 % Formulas that are not ordinary clauses:
% 0.46/1.01 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.46/1.01 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].
% 0.46/1.01 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].
% 0.46/1.01 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].
% 0.46/1.01 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.46/1.01 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.46/1.01 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 13.56/13.86 14 -(all X0 all X1 (join(X0,one) = one -> meet(composition(X0,top),X1) = composition(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 13.56/13.86
% 13.56/13.86 ============================== end of process non-clausal formulas ===
% 13.56/13.86
% 13.56/13.86 ============================== PROCESS INITIAL CLAUSES ===============
% 13.56/13.86
% 13.56/13.86 ============================== PREDICATE ELIMINATION =================
% 13.56/13.86
% 13.56/13.86 ============================== end predicate elimination =============
% 13.56/13.86
% 13.56/13.86 Auto_denials:
% 13.56/13.86 % copying label goals to answer in negative clause
% 13.56/13.86
% 13.56/13.86 Term ordering decisions:
% 13.56/13.86 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 13.56/13.86
% 13.56/13.86 ============================== end of process initial clauses ========
% 13.56/13.86
% 13.56/13.86 ============================== CLAUSES FOR SEARCH ====================
% 13.56/13.86
% 13.56/13.86 ============================== end of clauses for search =============
% 13.56/13.86
% 13.56/13.86 ============================== SEARCH ================================
% 13.56/13.86
% 13.56/13.86 % Starting search at 0.01 seconds.
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=43.000, iters=3352
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=35.000, iters=3360
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=33.000, iters=3376
% 13.56/13.86
% 13.56/13.86 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 1.10 sec).
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=32.000, iters=3375
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=31.000, iters=3411
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=30.000, iters=3355
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=29.000, iters=3336
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=27.000, iters=3334
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=26.000, iters=3377
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=25.000, iters=3333
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=24.000, iters=3345
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=23.000, iters=3339
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=22.000, iters=3370
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=21.000, iters=3353
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=20.000, iters=3353
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=19.000, iters=3345
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=4399, wt=46.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=7095, wt=45.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=7270, wt=44.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=7436, wt=43.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=7261, wt=42.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=7243, wt=41.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=5066, wt=40.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=6763, wt=39.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=7271, wt=38.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=13468, wt=16.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=13474, wt=15.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=13505, wt=14.000
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=13681, wt=13.000
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=18.000, iters=3335
% 13.56/13.86
% 13.56/13.86 Low Water (displace): id=17732, wt=12.000
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=17.000, iters=3336
% 13.56/13.86
% 13.56/13.86 Low Water (keep): wt=16.000, iters=3337
% 13.56/13.86
% 13.56/13.86 ============================== PROOF =================================
% 13.56/13.86 % SZS status Theorem
% 13.56/13.86 % SZS output start Refutation
% 13.56/13.86
% 13.56/13.86 % Proof 1 at 12.49 (+ 0.38) seconds: goals.
% 13.56/13.86 % Length of proof is 162.
% 13.56/13.86 % Level of proof is 37.
% 13.56/13.86 % Maximum clause weight is 21.000.
% 13.56/13.86 % Given clauses 1922.
% 13.56/13.86
% 13.56/13.86 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 13.56/13.86 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].
% 13.56/13.86 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].
% 13.56/13.86 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].
% 13.56/13.86 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].
% 13.56/13.86 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 13.56/13.86 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].
% 13.56/13.86 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 13.56/13.86 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 13.56/13.86 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 13.56/13.86 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].
% 13.56/13.86 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 13.56/13.86 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 13.56/13.86 14 -(all X0 all X1 (join(X0,one) = one -> meet(composition(X0,top),X1) = composition(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 13.56/13.86 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 13.56/13.86 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 13.56/13.86 17 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(14)].
% 13.56/13.86 18 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 13.56/13.86 19 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 13.56/13.86 20 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 13.56/13.86 21 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 13.56/13.86 22 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 13.56/13.86 23 join(converse(A),converse(B)) = converse(join(A,B)). [copy(22),flip(a)].
% 13.56/13.86 24 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 13.56/13.86 25 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(24),flip(a)].
% 13.56/13.86 26 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 13.56/13.86 27 join(A,join(B,C)) = join(C,join(A,B)). [copy(26),rewrite([20(2)]),flip(a)].
