TSTP Solution File: LAT241-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT241-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 06:26:20 EDT 2022
% Result : Unsatisfiable 101.64s 101.93s
% Output : Refutation 101.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT241-10 : TPTP v8.1.0. Released v7.5.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.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 01:19:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 6.27/6.57 ============================== Prover9 ===============================
% 6.27/6.57 Prover9 (32) version 2009-11A, November 2009.
% 6.27/6.57 Process 13163 was started by sandbox on n026.cluster.edu,
% 6.27/6.57 Wed Jun 29 01:19:03 2022
% 6.27/6.57 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13009_n026.cluster.edu".
% 6.27/6.57 ============================== end of head ===========================
% 6.27/6.57
% 6.27/6.57 ============================== INPUT =================================
% 6.27/6.57
% 6.27/6.57 % Reading from file /tmp/Prover9_13009_n026.cluster.edu
% 6.27/6.57
% 6.27/6.57 set(prolog_style_variables).
% 6.27/6.57 set(auto2).
% 6.27/6.57 % set(auto2) -> set(auto).
% 6.27/6.57 % set(auto) -> set(auto_inference).
% 6.27/6.57 % set(auto) -> set(auto_setup).
% 6.27/6.57 % set(auto_setup) -> set(predicate_elim).
% 6.27/6.57 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.27/6.57 % set(auto) -> set(auto_limits).
% 6.27/6.57 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.27/6.57 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.27/6.57 % set(auto) -> set(auto_denials).
% 6.27/6.57 % set(auto) -> set(auto_process).
% 6.27/6.57 % set(auto2) -> assign(new_constants, 1).
% 6.27/6.57 % set(auto2) -> assign(fold_denial_max, 3).
% 6.27/6.57 % set(auto2) -> assign(max_weight, "200.000").
% 6.27/6.57 % set(auto2) -> assign(max_hours, 1).
% 6.27/6.57 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.27/6.57 % set(auto2) -> assign(max_seconds, 0).
% 6.27/6.57 % set(auto2) -> assign(max_minutes, 5).
% 6.27/6.57 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.27/6.57 % set(auto2) -> set(sort_initial_sos).
% 6.27/6.57 % set(auto2) -> assign(sos_limit, -1).
% 6.27/6.57 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.27/6.57 % set(auto2) -> assign(max_megs, 400).
% 6.27/6.57 % set(auto2) -> assign(stats, some).
% 6.27/6.57 % set(auto2) -> clear(echo_input).
% 6.27/6.57 % set(auto2) -> set(quiet).
% 6.27/6.57 % set(auto2) -> clear(print_initial_clauses).
% 6.27/6.57 % set(auto2) -> clear(print_given).
% 6.27/6.57 assign(lrs_ticks,-1).
% 6.27/6.57 assign(sos_limit,10000).
% 6.27/6.57 assign(order,kbo).
% 6.27/6.57 set(lex_order_vars).
% 6.27/6.57 clear(print_given).
% 6.27/6.57
% 6.27/6.57 % formulas(sos). % not echoed (15 formulas)
% 6.27/6.57
% 6.27/6.57 ============================== end of input ==========================
% 6.27/6.57
% 6.27/6.57 % From the command line: assign(max_seconds, 300).
% 6.27/6.57
% 6.27/6.57 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.27/6.57
% 6.27/6.57 % Formulas that are not ordinary clauses:
% 6.27/6.57
% 6.27/6.57 ============================== end of process non-clausal formulas ===
% 6.27/6.57
% 6.27/6.57 ============================== PROCESS INITIAL CLAUSES ===============
% 6.27/6.57
% 6.27/6.57 ============================== PREDICATE ELIMINATION =================
% 6.27/6.57
% 6.27/6.57 ============================== end predicate elimination =============
% 6.27/6.57
% 6.27/6.57 Auto_denials:
% 6.27/6.57 % copying label prove_distributivity to answer in negative clause
% 6.27/6.57
% 6.27/6.57 Term ordering decisions:
% 6.27/6.57
% 6.27/6.57 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 6.27/6.57 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. ifeq=1. complement=0.
