TSTP Solution File: LAT066-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT066-1 : TPTP v8.1.0. Released v2.5.0.
% 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 06:25:23 EDT 2022
% Result : Unsatisfiable 10.62s 10.91s
% Output : Refutation 10.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT066-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 12:48:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 8.27/8.52 ============================== Prover9 ===============================
% 8.27/8.52 Prover9 (32) version 2009-11A, November 2009.
% 8.27/8.52 Process 7468 was started by sandbox on n004.cluster.edu,
% 8.27/8.52 Wed Jun 29 12:48:38 2022
% 8.27/8.52 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7314_n004.cluster.edu".
% 8.27/8.52 ============================== end of head ===========================
% 8.27/8.52
% 8.27/8.52 ============================== INPUT =================================
% 8.27/8.52
% 8.27/8.52 % Reading from file /tmp/Prover9_7314_n004.cluster.edu
% 8.27/8.52
% 8.27/8.52 set(prolog_style_variables).
% 8.27/8.52 set(auto2).
% 8.27/8.52 % set(auto2) -> set(auto).
% 8.27/8.52 % set(auto) -> set(auto_inference).
% 8.27/8.52 % set(auto) -> set(auto_setup).
% 8.27/8.52 % set(auto_setup) -> set(predicate_elim).
% 8.27/8.52 % set(auto_setup) -> assign(eq_defs, unfold).
% 8.27/8.52 % set(auto) -> set(auto_limits).
% 8.27/8.52 % set(auto_limits) -> assign(max_weight, "100.000").
% 8.27/8.52 % set(auto_limits) -> assign(sos_limit, 20000).
% 8.27/8.52 % set(auto) -> set(auto_denials).
% 8.27/8.52 % set(auto) -> set(auto_process).
% 8.27/8.52 % set(auto2) -> assign(new_constants, 1).
% 8.27/8.52 % set(auto2) -> assign(fold_denial_max, 3).
% 8.27/8.52 % set(auto2) -> assign(max_weight, "200.000").
% 8.27/8.52 % set(auto2) -> assign(max_hours, 1).
% 8.27/8.52 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 8.27/8.52 % set(auto2) -> assign(max_seconds, 0).
% 8.27/8.52 % set(auto2) -> assign(max_minutes, 5).
% 8.27/8.52 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 8.27/8.52 % set(auto2) -> set(sort_initial_sos).
% 8.27/8.52 % set(auto2) -> assign(sos_limit, -1).
% 8.27/8.52 % set(auto2) -> assign(lrs_ticks, 3000).
% 8.27/8.52 % set(auto2) -> assign(max_megs, 400).
% 8.27/8.52 % set(auto2) -> assign(stats, some).
% 8.27/8.52 % set(auto2) -> clear(echo_input).
% 8.27/8.52 % set(auto2) -> set(quiet).
% 8.27/8.52 % set(auto2) -> clear(print_initial_clauses).
% 8.27/8.52 % set(auto2) -> clear(print_given).
% 8.27/8.52 assign(lrs_ticks,-1).
% 8.27/8.52 assign(sos_limit,10000).
% 8.27/8.52 assign(order,kbo).
% 8.27/8.52 set(lex_order_vars).
% 8.27/8.52 clear(print_given).
% 8.27/8.52
% 8.27/8.52 % formulas(sos). % not echoed (13 formulas)
% 8.27/8.52
% 8.27/8.52 ============================== end of input ==========================
% 8.27/8.52
% 8.27/8.52 % From the command line: assign(max_seconds, 300).
% 8.27/8.52
% 8.27/8.52 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 8.27/8.52
% 8.27/8.52 % Formulas that are not ordinary clauses:
% 8.27/8.52
% 8.27/8.52 ============================== end of process non-clausal formulas ===
% 8.27/8.52
% 8.27/8.52 ============================== PROCESS INITIAL CLAUSES ===============
% 8.27/8.52
% 8.27/8.52 ============================== PREDICATE ELIMINATION =================
% 8.27/8.52
% 8.27/8.52 ============================== end predicate elimination =============
% 8.27/8.52
% 8.27/8.52 Auto_denials:
% 8.27/8.52 % copying label prove_distributivity to answer in negative clause
% 8.27/8.52
% 8.27/8.52 Term ordering decisions:
% 8.27/8.52
% 8.27/8.52 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 8.27/8.52 Function symbol KB weights: n0=1. n1=1. a=1. b=1. c=1. join=1. meet=1. complement=0.
