TSTP Solution File: REL042+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL042+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 19:54:25 EDT 2022
% Result : Theorem 46.89s 47.20s
% Output : Refutation 46.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL042+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n016.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 12:43:23 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 16055 was started by sandbox on n016.cluster.edu,
% 0.42/0.98 Fri Jul 8 12:43:24 2022
% 0.42/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15902_n016.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_15902_n016.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 (14 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].
% 46.89/47.20 14 -(all X0 ((all X1 meet(composition(X0,X1),composition(X0,complement(X1))) = zero) -> join(composition(converse(X0),X0),one) = one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 46.89/47.20
% 46.89/47.20 ============================== end of process non-clausal formulas ===
% 46.89/47.20
% 46.89/47.20 ============================== PROCESS INITIAL CLAUSES ===============
% 46.89/47.20
% 46.89/47.20 ============================== PREDICATE ELIMINATION =================
% 46.89/47.20
% 46.89/47.20 ============================== end predicate elimination =============
% 46.89/47.20
% 46.89/47.20 Auto_denials:
% 46.89/47.20 % copying label goals to answer in negative clause
% 46.89/47.20
% 46.89/47.20 Term ordering decisions:
% 46.89/47.20 Function symbol KB weights: zero=1. one=1. top=1. c1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 46.89/47.20
% 46.89/47.20 ============================== end of process initial clauses ========
% 46.89/47.20
% 46.89/47.20 ============================== CLAUSES FOR SEARCH ====================
% 46.89/47.20
% 46.89/47.20 ============================== end of clauses for search =============
% 46.89/47.20
% 46.89/47.20 ============================== SEARCH ================================
% 46.89/47.20
% 46.89/47.20 % Starting search at 0.01 seconds.
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=35.000, iters=3355
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=31.000, iters=3404
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=28.000, iters=3335
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=27.000, iters=3335
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=26.000, iters=3376
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=25.000, iters=3342
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=24.000, iters=3366
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=23.000, iters=3355
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=22.000, iters=3336
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=21.000, iters=3345
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=20.000, iters=3333
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=19.000, iters=3336
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=3045, wt=46.000
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=5834, wt=41.000
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=6728, wt=40.000
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=6805, wt=39.000
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=5808, wt=38.000
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=13405, wt=18.000
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=13413, wt=17.000
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=13415, wt=16.000
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=18.000, iters=3336
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=13964, wt=14.000
% 46.89/47.20
% 46.89/47.20 Low Water (displace): id=14009, wt=13.000
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=17.000, iters=3350
% 46.89/47.20
% 46.89/47.20 Low Water (keep): wt=16.000, iters=3333
% 46.89/47.20
% 46.89/47.20 ============================== PROOF =================================
% 46.89/47.20 % SZS status Theorem
% 46.89/47.20 % SZS output start Refutation
% 46.89/47.20
% 46.89/47.20 % Proof 1 at 44.79 (+ 1.44) seconds: goals.
% 46.89/47.20 % Length of proof is 145.
% 46.89/47.20 % Level of proof is 29.
% 46.89/47.20 % Maximum clause weight is 21.000.
% 46.89/47.20 % Given clauses 3147.
% 46.89/47.20
% 46.89/47.20 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.20 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].
% 46.89/47.20 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].
% 46.89/47.20 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].
% 46.89/47.20 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].
% 46.89/47.20 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.20 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].
% 46.89/47.20 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.20 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.20 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.20 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].
% 46.89/47.20 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.20 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.20 14 -(all X0 ((all X1 meet(composition(X0,X1),composition(X0,complement(X1))) = zero) -> join(composition(converse(X0),X0),one) = one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 46.89/47.20 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 46.89/47.20 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 46.89/47.20 17 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 46.89/47.20 18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 46.89/47.20 19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 46.89/47.20 20 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 46.89/47.20 21 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 46.89/47.20 22 join(converse(A),converse(B)) = converse(join(A,B)). [copy(21),flip(a)].
