TSTP Solution File: REL043+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL043+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 19:54:27 EDT 2022
% Result : Theorem 3.58s 3.85s
% Output : Refutation 3.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL043+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 12:40:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/0.98 ============================== Prover9 ===============================
% 0.42/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.98 Process 26112 was started by sandbox on n022.cluster.edu,
% 0.42/0.98 Fri Jul 8 12:40:11 2022
% 0.42/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25662_n022.cluster.edu".
% 0.42/0.98 ============================== end of head ===========================
% 0.42/0.98
% 0.42/0.98 ============================== INPUT =================================
% 0.42/0.98
% 0.42/0.98 % Reading from file /tmp/Prover9_25662_n022.cluster.edu
% 0.42/0.98
% 0.42/0.98 set(prolog_style_variables).
% 0.42/0.98 set(auto2).
% 0.42/0.98 % set(auto2) -> set(auto).
% 0.42/0.98 % set(auto) -> set(auto_inference).
% 0.42/0.98 % set(auto) -> set(auto_setup).
% 0.42/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.98 % set(auto) -> set(auto_limits).
% 0.42/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.98 % set(auto) -> set(auto_denials).
% 0.42/0.98 % set(auto) -> set(auto_process).
% 0.42/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.98 % set(auto2) -> assign(stats, some).
% 0.42/0.98 % set(auto2) -> clear(echo_input).
% 0.42/0.98 % set(auto2) -> set(quiet).
% 0.42/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.98 % set(auto2) -> clear(print_given).
% 0.42/0.98 assign(lrs_ticks,-1).
% 0.42/0.98 assign(sos_limit,10000).
% 0.42/0.98 assign(order,kbo).
% 0.42/0.98 set(lex_order_vars).
% 0.42/0.98 clear(print_given).
% 0.42/0.98
% 0.42/0.98 % formulas(sos). % not echoed (17 formulas)
% 0.42/0.98
% 0.42/0.98 ============================== end of input ==========================
% 0.42/0.98
% 0.42/0.98 % From the command line: assign(max_seconds, 300).
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.98
% 0.42/0.98 % Formulas that are not ordinary clauses:
% 0.42/0.98 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.84 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].
% 3.58/3.84 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].
% 3.58/3.84 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].
% 3.58/3.84 17 -(all X0 all X1 all X2 (join(composition(X0,converse(X1)),X2) = X2 -> join(composition(complement(X2),X1),complement(X0)) = complement(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.58/3.84
% 3.58/3.84 ============================== end of process non-clausal formulas ===
% 3.58/3.84
% 3.58/3.84 ============================== PROCESS INITIAL CLAUSES ===============
% 3.58/3.84
% 3.58/3.84 ============================== PREDICATE ELIMINATION =================
% 3.58/3.84
% 3.58/3.84 ============================== end predicate elimination =============
% 3.58/3.84
% 3.58/3.84 Auto_denials:
% 3.58/3.84 % copying label goals to answer in negative clause
% 3.58/3.84
% 3.58/3.84 Term ordering decisions:
% 3.58/3.84 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. c3=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 3.58/3.84
% 3.58/3.84 ============================== end of process initial clauses ========
% 3.58/3.84
% 3.58/3.84 ============================== CLAUSES FOR SEARCH ====================
% 3.58/3.84
% 3.58/3.84 ============================== end of clauses for search =============
% 3.58/3.84
% 3.58/3.84 ============================== SEARCH ================================
% 3.58/3.84
% 3.58/3.84 % Starting search at 0.01 seconds.
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=125.000, iters=3430
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=105.000, iters=3419
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=104.000, iters=3508
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=72.000, iters=3353
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=71.000, iters=3346
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=70.000, iters=3441
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=67.000, iters=3337
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=66.000, iters=3430
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=65.000, iters=3461
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=64.000, iters=3377
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=62.000, iters=3345
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=61.000, iters=3428
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=60.000, iters=3405
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=58.000, iters=3386
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=57.000, iters=3391
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=56.000, iters=3403
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=55.000, iters=3540
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=53.000, iters=3418
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=52.000, iters=3347
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=51.000, iters=3456
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=49.000, iters=3341
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=48.000, iters=3336
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=47.000, iters=3333
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=45.000, iters=3415
% 3.58/3.84
% 3.58/3.84 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 28 (0.00 of 2.28 sec).
