TSTP Solution File: LAT199-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT199-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 06:26:04 EDT 2022
% Result : Unsatisfiable 12.89s 13.16s
% Output : Refutation 12.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT199-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 29 13:30:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 6.70/6.98 ============================== Prover9 ===============================
% 6.70/6.98 Prover9 (32) version 2009-11A, November 2009.
% 6.70/6.98 Process 26099 was started by sandbox2 on n029.cluster.edu,
% 6.70/6.98 Wed Jun 29 13:30:53 2022
% 6.70/6.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25946_n029.cluster.edu".
% 6.70/6.98 ============================== end of head ===========================
% 6.70/6.98
% 6.70/6.98 ============================== INPUT =================================
% 6.70/6.98
% 6.70/6.98 % Reading from file /tmp/Prover9_25946_n029.cluster.edu
% 6.70/6.98
% 6.70/6.98 set(prolog_style_variables).
% 6.70/6.98 set(auto2).
% 6.70/6.98 % set(auto2) -> set(auto).
% 6.70/6.98 % set(auto) -> set(auto_inference).
% 6.70/6.98 % set(auto) -> set(auto_setup).
% 6.70/6.98 % set(auto_setup) -> set(predicate_elim).
% 6.70/6.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.70/6.98 % set(auto) -> set(auto_limits).
% 6.70/6.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.70/6.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.70/6.98 % set(auto) -> set(auto_denials).
% 6.70/6.98 % set(auto) -> set(auto_process).
% 6.70/6.98 % set(auto2) -> assign(new_constants, 1).
% 6.70/6.98 % set(auto2) -> assign(fold_denial_max, 3).
% 6.70/6.98 % set(auto2) -> assign(max_weight, "200.000").
% 6.70/6.98 % set(auto2) -> assign(max_hours, 1).
% 6.70/6.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.70/6.98 % set(auto2) -> assign(max_seconds, 0).
% 6.70/6.98 % set(auto2) -> assign(max_minutes, 5).
% 6.70/6.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.70/6.98 % set(auto2) -> set(sort_initial_sos).
% 6.70/6.98 % set(auto2) -> assign(sos_limit, -1).
% 6.70/6.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.70/6.98 % set(auto2) -> assign(max_megs, 400).
% 6.70/6.98 % set(auto2) -> assign(stats, some).
% 6.70/6.98 % set(auto2) -> clear(echo_input).
% 6.70/6.98 % set(auto2) -> set(quiet).
% 6.70/6.98 % set(auto2) -> clear(print_initial_clauses).
% 6.70/6.98 % set(auto2) -> clear(print_given).
% 6.70/6.98 assign(lrs_ticks,-1).
% 6.70/6.98 assign(sos_limit,10000).
% 6.70/6.98 assign(order,kbo).
% 6.70/6.98 set(lex_order_vars).
% 6.70/6.98 clear(print_given).
% 6.70/6.98
% 6.70/6.98 % formulas(sos). % not echoed (13 formulas)
% 6.70/6.98
% 6.70/6.98 ============================== end of input ==========================
% 6.70/6.98
% 6.70/6.98 % From the command line: assign(max_seconds, 300).
% 6.70/6.98
% 6.70/6.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.70/6.98
% 6.70/6.98 % Formulas that are not ordinary clauses:
% 6.70/6.98
% 6.70/6.98 ============================== end of process non-clausal formulas ===
% 6.70/6.98
% 6.70/6.98 ============================== PROCESS INITIAL CLAUSES ===============
% 6.70/6.98
% 6.70/6.98 ============================== PREDICATE ELIMINATION =================
% 6.70/6.98
% 6.70/6.98 ============================== end predicate elimination =============
% 6.70/6.98
% 6.70/6.98 Auto_denials:
% 6.70/6.98 % copying label prove_distributivity to answer in negative clause
% 6.70/6.98
% 6.70/6.98 Term ordering decisions:
% 6.70/6.98
% 6.70/6.98 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 6.70/6.98 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. join=1. meet=1. complement=0.
% 6.70/6.98
% 6.70/6.98 ============================== end of process initial clauses ========
% 6.70/6.98
% 6.70/6.98 ============================== CLAUSES FOR SEARCH ====================
% 6.70/6.98
% 6.70/6.98 ============================== end of clauses for search =============
% 6.70/6.98
% 6.70/6.98 ============================== SEARCH ================================
% 6.70/6.98
% 6.70/6.98 % Starting search at 0.01 seconds.