% 46.89/47.20 23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 46.89/47.20 24 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(23),flip(a)].
% 46.89/47.20 25 meet(composition(c1,A),composition(c1,complement(A))) = zero # label(goals) # label(negated_conjecture). [clausify(14)].
% 46.89/47.20 26 complement(join(complement(composition(c1,A)),complement(composition(c1,complement(A))))) = zero. [copy(25),rewrite([20(6)])].
% 46.89/47.20 27 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 46.89/47.20 28 join(A,join(B,C)) = join(C,join(A,B)). [copy(27),rewrite([19(2)]),flip(a)].
% 46.89/47.20 29 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 46.89/47.20 30 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 46.89/47.20 31 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(30),flip(a)].
% 46.89/47.20 32 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 46.89/47.20 33 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(32),rewrite([19(7)]),flip(a)].
% 46.89/47.20 34 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 46.89/47.20 35 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(34),rewrite([19(6),19(8)]),rewrite([19(6)])].
% 46.89/47.20 36 join(composition(converse(c1),c1),one) != one # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 46.89/47.20 37 join(one,composition(converse(c1),c1)) != one # answer(goals). [copy(36),rewrite([19(6)])].
% 46.89/47.20 38 complement(top) = zero. [back_rewrite(18),rewrite([20(2),17(4)])].
% 46.89/47.20 39 converse(join(A,converse(B))) = join(B,converse(A)). [para(16(a,1),22(a,1,1)),rewrite([19(4)]),flip(a)].
% 46.89/47.20 40 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(16(a,1),24(a,1,1)),flip(a)].
% 46.89/47.20 41 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),24(a,1,2)),flip(a)].
% 46.89/47.20 42 complement(join(complement(c1),complement(composition(c1,complement(one))))) = zero. [para(15(a,1),26(a,1,1,1,1))].
% 46.89/47.20 45 join(A,join(B,complement(A))) = join(B,top). [para(17(a,1),28(a,2,2)),rewrite([19(2)])].
% 46.89/47.20 46 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),29(a,1,1)),flip(a)].
% 46.89/47.20 48 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(24(a,1),31(a,1,1)),rewrite([19(7)])].
% 46.89/47.20 50 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(29(a,1),31(a,1,1)),rewrite([19(6)])].
% 46.89/47.20 52 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(15(a,1),33(a,1,2,2,1))].
% 46.89/47.20 54 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(33(a,1),22(a,2,1)),rewrite([41(7)])].
% 46.89/47.20 58 join(zero,complement(join(complement(A),complement(A)))) = A. [para(17(a,1),35(a,1,1,1)),rewrite([38(2)])].
% 46.89/47.20 61 join(complement(composition(c1,A)),complement(composition(c1,complement(A)))) = join(complement(join(B,zero)),complement(join(zero,complement(B)))). [para(26(a,1),35(a,1,1,1,2)),rewrite([26(13),19(6)]),flip(a)].
% 46.89/47.20 64 join(zero,complement(join(composition(c1,A),complement(composition(c1,complement(A)))))) = composition(c1,complement(A)). [para(26(a,1),35(a,1,2)),rewrite([19(10)])].
% 46.89/47.20 66 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(35(a,1),35(a,1,2,1)),rewrite([19(10)])].
% 46.89/47.20 67 join(complement(composition(c1,A)),complement(composition(c1,complement(A)))) = c_0. [new_symbol(61)].
% 46.89/47.20 69 join(complement(join(A,zero)),complement(join(zero,complement(A)))) = c_0. [back_rewrite(61),rewrite([67(8)]),flip(a)].
% 46.89/47.20 74 join(zero,top) = top. [para(38(a,1),17(a,1,2)),rewrite([19(3)])].
% 46.89/47.20 76 c_0 = top. [para(38(a,1),35(a,1,1,1,2)),rewrite([38(6),19(6),69(8)])].
% 46.89/47.20 77 join(complement(join(zero,complement(A))),complement(join(top,complement(A)))) = A. [para(38(a,1),35(a,1,2,1,1)),rewrite([19(9)])].
