TSTP Solution File: REL028+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL028+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 19:54:03 EDT 2022
% Result : Theorem 10.31s 10.65s
% Output : Refutation 10.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : REL028+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 12:30:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.97 ============================== Prover9 ===============================
% 0.41/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.97 Process 798 was started by sandbox on n027.cluster.edu,
% 0.41/0.97 Fri Jul 8 12:30:31 2022
% 0.41/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_613_n027.cluster.edu".
% 0.41/0.97 ============================== end of head ===========================
% 0.41/0.97
% 0.41/0.97 ============================== INPUT =================================
% 0.41/0.97
% 0.41/0.97 % Reading from file /tmp/Prover9_613_n027.cluster.edu
% 0.41/0.97
% 0.41/0.97 set(prolog_style_variables).
% 0.41/0.97 set(auto2).
% 0.41/0.97 % set(auto2) -> set(auto).
% 0.41/0.97 % set(auto) -> set(auto_inference).
% 0.41/0.97 % set(auto) -> set(auto_setup).
% 0.41/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.97 % set(auto) -> set(auto_limits).
% 0.41/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.97 % set(auto) -> set(auto_denials).
% 0.41/0.97 % set(auto) -> set(auto_process).
% 0.41/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.97 % set(auto2) -> assign(stats, some).
% 0.41/0.97 % set(auto2) -> clear(echo_input).
% 0.41/0.97 % set(auto2) -> set(quiet).
% 0.41/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.97 % set(auto2) -> clear(print_given).
% 0.41/0.97 assign(lrs_ticks,-1).
% 0.41/0.97 assign(sos_limit,10000).
% 0.41/0.97 assign(order,kbo).
% 0.41/0.97 set(lex_order_vars).
% 0.41/0.97 clear(print_given).
% 0.41/0.97
% 0.41/0.97 % formulas(sos). % not echoed (17 formulas)
% 0.41/0.97
% 0.41/0.97 ============================== end of input ==========================
% 0.41/0.97
% 0.41/0.97 % From the command line: assign(max_seconds, 300).
% 0.41/0.97
% 0.41/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.97
% 0.41/0.97 % Formulas that are not ordinary clauses:
% 0.41/0.97 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 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].
% 0.41/0.97 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].
% 0.41/0.97 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].
% 0.41/0.97 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].
% 0.41/0.97 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 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].
% 0.41/0.97 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 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].
% 0.41/0.97 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.97 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 5.48/5.85 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].
% 5.48/5.85 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].
% 5.48/5.85 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].
% 5.48/5.85 17 -(all X0 all X1 (join(X0,one) = one & join(X1,one) = one -> composition(X0,X1) = meet(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.48/5.85
% 5.48/5.85 ============================== end of process non-clausal formulas ===
% 5.48/5.85
% 5.48/5.85 ============================== PROCESS INITIAL CLAUSES ===============
% 5.48/5.85
% 5.48/5.85 ============================== PREDICATE ELIMINATION =================
% 5.48/5.85
% 5.48/5.85 ============================== end predicate elimination =============
% 5.48/5.85
% 5.48/5.85 Auto_denials:
% 5.48/5.85 % copying label goals to answer in negative clause
% 5.48/5.85
% 5.48/5.85 Term ordering decisions:
% 5.48/5.85 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 5.48/5.85
% 5.48/5.85 ============================== end of process initial clauses ========
% 5.48/5.85
% 5.48/5.85 ============================== CLAUSES FOR SEARCH ====================
% 5.48/5.85
% 5.48/5.85 ============================== end of clauses for search =============
% 5.48/5.85
% 5.48/5.85 ============================== SEARCH ================================
% 5.48/5.85
% 5.48/5.85 % Starting search at 0.02 seconds.
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=128.000, iters=3360
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=104.000, iters=3346
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=96.000, iters=3685
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=78.000, iters=3538
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=71.000, iters=3442
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=70.000, iters=3348
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=68.000, iters=3353
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=67.000, iters=3333
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=66.000, iters=3363
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=65.000, iters=3356
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=63.000, iters=3353
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=62.000, iters=3383
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=61.000, iters=3335
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=59.000, iters=3349
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=58.000, iters=3355
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=56.000, iters=3335
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=55.000, iters=3348
% 5.48/5.85
% 5.48/5.85 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 49 (0.00 of 1.96 sec).
