TSTP Solution File: LAT241-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT241-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 : Sun Jul 17 06:26:21 EDT 2022
% Result : Unsatisfiable 244.14s 244.43s
% Output : Refutation 244.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT241-1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 01:33:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 10.07/10.37 ============================== Prover9 ===============================
% 10.07/10.37 Prover9 (32) version 2009-11A, November 2009.
% 10.07/10.37 Process 3850 was started by sandbox on n004.cluster.edu,
% 10.07/10.37 Wed Jun 29 01:33:53 2022
% 10.07/10.37 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3697_n004.cluster.edu".
% 10.07/10.37 ============================== end of head ===========================
% 10.07/10.37
% 10.07/10.37 ============================== INPUT =================================
% 10.07/10.37
% 10.07/10.37 % Reading from file /tmp/Prover9_3697_n004.cluster.edu
% 10.07/10.37
% 10.07/10.37 set(prolog_style_variables).
% 10.07/10.37 set(auto2).
% 10.07/10.37 % set(auto2) -> set(auto).
% 10.07/10.37 % set(auto) -> set(auto_inference).
% 10.07/10.37 % set(auto) -> set(auto_setup).
% 10.07/10.37 % set(auto_setup) -> set(predicate_elim).
% 10.07/10.37 % set(auto_setup) -> assign(eq_defs, unfold).
% 10.07/10.37 % set(auto) -> set(auto_limits).
% 10.07/10.37 % set(auto_limits) -> assign(max_weight, "100.000").
% 10.07/10.37 % set(auto_limits) -> assign(sos_limit, 20000).
% 10.07/10.37 % set(auto) -> set(auto_denials).
% 10.07/10.37 % set(auto) -> set(auto_process).
% 10.07/10.37 % set(auto2) -> assign(new_constants, 1).
% 10.07/10.37 % set(auto2) -> assign(fold_denial_max, 3).
% 10.07/10.37 % set(auto2) -> assign(max_weight, "200.000").
% 10.07/10.37 % set(auto2) -> assign(max_hours, 1).
% 10.07/10.37 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 10.07/10.37 % set(auto2) -> assign(max_seconds, 0).
% 10.07/10.37 % set(auto2) -> assign(max_minutes, 5).
% 10.07/10.37 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 10.07/10.37 % set(auto2) -> set(sort_initial_sos).
% 10.07/10.37 % set(auto2) -> assign(sos_limit, -1).
% 10.07/10.37 % set(auto2) -> assign(lrs_ticks, 3000).
% 10.07/10.37 % set(auto2) -> assign(max_megs, 400).
% 10.07/10.37 % set(auto2) -> assign(stats, some).
% 10.07/10.37 % set(auto2) -> clear(echo_input).
% 10.07/10.37 % set(auto2) -> set(quiet).
% 10.07/10.37 % set(auto2) -> clear(print_initial_clauses).
% 10.07/10.37 % set(auto2) -> clear(print_given).
% 10.07/10.37 assign(lrs_ticks,-1).
% 10.07/10.37 assign(sos_limit,10000).
% 10.07/10.37 assign(order,kbo).
% 10.07/10.37 set(lex_order_vars).
% 10.07/10.37 clear(print_given).
% 10.07/10.37
% 10.07/10.37 % formulas(sos). % not echoed (14 formulas)
% 10.07/10.37
% 10.07/10.37 ============================== end of input ==========================
% 10.07/10.37
% 10.07/10.37 % From the command line: assign(max_seconds, 300).