% 13.56/13.86 28 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 13.56/13.86 29 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 13.56/13.86 30 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(29),flip(a)].
% 13.56/13.86 31 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 13.56/13.86 32 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(31),rewrite([20(7)]),flip(a)].
% 13.56/13.86 33 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 13.56/13.86 34 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(33),rewrite([20(6),20(8)]),rewrite([20(6)])].
% 13.56/13.86 35 composition(c1,c2) != meet(composition(c1,top),c2) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 13.56/13.86 36 complement(join(complement(c2),complement(composition(c1,top)))) != composition(c1,c2) # answer(goals). [copy(35),rewrite([21(8),20(10)]),flip(a)].
% 13.56/13.86 37 join(one,c1) = one. [back_rewrite(17),rewrite([20(3)])].
% 13.56/13.86 38 complement(top) = zero. [back_rewrite(19),rewrite([21(2),18(4)])].
% 13.56/13.86 39 converse(join(A,converse(B))) = join(B,converse(A)). [para(16(a,1),23(a,1,1)),rewrite([20(4)]),flip(a)].
% 13.56/13.86 40 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(16(a,1),25(a,1,1)),flip(a)].
% 13.56/13.86 41 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),25(a,1,2)),flip(a)].
% 13.56/13.86 42 join(A,join(B,complement(A))) = join(B,top). [para(18(a,1),27(a,2,2)),rewrite([20(2)])].
% 13.56/13.86 43 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),28(a,1,1)),flip(a)].
% 13.56/13.86 45 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(25(a,1),30(a,1,1)),rewrite([20(7)])].
% 13.56/13.86 47 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(28(a,1),30(a,1,1)),rewrite([20(6)])].
% 13.56/13.86 49 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(15(a,1),32(a,1,2,2,1))].
% 13.56/13.86 52 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(25(a,1),32(a,1,2,2,1)),rewrite([16(4)])].
% 13.56/13.86 54 join(zero,complement(join(complement(A),complement(A)))) = A. [para(18(a,1),34(a,1,1,1)),rewrite([38(2)])].
% 13.56/13.86 58 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(34(a,1),34(a,1,2,1)),rewrite([20(10)])].
% 13.56/13.86 60 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(38(a,1),32(a,1,1)),rewrite([38(9)])].
% 13.56/13.86 62 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(38(a,1),34(a,1,2,1,1))].
% 13.56/13.86 63 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(39(a,1),23(a,1,1)),rewrite([20(7),27(7,R),20(6)]),flip(a)].
% 13.56/13.86 64 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(39(a,1),23(a,1,2)),rewrite([27(4,R),20(3),23(3),63(7)]),flip(a)].
% 13.56/13.86 68 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(39(a,1),39(a,2,2)),rewrite([64(4),39(4),27(6,R),20(5)])].
% 13.56/13.86 69 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(63),rewrite([68(8),23(7)])].
% 13.56/13.86 71 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(40(a,1),23(a,1,1)),rewrite([20(7)]),flip(a)].
% 13.56/13.86 75 composition(converse(one),A) = A. [para(15(a,1),41(a,1,1)),rewrite([16(2)]),flip(a)].
% 13.56/13.86 81 converse(one) = one. [para(75(a,1),15(a,1)),flip(a)].
% 13.56/13.86 83 composition(join(A,one),B) = join(B,composition(A,B)). [para(75(a,1),30(a,1,1)),rewrite([81(4),20(4)]),flip(a)].
% 13.56/13.86 85 join(complement(A),complement(composition(one,A))) = complement(A). [para(75(a,1),32(a,1,2))].
% 13.56/13.86 86 composition(one,A) = A. [para(75(a,1),43(a,2)),rewrite([81(2),43(4)])].
% 13.56/13.86 87 join(complement(A),complement(A)) = complement(A). [back_rewrite(85),rewrite([86(3)])].
% 13.56/13.86 88 join(zero,complement(complement(A))) = A. [back_rewrite(54),rewrite([87(4)])].
% 13.56/13.86 89 converse(join(A,one)) = join(one,converse(A)). [para(81(a,1),23(a,1,1)),rewrite([20(5)]),flip(a)].
% 13.56/13.86 93 join(top,complement(A)) = top. [para(87(a,1),42(a,1,2)),rewrite([18(2),20(4)]),flip(a)].