% 6.27/6.57
% 6.27/6.57 ============================== end of process initial clauses ========
% 6.27/6.57
% 6.27/6.57 ============================== CLAUSES FOR SEARCH ====================
% 6.27/6.57
% 6.27/6.57 ============================== end of clauses for search =============
% 6.27/6.57
% 6.27/6.57 ============================== SEARCH ================================
% 6.27/6.57
% 6.27/6.57 % Starting search at 0.01 seconds.
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=84.000, iters=3438
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=76.000, iters=3404
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=74.000, iters=3379
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=72.000, iters=3371
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=68.000, iters=3339
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=64.000, iters=3340
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=61.000, iters=3363
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=59.000, iters=3340
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=51.000, iters=3362
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=50.000, iters=3374
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=49.000, iters=3435
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=47.000, iters=3381
% 6.27/6.57
% 6.27/6.57 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 3.70 sec).
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=46.000, iters=3360
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=44.000, iters=3374
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=43.000, iters=3336
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=42.000, iters=3364
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=40.000, iters=3337
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=39.000, iters=3418
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=38.000, iters=3343
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=37.000, iters=3441
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=36.000, iters=3376
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=35.000, iters=3346
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=34.000, iters=3333
% 6.27/6.57
% 6.27/6.57 Low Water (keep): wt=33.000, iters=3339
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=32.000, iters=3354
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=31.000, iters=3341
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=30.000, iters=3380
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=29.000, iters=3351
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=28.000, iters=3365
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=27.000, iters=3336
% 101.64/101.93
% 101.64/101.93 Low Water (displace): id=5186, wt=172.000
% 101.64/101.93
% 101.64/101.93 Low Water (displace): id=6514, wt=152.000
% 101.64/101.93
% 101.64/101.93 Low Water (displace): id=13942, wt=22.000
% 101.64/101.93
% 101.64/101.93 Low Water (displace): id=13943, wt=17.000
% 101.64/101.93
% 101.64/101.93 Low Water (displace): id=13947, wt=16.000
% 101.64/101.93
% 101.64/101.93 Low Water (displace): id=14180, wt=15.000
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=26.000, iters=3333
% 101.64/101.93
% 101.64/101.93 Low Water (displace): id=14662, wt=14.000
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=25.000, iters=3347
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=24.000, iters=3361
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=23.000, iters=3379
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=22.000, iters=3356
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=21.000, iters=3342
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=20.000, iters=3333
% 101.64/101.93
% 101.64/101.93 Low Water (keep): wt=19.000, iters=3335
% 101.64/101.93
% 101.64/101.93 ============================== PROOF =================================
% 101.64/101.93 % SZS status Unsatisfiable
% 101.64/101.93 % SZS output start Refutation
% 101.64/101.93
% 101.64/101.93 % Proof 1 at 99.76 (+ 1.16) seconds: prove_distributivity.
% 101.64/101.93 % Length of proof is 84.
% 101.64/101.93 % Level of proof is 30.
% 101.64/101.93 % Maximum clause weight is 31.000.
% 101.64/101.93 % Given clauses 2139.
% 101.64/101.93
% 101.64/101.93 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 101.64/101.93 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 101.64/101.93 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 101.64/101.93 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 101.64/101.93 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 101.64/101.93 6 ifeq(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 101.64/101.93 7 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 101.64/101.93 8 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 101.64/101.93 9 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 101.64/101.93 10 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 101.64/101.93 11 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 101.64/101.93 12 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(11),rewrite([9(2)]),flip(a)].
% 101.64/101.93 13 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 101.64/101.93 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([10(2)]),flip(a)].
% 101.64/101.93 15 ifeq(join(A,B),one,ifeq(meet(A,B),zero,complement(A),B),B) = B # label(meet_join_complement) # label(axiom). [assumption].
% 101.64/101.93 16 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].