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=167.000, iters=3366
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=135.000, iters=3346
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=127.000, iters=3335
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=111.000, iters=3501
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=93.000, iters=3397
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=87.000, iters=3345
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=78.000, iters=3353
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=77.000, iters=3385
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=75.000, iters=3350
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=72.000, iters=3368
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=71.000, iters=3339
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=70.000, iters=3337
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=69.000, iters=3390
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=68.000, iters=3343
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=65.000, iters=3335
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=64.000, iters=3366
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=63.000, iters=3376
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=62.000, iters=3336
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=61.000, iters=3408
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=60.000, iters=3374
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=59.000, iters=3348
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=57.000, iters=3346
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=55.000, iters=3410
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=54.000, iters=3357
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=53.000, iters=3355
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=52.000, iters=3406
% 6.70/6.98
% 6.70/6.98 Low Water (keep): wt=51.000, iters=3350
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=49.000, iters=3345
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=48.000, iters=3351
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=47.000, iters=3410
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=46.000, iters=3346
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=45.000, iters=3335
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=44.000, iters=3363
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=43.000, iters=3339
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=42.000, iters=3380
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=41.000, iters=3338
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=40.000, iters=3348
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=39.000, iters=3350
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=38.000, iters=3351
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=37.000, iters=3346
% 12.89/13.16
% 12.89/13.16 Low Water (displace): id=7427, wt=177.000
% 12.89/13.16
% 12.89/13.16 Low Water (displace): id=8448, wt=175.000
% 12.89/13.16
% 12.89/13.16 Low Water (displace): id=7656, wt=169.000
% 12.89/13.16
% 12.89/13.16 Low Water (displace): id=8630, wt=167.000
% 12.89/13.16
% 12.89/13.16 Low Water (displace): id=14507, wt=26.000
% 12.89/13.16
% 12.89/13.16 Low Water (displace): id=14511, wt=16.000
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=36.000, iters=3376
% 12.89/13.16
% 12.89/13.16 Low Water (displace): id=15333, wt=15.000
% 12.89/13.16
% 12.89/13.16 Low Water (keep): wt=35.000, iters=3340
% 12.89/13.16
% 12.89/13.16 ============================== PROOF =================================
% 12.89/13.16 % SZS status Unsatisfiable
% 12.89/13.16 % SZS output start Refutation
% 12.89/13.16
% 12.89/13.16 % Proof 1 at 12.10 (+ 0.11) seconds: prove_distributivity.
% 12.89/13.16 % Length of proof is 117.
% 12.89/13.16 % Level of proof is 32.
% 12.89/13.16 % Maximum clause weight is 49.000.
% 12.89/13.16 % Given clauses 490.
% 12.89/13.16
% 12.89/13.16 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 12.89/13.16 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 12.89/13.16 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 12.89/13.16 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 12.89/13.16 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 12.89/13.16 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 12.89/13.16 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 12.89/13.16 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 12.89/13.16 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 12.89/13.16 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 12.89/13.16 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 12.89/13.16 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 12.89/13.16 13 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))) # label(equation_H49) # label(axiom). [assumption].
% 12.89/13.16 14 meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))) = meet(A,join(B,meet(C,join(A,D)))). [copy(13),flip(a)].
% 12.89/13.16 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 12.89/13.16 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 12.89/13.16 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 12.89/13.16 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 12.89/13.16 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 12.89/13.16 20 meet(A,meet(A,B)) = meet(A,B). [para(10(a,1),1(a,1)),rewrite([7(1),7(2),10(2,R),1(1),7(3)])].
% 12.89/13.16 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 12.89/13.16 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 12.89/13.16 23 join(A,join(A,B)) = join(A,B). [para(12(a,1),2(a,1)),rewrite([8(1),8(2),12(2,R),2(1),8(3)])].
% 12.89/13.16 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 12.89/13.16 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 12.89/13.16 27 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(2(a,1),14(a,1,2,2,2,2)),rewrite([7(2),25(4)]),flip(a)].
% 12.89/13.16 28 meet(A,join(B,join(meet(A,C),meet(C,join(A,B))))) = meet(A,join(B,meet(A,C))). [para(2(a,1),14(a,2,2,2,2)),rewrite([8(2),7(7)])].