% 8.27/8.52
% 8.27/8.52 ============================== end of process initial clauses ========
% 8.27/8.52
% 8.27/8.52 ============================== CLAUSES FOR SEARCH ====================
% 8.27/8.52
% 8.27/8.52 ============================== end of clauses for search =============
% 8.27/8.52
% 8.27/8.52 ============================== SEARCH ================================
% 8.27/8.52
% 8.27/8.52 % Starting search at 0.01 seconds.
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=153.000, iters=3465
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=150.000, iters=3456
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=129.000, iters=3378
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=125.000, iters=3351
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=124.000, iters=3340
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=123.000, iters=3337
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=107.000, iters=3351
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=106.000, iters=3338
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=105.000, iters=3335
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=95.000, iters=3355
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=94.000, iters=3351
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=88.000, iters=3362
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=87.000, iters=3352
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=85.000, iters=3392
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=83.000, iters=3361
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=81.000, iters=3371
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=80.000, iters=3333
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=79.000, iters=3334
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=77.000, iters=3368
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=76.000, iters=3355
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=75.000, iters=3339
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=74.000, iters=3398
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=73.000, iters=3385
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=72.000, iters=3410
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=71.000, iters=3399
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=70.000, iters=3373
% 8.27/8.52
% 8.27/8.52 Low Water (keep): wt=67.000, iters=3344
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=66.000, iters=3375
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=65.000, iters=3339
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=64.000, iters=3365
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=63.000, iters=3340
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=62.000, iters=3339
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=60.000, iters=3341
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=59.000, iters=3355
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=57.000, iters=3366
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=56.000, iters=3371
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=55.000, iters=3441
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=54.000, iters=3346
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=53.000, iters=3334
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=52.000, iters=3381
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=51.000, iters=3371
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=50.000, iters=3385
% 10.62/10.91
% 10.62/10.91 Low Water (keep): wt=49.000, iters=3358
% 10.62/10.91
% 10.62/10.91 ============================== PROOF =================================
% 10.62/10.91 % SZS status Unsatisfiable
% 10.62/10.91 % SZS output start Refutation
% 10.62/10.91
% 10.62/10.91 % Proof 1 at 9.86 (+ 0.09) seconds: prove_distributivity.
% 10.62/10.91 % Length of proof is 142.
% 10.62/10.91 % Level of proof is 47.
% 10.62/10.91 % Maximum clause weight is 49.000.
% 10.62/10.91 % Given clauses 463.
% 10.62/10.91
% 10.62/10.91 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 10.62/10.91 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 10.62/10.91 3 join(A,complement(A)) = n1 # label(top) # label(axiom). [assumption].
% 10.62/10.91 4 meet(A,complement(A)) = n0 # label(bottom) # label(axiom). [assumption].
% 10.62/10.91 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 10.62/10.91 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 10.62/10.91 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 10.62/10.91 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 10.62/10.91 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 10.62/10.91 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 10.62/10.91 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 10.62/10.91 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 10.62/10.91 13 meet(A,join(B,join(C,meet(D,join(A,meet(B,C)))))) = meet(A,join(B,join(C,meet(A,D)))) # label(g61) # label(axiom). [assumption].
% 10.62/10.91 14 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 10.62/10.91 15 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(14),flip(a)].
% 10.62/10.91 16 join(A,B) != n1 | meet(A,B) != n0 | complement(A) = B # label(complements_are_unique) # label(axiom). [assumption].
% 10.62/10.91 17 meet(A,n1) = A. [para(3(a,1),5(a,1,2))].
% 10.62/10.91 18 join(A,n0) = A. [para(4(a,1),6(a,1,2))].
% 10.62/10.91 19 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)])].