% 46.89/47.20 79 join(complement(join(A,zero)),complement(join(zero,complement(A)))) = top. [back_rewrite(69),rewrite([76(9)])].
% 46.89/47.20 80 join(complement(composition(c1,A)),complement(composition(c1,complement(A)))) = top. [back_rewrite(67),rewrite([76(9)])].
% 46.89/47.20 81 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(39(a,1),22(a,1,1)),rewrite([19(7),28(7,R),19(6)]),flip(a)].
% 46.89/47.20 82 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(39(a,1),22(a,1,2)),rewrite([28(4,R),19(3),22(3),81(7)]),flip(a)].
% 46.89/47.20 86 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(39(a,1),39(a,2,2)),rewrite([82(4),39(4),28(6,R),19(5)])].
% 46.89/47.20 89 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(40(a,1),22(a,1,1)),rewrite([19(7)]),flip(a)].
% 46.89/47.20 93 composition(converse(one),A) = A. [para(15(a,1),41(a,1,1)),rewrite([16(2)]),flip(a)].
% 46.89/47.20 97 converse(one) = one. [para(93(a,1),15(a,1)),flip(a)].
% 46.89/47.20 99 composition(join(A,one),B) = join(B,composition(A,B)). [para(93(a,1),31(a,1,1)),rewrite([97(4),19(4)]),flip(a)].
% 46.89/47.20 101 join(complement(A),complement(composition(one,A))) = complement(A). [para(93(a,1),33(a,1,2))].
% 46.89/47.20 102 composition(one,A) = A. [para(93(a,1),46(a,2)),rewrite([97(2),46(4)])].
% 46.89/47.20 103 join(complement(A),complement(A)) = complement(A). [back_rewrite(101),rewrite([102(3)])].
% 46.89/47.20 104 join(zero,complement(complement(A))) = A. [back_rewrite(58),rewrite([103(4)])].
% 46.89/47.20 105 converse(join(A,one)) = join(one,converse(A)). [para(97(a,1),22(a,1,1)),rewrite([19(5)]),flip(a)].
% 46.89/47.20 109 join(complement(c1),complement(composition(c1,complement(one)))) = top. [para(42(a,1),35(a,1,1,1,2)),rewrite([42(13),19(6),79(8)]),flip(a)].
% 46.89/47.20 111 join(zero,complement(join(c1,complement(composition(c1,complement(one)))))) = composition(c1,complement(one)). [para(42(a,1),35(a,1,2)),rewrite([19(10)])].
% 46.89/47.20 117 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(105(a,1),24(a,1,1))].
% 46.89/47.20 122 join(top,complement(A)) = top. [para(103(a,1),45(a,1,2)),rewrite([17(2),19(4)]),flip(a)].
% 46.89/47.20 123 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(77),rewrite([122(7),38(6),19(6)])].
% 46.89/47.20 124 join(top,top) = join(A,top). [para(122(a,1),45(a,1,2)),flip(a)].
% 46.89/47.20 129 join(top,top) = top. [para(124(a,2),74(a,1))].
% 46.89/47.20 131 join(A,top) = top. [para(124(a,2),45(a,2)),rewrite([45(3),129(5)])].
% 46.89/47.20 133 join(A,join(B,complement(A))) = top. [back_rewrite(45),rewrite([131(5)])].
% 46.89/47.20 139 join(zero,complement(A)) = complement(A). [para(104(a,1),123(a,1,2,1))].
% 46.89/47.20 140 complement(complement(A)) = A. [back_rewrite(123),rewrite([139(4),139(4)])].
% 46.89/47.20 141 complement(join(c1,complement(composition(c1,complement(one))))) = composition(c1,complement(one)). [back_rewrite(111),rewrite([139(10)])].
% 46.89/47.20 143 join(A,zero) = A. [back_rewrite(104),rewrite([140(3),19(2)])].