% 10.07/10.37
% 10.07/10.37 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 10.07/10.37
% 10.07/10.37 % Formulas that are not ordinary clauses:
% 10.07/10.37
% 10.07/10.37 ============================== end of process non-clausal formulas ===
% 10.07/10.37
% 10.07/10.37 ============================== PROCESS INITIAL CLAUSES ===============
% 10.07/10.37
% 10.07/10.37 ============================== PREDICATE ELIMINATION =================
% 10.07/10.37
% 10.07/10.37 ============================== end predicate elimination =============
% 10.07/10.37
% 10.07/10.37 Auto_denials:
% 10.07/10.37 % copying label prove_distributivity to answer in negative clause
% 10.07/10.37
% 10.07/10.37 Term ordering decisions:
% 10.07/10.37
% 10.07/10.37 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 10.07/10.37 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 10.07/10.37
% 10.07/10.37 ============================== end of process initial clauses ========
% 10.07/10.37
% 10.07/10.37 ============================== CLAUSES FOR SEARCH ====================
% 10.07/10.37
% 10.07/10.37 ============================== end of clauses for search =============
% 10.07/10.37
% 10.07/10.37 ============================== SEARCH ================================
% 10.07/10.37
% 10.07/10.37 % Starting search at 0.01 seconds.
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=115.000, iters=3495
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=79.000, iters=3385
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=69.000, iters=3361
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=67.000, iters=3342
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=66.000, iters=3375
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=55.000, iters=3334
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=49.000, iters=3362
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=47.000, iters=3478
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=45.000, iters=3398
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=44.000, iters=3390
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=43.000, iters=3365
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=42.000, iters=3427
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=41.000, iters=3382
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=40.000, iters=3354
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=39.000, iters=3335
% 10.07/10.37
% 10.07/10.37 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 27 (0.00 of 6.23 sec).
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=38.000, iters=3356
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=37.000, iters=3335
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=36.000, iters=3335
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=35.000, iters=3365
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=34.000, iters=3333
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=33.000, iters=3334
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=32.000, iters=3381
% 10.07/10.37
% 10.07/10.37 Low Water (keep): wt=31.000, iters=3355
% 10.07/10.37
% 10.07/10.37 Low Water (displace): id=8139, wt=137.000
% 10.07/10.37
% 10.07/10.37 Low Water (displace): id=15095, wt=27.000
% 244.14/244.43
% 244.14/244.43 Low Water (displace): id=15096, wt=23.000
% 244.14/244.43
% 244.14/244.43 Low Water (displace): id=15097, wt=15.000
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=30.000, iters=3446
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=29.000, iters=3343
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=28.000, iters=3355
% 244.14/244.43
% 244.14/244.43 Low Water (displace): id=17058, wt=14.000
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=27.000, iters=3388
% 244.14/244.43
% 244.14/244.43 Low Water (displace): id=18058, wt=13.000
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=26.000, iters=3345
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=25.000, iters=3403
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=24.000, iters=3333
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=23.000, iters=3545
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=22.000, iters=3335
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=21.000, iters=3333
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=19.000, iters=4242
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=18.000, iters=3357
% 244.14/244.43
% 244.14/244.43 Low Water (keep): wt=17.000, iters=3611
% 244.14/244.43
% 244.14/244.43 ============================== PROOF =================================
% 244.14/244.43 % SZS status Unsatisfiable
% 244.14/244.43 % SZS output start Refutation
% 244.14/244.43
% 244.14/244.43 % Proof 1 at 240.66 (+ 2.78) seconds: prove_distributivity.
% 244.14/244.43 % Length of proof is 124.
% 244.14/244.43 % Level of proof is 26.
% 244.14/244.43 % Maximum clause weight is 39.000.
% 244.14/244.43 % Given clauses 3433.
% 244.14/244.43
% 244.14/244.43 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 244.14/244.43 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 244.14/244.43 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 244.14/244.43 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 244.14/244.43 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 244.14/244.43 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 244.14/244.43 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 244.14/244.43 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 244.14/244.43 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 244.14/244.43 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 244.14/244.43 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 244.14/244.43 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 244.14/244.43 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 244.14/244.43 14 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,join(meet(A,C),meet(C,D)))) # label(equation_H51) # label(axiom). [assumption].
% 244.14/244.43 15 meet(A,join(B,join(meet(A,C),meet(C,D)))) = meet(A,join(B,meet(C,join(A,D)))). [copy(14),flip(a)].