% 13.56/13.86 94 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(62),rewrite([93(3),38(2)])].
% 13.56/13.86 95 join(top,top) = join(A,top). [para(93(a,1),42(a,1,2)),flip(a)].
% 13.56/13.86 100 join(A,top) = join(B,top). [para(95(a,1),42(a,2)),rewrite([93(3)])].
% 13.56/13.86 101 join(A,top) = c_0. [new_symbol(100)].
% 13.56/13.86 104 join(A,join(B,complement(A))) = c_0. [back_rewrite(42),rewrite([101(5)])].
% 13.56/13.86 110 converse(join(A,composition(A,B))) = composition(join(one,converse(B)),converse(A)). [para(86(a,1),45(a,1,2)),rewrite([20(4),23(4)])].
% 13.56/13.86 115 c_0 = top. [para(88(a,1),104(a,1,2)),rewrite([20(2),18(2)]),flip(a)].
% 13.56/13.86 116 join(A,join(B,complement(A))) = top. [back_rewrite(104),rewrite([115(4)])].
% 13.56/13.86 118 join(A,top) = top. [back_rewrite(101),rewrite([115(3)])].
% 13.56/13.86 128 converse(join(A,join(B,one))) = join(one,converse(join(A,B))). [para(89(a,1),23(a,1,1)),rewrite([68(5),23(4),20(7),27(7,R),20(6)]),flip(a)].
% 13.56/13.86 129 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(89(a,1),25(a,1,1))].
% 13.56/13.86 136 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(110),rewrite([129(8)]),flip(a)].
% 13.56/13.86 139 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(86(a,1),47(a,1,2)),rewrite([20(3)]),flip(a)].
% 13.56/13.86 143 join(zero,complement(A)) = complement(A). [para(88(a,1),94(a,1,2,1))].
% 13.56/13.86 144 complement(complement(A)) = A. [back_rewrite(94),rewrite([143(4),143(4)])].
% 13.56/13.86 145 join(A,zero) = A. [back_rewrite(88),rewrite([144(3),20(2)])].
% 13.56/13.86 150 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(144(a,1),34(a,1,1,1,2)),rewrite([144(5),20(4)])].
% 13.56/13.86 152 join(A,A) = A. [para(144(a,1),87(a,1,1)),rewrite([144(2),144(3)])].
% 13.56/13.86 156 join(A,join(A,B)) = join(A,B). [para(152(a,1),27(a,1)),rewrite([20(3),27(4,R),20(3),27(3,R),152(2)]),flip(a)].
% 13.56/13.86 157 join(A,complement(join(B,complement(A)))) = A. [para(34(a,1),156(a,1,2)),rewrite([20(4),34(12)])].
% 13.56/13.86 159 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(157(a,1),27(a,2,2)),rewrite([20(4),20(6)])].
% 13.56/13.86 162 join(complement(A),complement(join(A,B))) = complement(A). [para(144(a,1),157(a,1,2,1,2)),rewrite([20(2)])].
% 13.56/13.86 170 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(144(a,1),49(a,1,2,2))].
% 13.56/13.86 173 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(23(a,1),162(a,1,2,1))].
% 13.56/13.86 184 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(60(a,1),23(a,2,1)),rewrite([41(8)])].
% 13.56/13.86 197 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(83(a,1),30(a,1,2)),rewrite([27(4,R),30(3),20(1)]),flip(a)].
% 13.56/13.86 224 join(complement(one),converse(complement(one))) = complement(one). [para(15(a,1),170(a,1,2))].
% 13.56/13.86 228 converse(complement(one)) = complement(one). [para(224(a,1),23(a,2,1)),rewrite([16(7),20(6),224(6)]),flip(a)].
% 13.56/13.86 229 converse(join(A,complement(one))) = join(complement(one),converse(A)). [para(228(a,1),23(a,1,1)),rewrite([20(7)]),flip(a)].
% 13.56/13.86 233 converse(top) = top. [para(228(a,1),89(a,2,2)),rewrite([20(4),18(4),18(6)])].
% 13.56/13.86 237 join(top,converse(A)) = top. [para(233(a,1),23(a,1,1)),rewrite([20(5),118(5),233(5)])].
% 13.56/13.86 238 converse(composition(A,top)) = composition(top,converse(A)). [para(233(a,1),25(a,1,1)),flip(a)].