% 12.89/13.16 30 meet(A,join(B,join(C,meet(A,C)))) = meet(A,join(B,meet(C,join(A,complement(B))))). [para(3(a,1),14(a,1,2,2,2,2)),rewrite([18(3),8(2)])].
% 12.89/13.16 32 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(5(a,1),14(a,1,2,2,1)),rewrite([12(5,R),8(4),5(6)]),flip(a)].
% 12.89/13.16 33 meet(A,join(B,meet(A,B))) = meet(A,B). [para(5(a,1),14(a,1,2,2,2)),rewrite([8(2),23(3),6(6)])].
% 12.89/13.16 34 meet(A,join(B,meet(C,join(A,meet(B,D))))) = meet(A,join(B,meet(A,C))). [para(6(a,1),14(a,1,2,2,2,2)),rewrite([7(2),25(4)]),flip(a)].
% 12.89/13.16 37 meet(A,join(B,join(meet(A,join(C,meet(D,join(A,E)))),meet(join(C,join(meet(A,D),meet(D,join(C,E)))),join(B,F))))) = meet(A,join(B,meet(join(C,join(meet(A,D),meet(D,join(C,E)))),join(A,F)))). [para(14(a,1),14(a,1,2,2,1))].
% 12.89/13.16 41 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(7(a,1),17(a,1)),rewrite([8(4)])].
% 12.89/13.16 47 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 12.89/13.16 50 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([47(5)])].
% 12.89/13.16 51 complement(one) = zero. [hyper(17,a,47,a,b,19,a)].
% 12.89/13.16 53 one != A | complement(A) = zero. [para(47(a,1),17(a,1)),rewrite([19(5)]),flip(b),xx(a)].
% 12.89/13.16 57 complement(join(A,one)) = zero. [hyper(53,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 12.89/13.16 59 join(A,one) = one. [para(57(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 12.89/13.16 61 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([59(5)])].
% 12.89/13.16 63 meet(A,join(B,join(C,meet(A,C)))) = meet(A,join(B,C)). [para(59(a,1),14(a,1,2,2,2,2)),rewrite([18(3),8(2),59(6),18(6)])].
% 12.89/13.16 64 meet(A,join(B,meet(C,join(A,complement(B))))) = meet(A,join(B,C)). [back_rewrite(30),rewrite([63(4)]),flip(a)].
% 12.89/13.16 72 join(A,join(B,join(C,complement(A)))) = one. [para(61(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),59(6)])].
% 12.89/13.16 84 meet(A,B) != zero | join(A,B) != one | join(B,meet(A,B)) = complement(A). [para(33(a,1),17(a,1)),rewrite([25(6)]),flip(c)].
% 12.89/13.16 86 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(50(a,1),33(a,1,2,2)),rewrite([8(4),50(8)])].
% 12.89/13.16 89 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),86(a,1,2,2))].
% 12.89/13.16 90 meet(A,meet(B,join(zero,meet(C,complement(A))))) = zero. [para(86(a,1),10(a,2,2)),rewrite([7(5),47(8)])].
% 12.89/13.16 95 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(3(a,1),27(a,1,2,2,2)),rewrite([18(3),8(2)]),flip(a)].
% 12.89/13.16 97 meet(A,meet(B,join(C,meet(D,join(A,C))))) = meet(A,meet(B,join(C,meet(A,D)))). [para(27(a,1),10(a,2,2)),rewrite([7(4),10(9,R),7(8)])].
% 12.89/13.16 102 meet(A,join(one,meet(A,B))) = A. [para(59(a,1),27(a,1,2,2,2)),rewrite([18(3),8(2),59(2),18(2)]),flip(a)].
% 12.89/13.16 104 meet(A,join(join(B,complement(A)),meet(A,C))) = meet(A,join(B,join(C,complement(A)))). [para(61(a,1),27(a,1,2,2,2)),rewrite([18(4),8(3),12(3,R),8(2)]),flip(a)].
% 12.89/13.16 106 meet(A,join(join(B,join(C,complement(A))),meet(A,D))) = meet(A,join(B,join(C,join(D,complement(A))))). [para(72(a,1),27(a,1,2,2,2)),rewrite([18(5),8(4),12(4,R),8(3),12(3,R),8(2)]),flip(a)].
% 12.89/13.16 109 join(zero,complement(A)) = complement(A). [hyper(17,a,89,a,b,61,a),flip(a)].