% 244.14/244.43 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 244.14/244.43 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 244.14/244.43 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 244.14/244.43 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 244.14/244.43 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 244.14/244.43 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 244.14/244.43 22 meet(A,meet(A,B)) = meet(A,B). [para(11(a,1),1(a,1)),rewrite([8(1),8(2),11(2,R),1(1),8(3)])].
% 244.14/244.43 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 244.14/244.43 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 244.14/244.43 25 join(A,join(A,B)) = join(A,B). [para(13(a,1),2(a,1)),rewrite([9(1),9(2),13(2,R),2(1),9(3)])].
% 244.14/244.43 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 244.14/244.43 27 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 244.14/244.43 28 meet(A,join(B,join(C,meet(A,C)))) = meet(A,join(B,meet(C,join(A,C)))). [para(1(a,1),15(a,1,2,2,2)),rewrite([9(2)])].
% 244.14/244.43 29 meet(A,join(meet(B,C),meet(B,join(A,C)))) = meet(A,join(meet(A,B),meet(B,C))). [para(2(a,1),15(a,1,2)),rewrite([9(10),13(10),9(9),15(11),25(7)]),flip(a)].
% 244.14/244.43 30 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(2(a,1),15(a,2,2)),rewrite([13(6),9(5),15(7),25(3),29(5),24(7)])].
% 244.14/244.43 33 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(6(a,1),15(a,1,2,2,1)),rewrite([8(2),13(4,R),9(3),6(5)]),flip(a)].
% 244.14/244.43 34 meet(A,join(B,meet(C,join(A,join(C,D))))) = meet(A,join(B,meet(C,join(A,C)))). [para(6(a,1),15(a,1,2,2,2)),rewrite([9(2),28(4)]),flip(a)].
% 244.14/244.43 36 meet(A,join(B,meet(A,B))) = meet(A,B). [para(7(a,1),15(a,2,2)),rewrite([27(4)])].
% 244.14/244.43 37 meet(A,join(B,join(meet(C,D),meet(A,C)))) = meet(A,join(B,meet(C,join(A,D)))). [para(9(a,1),15(a,1,2,2))].
% 244.14/244.43 38 meet(A,meet(B,join(C,join(meet(A,D),meet(D,E))))) = meet(A,meet(B,join(C,meet(D,join(A,E))))). [para(15(a,1),11(a,2,2)),rewrite([8(5),11(11,R),8(10)])].
% 244.14/244.43 39 meet(A,join(B,join(meet(A,meet(C,D)),meet(C,meet(D,E))))) = meet(A,join(B,meet(meet(C,D),join(A,E)))). [para(11(a,1),15(a,1,2,2,1)),rewrite([11(2,R),8(1),8(3),8(4),11(4),8(3),11(4,R),8(3),8(8)])].
% 244.14/244.43 42 meet(A,join(B,meet(C,join(A,meet(D,join(C,E)))))) = meet(A,join(B,meet(C,join(A,D)))). [para(15(a,1),15(a,2,2,2)),rewrite([30(5),15(5)]),flip(a)].
% 244.14/244.43 48 meet(A,join(B,meet(one,join(A,C)))) = A. [para(20(a,1),15(a,1,2,2,1)),rewrite([8(2),20(2),13(2,R),9(1),6(3)]),flip(a)].
% 244.14/244.43 49 meet(A,join(B,meet(C,join(A,one)))) = meet(A,join(B,meet(C,join(A,C)))). [para(20(a,1),15(a,1,2,2,2)),rewrite([9(2),28(4)]),flip(a)].
% 244.14/244.43 50 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 244.14/244.43 51 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 244.14/244.43 54 one != A | complement(A) = zero. [back_rewrite(50),rewrite([51(2)]),xx(a)].
% 244.14/244.43 55 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([51(5)])].
% 244.14/244.43 58 meet(A,join(B,join(zero,meet(A,C)))) = meet(A,join(B,meet(A,C))). [para(51(a,1),15(a,1,2,2,2)),rewrite([9(3),21(7),8(6)])].