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=39.000, iters=3429
% 3.58/3.84
% 3.58/3.84 Low Water (keep): wt=37.000, iters=3441
% 3.58/3.85
% 3.58/3.85 Low Water (keep): wt=36.000, iters=3401
% 3.58/3.85
% 3.58/3.85 Low Water (keep): wt=35.000, iters=3358
% 3.58/3.85
% 3.58/3.85 Low Water (keep): wt=34.000, iters=3335
% 3.58/3.85
% 3.58/3.85 ============================== PROOF =================================
% 3.58/3.85 % SZS status Theorem
% 3.58/3.85 % SZS output start Refutation
% 3.58/3.85
% 3.58/3.85 % Proof 1 at 2.81 (+ 0.06) seconds: goals.
% 3.58/3.85 % Length of proof is 105.
% 3.58/3.85 % Level of proof is 30.
% 3.58/3.85 % Maximum clause weight is 48.000.
% 3.58/3.85 % Given clauses 531.
% 3.58/3.85
% 3.58/3.85 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.85 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].
% 3.58/3.85 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].
% 3.58/3.85 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].
% 3.58/3.85 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].
% 3.58/3.85 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.85 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].
% 3.58/3.85 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.85 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.85 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.85 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].
% 3.58/3.85 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.85 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.85 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].
% 3.58/3.85 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].
% 3.58/3.85 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].
% 3.58/3.85 17 -(all X0 all X1 all X2 (join(composition(X0,converse(X1)),X2) = X2 -> join(composition(complement(X2),X1),complement(X0)) = complement(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.58/3.85 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 3.58/3.85 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 3.58/3.85 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 3.58/3.85 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 3.58/3.85 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 3.58/3.85 23 join(composition(c1,converse(c2)),c3) = c3 # label(goals) # label(negated_conjecture). [clausify(17)].
% 3.58/3.85 24 join(c3,composition(c1,converse(c2))) = c3. [copy(23),rewrite([22(6)])].
% 3.58/3.85 25 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 3.58/3.85 26 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 3.58/3.85 27 join(converse(A),converse(B)) = converse(join(A,B)). [copy(26),flip(a)].
% 3.58/3.85 28 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 3.58/3.85 29 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(28),flip(a)].
% 3.58/3.85 30 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 3.58/3.85 31 join(A,join(B,C)) = join(C,join(A,B)). [copy(30),rewrite([22(2)]),flip(a)].
% 3.58/3.85 32 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 3.58/3.85 33 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 3.58/3.85 34 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(33),flip(a)].
% 3.58/3.85 35 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 3.58/3.85 36 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(35),rewrite([22(7)]),flip(a)].
% 3.58/3.85 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)].
% 3.58/3.85 38 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(37),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 3.58/3.85 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)].
% 3.58/3.85 40 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A)))))))). [copy(39),rewrite([25(3),25(8),22(10),25(13),22(15),25(19),25(24),22(26)]),flip(a)].
% 3.58/3.85 41 meet(composition(meet(A,composition(B,converse(C))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)) # label(modular_law_2) # label(axiom). [clausify(16)].
% 3.58/3.85 42 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C))))) = complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C)))). [copy(41),rewrite([25(3),25(8),22(10),25(13),22(15),25(19),25(24),22(26)]),flip(a)].
% 3.58/3.85 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)].
% 3.58/3.85 44 join(complement(join(complement(A),complement(composition(B,C)))),composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A))))). [copy(43),rewrite([25(3),25(9),25(15),22(17),25(21),25(27)]),flip(a)].
% 3.58/3.85 45 complement(c1) != join(composition(complement(c3),c2),complement(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 3.58/3.85 46 join(complement(c1),composition(complement(c3),c2)) != complement(c1) # answer(goals). [copy(45),rewrite([22(9)]),flip(a)].
% 3.58/3.85 47 complement(top) = zero. [back_rewrite(21),rewrite([25(2),20(4)])].
% 3.58/3.85 49 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),29(a,1,1)),flip(a)].
% 3.58/3.85 50 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),29(a,1,2)),flip(a)].
% 3.58/3.85 51 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),31(a,2,2)),rewrite([22(2)])].
% 3.58/3.85 52 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),32(a,1,1)),flip(a)].
% 3.58/3.85 57 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(32(a,1),34(a,1,1)),rewrite([22(6)])].
% 3.58/3.85 59 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(18(a,1),36(a,1,2,2,1))].
% 3.58/3.85 64 join(zero,complement(join(complement(A),complement(A)))) = A. [para(20(a,1),38(a,1,1,1)),rewrite([47(2)])].