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=54.000, iters=3478
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=53.000, iters=3425
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=52.000, iters=3393
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=51.000, iters=3413
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=50.000, iters=3494
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=48.000, iters=3360
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=47.000, iters=3421
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=46.000, iters=3399
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=45.000, iters=3367
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=43.000, iters=3346
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=42.000, iters=3348
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=36.000, iters=3439
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=34.000, iters=3338
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=33.000, iters=3346
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=31.000, iters=3363
% 5.48/5.85
% 5.48/5.85 Low Water (displace): id=5342, wt=171.000
% 5.48/5.85
% 5.48/5.85 Low Water (displace): id=5229, wt=166.000
% 5.48/5.85
% 5.48/5.85 Low Water (displace): id=3947, wt=157.000
% 5.48/5.85
% 5.48/5.85 Low Water (displace): id=12064, wt=17.000
% 5.48/5.85
% 5.48/5.85 Low Water (displace): id=12066, wt=16.000
% 5.48/5.85
% 5.48/5.85 Low Water (displace): id=12109, wt=15.000
% 5.48/5.85
% 5.48/5.85 Low Water (displace): id=12119, wt=14.000
% 5.48/5.85
% 5.48/5.85 Low Water (displace): id=12133, wt=13.000
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=30.000, iters=3359
% 5.48/5.85
% 5.48/5.85 Low Water (displace): id=12216, wt=12.000
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=29.000, iters=3394
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=28.000, iters=3351
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=27.000, iters=3339
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=26.000, iters=3393
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=25.000, iters=3341
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=24.000, iters=3335
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=23.000, iters=3441
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=22.000, iters=3336
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=21.000, iters=3335
% 5.48/5.85
% 5.48/5.85 Low Water (keep): wt=20.000, iters=3358
% 10.31/10.65
% 10.31/10.65 Low Water (keep): wt=19.000, iters=3376
% 10.31/10.65
% 10.31/10.65 Low Water (keep): wt=18.000, iters=3335
% 10.31/10.65
% 10.31/10.65 Low Water (keep): wt=17.000, iters=3333
% 10.31/10.65
% 10.31/10.65 ============================== PROOF =================================
% 10.31/10.65 % SZS status Theorem
% 10.31/10.65 % SZS output start Refutation
% 10.31/10.65
% 10.31/10.65 % Proof 1 at 9.51 (+ 0.18) seconds: goals.
% 10.31/10.65 % Length of proof is 158.
% 10.31/10.65 % Level of proof is 35.
% 10.31/10.65 % Maximum clause weight is 48.000.
% 10.31/10.65 % Given clauses 1439.
% 10.31/10.65
% 10.31/10.65 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 10.31/10.65 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].
% 10.31/10.65 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].
% 10.31/10.65 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].
% 10.31/10.65 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].
% 10.31/10.65 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 10.31/10.65 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].
% 10.31/10.65 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 10.31/10.65 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 10.31/10.65 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 10.31/10.65 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].
% 10.31/10.65 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 10.31/10.65 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 10.31/10.65 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].
% 10.31/10.65 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].
% 10.31/10.65 17 -(all X0 all X1 (join(X0,one) = one & join(X1,one) = one -> composition(X0,X1) = meet(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 10.31/10.65 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 10.31/10.65 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 10.31/10.65 20 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(17)].
% 10.31/10.65 21 join(c2,one) = one # label(goals) # label(negated_conjecture). [clausify(17)].
% 10.31/10.65 22 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 10.31/10.65 23 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 10.31/10.65 24 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 10.31/10.65 25 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 10.31/10.65 26 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 10.31/10.65 27 join(converse(A),converse(B)) = converse(join(A,B)). [copy(26),flip(a)].
% 10.31/10.65 28 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 10.31/10.65 29 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(28),flip(a)].
% 10.31/10.65 30 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 10.31/10.65 31 join(A,join(B,C)) = join(C,join(A,B)). [copy(30),rewrite([24(2)]),flip(a)].
% 10.31/10.65 32 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 10.31/10.65 33 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 10.31/10.65 34 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(33),flip(a)].
% 10.31/10.65 35 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 10.31/10.65 36 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(35),rewrite([24(7)]),flip(a)].
% 10.31/10.65 37 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 10.31/10.65 38 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(37),rewrite([24(6),24(8)]),rewrite([24(6)])].