% 244.14/244.43 60 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(24(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),11(6),8(5),11(6,R),8(5)])].
% 244.14/244.43 63 complement(join(A,one)) = zero. [hyper(54,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 244.14/244.43 65 join(A,one) = one. [para(63(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 244.14/244.43 66 meet(A,join(B,meet(C,join(A,C)))) = meet(A,join(B,C)). [back_rewrite(49),rewrite([65(2),20(2)]),flip(a)].
% 244.14/244.43 67 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([65(5)])].
% 244.14/244.43 69 meet(A,join(B,meet(C,join(A,join(C,D))))) = meet(A,join(B,C)). [back_rewrite(34),rewrite([66(9)])].
% 244.14/244.43 70 meet(A,join(B,join(C,meet(A,C)))) = meet(A,join(B,C)). [back_rewrite(28),rewrite([66(8)])].
% 244.14/244.43 83 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(27(a,1),13(a,2,2)),rewrite([9(3),13(3,R),9(2),13(6),9(5),13(6,R),9(5)])].
% 244.14/244.43 84 meet(A,join(B,meet(A,C))) != zero | join(A,B) != one | join(B,meet(A,C)) = complement(A). [para(27(a,1),18(b,1)),flip(c)].
% 244.14/244.43 95 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(9(a,1),30(a,1,2))].
% 244.14/244.43 140 meet(A,join(join(B,join(meet(A,C),meet(C,D))),meet(A,join(B,meet(C,join(A,D)))))) = meet(A,join(B,meet(C,join(A,D)))). [para(15(a,1),36(a,1,2,2)),rewrite([15(15)])].
% 244.14/244.43 188 meet(A,join(B,join(meet(C,D),meet(C,A)))) = meet(A,join(B,meet(C,join(D,A)))). [para(37(a,1),8(a,2)),rewrite([8(2),8(5),9(6)])].
% 244.14/244.43 212 meet(A,join(meet(B,C),meet(B,A))) = meet(B,A). [para(95(a,1),8(a,2)),rewrite([8(2),8(4),8(5)])].
% 244.14/244.43 213 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(8(a,1),95(a,1,2,1))].
% 244.14/244.43 222 meet(meet(A,B),join(A,C)) = meet(A,B). [para(95(a,1),48(a,1,2,2)),rewrite([8(3),20(3),9(2)])].
% 244.14/244.43 282 meet(meet(A,B),join(B,C)) = meet(A,B). [para(8(a,1),222(a,1,1)),rewrite([8(4)])].
% 244.14/244.43 287 meet(meet(A,B),meet(join(A,C),join(D,meet(A,B)))) = meet(A,B). [para(222(a,1),24(a,2)),rewrite([9(4)])].
% 244.14/244.43 293 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(222(a,1),222(a,1,1)),rewrite([9(3),222(7)])].
% 244.14/244.43 336 meet(A,join(B,meet(meet(C,D),join(A,E)))) = meet(A,join(B,meet(C,meet(D,join(A,E))))). [para(8(a,1),39(a,2,2,2)),rewrite([39(7),11(8),8(7),11(8,R),8(7)])].
% 244.14/244.43 353 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(27(a,1),39(a,1,2)),rewrite([336(9),7(8)])].
% 244.14/244.43 623 meet(complement(A),join(zero,meet(A,B))) = zero. [para(5(a,1),212(a,1,2,2)),rewrite([9(4),5(7)])].
% 244.14/244.43 626 meet(b,join(a,meet(A,a))) = a. [para(19(a,1),212(a,1,2,2)),rewrite([8(3),9(5),19(9)])].
% 244.14/244.43 628 meet(meet(A,complement(B)),join(zero,meet(B,C))) = zero. [para(55(a,1),212(a,1,2,2)),rewrite([9(5),55(9)])].
% 244.14/244.43 640 meet(join(A,join(meet(B,C),meet(B,D))),join(meet(D,E),meet(D,join(A,meet(B,join(C,D)))))) = meet(D,join(A,meet(B,join(C,D)))). [para(37(a,1),212(a,1,2,2)),rewrite([8(2),9(6),8(13),188(16)])].