% 10.62/10.91 20 meet(A,meet(B,complement(A))) = meet(B,n0). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 10.62/10.91 21 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 10.62/10.91 22 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)])].
% 10.62/10.91 23 join(A,join(B,complement(A))) = join(B,n1). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 10.62/10.91 24 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 10.62/10.91 25 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(1(a,1),13(a,1,2,2,2,2,2)),rewrite([22(4),22(7)])].
% 10.62/10.91 27 meet(A,join(B,join(join(B,C),meet(D,join(A,B))))) = meet(A,join(B,join(join(B,C),meet(A,D)))). [para(5(a,1),13(a,1,2,2,2,2,2))].
% 10.62/10.91 28 meet(A,join(B,join(C,meet(A,C)))) = meet(A,join(B,C)). [para(6(a,1),13(a,1,2,2)),flip(a)].
% 10.62/10.91 30 meet(A,join(join(B,C),meet(D,join(A,meet(B,C))))) = meet(A,join(B,join(C,meet(A,D)))). [para(12(a,1),13(a,1,2)),rewrite([8(5)])].
% 10.62/10.91 31 meet(A,join(B,join(join(C,join(D,meet(E,join(B,meet(C,D))))),meet(F,join(A,meet(B,join(C,join(D,meet(B,E))))))))) = meet(A,join(B,join(join(C,join(D,meet(E,join(B,meet(C,D))))),meet(A,F)))). [para(13(a,1),13(a,1,2,2,2,2,2))].
% 10.62/10.91 37 meet(A,n0) = n0. [para(4(a,1),19(a,1,2)),rewrite([4(4)])].
% 10.62/10.91 40 meet(A,meet(B,complement(A))) = n0. [back_rewrite(20),rewrite([37(5)])].
% 10.62/10.91 41 complement(n1) = n0. [hyper(16,a,18,a,b,37,a)].
% 10.62/10.91 42 n1 != A | complement(A) = n0. [para(37(a,1),16(b,1)),rewrite([18(2)]),flip(a),xx(b)].
% 10.62/10.91 43 join(n0,n1) = n1. [para(41(a,1),3(a,1,2)),rewrite([8(3)])].
% 10.62/10.91 46 join(A,meet(B,join(A,C))) != n1 | meet(A,B) != n0 | meet(B,join(A,C)) = complement(A). [para(21(a,1),16(b,1)),flip(c)].
% 10.62/10.91 47 complement(n0) = n1. [hyper(16,a,43,a,b,17,a)].
% 10.62/10.91 48 complement(join(A,n1)) = n0. [hyper(42,a,6,a(flip)),rewrite([7(3),17(3),8(2)])].
% 10.62/10.91 50 join(A,n1) = n1. [para(48(a,1),3(a,1,2)),rewrite([8(4),12(4,R),8(3),43(3)])].
% 10.62/10.91 52 join(A,join(B,complement(A))) = n1. [back_rewrite(23),rewrite([50(5)])].
% 10.62/10.91 55 join(A,join(B,join(C,complement(A)))) = n1. [para(52(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),50(6)])].
% 10.62/10.91 56 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(24(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),12(6),8(5),12(6,R),8(5)])].
% 10.62/10.91 63 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(3(a,1),25(a,1,2,2,2)),rewrite([17(3),8(2)]),flip(a)].
% 10.62/10.91 64 meet(A,join(B,meet(A,B))) = meet(A,B). [para(6(a,1),25(a,1,2)),flip(a)].
% 10.62/10.91 65 meet(A,join(B,meet(C,join(B,A)))) = meet(A,join(B,meet(C,A))). [para(25(a,1),7(a,2)),rewrite([8(1),7(4),7(5)])].
% 10.62/10.91 72 meet(A,join(n1,meet(A,B))) = A. [para(50(a,1),25(a,1,2,2,2)),rewrite([17(3),8(2),50(2),17(2)]),flip(a)].
% 10.62/10.91 75 meet(A,join(join(B,join(C,complement(A))),meet(A,D))) = meet(A,join(B,join(C,join(D,complement(A))))). [para(55(a,1),25(a,1,2,2,2)),rewrite([17(5),8(4),12(4,R),8(3),12(3,R),8(2)]),flip(a)].
