TSTP Solution File: REL026+4 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL026+4 : 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 19:53:59 EDT 2022
% Result : Theorem 27.81s 28.10s
% Output : Refutation 27.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : REL026+4 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.37 % Computer : n003.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Fri Jul 8 09:36:58 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.37/1.07 ============================== Prover9 ===============================
% 0.37/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.37/1.07 Process 27934 was started by sandbox on n003.cluster.edu,
% 0.37/1.07 Fri Jul 8 09:36:58 2022
% 0.37/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27781_n003.cluster.edu".
% 0.37/1.07 ============================== end of head ===========================
% 0.37/1.07
% 0.37/1.07 ============================== INPUT =================================
% 0.37/1.07
% 0.37/1.07 % Reading from file /tmp/Prover9_27781_n003.cluster.edu
% 0.37/1.07
% 0.37/1.07 set(prolog_style_variables).
% 0.37/1.07 set(auto2).
% 0.37/1.07 % set(auto2) -> set(auto).
% 0.37/1.07 % set(auto) -> set(auto_inference).
% 0.37/1.07 % set(auto) -> set(auto_setup).
% 0.37/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.37/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.37/1.07 % set(auto) -> set(auto_limits).
% 0.37/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.37/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.37/1.07 % set(auto) -> set(auto_denials).
% 0.37/1.07 % set(auto) -> set(auto_process).
% 0.37/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.37/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.37/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.37/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.37/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.37/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.37/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.37/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.37/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.37/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.37/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.37/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.37/1.07 % set(auto2) -> assign(stats, some).
% 0.37/1.07 % set(auto2) -> clear(echo_input).
% 0.37/1.07 % set(auto2) -> set(quiet).
% 0.37/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.37/1.07 % set(auto2) -> clear(print_given).
% 0.37/1.07 assign(lrs_ticks,-1).
% 0.37/1.07 assign(sos_limit,10000).
% 0.37/1.07 assign(order,kbo).
% 0.37/1.07 set(lex_order_vars).
% 0.37/1.07 clear(print_given).
% 0.37/1.07
% 0.37/1.07 % formulas(sos). % not echoed (17 formulas)
% 0.37/1.07
% 0.37/1.07 ============================== end of input ==========================
% 0.37/1.07
% 0.37/1.07 % From the command line: assign(max_seconds, 300).
% 0.37/1.07
% 0.37/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.37/1.07
% 0.37/1.07 % Formulas that are not ordinary clauses:
% 0.37/1.07 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.37/1.07 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].
% 0.37/1.07 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].
% 0.37/1.07 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].
% 0.37/1.07 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].
% 0.37/1.07 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.37/1.07 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].
% 0.37/1.07 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.37/1.07 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.37/1.07 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.37/1.07 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].
% 0.37/1.07 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.37/1.07 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 5.23/5.53 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].
% 5.23/5.53 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].
% 5.23/5.53 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].
% 5.23/5.53 17 -(all X0 all X1 (join(X0,one) = one -> join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1) & join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.23/5.53
% 5.23/5.53 ============================== end of process non-clausal formulas ===
% 5.23/5.53
% 5.23/5.53 ============================== PROCESS INITIAL CLAUSES ===============
% 5.23/5.53
% 5.23/5.53 ============================== PREDICATE ELIMINATION =================
% 5.23/5.53
% 5.23/5.53 ============================== end predicate elimination =============
% 5.23/5.53
% 5.23/5.53 Auto_denials:
% 5.23/5.53 % copying label goals to answer in negative clause
% 5.23/5.53
% 5.23/5.53 Term ordering decisions:
% 5.23/5.53 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 5.23/5.53
% 5.23/5.53 ============================== end of process initial clauses ========
% 5.23/5.53
% 5.23/5.53 ============================== CLAUSES FOR SEARCH ====================
% 5.23/5.53
% 5.23/5.53 ============================== end of clauses for search =============
% 5.23/5.53
% 5.23/5.53 ============================== SEARCH ================================
% 5.23/5.53
% 5.23/5.53 % Starting search at 0.01 seconds.