% 101.64/101.93 17 meet(A,join(B,join(meet(A,C),meet(C,D)))) = meet(A,join(B,meet(C,join(A,D)))). [copy(16),flip(a)].
% 101.64/101.93 18 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 101.64/101.93 19 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(18),rewrite([10(5)])].
% 101.64/101.93 20 meet(a,b) = a. [back_rewrite(3),rewrite([9(3)])].
% 101.64/101.93 21 meet(A,one) = A. [para(4(a,1),7(a,1,2))].
% 101.64/101.93 22 join(A,zero) = A. [para(5(a,1),8(a,1,2))].
% 101.64/101.93 23 meet(A,meet(A,B)) = meet(A,B). [para(12(a,1),1(a,1)),rewrite([9(1),9(2),12(2,R),1(1),9(3)])].
% 101.64/101.93 24 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),12(a,2,2)),rewrite([9(2)])].
% 101.64/101.93 25 meet(A,meet(B,join(A,C))) = meet(A,B). [para(7(a,1),12(a,2,2)),rewrite([9(2),9(4)])].
% 101.64/101.93 26 join(A,join(A,B)) = join(A,B). [para(14(a,1),2(a,1)),rewrite([10(1),10(2),14(2,R),2(1),10(3)])].
% 101.64/101.93 27 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),14(a,2,2)),rewrite([10(2)])].
% 101.64/101.93 28 join(A,join(B,meet(A,C))) = join(A,B). [para(8(a,1),14(a,2,2)),rewrite([10(2),10(4)])].
% 101.64/101.93 32 ifeq(join(A,B),one,ifeq(meet(A,B),zero,complement(B),A),A) = A. [para(10(a,1),15(a,1,1)),rewrite([9(3)])].
% 101.64/101.93 34 ifeq(join(A,join(B,C)),one,ifeq(meet(C,join(A,B)),zero,complement(C),join(A,B)),join(A,B)) = join(A,B). [para(14(a,2),15(a,1,1))].
% 101.64/101.93 36 meet(A,join(meet(B,C),meet(B,join(A,C)))) = meet(A,join(meet(A,B),meet(B,C))). [para(2(a,1),17(a,1,2)),rewrite([10(10),14(10),10(9),17(11),26(7)]),flip(a)].
% 101.64/101.93 37 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(2(a,1),17(a,2,2)),rewrite([14(6),10(5),17(7),26(3),36(5),25(7)])].
% 101.64/101.93 43 meet(A,join(B,meet(A,B))) = meet(A,B). [para(8(a,1),17(a,2,2)),rewrite([28(4)])].
% 101.64/101.93 46 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(12(a,1),17(a,1,2,2,1)),rewrite([12(2,R),9(1),9(3),9(4),12(4),9(3),12(4,R),9(3),9(8)])].
% 101.64/101.93 56 meet(A,join(B,meet(one,join(A,C)))) = A. [para(21(a,1),17(a,1,2,2,1)),rewrite([9(2),21(2),14(2,R),10(1),7(3)]),flip(a)].
% 101.64/101.93 59 meet(A,zero) = zero. [para(5(a,1),23(a,1,2)),rewrite([5(4)])].
% 101.64/101.93 63 meet(A,meet(B,complement(A))) = zero. [back_rewrite(24),rewrite([59(5)])].
% 101.64/101.93 77 join(A,one) = one. [para(4(a,1),26(a,1,2)),rewrite([4(4)])].
% 101.64/101.93 81 join(A,join(B,complement(A))) = one. [back_rewrite(27),rewrite([77(5)])].
% 101.64/101.93 112 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(17(a,1),43(a,1,2,2)),rewrite([17(15)])].
% 101.64/101.93 113 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(63(a,1),43(a,1,2,2)),rewrite([10(4),63(8)])].
% 101.64/101.93 115 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),113(a,1,2,2))].
% 101.64/101.93 121 join(zero,complement(A)) = complement(A). [para(115(a,1),15(a,1,3,1)),rewrite([81(4),6(9),6(7)]),flip(a)].