% 10.62/10.91 84 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(21(a,1),64(a,1,2,2)),rewrite([8(4),21(8)])].
% 10.62/10.91 85 meet(A,join(n0,meet(B,complement(A)))) = n0. [para(40(a,1),64(a,1,2,2)),rewrite([8(4),40(8)])].
% 10.62/10.91 89 meet(A,join(n0,complement(A))) = n0. [para(1(a,1),85(a,1,2,2))].
% 10.62/10.91 92 join(n0,complement(A)) = complement(A). [hyper(16,a,52,a,b,89,a),flip(a)].
% 10.62/10.91 96 meet(A,join(B,join(join(B,C),meet(A,D)))) = meet(A,join(B,join(C,meet(D,join(A,B))))). [para(8(a,1),27(a,1,2,2)),rewrite([12(4),8(3),12(4,R),8(3),22(5)]),flip(a)].
% 10.62/10.91 97 meet(A,join(B,join(C,meet(D,join(A,B))))) = meet(A,join(B,join(C,meet(A,D)))). [para(8(a,1),27(a,2,2,2)),rewrite([27(6),96(5),12(8),8(7),12(8,R),8(7),22(9)])].
% 10.62/10.91 111 meet(n0,complement(A)) = n0. [para(92(a,1),5(a,1,2))].
% 10.62/10.91 117 join(A,join(B,C)) != n1 | meet(A,join(B,C)) != n0 | join(B,join(C,meet(A,C))) = complement(A). [para(28(a,1),16(b,1)),rewrite([56(4)]),flip(c)].
% 10.62/10.91 123 meet(A,join(B,join(n1,meet(A,C)))) = A. [para(72(a,1),28(a,1,2,2,2)),rewrite([8(4),24(4),50(2),50(2),17(2)]),flip(a)].
% 10.62/10.91 130 meet(A,join(join(n1,meet(B,C)),meet(A,B))) = A. [para(123(a,1),25(a,1,2,2)),rewrite([8(4),24(4),50(2),17(2)]),flip(a)].
% 10.62/10.91 196 meet(A,join(B,join(complement(B),meet(A,C)))) = A. [para(3(a,1),30(a,1,2,1)),rewrite([4(3),18(3),7(2),72(4)]),flip(a)].
% 10.62/10.91 199 meet(A,join(join(A,B),meet(A,C))) = A. [para(5(a,1),30(a,2)),rewrite([6(3),7(2)])].
% 10.62/10.91 208 meet(A,join(n1,meet(B,join(A,C)))) = A. [para(17(a,1),30(a,1,2,2,2,2)),rewrite([50(2),123(10)])].
% 10.62/10.91 247 meet(A,join(B,join(join(A,C),meet(A,D)))) = A. [para(199(a,1),28(a,1,2,2,2)),rewrite([8(4),24(4),22(2),12(2,R),8(1),5(3)]),flip(a)].
% 10.62/10.91 261 join(n1,meet(A,B)) = n1. [para(130(a,1),208(a,1,2,2)),rewrite([8(5),50(5),7(5),5(5)]),flip(a)].
% 10.62/10.91 262 meet(n1,join(A,B)) = join(A,B). [para(30(a,1),208(a,1,2,2)),rewrite([261(7),7(3)])].
% 10.62/10.91 266 meet(n1,complement(A)) = complement(A). [para(92(a,1),262(a,1,2)),rewrite([92(6)])].
% 10.62/10.91 276 meet(A,join(B,join(join(C,join(D,meet(E,join(B,meet(C,D))))),meet(A,F)))) = meet(A,join(B,join(C,join(join(D,meet(E,join(B,meet(C,D)))),meet(A,F))))). [para(8(a,1),31(a,2,2,2)),rewrite([31(14),12(16,R)])].
% 10.62/10.91 286 meet(A,join(B,join(join(C,join(D,meet(n0,join(B,meet(C,D))))),meet(E,join(A,meet(B,join(C,D))))))) = meet(A,join(B,join(C,join(join(D,meet(n0,join(B,meet(C,D)))),meet(A,E))))). [para(37(a,1),31(a,1,2,2,2,2,2,2,2,2)),rewrite([18(8),276(23)])].