% 10.31/10.65 39 meet(composition(A,meet(B,composition(converse(A),C))),C) = join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) # label(modular_law_1) # label(axiom). [clausify(15)].
% 10.31/10.65 40 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A)))))))). [copy(39),rewrite([25(3),25(8),24(10),25(13),24(15),25(19),25(24),24(26)]),flip(a)].
% 10.31/10.65 43 composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))) # label(dedekind_law) # label(axiom). [clausify(14)].
% 10.31/10.65 44 join(complement(join(complement(A),complement(composition(B,C)))),composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A))))). [copy(43),rewrite([25(3),25(9),25(15),24(17),25(21),25(27)]),flip(a)].
% 10.31/10.65 45 composition(c1,c2) != meet(c1,c2) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 10.31/10.65 46 complement(join(complement(c1),complement(c2))) != composition(c1,c2) # answer(goals). [copy(45),rewrite([25(6)]),flip(a)].
% 10.31/10.65 47 join(one,c2) = one. [back_rewrite(21),rewrite([24(3)])].
% 10.31/10.65 48 join(one,c1) = one. [back_rewrite(20),rewrite([24(3)])].
% 10.31/10.65 49 complement(top) = zero. [back_rewrite(23),rewrite([25(2),22(4)])].
% 10.31/10.65 50 converse(join(A,converse(B))) = join(B,converse(A)). [para(19(a,1),27(a,1,1)),rewrite([24(4)]),flip(a)].
% 10.31/10.65 51 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),29(a,1,1)),flip(a)].
% 10.31/10.65 52 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),29(a,1,2)),flip(a)].
% 10.31/10.65 53 join(A,join(B,complement(A))) = join(B,top). [para(22(a,1),31(a,2,2)),rewrite([24(2)])].
% 10.31/10.65 54 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),32(a,1,1)),flip(a)].
% 10.31/10.65 56 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(29(a,1),34(a,1,1)),rewrite([24(7)])].
% 10.31/10.65 60 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(18(a,1),36(a,1,2,2,1))].
% 10.31/10.65 65 join(zero,complement(join(complement(A),complement(A)))) = A. [para(22(a,1),38(a,1,1,1)),rewrite([49(2)])].
% 10.31/10.65 66 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(22(a,1),38(a,1,2,1)),rewrite([49(6),24(6)])].
% 10.38/10.65 69 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(38(a,1),38(a,1,2,1)),rewrite([24(10)])].
% 10.38/10.65 70 join(complement(join(complement(A),complement(B))),complement(join(complement(A),complement(composition(B,complement(join(complement(one),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(one),complement(composition(converse(B),A)))))))). [para(18(a,1),40(a,1,1,1,2,1))].
% 10.38/10.65 72 join(complement(join(complement(A),complement(composition(converse(B),C)))),complement(join(complement(A),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A))))))))) = complement(join(complement(A),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A)))))))). [para(19(a,1),40(a,1,2,1,2,1,2,1,2,1,1)),rewrite([19(23)])].
% 10.38/10.65 86 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),44(a,1,1,1,2,1))].
% 10.38/10.65 105 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(50(a,1),27(a,1,1)),rewrite([24(7),31(7,R),24(6)]),flip(a)].
% 10.38/10.65 106 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(50(a,1),27(a,1,2)),rewrite([31(4,R),24(3),27(3),105(7)]),flip(a)].
% 10.38/10.65 114 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(50(a,1),50(a,2,2)),rewrite([106(4),50(4),31(6,R),24(5)])].
% 10.38/10.65 115 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(105),rewrite([114(8),27(7)])].
% 10.38/10.65 122 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(51(a,1),27(a,1,1)),rewrite([24(7)]),flip(a)].
% 10.38/10.65 124 converse(composition(A,composition(converse(B),C))) = composition(converse(C),composition(B,converse(A))). [para(51(a,1),29(a,1,2)),rewrite([32(7)]),flip(a)].
% 10.38/10.65 130 composition(converse(one),A) = A. [para(18(a,1),52(a,1,1)),rewrite([19(2)]),flip(a)].
% 10.38/10.65 131 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(52(a,1),27(a,1,1)),rewrite([24(7)]),flip(a)].
% 10.38/10.65 139 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(38(a,1),53(a,1,2)),rewrite([24(4),53(4),24(3),24(8)]),flip(a)].