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=119.000, iters=3917
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=97.000, iters=3903
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=76.000, iters=3394
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=74.000, iters=3375
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=72.000, iters=3337
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=71.000, iters=3382
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=69.000, iters=3345
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=67.000, iters=3383
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=66.000, iters=3405
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=65.000, iters=3358
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=64.000, iters=3376
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=62.000, iters=3353
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=61.000, iters=3335
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=60.000, iters=3355
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=59.000, iters=3352
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=58.000, iters=3356
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=57.000, iters=3400
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=56.000, iters=3339
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=55.000, iters=3414
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=54.000, iters=3335
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=53.000, iters=3333
% 5.23/5.53
% 5.23/5.53 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 2.46 sec).
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=51.000, iters=3361
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=49.000, iters=3370
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=48.000, iters=3421
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=46.000, iters=3348
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=45.000, iters=3362
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=44.000, iters=3365
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=43.000, iters=3371
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=41.000, iters=3335
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=40.000, iters=3340
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=39.000, iters=3366
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=38.000, iters=3346
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=37.000, iters=3420
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=35.000, iters=3355
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=33.000, iters=3357
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=30.000, iters=3346
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=29.000, iters=3387
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=28.000, iters=3373
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=27.000, iters=3384
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=26.000, iters=3376
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=25.000, iters=3333
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=24.000, iters=3384
% 5.23/5.53
% 5.23/5.53 Low Water (keep): wt=23.000, iters=3368
% 5.23/5.53
% 5.23/5.53 Low Water (displace): id=5253, wt=166.000
% 5.23/5.53
% 5.23/5.53 Low Water (displace): id=4126, wt=157.000
% 5.23/5.53
% 5.23/5.53 Low Water (displace): id=16743, wt=20.000
% 5.23/5.53
% 5.23/5.53 Low Water (displace): id=16744, wt=15.000
% 5.23/5.53
% 5.23/5.53 Low Water (displace): id=16775, wt=13.000
% 5.23/5.53
% 5.23/5.53 Low Water (displace): id=16845, wt=12.000
% 27.81/28.10
% 27.81/28.10 Low Water (keep): wt=22.000, iters=3363
% 27.81/28.10
% 27.81/28.10 Low Water (keep): wt=21.000, iters=3333
% 27.81/28.10
% 27.81/28.10 Low Water (keep): wt=20.000, iters=3342
% 27.81/28.10
% 27.81/28.10 Low Water (keep): wt=19.000, iters=3333
% 27.81/28.10
% 27.81/28.10 Low Water (keep): wt=18.000, iters=3337
% 27.81/28.10
% 27.81/28.10 Low Water (keep): wt=17.000, iters=3355
% 27.81/28.10
% 27.81/28.10 Low Water (keep): wt=16.000, iters=3355
% 27.81/28.10
% 27.81/28.10 ============================== PROOF =================================
% 27.81/28.10 % SZS status Theorem
% 27.81/28.10 % SZS output start Refutation
% 27.81/28.10
% 27.81/28.10 % Proof 1 at 26.51 (+ 0.53) seconds: goals.
% 27.81/28.10 % Length of proof is 152.
% 27.81/28.10 % Level of proof is 37.
% 27.81/28.10 % Maximum clause weight is 49.000.
% 27.81/28.10 % Given clauses 2078.
% 27.81/28.10
% 27.81/28.10 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 27.81/28.10 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].
% 27.81/28.10 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].
% 27.81/28.10 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].
% 27.81/28.10 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].
% 27.81/28.10 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 27.81/28.10 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].
% 27.81/28.10 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 27.81/28.10 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 27.81/28.10 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 27.81/28.10 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].
% 27.81/28.10 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 27.81/28.10 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 27.81/28.10 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].
% 27.81/28.10 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].
% 27.81/28.10 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].
% 27.81/28.10 17 -(all X0 all X1 (join(X0,one) = one -> join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1) & join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 27.81/28.10 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 27.81/28.10 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 27.81/28.10 20 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(17)].
% 27.81/28.10 21 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 27.81/28.10 22 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 27.81/28.10 23 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 27.81/28.10 24 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 27.81/28.10 25 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 27.81/28.10 26 join(converse(A),converse(B)) = converse(join(A,B)). [copy(25),flip(a)].
% 27.81/28.10 27 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 27.81/28.10 28 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(27),flip(a)].