% 10.62/10.91 331 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(266(a,1),30(a,2,2,2,2)),rewrite([261(6),17(5),262(5),262(8)])].
% 10.62/10.91 339 join(A,join(complement(A),complement(B))) = n1. [para(266(a,1),196(a,1,2,2,2)),rewrite([262(6)])].
% 10.62/10.91 428 meet(n0,join(A,B)) = n0. [para(111(a,1),247(a,1,2,2,2)),rewrite([8(3),18(3),18(3)])].
% 10.62/10.91 435 meet(A,join(B,join(join(C,D),meet(A,E)))) = meet(A,join(B,join(C,join(D,meet(A,E))))). [back_rewrite(286),rewrite([428(4),18(2),13(8),428(9),18(7)])].
% 10.62/10.91 517 join(A,join(B,complement(join(A,B)))) = n1. [para(331(a,1),3(a,1))].
% 10.62/10.91 518 meet(join(A,B),join(A,join(B,complement(C)))) = join(A,B). [para(331(a,1),5(a,1,2))].
% 10.62/10.91 519 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(6(a,1),331(a,1,1)),flip(a)].
% 10.62/10.91 523 join(n0,join(complement(A),complement(B))) = join(complement(A),complement(B)). [para(92(a,1),331(a,1,1)),flip(a)].
% 10.62/10.91 532 join(A,join(B,join(C,complement(join(A,B))))) = n1. [para(517(a,1),12(a,2,2)),rewrite([8(4),12(4,R),8(3),50(7)])].
% 10.62/10.91 538 join(A,join(B,join(C,complement(join(A,C))))) = n1. [para(532(a,1),8(a,1)),rewrite([8(2),8(6),12(6,R),8(5),12(5,R),8(4)]),flip(a)].
% 10.62/10.91 617 join(complement(A),meet(B,complement(A))) = complement(A). [para(2(a,1),519(a,2)),rewrite([7(3),8(5),22(6)])].
% 10.62/10.91 618 join(A,complement(meet(A,B))) = n1. [para(3(a,1),519(a,1,2)),rewrite([50(2)]),flip(a)].
% 10.62/10.91 624 join(A,join(B,complement(join(A,meet(B,C))))) = n1. [para(519(a,1),538(a,1,2))].
% 10.62/10.91 629 join(A,join(B,complement(meet(C,join(A,B))))) = n1. [para(618(a,1),331(a,1)),rewrite([7(3)]),flip(a)].
% 10.62/10.91 633 join(A,B) != n1 | n0 != A | complement(join(A,B)) = A. [para(199(a,1),46(a,1,2)),rewrite([8(2),22(2),7(5),5(5),199(9)]),flip(b),flip(c)].
% 10.62/10.91 648 join(A,join(B,complement(join(B,meet(A,C))))) = n1. [para(624(a,1),12(a,2)),rewrite([8(4)])].
% 10.62/10.91 662 join(complement(A),complement(meet(B,complement(A)))) = n1. [para(92(a,1),629(a,1,2,2,1,2)),rewrite([523(7)])].
% 10.62/10.91 679 join(A,complement(B)) != n1 | meet(A,complement(B)) != n0 | complement(complement(B)) = A. [para(662(a,1),46(a,1,2,2)),rewrite([17(3),8(2),7(6),662(13),17(10)]),flip(c)].
% 10.62/10.91 697 join(A,complement(join(meet(A,B),meet(A,C)))) = n1. [para(648(a,1),519(a,1)),flip(a)].
% 10.62/10.91 876 meet(meet(A,B),join(join(A,C),meet(A,B))) = meet(meet(A,B),join(A,C)). [para(199(a,1),65(a,1,2,2)),rewrite([8(3),22(3),19(7)]),flip(a)].
% 10.62/10.91 1189 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(518(a,1),199(a,1,2,2)),rewrite([8(3),12(3),8(2),12(3,R),8(2),8(5),12(5,R),12(4),8(3),12(4,R),8(3),22(3),22(4)])].