% 101.64/101.93 132 complement(complement(A)) = A. [para(4(a,1),32(a,1,1)),rewrite([5(4),6(7),6(5)])].
% 101.64/101.93 156 meet(complement(A),join(zero,meet(A,B))) = zero. [para(132(a,1),113(a,1,2,2,2)),rewrite([9(3)])].
% 101.64/101.93 198 ifeq(meet(complement(A),join(A,B)),zero,A,join(A,B)) = join(A,B). [para(81(a,1),34(a,1,1)),rewrite([132(8),6(10)])].
% 101.64/101.93 215 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(10(a,1),37(a,1,2))].
% 101.64/101.93 290 meet(A,join(meet(B,C),meet(B,A))) = meet(B,A). [para(215(a,1),9(a,2)),rewrite([9(2),9(4),9(5)])].
% 101.64/101.93 291 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(9(a,1),215(a,1,2,1))].
% 101.64/101.93 300 meet(meet(A,B),join(A,C)) = meet(A,B). [para(215(a,1),56(a,1,2,2)),rewrite([9(3),21(3),10(2)])].
% 101.64/101.93 326 meet(complement(meet(A,B)),join(zero,meet(A,B))) = zero. [para(300(a,1),156(a,1,2,2))].
% 101.64/101.93 497 meet(A,join(B,meet(meet(C,D),join(A,E)))) = meet(A,join(B,meet(C,meet(D,join(A,E))))). [para(9(a,1),46(a,2,2,2)),rewrite([46(7),12(8),9(7),12(8,R),9(7)])].
% 101.64/101.93 515 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(28(a,1),46(a,1,2)),rewrite([497(9),8(8)])].
% 101.64/101.93 576 join(zero,meet(A,B)) = meet(A,B). [para(326(a,1),15(a,1,3,1)),rewrite([14(6),10(5),121(5),4(4),132(7),6(9),6(7)]),flip(a)].
% 101.64/101.93 580 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [para(326(a,1),37(a,1,2,1)),rewrite([576(6),9(5),12(5),9(4),12(5,R),9(4),576(6),12(5,R),576(10),9(9),5(9)])].
% 101.64/101.93 613 meet(A,meet(meet(B,C),complement(meet(A,C)))) = zero. [para(9(a,1),580(a,1,2,1))].
% 101.64/101.93 896 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(7(a,1),613(a,1,2,1))].
% 101.64/101.93 1175 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(896(a,1),12(a,1)),rewrite([9(6)]),flip(a)].
% 101.64/101.93 1315 meet(A,complement(join(A,B))) = zero. [para(1(a,1),1175(a,1,2,1)),rewrite([9(2),7(2)])].
% 101.64/101.93 1316 meet(meet(A,B),complement(meet(B,join(A,C)))) = zero. [para(9(a,1),1175(a,1,1))].
% 101.64/101.93 1343 meet(A,join(B,meet(complement(join(A,C)),join(A,D)))) = meet(A,join(B,meet(D,complement(join(A,C))))). [para(1315(a,1),17(a,1,2,2,1)),rewrite([9(4),576(5)]),flip(a)].
% 101.64/101.93 1522 meet(A,complement(meet(one,join(A,B)))) = zero. [para(21(a,1),1316(a,1,1))].
% 101.64/101.93 1928 meet(b,join(a,meet(A,a))) = a. [para(20(a,1),290(a,1,2,2)),rewrite([9(3),10(5),20(9)])].
% 101.64/101.93 1979 join(a,b) = b. [para(1928(a,1),8(a,1,2)),rewrite([10(3)])].
% 101.64/101.93 2855 meet(join(A,B),complement(meet(one,join(A,B)))) = zero. [para(112(a,1),1522(a,1,2,1)),rewrite([9(2),21(2),8(2),10(4),77(4),21(4)])].
% 101.64/101.93 3532 meet(A,join(one,meet(A,B))) = A. [para(21(a,1),515(a,2)),rewrite([9(3),21(3)])].