% 27.81/28.10 29 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 27.81/28.10 30 join(A,join(B,C)) = join(C,join(A,B)). [copy(29),rewrite([23(2)]),flip(a)].
% 27.81/28.10 31 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 27.81/28.10 32 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 27.81/28.10 33 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(32),flip(a)].
% 27.81/28.10 34 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 27.81/28.10 35 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(34),rewrite([23(7)]),flip(a)].
% 27.81/28.10 36 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 27.81/28.10 37 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(36),rewrite([23(6),23(8)]),rewrite([23(6)])].
% 27.81/28.10 38 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)].
% 27.81/28.10 39 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(38),rewrite([24(3),24(8),23(10),24(13),23(15),24(19),24(24),23(26)]),flip(a)].
% 27.81/28.10 40 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)].
% 27.81/28.10 41 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(40),rewrite([24(3),24(8),23(10),24(13),23(15),24(19),24(24),23(26)]),flip(a)].
% 27.81/28.10 42 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)].
% 27.81/28.10 43 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(42),rewrite([24(3),24(9),24(15),23(17),24(21),24(27)]),flip(a)].
% 27.81/28.10 44 composition(c1,c2) != join(meet(composition(c1,top),c2),composition(c1,c2)) | meet(composition(c1,top),c2) != join(composition(c1,c2),meet(composition(c1,top),c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 27.81/28.10 45 join(composition(c1,c2),complement(join(complement(c2),complement(composition(c1,top))))) != composition(c1,c2) | join(composition(c1,c2),complement(join(complement(c2),complement(composition(c1,top))))) != complement(join(complement(c2),complement(composition(c1,top)))) # answer(goals). [copy(44),rewrite([24(8),23(10),23(15),24(21),23(23),24(32),23(34)]),flip(a),flip(b)].
% 27.81/28.10 46 join(one,c1) = one. [back_rewrite(20),rewrite([23(3)])].
% 27.81/28.10 47 complement(top) = zero. [back_rewrite(22),rewrite([24(2),21(4)])].
% 27.81/28.10 48 converse(join(A,converse(B))) = join(B,converse(A)). [para(19(a,1),26(a,1,1)),rewrite([23(4)]),flip(a)].
% 27.81/28.10 49 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),28(a,1,1)),flip(a)].
% 27.81/28.10 50 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),28(a,1,2)),flip(a)].
% 27.81/28.10 51 join(A,join(B,complement(A))) = join(B,top). [para(21(a,1),30(a,2,2)),rewrite([23(2)])].
% 27.81/28.10 52 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),31(a,1,1)),flip(a)].
% 27.81/28.10 53 composition(converse(A),composition(converse(B),C)) = composition(converse(composition(B,A)),C). [para(28(a,1),31(a,1,1)),flip(a)].
% 27.81/28.10 54 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(28(a,1),33(a,1,1)),rewrite([23(7)])].
% 27.81/28.10 56 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(31(a,1),33(a,1,1)),rewrite([23(6)])].
% 27.81/28.10 57 join(composition(A,B),composition(C,composition(D,B))) = composition(join(A,composition(C,D)),B). [para(31(a,1),33(a,1,2))].
% 27.81/28.10 58 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(18(a,1),35(a,1,2,2,1))].
% 27.81/28.10 62 join(complement(A),composition(converse(composition(B,C)),complement(composition(B,composition(C,A))))) = complement(A). [para(31(a,1),35(a,1,2,2,1))].
% 27.81/28.10 63 join(zero,complement(join(complement(A),complement(A)))) = A. [para(21(a,1),37(a,1,1,1)),rewrite([47(2)])].
% 27.81/28.10 64 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(21(a,1),37(a,1,2,1)),rewrite([47(6),23(6)])].
% 27.81/28.10 67 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(37(a,1),37(a,1,2,1)),rewrite([23(10)])].
% 27.81/28.10 84 join(complement(join(complement(A),complement(B))),composition(complement(join(complement(B),complement(composition(A,converse(one))))),complement(join(complement(one),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(one))))),complement(join(complement(one),complement(composition(converse(B),A))))). [para(18(a,1),43(a,1,1,1,2,1))].