% 3.58/3.85 65 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(20(a,1),38(a,1,2,1)),rewrite([47(6),22(6)])].
% 3.58/3.85 94 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(47(a,1),36(a,1,1)),rewrite([47(9)])].
% 3.58/3.85 129 composition(converse(one),A) = A. [para(18(a,1),50(a,1,1)),rewrite([19(2)]),flip(a)].
% 3.58/3.85 138 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(38(a,1),51(a,1,2)),rewrite([22(4),51(4),22(3),22(8)]),flip(a)].
% 3.58/3.85 139 join(top,complement(complement(A))) = top. [para(40(a,1),51(a,1,2)),rewrite([20(22),22(8),138(8)]),flip(a)].
% 3.58/3.85 140 converse(one) = one. [para(129(a,1),18(a,1)),flip(a)].
% 3.58/3.85 142 composition(join(A,one),B) = join(B,composition(A,B)). [para(129(a,1),34(a,1,1)),rewrite([140(4),22(4)]),flip(a)].
% 3.58/3.85 144 join(complement(A),complement(composition(one,A))) = complement(A). [para(129(a,1),36(a,1,2))].
% 3.58/3.85 158 composition(one,A) = A. [para(129(a,1),52(a,2)),rewrite([140(2),52(4)])].
% 3.58/3.85 164 join(complement(A),complement(A)) = complement(A). [back_rewrite(144),rewrite([158(3)])].
% 3.58/3.85 165 join(zero,complement(complement(A))) = A. [back_rewrite(64),rewrite([164(4)])].
% 3.58/3.85 166 converse(join(A,one)) = join(one,converse(A)). [para(140(a,1),27(a,1,1)),rewrite([22(5)]),flip(a)].
% 3.58/3.85 167 join(zero,complement(A)) = complement(A). [para(139(a,1),38(a,1,1,1)),rewrite([47(2),47(3),165(5)])].
% 3.58/3.85 169 join(top,complement(A)) = join(top,top). [para(139(a,1),51(a,1,2)),rewrite([22(3)])].
% 3.58/3.85 170 complement(complement(A)) = A. [back_rewrite(165),rewrite([167(4)])].
% 3.58/3.85 180 complement(join(A,A)) = complement(A). [back_rewrite(65),rewrite([170(3),167(4)])].
% 3.58/3.85 182 join(A,top) = top. [back_rewrite(139),rewrite([170(3),22(2)])].
% 3.58/3.85 188 join(top,complement(A)) = top. [back_rewrite(169),rewrite([182(6)])].
% 3.58/3.85 198 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(170(a,1),38(a,1,1,1,2)),rewrite([170(5),22(4)])].
% 3.58/3.85 202 join(complement(join(complement(A),complement(composition(complement(B),C)))),complement(join(complement(A),complement(composition(complement(join(B,complement(composition(A,converse(C))))),C))))) = complement(join(complement(A),complement(composition(complement(join(B,complement(composition(A,converse(C))))),C)))). [para(170(a,1),42(a,1,2,1,2,1,1,1,1)),rewrite([170(20)])].
% 3.58/3.85 206 complement(zero) = top. [para(47(a,1),170(a,1,1))].
% 3.58/3.85 221 join(A,A) = A. [para(180(a,1),38(a,1,1,1,2)),rewrite([180(6),38(8)]),flip(a)].
% 3.58/3.85 228 join(A,join(A,B)) = join(A,B). [para(221(a,1),31(a,1)),rewrite([22(3),31(4,R),22(3),31(3,R),221(2)]),flip(a)].
% 3.58/3.85 246 join(A,complement(join(B,complement(A)))) = A. [para(38(a,1),228(a,1,2)),rewrite([22(4),38(12)])].
% 3.58/3.85 248 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(246(a,1),31(a,2,2)),rewrite([22(4),22(6)])].
% 3.58/3.85 269 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(170(a,1),59(a,1,2,2))].
% 3.58/3.85 282 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(166(a,1),94(a,1,2,1))].
% 3.58/3.85 318 join(complement(one),converse(complement(one))) = complement(one). [para(18(a,1),269(a,1,2))].
% 3.58/3.85 322 converse(complement(one)) = complement(one). [para(318(a,1),27(a,2,1)),rewrite([19(7),22(6),318(6)]),flip(a)].
% 3.58/3.85 331 converse(top) = top. [para(322(a,1),166(a,2,2)),rewrite([22(4),20(4),20(6)])].