% 10.38/10.65 140 join(top,complement(complement(A))) = top. [para(40(a,1),53(a,1,2)),rewrite([22(22),24(8),139(8)]),flip(a)].
% 10.38/10.65 141 converse(one) = one. [para(130(a,1),18(a,1)),flip(a)].
% 10.38/10.65 145 join(complement(A),complement(composition(one,A))) = complement(A). [para(130(a,1),36(a,1,2))].
% 10.38/10.65 159 composition(one,A) = A. [para(130(a,1),54(a,2)),rewrite([141(2),54(4)])].
% 10.38/10.65 160 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(86),rewrite([141(7),18(7),24(7),141(20),18(20),24(20)])].
% 10.38/10.65 165 join(complement(A),complement(A)) = complement(A). [back_rewrite(145),rewrite([159(3)])].
% 10.38/10.65 166 join(zero,complement(complement(A))) = A. [back_rewrite(65),rewrite([165(4)])].
% 10.38/10.65 167 converse(join(A,one)) = join(one,converse(A)). [para(141(a,1),27(a,1,1)),rewrite([24(5)]),flip(a)].
% 10.38/10.65 168 join(zero,complement(A)) = complement(A). [para(140(a,1),38(a,1,1,1)),rewrite([49(2),49(3),166(5)])].
% 10.38/10.65 171 complement(complement(A)) = A. [back_rewrite(166),rewrite([168(4)])].
% 10.38/10.65 181 complement(join(A,A)) = complement(A). [back_rewrite(66),rewrite([171(3),168(4)])].
% 10.38/10.65 183 join(A,top) = top. [back_rewrite(140),rewrite([171(3),24(2)])].
% 10.38/10.65 191 join(A,join(B,complement(A))) = top. [back_rewrite(53),rewrite([183(5)])].
% 10.38/10.65 199 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(171(a,1),38(a,1,1,1,2)),rewrite([171(5),24(4)])].
% 10.38/10.65 217 converse(join(A,composition(A,B))) = composition(join(one,converse(B)),converse(A)). [para(159(a,1),56(a,1,2)),rewrite([24(4),27(4)])].
% 10.38/10.65 222 join(A,A) = A. [para(181(a,1),38(a,1,1,1,2)),rewrite([181(6),38(8)]),flip(a)].
% 10.38/10.65 229 join(A,join(A,B)) = join(A,B). [para(222(a,1),31(a,1)),rewrite([24(3),31(4,R),24(3),31(3,R),222(2)]),flip(a)].
% 10.38/10.65 235 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(167(a,1),29(a,1,1))].
% 10.38/10.65 246 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(217),rewrite([235(8)]),flip(a)].
% 10.38/10.65 247 join(A,complement(join(B,complement(A)))) = A. [para(38(a,1),229(a,1,2)),rewrite([24(4),38(12)])].
% 10.38/10.65 252 join(complement(A),complement(join(A,B))) = complement(A). [para(171(a,1),247(a,1,2,1,2)),rewrite([24(2)])].
% 10.38/10.65 257 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(27(a,1),252(a,1,2,1))].
% 10.38/10.65 258 join(complement(composition(A,B)),complement(composition(join(A,C),B))) = complement(composition(A,B)). [para(34(a,1),252(a,1,2,1))].
% 10.38/10.65 270 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(171(a,1),60(a,1,2,2))].
% 10.38/10.65 319 join(complement(one),converse(complement(one))) = complement(one). [para(18(a,1),270(a,1,2))].
% 10.38/10.65 323 converse(complement(one)) = complement(one). [para(319(a,1),27(a,2,1)),rewrite([19(7),24(6),319(6)]),flip(a)].
% 10.38/10.65 332 converse(top) = top. [para(323(a,1),167(a,2,2)),rewrite([24(4),22(4),22(6)])].
% 10.38/10.65 343 join(top,converse(A)) = top. [para(332(a,1),27(a,1,1)),rewrite([24(5),183(5),332(5)])].
% 10.38/10.65 350 join(top,composition(A,converse(B))) = top. [para(51(a,1),343(a,1,2))].
% 10.38/10.65 352 join(top,composition(A,B)) = top. [para(19(a,1),350(a,1,2,2))].
% 10.38/10.65 452 join(complement(A),complement(join(B,A))) = complement(A). [para(247(a,1),69(a,2)),rewrite([171(2),171(4),171(8),69(13)])].