% 27.81/28.10 86 join(complement(join(complement(A),complement(composition(B,converse(C))))),composition(complement(join(complement(B),complement(composition(A,C)))),complement(join(complement(converse(C)),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,C)))),complement(join(complement(converse(C)),complement(composition(converse(B),A))))). [para(19(a,1),43(a,1,2,1,1,2,1,2)),rewrite([19(23)])].
% 27.81/28.10 93 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(47(a,1),35(a,1,1)),rewrite([47(9)])].
% 27.81/28.10 95 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(47(a,1),37(a,1,2,1,1))].
% 27.81/28.10 103 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(48(a,1),26(a,1,1)),rewrite([23(7),30(7,R),23(6)]),flip(a)].
% 27.81/28.10 104 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(48(a,1),26(a,1,2)),rewrite([30(4,R),23(3),26(3),103(7)]),flip(a)].
% 27.81/28.10 112 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(48(a,1),48(a,2,2)),rewrite([104(4),48(4),30(6,R),23(5)])].
% 27.81/28.10 120 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(49(a,1),26(a,1,1)),rewrite([23(7)]),flip(a)].
% 27.81/28.10 128 composition(converse(one),A) = A. [para(18(a,1),50(a,1,1)),rewrite([19(2)]),flip(a)].
% 27.81/28.10 129 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(50(a,1),26(a,1,1)),rewrite([23(7)]),flip(a)].
% 27.81/28.10 137 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(37(a,1),51(a,1,2)),rewrite([23(4),51(4),23(3),23(8)]),flip(a)].
% 27.81/28.10 138 join(top,complement(complement(A))) = top. [para(39(a,1),51(a,1,2)),rewrite([21(22),23(8),137(8)]),flip(a)].
% 27.81/28.10 139 converse(one) = one. [para(128(a,1),18(a,1)),flip(a)].
% 27.81/28.10 141 composition(join(A,one),B) = join(B,composition(A,B)). [para(128(a,1),33(a,1,1)),rewrite([139(4),23(4)]),flip(a)].
% 27.81/28.10 143 join(complement(A),complement(composition(one,A))) = complement(A). [para(128(a,1),35(a,1,2))].
% 27.81/28.10 149 join(complement(join(complement(A),complement(B))),complement(join(complement(A),complement(composition(complement(join(complement(one),complement(composition(A,converse(B))))),B))))) = complement(join(complement(A),complement(composition(complement(join(complement(one),complement(composition(A,converse(B))))),B)))). [para(128(a,1),41(a,1,1,1,2,1)),rewrite([139(7),139(20)])].
% 27.81/28.10 157 composition(one,A) = A. [para(128(a,1),52(a,2)),rewrite([139(2),52(4)])].
% 27.81/28.10 158 join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(B),A)))))) = composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(B),A))))). [back_rewrite(84),rewrite([139(7),18(7),23(7),139(20),18(20),23(20)])].
% 27.81/28.10 163 join(complement(A),complement(A)) = complement(A). [back_rewrite(143),rewrite([157(3)])].
% 27.81/28.10 164 join(zero,complement(complement(A))) = A. [back_rewrite(63),rewrite([163(4)])].
% 27.81/28.10 165 converse(join(A,one)) = join(one,converse(A)). [para(139(a,1),26(a,1,1)),rewrite([23(5)]),flip(a)].
% 27.81/28.10 166 join(zero,complement(A)) = complement(A). [para(138(a,1),37(a,1,1,1)),rewrite([47(2),47(3),164(5)])].
% 27.81/28.10 168 join(top,complement(A)) = join(top,top). [para(138(a,1),51(a,1,2)),rewrite([23(3)])].
% 27.81/28.10 169 complement(complement(A)) = A. [back_rewrite(164),rewrite([166(4)])].
% 27.81/28.10 177 join(A,complement(join(top,top))) = A. [back_rewrite(95),rewrite([168(3),166(7),169(6),23(5)])].
% 27.81/28.10 179 complement(join(A,A)) = complement(A). [back_rewrite(64),rewrite([169(3),166(4)])].
% 27.81/28.10 181 join(A,top) = top. [back_rewrite(138),rewrite([169(3),23(2)])].
% 27.81/28.10 186 join(A,zero) = A. [back_rewrite(177),rewrite([181(3),47(2)])].