% 10.62/10.91 1197 meet(complement(A),join(B,complement(A))) = complement(A). [para(92(a,1),1189(a,1,1)),rewrite([8(4),12(5,R),18(4),92(7)])].
% 10.62/10.91 1330 meet(A,join(B,join(C,join(complement(A),meet(D,join(A,E)))))) = meet(A,join(B,join(C,join(D,complement(A))))). [para(21(a,1),75(a,1,2,2)),rewrite([75(6),8(9)]),flip(a)].
% 10.62/10.91 1413 join(A,B) != n1 | n0 != B | complement(join(A,B)) = B. [para(8(a,1),633(a,1)),rewrite([8(6)])].
% 10.62/10.91 1805 meet(complement(A),join(n0,meet(A,join(B,complement(A))))) = n0. [para(63(a,1),84(a,1,2,2)),rewrite([7(3),4(3),7(9),4(9)])].
% 10.62/10.91 1856 meet(complement(meet(A,B)),join(n0,meet(A,B))) = n0. [para(618(a,1),1805(a,1,2,2,2)),rewrite([7(6),10(6),7(5),17(5),7(4)])].
% 10.62/10.91 1866 join(n0,meet(A,B)) = complement(complement(meet(A,B))). [para(1856(a,1),16(b,1)),rewrite([12(6),8(5),92(5),3(4)]),flip(c),xx(a),xx(b)].
% 10.62/10.91 2339 complement(complement(A)) = A. [para(1(a,1),1866(a,1,2)),rewrite([8(2),18(2),1(1)]),flip(a)].
% 10.62/10.91 2342 join(n0,join(meet(A,B),complement(C))) = join(meet(A,B),complement(C)). [para(1866(a,1),331(a,1,1)),rewrite([2339(3)]),flip(a)].
% 10.62/10.91 2343 join(meet(A,B),complement(meet(A,meet(B,C)))) = n1. [para(1866(a,1),629(a,1,2,2,1,2)),rewrite([2339(5),10(4),7(3),10(4,R),7(3),2342(7)])].
% 10.62/10.91 2345 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(1866(a,1),1189(a,1,1)),rewrite([2339(3),8(4),12(5,R),8(4),1866(4),2339(4),1866(7),2339(7)])].
% 10.62/10.91 2452 join(n0,meet(A,B)) = meet(A,B). [back_rewrite(1866),rewrite([2339(6)])].
% 10.62/10.91 2468 join(A,complement(B)) != n1 | meet(A,complement(B)) != n0 | B = A. [back_rewrite(679),rewrite([2339(10)])].
% 10.62/10.91 2478 meet(meet(A,B),join(A,C)) = meet(A,B). [back_rewrite(876),rewrite([2345(5)]),flip(a)].
% 10.62/10.91 2590 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),2478(a,1,1)),rewrite([7(4)])].
% 10.62/10.91 2603 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(2478(a,1),65(a,1,2,2)),rewrite([6(2),7(3)]),flip(a)].
% 10.62/10.91 2765 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(21(a,1),2590(a,1,1)),rewrite([8(4),21(8)])].
% 10.62/10.91 3113 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(262(a,1),2603(a,2)),rewrite([7(5),10(6,R),7(5),262(5),262(6)])].
% 10.62/10.91 3244 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(2452(a,1),3113(a,1,1)),rewrite([2452(4),10(3),7(2),10(3,R),7(2),2452(7)])].
% 10.62/10.91 3245 join(join(A,B),meet(A,C)) = join(A,B). [para(2478(a,1),3113(a,1,2))].
% 10.62/10.91 3298 meet(A,join(B,join(C,join(D,meet(A,C))))) = meet(A,join(B,join(C,D))). [para(3245(a,1),13(a,1,2,2)),rewrite([435(8)]),flip(a)].
% 10.62/10.91 5000 join(A,B) != n1 | meet(A,B) != n0 | complement(B) = A. [para(2339(a,1),2468(b,1,2)),rewrite([2339(2)])].