% 13.56/13.86 246 join(top,composition(A,converse(B))) = top. [para(40(a,1),237(a,1,2))].
% 13.56/13.86 248 join(top,composition(A,B)) = top. [para(16(a,1),246(a,1,2,2))].
% 13.56/13.86 259 converse(composition(A,composition(B,top))) = composition(top,converse(composition(A,B))). [para(238(a,1),25(a,1,1)),rewrite([28(5),25(4)]),flip(a)].
% 13.56/13.86 264 composition(top,join(one,converse(A))) = top. [para(89(a,1),238(a,2,2)),rewrite([83(4),248(4),233(2)]),flip(a)].
% 13.56/13.86 269 composition(top,join(A,one)) = top. [para(16(a,1),264(a,1,2,2)),rewrite([20(3)])].
% 13.56/13.86 293 join(zero,composition(A,zero)) = zero. [para(269(a,1),52(a,1,2,2,1,1)),rewrite([233(2),38(2),233(5),38(5),83(5),156(6),233(6),38(6)])].
% 13.56/13.86 302 join(complement(A),complement(join(B,A))) = complement(A). [para(157(a,1),58(a,2)),rewrite([144(2),144(4),144(8),58(13)])].
% 13.56/13.86 303 join(A,complement(join(complement(A),complement(B)))) = A. [para(58(a,1),162(a,1,2,1)),rewrite([144(2),20(3),144(7)])].
% 13.56/13.86 308 join(A,composition(B,zero)) = A. [para(293(a,1),27(a,1,2)),rewrite([145(2),145(4),20(3)]),flip(a)].
% 13.56/13.86 312 composition(join(A,B),zero) = composition(A,zero). [para(308(a,1),30(a,1)),flip(a)].
% 13.56/13.86 314 composition(A,zero) = zero. [para(308(a,1),83(a,2)),rewrite([312(4)])].
% 13.56/13.86 316 composition(converse(zero),A) = converse(zero). [para(314(a,1),41(a,1,1)),flip(a)].
% 13.56/13.86 325 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(316(a,1),47(a,1,1,2)),flip(a)].
% 13.56/13.86 329 converse(zero) = zero. [para(316(a,1),314(a,1))].
% 13.56/13.86 332 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(325),rewrite([329(2),314(2),145(2),329(3),314(3)]),flip(a)].
% 13.56/13.86 335 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(184),rewrite([329(2),332(7),329(7)])].
% 13.56/13.86 359 join(zero,converse(A)) = converse(A). [para(329(a,1),23(a,1,1)),rewrite([20(5),145(5)])].
% 13.56/13.86 428 converse(composition(A,join(B,complement(composition(converse(A),top))))) = converse(composition(A,B)). [para(335(a,1),45(a,1,2)),rewrite([20(4),359(4),20(9),23(9),25(10)]),flip(a)].
% 13.56/13.86 560 join(complement(one),complement(c1)) = complement(c1). [para(37(a,1),302(a,1,2,1)),rewrite([20(5)])].
% 13.56/13.86 574 join(A,join(complement(A),complement(B))) = top. [para(303(a,1),116(a,1,2)),rewrite([20(4)])].
% 13.56/13.86 592 join(one,complement(c1)) = top. [para(560(a,1),574(a,1,2))].
% 13.56/13.86 595 join(zero,c1) = c1. [para(592(a,1),34(a,1,1,1)),rewrite([38(2),560(6),144(4)])].
% 13.56/13.86 998 join(one,converse(c1)) = one. [para(595(a,1),128(a,2,2,1)),rewrite([20(4),37(4),20(3),145(3),81(2)]),flip(a)].
% 13.56/13.86 1011 join(A,composition(converse(c1),A)) = A. [para(998(a,1),30(a,2,1)),rewrite([86(2),86(6)])].
% 13.56/13.86 1017 join(A,composition(A,c1)) = A. [para(1011(a,1),71(a,1,1)),rewrite([16(2),16(3),16(4),20(3)]),flip(a)].
% 13.56/13.86 1019 join(A,join(B,composition(A,c1))) = join(A,B). [para(1017(a,1),27(a,2,2)),rewrite([20(3),20(5)])].
% 13.56/13.86 1358 composition(A,join(B,one)) = join(A,composition(A,B)). [para(136(a,1),16(a,1,1)),rewrite([16(4)]),flip(a)].