% 27.81/28.10 187 join(top,complement(A)) = top. [back_rewrite(168),rewrite([181(6)])].
% 27.81/28.10 197 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(169(a,1),37(a,1,1,1,2)),rewrite([169(5),23(4)])].
% 27.81/28.10 205 complement(zero) = top. [para(47(a,1),169(a,1,1))].
% 27.81/28.10 220 join(A,A) = A. [para(179(a,1),37(a,1,1,1,2)),rewrite([179(6),37(8)]),flip(a)].
% 27.81/28.10 227 join(A,join(A,B)) = join(A,B). [para(220(a,1),30(a,1)),rewrite([23(3),30(4,R),23(3),30(3,R),220(2)]),flip(a)].
% 27.81/28.10 245 join(A,complement(join(B,complement(A)))) = A. [para(37(a,1),227(a,1,2)),rewrite([23(4),37(12)])].
% 27.81/28.10 247 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(245(a,1),30(a,2,2)),rewrite([23(4),23(6)])].
% 27.81/28.10 268 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(169(a,1),58(a,1,2,2))].
% 27.81/28.10 275 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(93(a,1),26(a,2,1)),rewrite([50(8)])].
% 27.81/28.10 281 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(165(a,1),93(a,1,2,1))].
% 27.81/28.10 317 join(complement(one),converse(complement(one))) = complement(one). [para(18(a,1),268(a,1,2))].
% 27.81/28.10 321 converse(complement(one)) = complement(one). [para(317(a,1),26(a,2,1)),rewrite([19(7),23(6),317(6)]),flip(a)].
% 27.81/28.10 330 converse(top) = top. [para(321(a,1),165(a,2,2)),rewrite([23(4),21(4),21(6)])].
% 27.81/28.10 341 join(top,converse(A)) = top. [para(330(a,1),26(a,1,1)),rewrite([23(5),181(5),330(5)])].
% 27.81/28.10 348 join(top,composition(A,converse(B))) = top. [para(49(a,1),341(a,1,2))].
% 27.81/28.10 350 join(top,composition(A,B)) = top. [para(19(a,1),348(a,1,2,2))].
% 27.81/28.10 351 composition(join(A,one),top) = top. [para(330(a,1),348(a,1,2,2)),rewrite([141(4,R)])].
% 27.81/28.10 352 composition(join(one,converse(A)),zero) = zero. [back_rewrite(281),rewrite([351(8),47(6),141(7,R),23(5),227(5)])].
% 27.81/28.10 379 composition(top,zero) = zero. [para(321(a,1),352(a,1,1,2)),rewrite([21(4)])].
% 27.81/28.10 383 composition(top,top) = top. [para(379(a,1),35(a,1,2,2,1)),rewrite([205(2),330(3),205(4),141(5,R),23(3),181(3),205(5)])].
% 27.81/28.10 384 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(379(a,1),43(a,1,1,1,2,1)),rewrite([205(3),23(3),187(3),47(2),47(3),166(7),169(6),205(6),330(7),187(9),47(6),31(6),47(9),166(13),169(12),205(12),330(13),187(15),47(12),31(12)])].
% 27.81/28.10 388 join(zero,composition(A,composition(B,zero))) = zero. [para(379(a,1),56(a,1,2)),rewrite([23(5),350(8),379(8)])].
% 27.81/28.10 391 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(384),rewrite([388(7)]),flip(a)].
% 27.81/28.10 450 join(complement(A),complement(join(B,A))) = complement(A). [para(245(a,1),67(a,2)),rewrite([169(2),169(4),169(8),67(13)])].
% 27.81/28.10 470 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(391(a,1),31(a,1,1)),rewrite([31(7)]),flip(a)].
% 27.81/28.10 471 composition(A,zero) = zero. [para(391(a,1),31(a,1)),rewrite([391(6)]),flip(a)].
% 27.81/28.10 472 composition(converse(zero),A) = converse(zero). [para(391(a,1),50(a,1,1)),rewrite([471(6)]),flip(a)].
% 27.81/28.10 477 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(470),rewrite([472(5)]),flip(a)].
% 27.81/28.10 479 composition(zero,A) = c_0. [new_symbol(477)].