% 10.62/10.91 5296 join(A,join(complement(meet(B,C)),meet(B,join(C,D)))) = n1. [para(2765(a,1),629(a,1,2,2,1)),rewrite([7(3),8(5)])].
% 10.62/10.91 5387 join(complement(meet(A,B)),meet(A,join(B,C))) = n1. [hyper(117,a,5296,a,b,428,a),rewrite([10(8,R),7(7),428(7),37(6),8(6),2452(6),47(7)])].
% 10.62/10.91 5430 join(complement(meet(A,B)),meet(B,join(A,C))) = n1. [para(7(a,1),5387(a,1,1,1))].
% 10.62/10.91 5641 join(A,complement(meet(B,meet(C,A)))) = n1. [para(2343(a,1),5430(a,1,2,2)),rewrite([7(2),10(2),7(1),10(2,R),7(1),17(5),8(4)])].
% 10.62/10.91 5742 join(meet(A,join(B,C)),complement(meet(A,meet(B,D)))) = n1. [para(21(a,1),5641(a,1,2,1,2)),rewrite([7(3),10(4),7(3),10(4,R),7(3)])].
% 10.62/10.91 6500 join(complement(meet(A,meet(B,C))),meet(A,join(B,D))) = n1. [para(5742(a,1),8(a,1)),flip(a)].
% 10.62/10.91 7446 join(complement(meet(A,meet(B,C))),meet(C,join(A,D))) = n1. [para(7(a,1),6500(a,1,1,1)),rewrite([7(2),10(2),7(1),10(2,R),7(1)])].
% 10.62/10.91 8376 join(complement(meet(A,B)),meet(join(B,C),join(A,D))) = n1. [para(5(a,1),7446(a,1,1,1,2))].
% 10.62/10.91 9043 join(complement(meet(A,complement(B))),meet(join(A,C),complement(B))) = n1. [para(617(a,1),8376(a,1,2,2)),rewrite([7(2)])].
% 10.62/10.91 9535 meet(A,complement(join(A,B))) = n0. [hyper(1413,a,9043,a,b,4,a(flip)),rewrite([4(8),8(6),92(6),2339(5),4(7)])].
% 10.62/10.91 9559 meet(join(A,B),complement(join(A,join(B,C)))) = n0. [hyper(1413,a,9043,a,b,9535,a(flip)),rewrite([8(2),12(2),8(1),12(2,R),8(1),9535(4),47(2),8(4),12(4),8(3),12(4,R),8(3),261(7),41(2),8(4),12(4),8(3),12(4,R),8(3)]),flip(a)].
% 10.62/10.91 9562 meet(A,join(complement(A),complement(join(A,B)))) = n0. [para(9535(a,1),63(a,1,2,2)),rewrite([18(3),4(2),8(5)]),flip(a)].
% 10.62/10.91 9587 join(complement(A),complement(join(A,B))) = complement(A). [hyper(117,a,339,a,b,9562,a),rewrite([9535(6),8(5),92(5)])].
% 10.62/10.91 9720 join(A,complement(join(B,complement(A)))) = A. [para(2339(a,1),9587(a,1,1)),rewrite([8(2),2339(6)])].
% 10.62/10.91 9736 join(A,complement(join(B,complement(meet(A,C))))) = A. [para(9720(a,1),519(a,1,2)),rewrite([6(2)]),flip(a)].
% 10.62/10.91 9742 meet(A,complement(join(B,complement(A)))) = complement(join(B,complement(A))). [para(9720(a,1),1197(a,1,2)),rewrite([7(4)])].
% 10.62/10.91 10497 meet(meet(A,B),complement(join(C,meet(A,B)))) = n0. [para(2452(a,1),9559(a,1,1)),rewrite([8(4),12(5,R),8(4),2452(4)])].
% 10.62/10.91 10836 meet(A,meet(meet(B,C),complement(meet(A,B)))) = n0. [para(3244(a,1),10497(a,1,2,1)),rewrite([7(5),10(5,R)])].
% 10.62/10.91 11383 meet(A,meet(meet(B,C),complement(meet(A,C)))) = n0. [para(7(a,1),10836(a,1,2,1))].