% 10.38/10.65 602 join(complement(A),join(join(complement(A),complement(composition(converse(B),C))),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A)))))))) = join(complement(A),complement(composition(converse(B),C))). [para(72(a,1),252(a,1,2,1)),rewrite([171(7),171(17),31(16,R),24(15),171(23)])].
% 10.38/10.65 772 join(complement(one),complement(c2)) = complement(c2). [para(47(a,1),452(a,1,2,1)),rewrite([24(5)])].
% 10.38/10.65 773 join(complement(one),complement(c1)) = complement(c1). [para(48(a,1),452(a,1,2,1)),rewrite([24(5)])].
% 10.38/10.65 2216 join(one,join(c2,converse(A))) = join(one,converse(A)). [para(47(a,1),114(a,1,1)),flip(a)].
% 10.38/10.65 2217 join(one,join(c1,converse(A))) = join(one,converse(A)). [para(48(a,1),114(a,1,1)),flip(a)].
% 10.38/10.65 3079 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(56(a,1),131(a,1,1)),rewrite([27(3),29(4),19(4),19(4),19(6)]),flip(a)].
% 10.38/10.65 4418 join(A,join(one,converse(c2))) = join(A,one). [para(2216(a,1),27(a,2,1)),rewrite([141(2),50(5),31(5,R),24(4),50(9),141(7)])].
% 10.38/10.65 4459 join(one,converse(c2)) = one. [para(222(a,1),4418(a,2)),rewrite([229(6)])].
% 10.38/10.65 4460 join(A,composition(converse(c2),A)) = A. [para(4459(a,1),34(a,2,1)),rewrite([159(2),159(6)])].
% 10.38/10.65 4462 join(complement(one),complement(converse(c2))) = complement(converse(c2)). [para(4459(a,1),452(a,1,2,1)),rewrite([24(6)])].
% 10.38/10.65 4469 join(complement(A),complement(composition(converse(c2),A))) = complement(composition(converse(c2),A)). [para(4460(a,1),452(a,1,2,1)),rewrite([24(6)])].
% 10.38/10.65 4473 join(A,composition(A,c2)) = A. [para(4460(a,1),122(a,1,1)),rewrite([19(2),19(3),19(4),24(3)]),flip(a)].
% 10.38/10.65 4511 composition(converse(c2),c2) = converse(c2). [para(4462(a,1),160(a,1,1,1)),rewrite([171(4),4462(8),171(6),19(9),18(9),772(9),171(7),4473(7),4462(8),171(6),19(9),18(9),772(9),171(7)]),flip(a)].
% 10.38/10.65 4517 converse(c2) = c2. [para(4511(a,1),29(a,2,1)),rewrite([19(5),4511(4),19(5)])].
% 10.38/10.65 4518 composition(c2,composition(c2,A)) = composition(c2,A). [para(4511(a,1),32(a,1,1)),rewrite([4517(2),4517(4)]),flip(a)].
% 10.38/10.65 4528 composition(c2,c2) = c2. [para(4511(a,1),52(a,1,1)),rewrite([4517(2),4517(2),4517(3)]),flip(a)].
% 10.38/10.65 4554 converse(composition(A,c2)) = composition(c2,converse(A)). [para(4511(a,1),124(a,1,1,2)),rewrite([4517(2),4517(5),4518(8)])].
% 10.38/10.65 4563 converse(join(A,c2)) = join(c2,converse(A)). [para(4511(a,1),131(a,1,1,2)),rewrite([4517(2),4517(5),4528(6)])].
% 10.38/10.65 4575 join(complement(A),complement(composition(c2,A))) = complement(composition(c2,A)). [back_rewrite(4469),rewrite([4517(3),4517(7)])].
% 10.38/10.65 4577 join(A,composition(c2,A)) = A. [back_rewrite(4460),rewrite([4517(2)])].
% 10.38/10.65 4609 converse(composition(c2,A)) = composition(converse(A),c2). [para(4517(a,1),29(a,1,2)),flip(a)].
% 10.38/10.65 5265 join(one,join(c1,c2)) = one. [para(4517(a,1),2217(a,1,2,2)),rewrite([4517(8),47(8)])].
% 10.38/10.65 5360 join(one,converse(c1)) = one. [para(5265(a,1),27(a,2,1)),rewrite([141(2),4563(5),2216(6),141(6)])].