% 27.81/28.10 480 composition(A,converse(zero)) = c_0. [back_rewrite(477),rewrite([479(2)]),flip(a)].
% 27.81/28.10 495 c_0 = zero. [para(479(a,1),18(a,1))].
% 27.81/28.10 496 converse(zero) = zero. [para(479(a,1),28(a,2,1)),rewrite([480(4),495(1),495(2)]),flip(a)].
% 27.81/28.10 497 join(zero,composition(A,B)) = composition(A,B). [para(479(a,1),33(a,1,1)),rewrite([495(1),23(5),186(5)])].
% 27.81/28.10 500 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(275),rewrite([496(2),497(7),496(7)])].
% 27.81/28.10 618 composition(converse(A),complement(composition(A,top))) = zero. [para(500(a,1),28(a,2,1)),rewrite([19(6),496(7)])].
% 27.81/28.10 667 composition(join(A,composition(A,converse(B))),top) = composition(A,top). [para(618(a,1),62(a,1,2,2,1,2)),rewrite([169(4),49(5),471(6),205(6),31(6),57(7),169(9)])].
% 27.81/28.10 770 join(complement(one),complement(c1)) = complement(c1). [para(46(a,1),450(a,1,2,1)),rewrite([23(5)])].
% 27.81/28.10 1051 composition(A,composition(converse(A),top)) = composition(A,top). [para(383(a,1),86(a,1,2,1,1,2,1)),rewrite([47(2),330(3),166(5),169(4),47(5),23(5),166(5),169(4),330(4),47(4),166(8),169(7),57(7),667(5),383(6),47(5),23(5),166(5),169(4),330(4),47(4),166(8),169(7)]),flip(a)].
% 27.81/28.10 2364 join(one,join(c1,converse(A))) = join(one,converse(A)). [para(46(a,1),112(a,1,1)),flip(a)].
% 27.81/28.10 3333 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(54(a,1),129(a,1,1)),rewrite([26(3),28(4),19(4),19(4),19(6)]),flip(a)].
% 27.81/28.10 3736 join(A,join(one,converse(c1))) = join(A,one). [para(2364(a,1),26(a,2,1)),rewrite([139(2),48(5),30(5,R),23(4),48(9),139(7)])].
% 27.81/28.10 3744 join(one,converse(c1)) = one. [para(220(a,1),3736(a,2)),rewrite([227(6)])].
% 27.81/28.10 3745 join(A,composition(converse(c1),A)) = A. [para(3744(a,1),33(a,2,1)),rewrite([157(2),157(6)])].
% 27.81/28.10 3747 join(complement(one),complement(converse(c1))) = complement(converse(c1)). [para(3744(a,1),450(a,1,2,1)),rewrite([23(6)])].
% 27.81/28.10 3751 join(A,join(B,composition(converse(c1),A))) = join(A,B). [para(3745(a,1),30(a,2,2)),rewrite([23(4),23(6)])].
% 27.81/28.10 3752 join(complement(A),complement(composition(converse(c1),A))) = complement(composition(converse(c1),A)). [para(3745(a,1),450(a,1,2,1)),rewrite([23(6)])].
% 27.81/28.10 3753 composition(join(c1,converse(c1)),top) = composition(c1,top). [para(1051(a,1),3745(a,1,2)),rewrite([19(3),33(8),19(9)])].
% 27.81/28.10 3756 join(A,composition(A,c1)) = A. [para(3745(a,1),120(a,1,1)),rewrite([19(2),19(3),19(4),23(3)]),flip(a)].
% 27.81/28.10 3875 join(complement(join(complement(A),complement(composition(c1,top)))),complement(join(complement(A),complement(composition(join(c1,converse(c1)),composition(join(c1,converse(c1)),A)))))) = complement(join(complement(A),complement(composition(join(c1,converse(c1)),composition(join(c1,converse(c1)),A))))). [para(3753(a,1),39(a,1,1,1,2,1)),rewrite([47(14),48(18),166(20),169(19),47(29),48(33),166(35),169(34)])].
% 27.81/28.10 4119 join(c1,complement(join(complement(one),complement(composition(converse(c1),c1))))) = complement(join(complement(one),complement(composition(converse(c1),c1)))). [para(770(a,1),149(a,1,1,1)),rewrite([169(3),157(9),3747(9),169(7),157(19),3747(19),169(17)])].