% 101.64/101.93 3652 meet(one,join(A,B)) = join(A,B). [para(2855(a,1),3532(a,1,2,2)),rewrite([22(4),9(3)])].
% 101.64/101.93 3765 meet(one,complement(A)) = complement(A). [para(121(a,1),3652(a,1,2)),rewrite([121(6)])].
% 101.64/101.93 3770 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(3652(a,1),1175(a,1,1)),rewrite([10(4),14(4),10(3),14(4,R),10(3),3652(5)])].
% 101.64/101.93 3773 join(A,meet(B,A)) = A. [para(3652(a,1),291(a,1)),rewrite([9(3),21(3),10(2),9(4),21(4)])].
% 101.64/101.93 3861 join(join(A,B),meet(A,C)) = join(A,B). [para(300(a,1),3773(a,1,2))].
% 101.64/101.93 4186 join(join(A,B),meet(B,C)) = join(A,B). [para(10(a,1),3861(a,1,1)),rewrite([10(4)])].
% 101.64/101.93 4246 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(28(a,1),4186(a,1,1)),rewrite([9(4),28(8)])].
% 101.64/101.93 4334 meet(meet(A,B),complement(join(C,meet(A,B)))) = zero. [para(576(a,1),3770(a,1,1)),rewrite([10(4),14(5,R),10(4),576(4)])].
% 101.64/101.93 28359 meet(A,meet(complement(join(B,C)),join(B,meet(C,D)))) = zero. [para(4246(a,1),4334(a,1,2,1)),rewrite([10(4),9(6),12(6,R),9(5)])].
% 101.64/101.93 28400 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [para(28359(a,1),1(a,1)),flip(a)].
% 101.64/101.93 28422 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(10(a,1),28400(a,1,1,1))].
% 101.64/101.93 28485 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [para(8(a,1),28422(a,1,1,1))].
% 101.64/101.93 30816 meet(complement(A),join(meet(A,B),complement(join(C,complement(A))))) = zero. [para(28485(a,1),1343(a,2)),rewrite([10(4),10(7),4(7),9(7),3765(7)])].
% 101.64/101.93 31235 meet(complement(A),join(A,complement(join(B,complement(A))))) = zero. [para(1(a,1),30816(a,1,2,1))].
% 101.64/101.93 31284 join(A,complement(join(B,complement(A)))) = A. [para(31235(a,1),198(a,1,1)),rewrite([6(7)]),flip(a)].
% 101.64/101.93 31286 join(complement(A),complement(join(A,B))) = complement(A). [para(132(a,1),31284(a,1,2,1,2)),rewrite([10(2)])].
% 101.64/101.93 31322 join(complement(a),complement(b)) = complement(a). [para(1979(a,1),31286(a,1,2,1))].
% 101.64/101.93 31323 $F # answer(prove_distributivity). [resolve(31322,a,19,a)].
% 101.64/101.93
% 101.64/101.93 % SZS output end Refutation
% 101.64/101.93 ============================== end of proof ==========================
% 101.64/101.93
% 101.64/101.93 ============================== STATISTICS ============================
% 101.64/101.93
% 101.64/101.93 Given=2139. Generated=2060968. Kept=31318. proofs=1.
% 101.64/101.93 Usable=1582. Sos=9766. Demods=11339. Limbo=1, Disabled=19983. Hints=0.
% 101.64/101.93 Megabytes=31.39.
% 101.64/101.93 User_CPU=99.76, System_CPU=1.16, Wall_clock=101.
% 101.64/101.93
% 101.64/101.93 ============================== end of statistics =====================
% 101.64/101.93
% 101.64/101.93 ============================== end of search =========================
% 101.64/101.93
% 101.64/101.93 THEOREM PROVED
% 101.64/101.93 % SZS status Unsatisfiable
% 101.64/101.93
% 101.64/101.93 Exiting with 1 proof.
% 101.64/101.93
% 101.64/101.93 Process 13163 exit (max_proofs) Wed Jun 29 01:20:44 2022
% 101.64/101.93 Prover9 interrupted
%------------------------------------------------------------------------------