% 244.14/244.43 645 meet(A,meet(join(A,B),join(meet(C,D),join(meet(A,C),meet(B,C))))) = meet(A,C). [para(212(a,1),38(a,2,2)),rewrite([8(4),24(11)])].
% 244.14/244.43 663 join(a,b) = b. [para(626(a,1),7(a,1,2)),rewrite([9(3)])].
% 244.14/244.43 857 meet(A,join(zero,meet(B,join(A,C)))) = meet(A,B). [para(95(a,1),58(a,2)),rewrite([13(5,R),15(6)])].
% 244.14/244.43 872 meet(complement(meet(A,B)),join(zero,meet(A,B))) = zero. [para(222(a,1),623(a,1,2,2))].
% 244.14/244.43 1060 meet(A,join(B,meet(join(C,complement(B)),join(A,join(C,join(D,complement(B))))))) = A. [para(67(a,1),69(a,2,2)),rewrite([9(5),13(5,R),9(4),20(11)])].
% 244.14/244.43 1155 meet(A,meet(B,join(C,join(meet(A,join(D,E)),meet(F,join(D,join(E,meet(A,E)))))))) = meet(A,meet(B,join(C,meet(join(D,join(E,meet(A,E))),join(A,F))))). [para(70(a,1),38(a,1,2,2,2,1)),rewrite([8(6)])].
% 244.14/244.43 1398 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(83(a,1),13(a,2,2)),rewrite([9(4),13(4,R),9(3),13(3,R),9(2),13(8,R),9(7),13(7),9(6),13(7,R),9(6)])].
% 244.14/244.43 1462 meet(A,complement(B)) != zero | join(A,complement(B)) != one | complement(complement(B)) = A. [para(623(a,1),84(a,1,2,2)),rewrite([21(3),8(2),9(6),623(13),21(10)]),flip(c)].
% 244.14/244.43 1816 meet(A,join(join(A,B),meet(A,C))) = A. [para(6(a,1),353(a,2)),rewrite([8(3),24(4)])].
% 244.14/244.43 1822 meet(A,join(one,meet(A,B))) = A. [para(20(a,1),353(a,2)),rewrite([8(3),20(3)])].
% 244.14/244.43 1917 meet(one,complement(meet(A,B))) = complement(meet(A,B)). [para(872(a,1),1822(a,1,2,2)),rewrite([21(5),8(4)])].
% 244.14/244.43 2261 meet(complement(A),join(B,complement(A))) = complement(A). [para(623(a,1),1816(a,1,2,2)),rewrite([9(3),9(5),13(5,R),21(4)])].
% 244.14/244.43 2272 meet(complement(A),join(B,join(C,complement(A)))) = complement(A). [para(2261(a,1),282(a,1,1)),rewrite([9(4),13(4,R),9(3),2261(9)])].
% 244.14/244.43 2397 meet(one,complement(A)) = complement(A). [para(1(a,1),1917(a,1,2,1)),rewrite([1(4)])].
% 244.14/244.43 2402 meet(complement(meet(A,B)),join(zero,meet(A,meet(B,C)))) = zero. [para(1917(a,1),628(a,1,1)),rewrite([8(5),11(5),8(4),11(5,R),8(4)])].
% 244.14/244.43 2474 join(one,complement(A)) = one. [para(2397(a,1),7(a,1,2))].
% 244.14/244.43 2539 meet(complement(A),join(B,join(C,join(D,complement(A))))) = complement(A). [para(2272(a,1),282(a,1,1)),rewrite([9(5),13(5,R),9(4),13(4,R),9(3),2272(11)])].
% 244.14/244.43 2937 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(293(a,1),857(a,1,2,2))].
% 244.14/244.43 2961 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [back_rewrite(2402),rewrite([2937(7),11(5,R)])].