% 27.81/28.10 4240 composition(converse(c1),c1) = converse(c1). [para(3747(a,1),158(a,1,1,1)),rewrite([169(4),3747(8),169(6),19(9),18(9),770(9),169(7),3756(7),3747(8),169(6),19(9),18(9),770(9),169(7)]),flip(a)].
% 27.81/28.10 4242 join(c1,converse(c1)) = converse(c1). [back_rewrite(4119),rewrite([4240(7),3747(7),169(5),4240(10),3747(10),169(8)])].
% 27.81/28.10 4270 join(complement(join(complement(A),complement(composition(c1,top)))),complement(join(complement(A),complement(composition(converse(composition(c1,c1)),A))))) = complement(join(complement(A),complement(composition(converse(composition(c1,c1)),A)))). [back_rewrite(3875),rewrite([4242(12),4242(14),53(14),4242(22),4242(24),53(24)])].
% 27.81/28.10 4273 converse(c1) = c1. [para(4240(a,1),28(a,2,1)),rewrite([19(5),4240(4),19(5)])].
% 27.81/28.10 4284 composition(c1,c1) = c1. [para(4240(a,1),50(a,1,1)),rewrite([4273(2),4273(2),4273(3)]),flip(a)].
% 27.81/28.10 4340 join(complement(A),complement(composition(c1,A))) = complement(composition(c1,A)). [back_rewrite(3752),rewrite([4273(3),4273(7)])].
% 27.81/28.10 4341 join(A,join(B,composition(c1,A))) = join(A,B). [back_rewrite(3751),rewrite([4273(2)])].
% 27.81/28.10 4349 join(composition(c1,A),complement(join(complement(A),complement(composition(c1,top))))) = composition(c1,A). [back_rewrite(4270),rewrite([4284(11),4273(10),4340(12),169(11),23(10),4284(14),4273(13),4340(15),169(14)])].
% 27.81/28.10 4355 complement(join(complement(c2),complement(composition(c1,top)))) != composition(c1,c2) # answer(goals). [back_rewrite(45),rewrite([4349(12),4349(19)]),flip(b),xx(a)].
% 27.81/28.10 9691 join(A,complement(join(A,B))) = join(A,complement(B)). [para(197(a,1),247(a,1,2)),flip(a)].
% 27.81/28.10 10648 join(A,complement(join(B,composition(c1,A)))) = join(A,complement(B)). [para(4341(a,1),9691(a,1,2,1)),rewrite([9691(3)]),flip(a)].
% 27.81/28.10 41476 join(complement(A),complement(composition(c1,top))) = complement(composition(c1,A)). [para(4340(a,1),10648(a,2)),rewrite([3333(7),21(4)])].
% 27.81/28.10 41482 $F # answer(goals). [back_rewrite(4355),rewrite([41476(7),169(5)]),xx(a)].
% 27.81/28.10
% 27.81/28.10 % SZS output end Refutation
% 27.81/28.10 ============================== end of proof ==========================
% 27.81/28.10
% 27.81/28.10 ============================== STATISTICS ============================
% 27.81/28.10
% 27.81/28.10 Given=2078. Generated=1005650. Kept=41454. proofs=1.
% 27.81/28.10 Usable=1614. Sos=9961. Demods=11295. Limbo=6, Disabled=29891. Hints=0.
% 27.81/28.10 Megabytes=39.27.
% 27.81/28.10 User_CPU=26.51, System_CPU=0.53, Wall_clock=27.
% 27.81/28.10
% 27.81/28.10 ============================== end of statistics =====================
% 27.81/28.10
% 27.81/28.10 ============================== end of search =========================
% 27.81/28.10
% 27.81/28.10 THEOREM PROVED
% 27.81/28.10 % SZS status Theorem
% 27.81/28.10
% 27.81/28.10 Exiting with 1 proof.
% 27.81/28.10
% 27.81/28.10 Process 27934 exit (max_proofs) Fri Jul 8 09:37:25 2022
% 27.81/28.10 Prover9 interrupted
%------------------------------------------------------------------------------