% 10.62/10.91 11733 meet(A,meet(B,complement(meet(A,join(B,C))))) = n0. [para(5(a,1),11383(a,1,2,1))].
% 10.62/10.91 12019 meet(meet(A,B),complement(meet(A,join(B,C)))) = n0. [para(11733(a,1),10(a,1)),rewrite([7(6)]),flip(a)].
% 10.62/10.91 12073 meet(meet(A,B),complement(meet(B,join(A,C)))) = n0. [para(7(a,1),12019(a,1,1))].
% 10.62/10.91 12126 meet(A,complement(meet(join(A,B),join(A,C)))) = n0. [para(5(a,1),12073(a,1,1))].
% 10.62/10.91 12365 meet(complement(A),join(B,complement(meet(A,C)))) = complement(A). [para(9736(a,1),9742(a,1,2,1)),rewrite([7(5),9736(10)])].
% 10.62/10.91 12423 meet(complement(A),complement(meet(A,B))) = complement(A). [para(2(a,1),12365(a,1,2))].
% 10.62/10.91 12455 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(12423(a,1),617(a,1,2)),rewrite([8(4)])].
% 10.62/10.91 12632 join(A,complement(meet(B,join(A,complement(B))))) = n1. [para(12455(a,1),629(a,1,2))].
% 10.62/10.91 12661 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(5000,a,12632,a,b,12126,a),rewrite([2339(7)])].
% 10.62/10.91 12985 meet(join(A,B),join(B,complement(join(A,B)))) = B. [para(8(a,1),12661(a,1,1)),rewrite([8(2)])].
% 10.62/10.91 13071 meet(A,join(B,complement(A))) = meet(A,B). [para(6(a,1),12985(a,1,1)),rewrite([6(3),8(3),63(4)])].
% 10.62/10.91 13441 meet(A,join(B,join(C,meet(A,D)))) = meet(A,join(B,join(C,join(D,complement(A))))). [para(13(a,1),13071(a,2)),rewrite([8(7),12(7,R),8(6),12(6,R),8(5),1330(8)]),flip(a)].
% 10.62/10.91 13442 meet(A,join(B,meet(A,C))) = meet(A,join(B,join(C,complement(A)))). [para(25(a,1),13071(a,2)),rewrite([8(5),12(5,R),8(4),97(6),13441(5),12(4,R),2(3)]),flip(a)].
% 10.62/10.91 13443 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [para(28(a,1),13071(a,2)),rewrite([8(5),12(5,R),8(4),12(4,R),8(3),3298(6)])].
% 10.62/10.91 13446 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [para(697(a,1),13071(a,1,2)),rewrite([7(5),262(5),7(7),13442(7),12(7),8(6),12(7,R),8(6),13441(8),12(7,R),2(6),12(6,R),8(5),13443(7)])].
% 10.62/10.91 13447 $F # answer(prove_distributivity). [resolve(13446,a,15,a)].
% 10.62/10.91
% 10.62/10.91 % SZS output end Refutation
% 10.62/10.91 ============================== end of proof ==========================
% 10.62/10.91
% 10.62/10.91 ============================== STATISTICS ============================
% 10.62/10.91
% 10.62/10.91 Given=463. Generated=153251. Kept=13443. proofs=1.
% 10.62/10.91 Usable=329. Sos=8293. Demods=7162. Limbo=6, Disabled=4827. Hints=0.
% 10.62/10.91 Megabytes=30.30.
% 10.62/10.91 User_CPU=9.86, System_CPU=0.09, Wall_clock=10.
% 10.62/10.91
% 10.62/10.91 ============================== end of statistics =====================
% 10.62/10.91
% 10.62/10.91 ============================== end of search =========================
% 10.62/10.91
% 10.62/10.91 THEOREM PROVED
% 10.62/10.91 % SZS status Unsatisfiable
% 10.62/10.91
% 10.62/10.91 Exiting with 1 proof.
% 10.62/10.91
% 10.62/10.91 Process 7468 exit (max_proofs) Wed Jun 29 12:48:48 2022
% 10.62/10.91 Prover9 interrupted
%------------------------------------------------------------------------------