% 244.14/244.43 3145 meet(A,meet(meet(B,C),complement(meet(A,C)))) = zero. [para(8(a,1),2961(a,1,2,1))].
% 244.14/244.43 3525 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(6(a,1),3145(a,1,2,1))].
% 244.14/244.43 4361 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(3525(a,1),11(a,1)),rewrite([8(6)]),flip(a)].
% 244.14/244.43 4363 meet(A,meet(B,complement(meet(B,join(A,C))))) = zero. [para(3525(a,1),11(a,2)),rewrite([8(4)])].
% 244.14/244.43 4612 meet(A,complement(join(A,B))) = zero. [para(1(a,1),4361(a,1,2,1)),rewrite([8(2),6(2)])].
% 244.14/244.43 4613 join(zero,meet(A,B)) = meet(A,B). [para(4361(a,1),7(a,1,2)),rewrite([9(3)])].
% 244.14/244.43 5083 meet(A,join(B,meet(complement(join(A,C)),join(A,D)))) = meet(A,join(B,meet(D,complement(join(A,C))))). [para(4612(a,1),15(a,1,2,2,1)),rewrite([8(4),4613(5)]),flip(a)].
% 244.14/244.43 5283 meet(A,complement(meet(one,join(A,B)))) = zero. [para(2397(a,1),4363(a,1,2))].
% 244.14/244.43 5298 meet(join(A,B),complement(meet(one,join(A,B)))) = zero. [para(140(a,1),5283(a,1,2,1)),rewrite([8(2),20(2),7(2),9(4),65(4),20(4)])].
% 244.14/244.43 5637 meet(one,join(A,B)) = join(A,B). [para(5298(a,1),1822(a,1,2,2)),rewrite([21(4),8(3)])].
% 244.14/244.43 5792 join(A,meet(B,A)) = A. [para(5637(a,1),213(a,1)),rewrite([8(3),20(3),9(2),8(4),20(4)])].
% 244.14/244.43 5796 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(5637(a,1),4361(a,1,1)),rewrite([9(4),13(4),9(3),13(4,R),9(3),5637(5)])].
% 244.14/244.43 5821 meet(A,meet(B,join(C,join(meet(A,join(D,E)),meet(F,join(D,E)))))) = meet(A,meet(B,join(C,meet(join(D,E),join(A,F))))). [back_rewrite(1155),rewrite([5792(4),5792(10)])].
% 244.14/244.43 5948 join(one,meet(A,B)) = one. [para(1822(a,1),5792(a,1,2)),rewrite([9(4),27(4),65(2)]),flip(a)].
% 244.14/244.43 13344 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(42(a,1),287(a,1,2)),rewrite([9(8),13(8),9(7),13(8,R),9(7),6(9),9(7),11(9,R),11(8,R),24(8),24(7),8(2),6(2)]),flip(a)].
% 244.14/244.43 13572 meet(A,join(join(A,B),complement(C))) = A. [para(2261(a,1),13344(a,1,2,2))].
% 244.14/244.43 13662 meet(a,join(b,complement(A))) = a. [para(663(a,1),13572(a,1,2,1))].
% 244.14/244.43 13668 join(A,join(join(A,B),complement(C))) = join(join(A,B),complement(C)). [para(13572(a,1),5792(a,1,2)),rewrite([9(4)])].
% 244.14/244.43 13701 join(a,join(b,complement(A))) = join(b,complement(A)). [para(13662(a,1),5792(a,1,2)),rewrite([9(5)])].
% 244.14/244.43 14096 join(a,join(complement(A),b)) = join(b,complement(A)). [para(9(a,1),13701(a,1,2))].
% 244.14/244.43 21124 meet(A,join(B,A)) = A. [para(33(a,1),640(a,2)),rewrite([8(2),6(2),8(2),6(2),2(1),2(4),8(4),6(4),212(6)])].
% 244.14/244.43 21621 meet(join(complement(A),b),join(b,complement(A))) = join(complement(A),b). [para(14096(a,1),21124(a,1,2))].