% 10.38/10.65 5364 join(A,composition(converse(c1),A)) = A. [para(5360(a,1),34(a,2,1)),rewrite([159(2),159(6)])].
% 10.38/10.65 5366 join(complement(one),complement(converse(c1))) = complement(converse(c1)). [para(5360(a,1),452(a,1,2,1)),rewrite([24(6)])].
% 10.38/10.65 5377 join(A,composition(A,c1)) = A. [para(5364(a,1),122(a,1,1)),rewrite([19(2),19(3),19(4),24(3)]),flip(a)].
% 10.38/10.65 5380 join(complement(A),complement(composition(A,c1))) = complement(composition(A,c1)). [para(5377(a,1),452(a,1,2,1)),rewrite([24(5)])].
% 10.38/10.65 5526 composition(converse(c1),c1) = converse(c1). [para(5366(a,1),160(a,1,1,1)),rewrite([171(4),5366(8),171(6),19(9),18(9),773(9),171(7),5377(7),5366(8),171(6),19(9),18(9),773(9),171(7)]),flip(a)].
% 10.38/10.65 5637 converse(c1) = c1. [para(5526(a,1),29(a,2,1)),rewrite([19(5),5526(4),19(5)])].
% 10.38/10.65 5638 composition(c1,composition(c1,A)) = composition(c1,A). [para(5526(a,1),32(a,1,1)),rewrite([5637(2),5637(4)]),flip(a)].
% 10.38/10.65 5674 converse(composition(A,c1)) = composition(c1,converse(A)). [para(5526(a,1),124(a,1,1,2)),rewrite([5637(2),5637(5),5638(8)])].
% 10.38/10.65 8784 composition(A,join(B,one)) = join(A,composition(A,B)). [para(246(a,1),19(a,1,1)),rewrite([19(4)]),flip(a)].
% 10.38/10.65 10036 join(complement(converse(A)),converse(join(A,B))) = top. [para(257(a,1),191(a,1,2)),rewrite([24(5)])].
% 10.38/10.65 10281 join(A,join(B,converse(complement(converse(A))))) = top. [para(10036(a,1),27(a,2,1)),rewrite([19(6),31(5),24(4),31(5,R),24(4),332(7)])].
% 10.38/10.65 10474 join(A,converse(complement(converse(A)))) = top. [para(222(a,1),10281(a,1,2))].
% 10.38/10.65 10505 join(complement(converse(A)),converse(join(B,A))) = top. [para(10474(a,1),115(a,1,1,2)),rewrite([183(2),332(2)]),flip(a)].
% 10.38/10.65 10574 join(converse(A),complement(composition(c2,converse(A)))) = top. [para(4473(a,1),10505(a,1,2,1)),rewrite([4554(3),24(6)])].
% 10.38/10.65 10575 join(converse(A),complement(composition(converse(A),c2))) = top. [para(4577(a,1),10505(a,1,2,1)),rewrite([4609(3),24(6)])].
% 10.38/10.65 10814 join(A,converse(complement(composition(c2,converse(A))))) = top. [para(10574(a,1),27(a,2,1)),rewrite([19(2),332(8)])].
% 10.38/10.65 10827 join(A,complement(composition(A,c2))) = top. [para(19(a,1),10575(a,1,1)),rewrite([19(2)])].
% 10.38/10.65 10914 join(A,join(B,complement(composition(A,c2)))) = top. [para(10827(a,1),31(a,2,2)),rewrite([24(4),183(7)])].
% 10.38/10.65 11089 join(one,converse(complement(composition(c2,c1)))) = top. [para(10814(a,1),2217(a,1,2)),rewrite([183(3),5637(5)]),flip(a)].
% 10.38/10.65 11148 join(one,complement(composition(c2,c1))) = top. [para(11089(a,1),27(a,2,1)),rewrite([141(2),19(7),332(8)])].
% 10.38/10.65 11156 complement(join(complement(one),complement(composition(c2,c1)))) = composition(c2,c1). [para(11148(a,1),38(a,1,1,1)),rewrite([49(2),168(10)])].
% 10.38/10.65 11157 join(complement(one),complement(composition(c2,c1))) = complement(composition(c2,c1)). [para(11148(a,1),69(a,1,2,1,1)),rewrite([11156(13),352(9),49(6),24(6),168(6)]),flip(a)].