% 12.89/13.16 129 meet(A,join(B,join(one,meet(A,B)))) = A. [para(59(a,1),28(a,1,2,2,2,2)),rewrite([18(4),8(3),12(4,R),8(3),102(9)])].
% 12.89/13.16 185 meet(A,join(one,join(zero,meet(B,complement(A))))) = A. [para(86(a,1),129(a,1,2,2,2)),rewrite([19(7),8(6)])].
% 12.89/13.16 276 meet(A,join(zero,meet(B,join(zero,meet(C,complement(A)))))) = zero. [para(90(a,1),33(a,1,2,2)),rewrite([8(7),90(14)])].
% 12.89/13.16 294 meet(A,join(join(B,C),meet(A,B))) = meet(A,join(B,C)). [para(32(a,1),34(a,1,2,2)),rewrite([8(2),23(2)]),flip(a)].
% 12.89/13.16 346 complement(complement(A)) = A. [hyper(41,a,4,a,b,3,a)].
% 12.89/13.16 351 meet(A,B) != zero | one != A | complement(meet(A,B)) = A. [para(20(a,1),41(a,1)),rewrite([6(5)]),flip(b)].
% 12.89/13.16 380 meet(complement(A),join(zero,meet(A,B))) = zero. [para(346(a,1),86(a,1,2,2,2)),rewrite([7(3)])].
% 12.89/13.16 460 meet(join(A,B),join(C,meet(join(A,B),join(A,join(B,D))))) = meet(join(A,B),join(A,join(B,C))). [para(2(a,1),37(a,1,2,2,2,1,2)),rewrite([8(5),12(5,R),2(4),1(5),23(4),1(4),1(5),23(4),6(6),12(3),8(2),12(3,R),8(2),1(8),1(9),2(8),23(7),8(8),12(8),8(7),12(8,R),8(7)]),flip(a)].
% 12.89/13.16 889 meet(complement(A),join(zero,meet(B,join(zero,meet(A,C))))) = zero. [para(346(a,1),276(a,1,2,2,2,2,2)),rewrite([7(4)])].
% 12.89/13.16 1146 meet(A,complement(join(A,B))) = zero. [para(32(a,1),889(a,1,2,2)),rewrite([8(4),19(4),7(3)])].
% 12.89/13.16 1161 meet(one,join(A,B)) = join(A,B). [para(1146(a,1),185(a,1,2,2,2)),rewrite([2(5),19(4),7(3)])].
% 12.89/13.16 1179 meet(one,complement(A)) = complement(A). [para(109(a,1),1161(a,1,2)),rewrite([109(6)])].
% 12.89/13.16 1268 meet(complement(A),join(A,meet(B,complement(A)))) = meet(complement(A),join(A,B)). [para(2(a,1),64(a,1,2,2,2))].
% 12.89/13.16 1913 meet(A,join(complement(A),complement(join(A,B)))) = zero. [para(1146(a,1),95(a,1,2,2)),rewrite([19(3),4(2),8(5)]),flip(a)].
% 12.89/13.16 2015 meet(complement(A),join(A,complement(join(B,complement(A))))) = zero. [para(346(a,1),1913(a,1,2,1)),rewrite([8(3)])].
% 12.89/13.16 2034 join(A,join(complement(A),complement(join(B,complement(A))))) != one | join(A,complement(join(B,complement(A)))) = A. [para(2015(a,1),17(a,1)),rewrite([12(9,R),8(8),346(13)]),flip(c),xx(a)].
% 12.89/13.16 2367 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(294(a,1),32(a,1,2,2)),rewrite([8(3),12(3),8(2),12(3,R),8(2),7(5),460(7)])].
% 12.89/13.16 2467 meet(complement(A),join(B,complement(A))) = complement(A). [para(109(a,1),2367(a,1,1)),rewrite([8(4),12(5,R),19(4),109(7)])].
% 12.89/13.16 2480 meet(complement(join(A,B)),join(zero,meet(C,join(A,B)))) = zero. [para(2367(a,1),889(a,1,2,2,2,2)),rewrite([12(6),8(5),19(5),8(4)])].
% 12.89/13.16 2543 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(2367(a,1),2480(a,1,2,2)),rewrite([12(6),8(5),19(5),8(4),7(5)])].
% 12.89/13.16 3628 meet(A,meet(complement(B),join(zero,meet(A,B)))) = zero. [para(380(a,1),97(a,1,2)),rewrite([47(2)]),flip(a)].