% 244.14/244.43 21754 meet(A,meet(join(A,B),join(meet(C,complement(A)),meet(B,complement(A))))) = zero. [para(5(a,1),645(a,1,2,2,2,1)),rewrite([8(3),4613(7),5(10)])].
% 244.14/244.43 21784 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(5796(a,1),645(a,1,2,2,1)),rewrite([5821(10),4613(6),60(6)])].
% 244.14/244.43 21861 meet(A,join(meet(B,complement(A)),meet(C,complement(A)))) = zero. [back_rewrite(21754),rewrite([21784(8)])].
% 244.14/244.43 27750 join(A,join(join(B,C),complement(D))) = join(A,join(B,join(C,complement(D)))). [para(2539(a,1),1398(a,1,2,2,2,2)),rewrite([13(6,R),9(5),13(5,R),9(4),13(4,R),2(3),13(8,R)]),flip(a)].
% 244.14/244.43 27796 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [back_rewrite(13668),rewrite([27750(4),25(4)]),flip(a)].
% 244.14/244.43 28103 join(one,join(meet(A,B),complement(C))) = one. [para(5948(a,1),27796(a,1,1)),rewrite([2474(3)]),flip(a)].
% 244.14/244.43 28305 join(one,join(complement(A),join(b,complement(B)))) = one. [para(21621(a,1),28103(a,1,2,1)),rewrite([27796(6)])].
% 244.14/244.43 28346 join(A,join(complement(A),complement(B))) = one. [para(28305(a,1),1060(a,1,2,2,2)),rewrite([9(4),8(6),5637(6),5637(6)])].
% 244.14/244.43 28356 meet(a,join(complement(a),complement(b))) != zero # answer(prove_distributivity). [ur(18,b,28346,a,c,17,a(flip))].
% 244.14/244.43 28601 complement(complement(A)) = A. [hyper(1462,a,5,a,b,4,a)].
% 244.14/244.43 28686 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [para(28601(a,1),21861(a,1,2,1,2)),rewrite([8(2),28601(4),8(3)])].
% 244.14/244.43 39035 meet(complement(A),join(meet(A,B),complement(join(C,complement(A))))) = zero. [para(28686(a,1),5083(a,2)),rewrite([9(4),9(7),4(7),8(7),2397(7)])].
% 244.14/244.43 39202 meet(A,join(complement(A),complement(join(A,B)))) = zero. [para(2539(a,1),39035(a,1,2,1)),rewrite([28601(2),28601(3),9(2)])].
% 244.14/244.43 39220 meet(a,join(complement(a),complement(b))) = zero. [para(663(a,1),39202(a,1,2,2,1))].
% 244.14/244.43 39221 $F # answer(prove_distributivity). [resolve(39220,a,28356,a)].
% 244.14/244.43
% 244.14/244.43 % SZS output end Refutation
% 244.14/244.43 ============================== end of proof ==========================
% 244.14/244.43
% 244.14/244.43 ============================== STATISTICS ============================
% 244.14/244.43
% 244.14/244.43 Given=3433. Generated=4945612. Kept=39216. proofs=1.
% 244.14/244.43 Usable=2256. Sos=9999. Demods=11781. Limbo=9, Disabled=26965. Hints=0.
% 244.14/244.43 Megabytes=37.23.
% 244.14/244.43 User_CPU=240.66, System_CPU=2.78, Wall_clock=244.
% 244.14/244.43
% 244.14/244.43 ============================== end of statistics =====================
% 244.14/244.43
% 244.14/244.43 ============================== end of search =========================
% 244.14/244.43
% 244.14/244.43 THEOREM PROVED
% 244.14/244.43 % SZS status Unsatisfiable
% 244.14/244.43
% 244.14/244.43 Exiting with 1 proof.
% 244.14/244.43
% 244.14/244.43 Process 3850 exit (max_proofs) Wed Jun 29 01:37:57 2022
% 244.14/244.43 Prover9 interrupted
%------------------------------------------------------------------------------