% 13.56/13.86 1770 join(A,composition(c1,A)) = A. [para(1017(a,1),139(a,1,1)),rewrite([86(2),86(4)]),flip(a)].
% 13.56/13.86 1797 join(A,join(B,composition(c1,A))) = join(A,B). [para(1770(a,1),27(a,2,2)),rewrite([20(3),20(5)])].
% 13.56/13.86 2073 join(A,complement(join(A,B))) = join(A,complement(B)). [para(150(a,1),159(a,1,2)),flip(a)].
% 13.56/13.86 2352 join(A,composition(join(A,B),c1)) = join(A,composition(B,c1)). [para(30(a,1),1019(a,1,2)),rewrite([20(1)])].
% 13.56/13.86 2435 join(complement(converse(A)),converse(join(A,B))) = top. [para(173(a,1),116(a,1,2)),rewrite([20(5)])].
% 13.56/13.86 2466 join(A,join(B,converse(complement(converse(A))))) = top. [para(2435(a,1),23(a,2,1)),rewrite([16(6),27(5),20(4),27(5,R),20(4),233(7)])].
% 13.56/13.86 2558 join(A,converse(complement(converse(A)))) = top. [para(152(a,1),2466(a,1,2))].
% 13.56/13.86 2580 join(complement(converse(A)),converse(join(B,A))) = top. [para(2558(a,1),69(a,1,1,2)),rewrite([118(2),233(2)]),flip(a)].
% 13.56/13.86 2686 join(converse(A),complement(composition(converse(A),c1))) = top. [para(1011(a,1),2580(a,1,2,1)),rewrite([41(4),20(6)])].
% 13.56/13.86 2716 join(A,converse(complement(composition(converse(A),c1)))) = top. [para(2686(a,1),23(a,2,1)),rewrite([16(2),233(8)])].
% 13.56/13.86 2888 join(complement(composition(converse(A),c1)),converse(join(B,A))) = top. [para(2716(a,1),69(a,1,1,2)),rewrite([118(2),233(2)]),flip(a)].
% 13.56/13.86 3616 join(A,composition(complement(one),A)) = composition(top,A). [para(49(a,1),197(a,2,2,1)),rewrite([20(7),27(8,R),20(7),49(7),18(4)]),flip(a)].
% 13.56/13.86 3745 join(A,composition(A,complement(one))) = composition(A,top). [para(3616(a,1),71(a,1,1)),rewrite([40(4),233(2),228(5),16(7),20(6)]),flip(a)].
% 13.56/13.86 3749 join(complement(one),composition(top,c1)) = join(c1,complement(one)). [para(3616(a,1),1019(a,1,2)),rewrite([20(10)])].
% 13.56/13.86 4577 join(complement(one),composition(c1,top)) = join(c1,complement(one)). [para(3745(a,1),1797(a,1,2)),rewrite([20(10)])].
% 13.56/13.86 5123 complement(join(complement(A),complement(join(B,complement(A))))) = complement(join(complement(A),complement(B))). [para(2073(a,1),21(a,2,1)),rewrite([20(2),21(3)])].
% 13.56/13.86 5137 join(complement(A),complement(join(B,complement(A)))) = join(complement(A),complement(B)). [para(2073(a,1),58(a,2)),rewrite([20(2),20(5),157(7),20(6),5123(9),303(8),20(5)])].
% 13.56/13.86 5218 join(A,complement(converse(complement(converse(A))))) = A. [para(2558(a,1),2073(a,1,2,1)),rewrite([38(2),145(2)]),flip(a)].
% 13.56/13.86 5302 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(16(a,1),5218(a,1,2,1,1,1))].
% 13.56/13.86 5305 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(5218(a,1),34(a,1,2,1)),rewrite([144(9),20(8),2073(8),144(6)])].
% 13.56/13.86 5489 converse(complement(converse(complement(A)))) = A. [para(5302(a,1),23(a,2,1)),rewrite([16(2),5305(5),16(6)])].
% 13.56/13.86 5517 complement(converse(complement(A))) = converse(A). [para(5489(a,1),16(a,1,1)),flip(a)].
% 13.56/13.86 5628 converse(complement(A)) = complement(converse(A)). [para(5517(a,1),144(a,1,1)),flip(a)].