% 12.89/13.16 3681 meet(meet(A,complement(B)),join(zero,meet(A,B))) = zero. [para(3628(a,1),10(a,1)),rewrite([7(7)]),flip(a)].
% 12.89/13.16 3717 join(zero,meet(A,complement(B))) = meet(A,complement(B)). [para(3681(a,1),6(a,1,2)),rewrite([8(4)])].
% 12.89/13.16 3877 join(zero,meet(A,B)) = meet(A,B). [para(346(a,1),3717(a,1,2,2)),rewrite([346(5)])].
% 12.89/13.16 4903 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(3877(a,1),2367(a,1,1)),rewrite([8(4),12(5,R),8(4),3877(4),3877(7)])].
% 12.89/13.16 4906 meet(meet(A,B),complement(join(C,meet(A,B)))) = zero. [para(3877(a,1),2543(a,1,1)),rewrite([8(4),12(5,R),8(4),3877(4)])].
% 12.89/13.16 5344 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(4903(a,1),34(a,1,2,2)),rewrite([6(2)]),flip(a)].
% 12.89/13.16 5399 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(1161(a,1),5344(a,2)),rewrite([7(5),10(6,R),7(5),1161(5),1161(6)])].
% 12.89/13.16 5400 join(complement(A),meet(B,complement(A))) = complement(A). [para(1179(a,1),5344(a,2)),rewrite([7(5),10(6,R),18(5),1161(6)])].
% 12.89/13.16 5542 meet(A,join(B,join(complement(A),meet(C,join(A,D))))) = meet(A,join(B,join(C,complement(A)))). [para(22(a,1),104(a,1,2,2)),rewrite([104(5),8(8)]),flip(a)].
% 12.89/13.16 5820 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(3877(a,1),5399(a,1,1)),rewrite([3877(4),10(3),7(2),10(3,R),7(2),3877(7)])].
% 12.89/13.16 6109 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(1179(a,1),106(a,1,2,2)),rewrite([51(3),19(3),1161(5),51(7),19(7),1161(8)])].
% 12.89/13.16 6464 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [para(5820(a,1),4906(a,1,2,1)),rewrite([7(5),10(5,R)])].
% 12.89/13.16 6609 meet(A,meet(meet(B,C),complement(meet(A,C)))) = zero. [para(7(a,1),6464(a,1,2,1))].
% 12.89/13.16 6729 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(5(a,1),6609(a,1,2,1))].
% 12.89/13.16 6958 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(6729(a,1),10(a,1)),rewrite([7(6)]),flip(a)].
% 12.89/13.16 7179 meet(meet(A,B),complement(meet(A,join(C,meet(A,B))))) = zero. [para(20(a,1),6958(a,1,1)),rewrite([8(3)])].
% 12.89/13.16 7307 join(A,join(B,complement(join(A,B)))) = one. [para(6109(a,1),3(a,1))].
% 12.89/13.16 7308 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(6(a,1),6109(a,1,1)),flip(a)].
% 12.89/13.16 7676 join(A,join(B,join(C,complement(join(A,B))))) = one. [hyper(351,a,2543,a,b,7307,a(flip)),rewrite([7307(4),8(5),12(5,R),8(4),1179(8),346(7),7307(9)])].
% 12.89/13.16 7818 join(A,join(B,join(C,complement(join(A,C))))) = one. [para(7676(a,1),8(a,1)),rewrite([8(2),8(6),12(6,R),8(5),12(5,R),8(4)]),flip(a)].
% 12.89/13.16 8055 join(A,complement(meet(A,B))) = one. [para(3(a,1),7308(a,1,2)),rewrite([59(2)]),flip(a)].
% 12.89/13.16 8078 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(7308(a,1),7818(a,1,2))].
% 12.89/13.16 8092 join(A,join(B,complement(meet(C,join(A,B))))) = one. [para(8055(a,1),6109(a,1)),rewrite([7(3)]),flip(a)].
% 12.89/13.16 8312 join(A,join(B,complement(join(B,meet(A,C))))) = one. [para(8078(a,1),12(a,2)),rewrite([8(4)])].
% 12.89/13.16 8319 join(A,join(complement(A),complement(B))) = one. [para(2015(a,1),8078(a,1,2,2,1,2)),rewrite([19(3),8(3)])].