% 10.38/10.65 11159 complement(join(one,composition(c2,c1))) = complement(one). [para(11148(a,1),199(a,1,2,1)),rewrite([24(5),49(8),24(8),168(8)])].
% 10.38/10.65 11163 join(one,composition(c2,c1)) = one. [para(11159(a,1),38(a,1,1,1,2)),rewrite([11159(11),38(10)]),flip(a)].
% 10.38/10.65 11211 join(one,composition(c1,c2)) = one. [para(11163(a,1),27(a,2,1)),rewrite([141(2),5674(5),4517(4),141(7)])].
% 10.38/10.65 11219 join(complement(one),complement(composition(c1,c2))) = complement(composition(c1,c2)). [para(11211(a,1),452(a,1,2,1)),rewrite([24(7)])].
% 10.38/10.65 11361 join(join(A,B),complement(composition(A,c2))) = top. [para(258(a,1),10914(a,1,2))].
% 10.38/10.65 11644 join(join(A,B),complement(composition(B,c2))) = top. [para(24(a,1),11361(a,1,1))].
% 10.38/10.65 11811 join(one,complement(composition(c2,composition(c1,c2)))) = top. [para(11163(a,1),11644(a,1,1)),rewrite([32(6)])].
% 10.38/10.65 12231 complement(join(complement(one),complement(composition(c2,composition(c1,c2))))) = composition(c2,composition(c1,c2)). [para(11811(a,1),38(a,1,1,1)),rewrite([49(2),168(12)])].
% 10.38/10.65 12232 join(complement(one),complement(composition(c2,composition(c1,c2)))) = complement(composition(c2,composition(c1,c2))). [para(11811(a,1),69(a,1,2,1,1)),rewrite([12231(17),352(13),49(8),24(8),168(8)]),flip(a)].
% 10.38/10.65 24964 composition(c2,composition(c1,c2)) = composition(c2,c1). [para(11157(a,1),70(a,1,1,1)),rewrite([171(5),5674(14),4517(13),18(15),11219(15),171(13),32(12),5638(11),12232(12),171(10),3079(9),8784(6,R),24(5),47(5),18(4),5674(14),4517(13),18(15),11219(15),171(13),32(12),5638(11),12232(12),171(10)]),flip(a)].
% 10.38/10.65 24975 join(complement(c1),complement(c2)) = complement(composition(c2,c1)). [para(11157(a,1),602(a,1,2,2,1,2,1)),rewrite([4517(6),18(7),4517(9),171(13),4518(12),24(12),31(12),24(11),4575(11),5380(9),4575(7),4517(8),18(9)]),flip(a)].
% 10.38/10.65 24983 composition(c2,c1) != composition(c1,c2) # answer(goals). [back_rewrite(46),rewrite([24975(5),171(5)])].
% 10.38/10.65 24984 composition(c2,c1) = composition(c1,c2). [para(24964(a,1),29(a,2,1)),rewrite([4554(4),5637(3),4517(5),32(5),24964(5),5674(7),4517(6)])].
% 10.38/10.65 24985 $F # answer(goals). [resolve(24984,a,24983,a)].
% 10.38/10.65
% 10.38/10.65 % SZS output end Refutation
% 10.38/10.65 ============================== end of proof ==========================
% 10.38/10.65
% 10.38/10.65 ============================== STATISTICS ============================
% 10.38/10.65
% 10.38/10.65 Given=1439. Generated=329437. Kept=24957. proofs=1.
% 10.38/10.65 Usable=1004. Sos=9930. Demods=10637. Limbo=0, Disabled=14041. Hints=0.
% 10.38/10.65 Megabytes=30.13.
% 10.38/10.65 User_CPU=9.51, System_CPU=0.18, Wall_clock=10.
% 10.38/10.65
% 10.38/10.65 ============================== end of statistics =====================
% 10.38/10.65
% 10.38/10.65 ============================== end of search =========================
% 10.38/10.65
% 10.38/10.65 THEOREM PROVED
% 10.38/10.65 % SZS status Theorem
% 10.38/10.65
% 10.38/10.65 Exiting with 1 proof.
% 10.38/10.65
% 10.38/10.65 Process 798 exit (max_proofs) Fri Jul 8 12:30:41 2022
% 10.38/10.65 Prover9 interrupted
%------------------------------------------------------------------------------