% 3.58/3.85 342 join(top,converse(A)) = top. [para(331(a,1),27(a,1,1)),rewrite([22(5),182(5),331(5)])].
% 3.58/3.85 349 join(top,composition(A,converse(B))) = top. [para(49(a,1),342(a,1,2))].
% 3.58/3.85 351 join(top,composition(A,B)) = top. [para(19(a,1),349(a,1,2,2))].
% 3.58/3.85 352 composition(join(A,one),top) = top. [para(331(a,1),349(a,1,2,2)),rewrite([142(4,R)])].
% 3.58/3.85 353 composition(join(one,converse(A)),zero) = zero. [back_rewrite(282),rewrite([352(8),47(6),142(7,R),22(5),228(5)])].
% 3.58/3.85 380 composition(top,zero) = zero. [para(322(a,1),353(a,1,1,2)),rewrite([20(4)])].
% 3.58/3.85 385 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(380(a,1),44(a,1,1,1,2,1)),rewrite([206(3),22(3),188(3),47(2),47(3),167(7),170(6),206(6),331(7),188(9),47(6),32(6),47(9),167(13),170(12),206(12),331(13),188(15),47(12),32(12)])].
% 3.58/3.85 389 join(zero,composition(A,composition(B,zero))) = zero. [para(380(a,1),57(a,1,2)),rewrite([22(5),351(8),380(8)])].
% 3.58/3.85 392 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(385),rewrite([389(7)]),flip(a)].
% 3.58/3.85 471 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(392(a,1),32(a,1,1)),rewrite([32(7)]),flip(a)].
% 3.58/3.85 472 composition(A,zero) = zero. [para(392(a,1),32(a,1)),rewrite([392(6)]),flip(a)].
% 3.58/3.85 473 composition(converse(zero),A) = converse(zero). [para(392(a,1),50(a,1,1)),rewrite([472(6)]),flip(a)].
% 3.58/3.85 478 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(471),rewrite([473(5)]),flip(a)].
% 3.58/3.85 480 composition(zero,A) = c_0. [new_symbol(478)].
% 3.58/3.85 496 c_0 = zero. [para(480(a,1),18(a,1))].
% 3.58/3.85 500 composition(zero,A) = zero. [back_rewrite(480),rewrite([496(3)])].
% 3.58/3.85 10338 join(A,complement(join(A,B))) = join(A,complement(B)). [para(198(a,1),248(a,1,2)),flip(a)].
% 3.58/3.85 10492 join(c3,complement(composition(c1,converse(c2)))) = top. [para(24(a,1),10338(a,1,2,1)),rewrite([20(4)]),flip(a)].
% 3.58/3.85 10831 complement(join(complement(c1),complement(composition(complement(c3),c2)))) = zero. [para(10492(a,1),202(a,1,2,1,2,1,1,1)),rewrite([47(13),500(14),206(13),22(13),188(13),47(11),22(11),167(11),10492(18),47(13),500(14),206(13),22(13),188(13),47(11)])].
% 3.58/3.85 13211 join(complement(c1),composition(complement(c3),c2)) = complement(c1). [para(10831(a,1),10338(a,1,2)),rewrite([22(4),167(4),170(10)]),flip(a)].
% 3.58/3.85 13212 $F # answer(goals). [resolve(13211,a,46,a)].
% 3.58/3.85
% 3.58/3.85 % SZS output end Refutation
% 3.58/3.85 ============================== end of proof ==========================
% 3.58/3.85
% 3.58/3.85 ============================== STATISTICS ============================
% 3.58/3.85
% 3.58/3.85 Given=531. Generated=82882. Kept=13183. proofs=1.
% 3.58/3.85 Usable=369. Sos=7271. Demods=7482. Limbo=8, Disabled=5552. Hints=0.
% 3.58/3.85 Megabytes=24.33.
% 3.58/3.85 User_CPU=2.81, System_CPU=0.06, Wall_clock=3.
% 3.58/3.85
% 3.58/3.85 ============================== end of statistics =====================
% 3.58/3.85
% 3.58/3.85 ============================== end of search =========================
% 3.58/3.85
% 3.58/3.85 THEOREM PROVED
% 3.58/3.85 % SZS status Theorem
% 3.58/3.85
% 3.58/3.85 Exiting with 1 proof.
% 3.58/3.85
% 3.58/3.85 Process 26112 exit (max_proofs) Fri Jul 8 12:40:14 2022
% 3.58/3.85 Prover9 interrupted
%------------------------------------------------------------------------------