% 46.89/47.20 144 complement(join(composition(c1,A),complement(composition(c1,complement(A))))) = composition(c1,complement(A)). [back_rewrite(64),rewrite([139(10)])].
% 46.89/47.20 149 join(A,composition(converse(B),complement(composition(B,complement(A))))) = A. [para(140(a,1),33(a,1,1)),rewrite([140(8)])].
% 46.89/47.20 150 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(140(a,1),35(a,1,1,1,2)),rewrite([140(5),19(4)])].
% 46.89/47.20 152 join(A,A) = A. [para(140(a,1),103(a,1,1)),rewrite([140(2),140(3)])].
% 46.89/47.20 159 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [para(102(a,1),48(a,1,2)),rewrite([19(4),22(4),117(8)]),flip(a)].
% 46.89/47.20 161 join(A,join(A,B)) = join(A,B). [para(152(a,1),28(a,1)),rewrite([19(3),28(4,R),19(3),28(3,R),152(2)]),flip(a)].
% 46.89/47.20 162 join(A,complement(join(B,complement(A)))) = A. [para(35(a,1),161(a,1,2)),rewrite([19(4),35(12)])].
% 46.89/47.20 164 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(162(a,1),28(a,2,2)),rewrite([19(4),19(6)])].
% 46.89/47.20 167 join(complement(A),complement(join(A,B))) = complement(A). [para(140(a,1),162(a,1,2,1,2)),rewrite([19(2)])].
% 46.89/47.20 175 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(22(a,1),167(a,1,2,1))].
% 46.89/47.20 181 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(102(a,1),50(a,1,2)),rewrite([19(3)]),flip(a)].
% 46.89/47.20 183 join(complement(one),composition(A,complement(converse(A)))) = complement(one). [para(16(a,1),52(a,1,2,1))].
% 46.89/47.20 190 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(140(a,1),52(a,1,2,2))].
% 46.89/47.20 209 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(99(a,1),31(a,1,2)),rewrite([28(4,R),31(3),19(1)]),flip(a)].
% 46.89/47.20 244 join(complement(one),converse(complement(one))) = complement(one). [para(15(a,1),190(a,1,2))].
% 46.89/47.20 254 converse(complement(one)) = complement(one). [para(244(a,1),22(a,2,1)),rewrite([16(7),19(6),244(6)]),flip(a)].
% 46.89/47.20 256 converse(composition(A,complement(one))) = composition(complement(one),converse(A)). [para(254(a,1),24(a,1,1)),flip(a)].
% 46.89/47.20 259 converse(top) = top. [para(254(a,1),105(a,2,2)),rewrite([19(4),17(4),17(6)])].
% 46.89/47.20 264 join(top,converse(A)) = top. [para(259(a,1),22(a,1,1)),rewrite([19(5),131(5),259(5)])].
% 46.89/47.20 265 converse(composition(A,top)) = composition(top,converse(A)). [para(259(a,1),24(a,1,1)),flip(a)].
% 46.89/47.20 269 join(top,composition(A,converse(B))) = top. [para(40(a,1),264(a,1,2))].
% 46.89/47.20 276 join(top,composition(A,B)) = top. [para(16(a,1),269(a,1,2,2))].
% 46.89/47.20 279 join(converse(A),composition(top,converse(B))) = converse(join(A,composition(B,top))). [para(265(a,1),22(a,1,2))].
% 46.89/47.20 337 join(complement(A),complement(join(B,A))) = complement(A). [para(162(a,1),66(a,2)),rewrite([140(2),140(4),140(8),66(13)])].
% 46.89/47.20 338 join(c1,complement(composition(c1,complement(one)))) = complement(composition(c1,complement(one))). [para(109(a,1),66(a,1,2,1,1)),rewrite([140(9),141(14),276(11),38(7),19(7),139(7),140(8)]),flip(a)].
% 46.89/47.20 369 join(composition(c1,A),complement(composition(c1,complement(A)))) = complement(composition(c1,complement(A))). [para(80(a,1),66(a,1,2,1,1)),rewrite([140(9),144(13),276(9),38(6),19(6),139(6),140(8)]),flip(a)].