% 13.56/13.86 6019 join(complement(converse(A)),converse(B)) = converse(join(B,complement(A))). [para(5628(a,1),23(a,1,1)),rewrite([20(6)])].
% 13.56/13.86 7632 join(complement(one),complement(composition(top,c1))) = complement(c1). [para(3749(a,1),2073(a,1,2,1)),rewrite([5137(8),560(5)]),flip(a)].
% 13.56/13.86 13238 join(join(complement(one),converse(c1)),complement(composition(top,composition(converse(c1),c1)))) = top. [para(4577(a,1),2888(a,1,2,1)),rewrite([238(4),28(6),229(12),20(13)])].
% 13.56/13.86 14072 composition(top,composition(A,converse(A))) = composition(top,converse(A)). [para(18(a,1),428(a,1,1,2)),rewrite([238(3),259(8),40(7)]),flip(a)].
% 13.56/13.86 14084 composition(top,composition(converse(A),A)) = composition(top,A). [para(16(a,1),14072(a,1,2,2)),rewrite([16(7)])].
% 13.56/13.86 14123 join(complement(c1),converse(c1)) = top. [back_rewrite(13238),rewrite([14084(11),20(10),27(10),20(9),7632(9),20(5)])].
% 13.56/13.86 14179 join(c1,complement(converse(c1))) = top. [para(14123(a,1),23(a,2,1)),rewrite([5628(3),16(6),20(5),233(7)])].
% 13.56/13.86 14185 join(complement(c1),complement(converse(c1))) = complement(c1). [para(14123(a,1),2073(a,1,2,1)),rewrite([38(4),20(4),143(4)]),flip(a)].
% 13.56/13.86 14190 converse(c1) = c1. [para(14179(a,1),34(a,1,1,1)),rewrite([38(2),14185(7),144(4),595(3)]),flip(a)].
% 13.56/13.86 14261 converse(composition(A,c1)) = composition(c1,converse(A)). [para(14190(a,1),25(a,1,1)),flip(a)].
% 13.56/13.86 16688 converse(join(converse(A),complement(B))) = join(A,complement(converse(B))). [para(16(a,1),6019(a,1,2)),rewrite([20(3)]),flip(a)].
% 13.56/13.86 25070 join(A,composition(complement(A),c1)) = join(A,composition(top,c1)). [para(18(a,1),2352(a,1,2,1)),flip(a)].
% 13.56/13.86 25173 join(A,complement(composition(top,c1))) = complement(composition(complement(A),c1)). [para(25070(a,1),150(a,1,1,1)),rewrite([20(10),1358(10,R),20(9),37(9),15(8),144(7),20(6),2073(6)])].
% 13.56/13.86 25265 join(A,complement(composition(c1,top))) = complement(composition(c1,complement(A))). [para(25173(a,1),16688(a,1,1)),rewrite([5628(6),14261(5),5628(4),16(3),14261(8),233(7)]),flip(a)].
% 13.56/13.86 25296 $F # answer(goals). [back_rewrite(36),rewrite([25265(7),144(4),144(5)]),xx(a)].
% 13.56/13.86
% 13.56/13.86 % SZS output end Refutation
% 13.56/13.86 ============================== end of proof ==========================
% 13.56/13.86
% 13.56/13.86 ============================== STATISTICS ============================
% 13.56/13.86
% 13.56/13.86 Given=1922. Generated=665342. Kept=25274. proofs=1.
% 13.56/13.86 Usable=1399. Sos=9893. Demods=11038. Limbo=31, Disabled=13966. Hints=0.
% 13.56/13.86 Megabytes=21.17.
% 13.56/13.86 User_CPU=12.49, System_CPU=0.38, Wall_clock=13.
% 13.56/13.86
% 13.56/13.86 ============================== end of statistics =====================
% 13.56/13.86
% 13.56/13.86 ============================== end of search =========================
% 13.56/13.86
% 13.56/13.86 THEOREM PROVED
% 13.56/13.86 % SZS status Theorem
% 13.56/13.86
% 13.56/13.86 Exiting with 1 proof.
% 13.56/13.86
% 13.56/13.86 Process 10071 exit (max_proofs) Fri Jul 8 09:06:41 2022
% 13.56/13.86 Prover9 interrupted
%------------------------------------------------------------------------------