% 12.89/13.16 8335 join(A,complement(join(B,complement(A)))) = A. [back_rewrite(2034),rewrite([8319(6)]),xx(a)].
% 12.89/13.16 8379 meet(A,complement(join(B,complement(A)))) = complement(join(B,complement(A))). [para(8335(a,1),2467(a,1,2)),rewrite([7(4)])].
% 12.89/13.16 8393 join(A,complement(join(B,complement(meet(A,C))))) = A. [para(8335(a,1),7308(a,1,2)),rewrite([6(2)]),flip(a)].
% 12.89/13.16 9309 join(A,complement(join(meet(A,B),meet(A,C)))) = one. [para(8312(a,1),7308(a,1)),flip(a)].
% 12.89/13.16 10446 meet(complement(A),join(B,complement(meet(A,C)))) = complement(A). [para(8393(a,1),8379(a,1,2,1)),rewrite([7(5),8393(10)])].
% 12.89/13.16 10555 meet(complement(A),complement(meet(A,B))) = complement(A). [para(2(a,1),10446(a,1,2))].
% 12.89/13.16 10598 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(10555(a,1),5400(a,1,2)),rewrite([8(4)])].
% 12.89/13.16 10817 join(A,complement(meet(B,join(A,complement(B))))) = one. [para(10598(a,1),8092(a,1,2))].
% 12.89/13.16 10832 join(A,complement(meet(complement(B),join(A,B)))) = one. [para(346(a,1),10817(a,1,2,1,2,2))].
% 12.89/13.16 10855 join(A,complement(meet(complement(B),join(B,A)))) = one. [para(10832(a,1),8(a,1)),rewrite([8(3),8(6)]),flip(a)].
% 12.89/13.16 16411 complement(meet(complement(A),join(A,B))) = complement(meet(B,complement(A))). [hyper(84,a,7179,a,b,10855,a),rewrite([7(3),1268(5),7(6),7(9),1268(11),5400(12),7(6)])].
% 12.89/13.16 16469 meet(complement(A),join(B,A)) = meet(B,complement(A)). [para(16411(a,1),346(a,1,1)),rewrite([346(4),8(4)]),flip(a)].
% 12.89/13.16 16595 meet(A,join(B,complement(A))) = meet(A,B). [para(346(a,1),16469(a,1,1)),rewrite([346(5),7(4)])].
% 12.89/13.16 16615 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [para(6109(a,1),16469(a,1,2)),rewrite([346(2),346(7),7(6)])].
% 12.89/13.16 17054 meet(A,join(B,join(complement(A),meet(C,join(A,D))))) = meet(A,join(B,C)). [back_rewrite(5542),rewrite([16615(10)])].
% 12.89/13.16 17222 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [para(27(a,1),16595(a,2)),rewrite([8(5),12(5,R),8(4),17054(6)]),flip(a)].
% 12.89/13.16 17257 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [para(9309(a,1),16595(a,1,2)),rewrite([7(5),1161(5),7(7),17222(7),8(5),17222(6),8(4)])].
% 12.89/13.16 17258 $F # answer(prove_distributivity). [resolve(17257,a,16,a)].
% 12.89/13.16
% 12.89/13.16 % SZS output end Refutation
% 12.89/13.16 ============================== end of proof ==========================
% 12.89/13.16
% 12.89/13.16 ============================== STATISTICS ============================
% 12.89/13.16
% 12.89/13.16 Given=490. Generated=194774. Kept=17253. proofs=1.
% 12.89/13.16 Usable=354. Sos=9274. Demods=8105. Limbo=38, Disabled=7599. Hints=0.
% 12.89/13.16 Megabytes=30.12.
% 12.89/13.16 User_CPU=12.10, System_CPU=0.11, Wall_clock=12.
% 12.89/13.16
% 12.89/13.16 ============================== end of statistics =====================
% 12.89/13.16
% 12.89/13.16 ============================== end of search =========================
% 12.89/13.16
% 12.89/13.16 THEOREM PROVED
% 12.89/13.16 % SZS status Unsatisfiable
% 12.89/13.16
% 12.89/13.16 Exiting with 1 proof.
% 12.89/13.16
% 12.89/13.16 Process 26099 exit (max_proofs) Wed Jun 29 13:31:05 2022
% 12.89/13.17 Prover9 interrupted
%------------------------------------------------------------------------------