% 46.89/47.20 523 join(join(A,B),composition(C,converse(D))) = join(A,join(B,composition(C,converse(D)))). [para(40(a,1),86(a,1,2)),rewrite([40(7)])].
% 46.89/47.20 588 join(one,complement(composition(A,complement(converse(A))))) = complement(composition(A,complement(converse(A)))). [para(183(a,1),337(a,1,2,1)),rewrite([140(7),19(6)])].
% 46.89/47.20 1545 composition(A,join(B,one)) = join(A,composition(A,B)). [para(159(a,1),16(a,1,1)),rewrite([16(4)]),flip(a)].
% 46.89/47.20 1644 composition(converse(complement(composition(A,complement(converse(A))))),A) = A. [para(149(a,1),159(a,2,1)),rewrite([19(7),588(7),41(7),16(8)])].
% 46.89/47.20 1743 join(A,complement(join(A,B))) = join(A,complement(B)). [para(150(a,1),164(a,1,2)),flip(a)].
% 46.89/47.20 1940 join(A,composition(A,join(B,one))) = join(A,composition(A,B)). [para(1545(a,2),161(a,1,2))].
% 46.89/47.20 2007 join(complement(converse(A)),converse(join(A,B))) = top. [para(175(a,1),133(a,1,2)),rewrite([19(5)])].
% 46.89/47.20 2033 join(A,join(B,converse(complement(converse(A))))) = top. [para(2007(a,1),22(a,2,1)),rewrite([16(6),28(5),19(4),28(5,R),19(4),259(7)])].
% 46.89/47.20 2075 join(A,converse(complement(converse(A)))) = top. [para(152(a,1),2033(a,1,2))].
% 46.89/47.20 2198 composition(A,complement(composition(converse(A),complement(A)))) = A. [para(1644(a,1),40(a,1,1)),rewrite([16(2),16(3),16(6)]),flip(a)].
% 46.89/47.20 2651 join(A,complement(converse(complement(converse(A))))) = A. [para(2075(a,1),1743(a,1,2,1)),rewrite([38(2),143(2)]),flip(a)].
% 46.89/47.20 2671 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(16(a,1),2651(a,1,2,1,1,1))].
% 46.89/47.20 2674 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(2651(a,1),35(a,1,2,1)),rewrite([140(9),19(8),1743(8),140(6)])].
% 46.89/47.20 2775 composition(join(one,composition(A,B)),A) = composition(A,join(one,composition(B,A))). [para(181(a,2),1545(a,2)),rewrite([19(3)]),flip(a)].
% 46.89/47.20 2810 converse(complement(converse(complement(A)))) = A. [para(2671(a,1),22(a,2,1)),rewrite([16(2),2674(5),16(6)])].
% 46.89/47.20 2831 complement(converse(complement(A))) = converse(A). [para(2810(a,1),16(a,1,1)),flip(a)].
% 46.89/47.20 2853 converse(complement(A)) = complement(converse(A)). [para(2831(a,1),140(a,1,1)),flip(a)].
% 46.89/47.20 2855 join(A,composition(complement(converse(composition(B,complement(converse(A))))),B)) = A. [para(2831(a,1),54(a,1,1,1)),rewrite([16(2),2853(2),2853(5),2853(9),140(10),16(9)])].
% 46.89/47.20 3052 join(converse(A),complement(converse(B))) = converse(join(A,complement(B))). [para(2853(a,1),22(a,1,2))].
% 46.89/47.20 3057 converse(composition(A,complement(converse(B)))) = composition(complement(B),converse(A)). [para(2853(a,1),40(a,1,1,2))].
% 46.89/47.20 3133 join(A,composition(complement(composition(complement(A),converse(B))),B)) = A. [back_rewrite(2855),rewrite([3057(4)])].
% 46.89/47.20 4498 join(A,composition(complement(one),A)) = composition(top,A). [para(52(a,1),209(a,2,2,1)),rewrite([19(7),28(8,R),19(7),52(7),17(4)]),flip(a)].
% 46.89/47.20 4558 join(A,composition(A,complement(one))) = composition(A,top). [para(4498(a,1),89(a,1,1)),rewrite([40(4),259(2),2853(5),97(4),16(7),19(6)]),flip(a)].
% 46.89/47.20 4562 join(A,complement(composition(complement(one),A))) = join(A,complement(composition(top,A))). [para(4498(a,1),1743(a,1,2,1)),flip(a)].
% 46.89/47.20 4572 join(A,complement(composition(A,complement(one)))) = join(A,complement(composition(A,top))). [para(4558(a,1),1743(a,1,2,1)),flip(a)].
% 46.89/47.20 4576 join(c1,complement(composition(c1,top))) = complement(composition(c1,complement(one))). [back_rewrite(338),rewrite([4572(7)])].
% 46.89/47.20 7019 join(converse(A),complement(composition(top,converse(B)))) = converse(join(A,complement(composition(B,top)))). [para(279(a,1),1743(a,1,2,1)),rewrite([3052(7),1743(5)]),flip(a)].
% 46.89/47.20 9502 join(complement(c1),composition(c1,composition(converse(c1),complement(c1)))) = complement(c1). [para(2198(a,1),369(a,1,2,1)),rewrite([19(10),2198(18)])].
% 46.89/47.20 9814 join(A,composition(complement(composition(complement(one),converse(B))),composition(B,A))) = A. [para(3133(a,1),181(a,1,1)),rewrite([102(2)]),flip(a)].
% 46.89/47.20 15725 join(join(A,B),composition(C,D)) = join(A,join(B,composition(C,D))). [para(16(a,1),523(a,1,2,2)),rewrite([16(5)])].
% 46.89/47.20 17556 join(A,composition(A,join(one,composition(B,A)))) = composition(A,join(one,composition(B,A))). [para(181(a,2),1940(a,2)),rewrite([19(3),2775(9)])].
% 46.89/47.20 22782 composition(join(one,composition(c1,converse(c1))),complement(c1)) = complement(c1). [para(9502(a,1),181(a,2))].
% 46.89/47.20 22798 composition(c1,join(one,composition(converse(c1),c1))) = c1. [para(22782(a,1),33(a,1,2,2,1)),rewrite([140(3),89(8),97(7),19(7),140(10),2775(9),17556(10),140(11)])].
% 46.89/47.20 32812 join(one,composition(converse(c1),c1)) = one. [para(22798(a,1),9814(a,1,2,2)),rewrite([15725(15),31(14),4562(10),7019(9),4576(7),2853(7),256(6),3133(10)]),flip(a)].
% 46.89/47.20 32813 $F # answer(goals). [resolve(32812,a,37,a)].
% 46.89/47.20
% 46.89/47.20 % SZS output end Refutation
% 46.89/47.20 ============================== end of proof ==========================
% 46.89/47.20
% 46.89/47.20 ============================== STATISTICS ============================
% 46.89/47.20
% 46.89/47.20 Given=3147. Generated=2663463. Kept=32790. proofs=1.
% 46.89/47.20 Usable=2726. Sos=9999. Demods=12543. Limbo=2, Disabled=20077. Hints=0.
% 46.89/47.20 Megabytes=25.29.
% 46.89/47.20 User_CPU=44.80, System_CPU=1.44, Wall_clock=46.
% 46.89/47.20
% 46.89/47.20 ============================== end of statistics =====================
% 46.89/47.20
% 46.89/47.20 ============================== end of search =========================
% 46.89/47.20
% 46.89/47.20 THEOREM PROVED
% 46.89/47.20 % SZS status Theorem
% 46.89/47.20
% 46.89/47.20 Exiting with 1 proof.
% 46.89/47.20
% 46.89/47.20 Process 16055 exit (max_proofs) Fri Jul 8 12:44:10 2022
% 46.89/47.20 Prover9 interrupted
%------------------------------------------------------------------------------