TSTP Solution File: LAT200-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT200-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 06:26:05 EDT 2022
% Result : Unsatisfiable 3.24s 3.58s
% Output : Refutation 3.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LAT200-1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n025.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 : Tue Jun 28 19:31:21 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.24/3.58 ============================== Prover9 ===============================
% 3.24/3.58 Prover9 (32) version 2009-11A, November 2009.
% 3.24/3.58 Process 13310 was started by sandbox on n025.cluster.edu,
% 3.24/3.58 Tue Jun 28 19:31:22 2022
% 3.24/3.58 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13156_n025.cluster.edu".
% 3.24/3.58 ============================== end of head ===========================
% 3.24/3.58
% 3.24/3.58 ============================== INPUT =================================
% 3.24/3.58
% 3.24/3.58 % Reading from file /tmp/Prover9_13156_n025.cluster.edu
% 3.24/3.58
% 3.24/3.58 set(prolog_style_variables).
% 3.24/3.58 set(auto2).
% 3.24/3.58 % set(auto2) -> set(auto).
% 3.24/3.58 % set(auto) -> set(auto_inference).
% 3.24/3.58 % set(auto) -> set(auto_setup).
% 3.24/3.58 % set(auto_setup) -> set(predicate_elim).
% 3.24/3.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.24/3.58 % set(auto) -> set(auto_limits).
% 3.24/3.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.24/3.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.24/3.58 % set(auto) -> set(auto_denials).
% 3.24/3.58 % set(auto) -> set(auto_process).
% 3.24/3.58 % set(auto2) -> assign(new_constants, 1).
% 3.24/3.58 % set(auto2) -> assign(fold_denial_max, 3).
% 3.24/3.58 % set(auto2) -> assign(max_weight, "200.000").
% 3.24/3.58 % set(auto2) -> assign(max_hours, 1).
% 3.24/3.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.24/3.58 % set(auto2) -> assign(max_seconds, 0).
% 3.24/3.58 % set(auto2) -> assign(max_minutes, 5).
% 3.24/3.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.24/3.58 % set(auto2) -> set(sort_initial_sos).
% 3.24/3.58 % set(auto2) -> assign(sos_limit, -1).
% 3.24/3.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.24/3.58 % set(auto2) -> assign(max_megs, 400).
% 3.24/3.58 % set(auto2) -> assign(stats, some).
% 3.24/3.58 % set(auto2) -> clear(echo_input).
% 3.24/3.58 % set(auto2) -> set(quiet).
% 3.24/3.58 % set(auto2) -> clear(print_initial_clauses).
% 3.24/3.58 % set(auto2) -> clear(print_given).
% 3.24/3.58 assign(lrs_ticks,-1).
% 3.24/3.58 assign(sos_limit,10000).
% 3.24/3.58 assign(order,kbo).
% 3.24/3.58 set(lex_order_vars).
% 3.24/3.58 clear(print_given).
% 3.24/3.58
% 3.24/3.58 % formulas(sos). % not echoed (13 formulas)
% 3.24/3.58
% 3.24/3.58 ============================== end of input ==========================
% 3.24/3.58
% 3.24/3.58 % From the command line: assign(max_seconds, 300).
% 3.24/3.58
% 3.24/3.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.24/3.58
% 3.24/3.58 % Formulas that are not ordinary clauses:
% 3.24/3.58
% 3.24/3.58 ============================== end of process non-clausal formulas ===
% 3.24/3.58
% 3.24/3.58 ============================== PROCESS INITIAL CLAUSES ===============
% 3.24/3.58
% 3.24/3.58 ============================== PREDICATE ELIMINATION =================
% 3.24/3.58
% 3.24/3.58 ============================== end predicate elimination =============
% 3.24/3.58
% 3.24/3.58 Auto_denials:
% 3.24/3.58 % copying label prove_distributivity to answer in negative clause
% 3.24/3.58
% 3.24/3.58 Term ordering decisions:
% 3.24/3.58
% 3.24/3.58 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 3.24/3.58 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. join=1. meet=1. complement=0.
% 3.24/3.58
% 3.24/3.58 ============================== end of process initial clauses ========
% 3.24/3.58
% 3.24/3.58 ============================== CLAUSES FOR SEARCH ====================
% 3.24/3.58
% 3.24/3.58 ============================== end of clauses for search =============
% 3.24/3.58
% 3.24/3.58 ============================== SEARCH ================================
% 3.24/3.58
% 3.24/3.58 % Starting search at 0.01 seconds.
% 3.24/3.58
% 3.24/3.58 ============================== PROOF =================================
% 3.24/3.58 % SZS status Unsatisfiable
% 3.24/3.58 % SZS output start Refutation
% 3.24/3.58
% 3.24/3.58 % Proof 1 at 2.55 (+ 0.05) seconds: prove_distributivity.
% 3.24/3.58 % Length of proof is 126.
% 3.24/3.58 % Level of proof is 35.
% 3.24/3.58 % Maximum clause weight is 51.000.
% 3.24/3.58 % Given clauses 322.
% 3.24/3.58
% 3.24/3.58 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 3.24/3.58 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 3.24/3.58 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 3.24/3.58 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 3.24/3.58 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 3.24/3.58 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 3.24/3.58 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 3.24/3.58 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 3.24/3.58 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 3.24/3.58 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 3.24/3.58 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 3.24/3.58 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 3.24/3.58 13 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(A,meet(C,join(B,D)))))) # label(equation_H50) # label(axiom). [assumption].
% 3.24/3.58 14 meet(A,join(B,meet(C,join(A,meet(C,join(B,D)))))) = meet(A,join(B,meet(C,join(A,D)))). [copy(13),flip(a)].
% 3.24/3.58 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 3.24/3.58 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 3.24/3.58 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 3.24/3.58 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 3.24/3.58 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 3.24/3.58 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)])].
% 3.24/3.58 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 3.24/3.58 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 3.24/3.58 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)])].
% 3.24/3.58 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 3.24/3.58 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 3.24/3.58 26 meet(A,join(B,meet(join(B,C),join(A,join(B,C))))) = meet(A,join(B,meet(join(B,C),join(A,C)))). [para(1(a,1),14(a,1,2,2,2,2))].
% 3.24/3.58 27 meet(A,join(B,meet(C,join(A,meet(B,C))))) = meet(A,join(B,meet(C,join(A,B)))). [para(2(a,1),14(a,1,2,2,2,2,2)),rewrite([7(1)])].
% 3.24/3.58 29 meet(A,join(B,meet(C,join(A,meet(C,join(A,B)))))) = meet(A,join(B,meet(A,C))). [para(2(a,1),14(a,2,2,2,2)),rewrite([8(1),7(7)])].
% 3.24/3.58 30 meet(A,join(meet(B,join(A,C)),meet(B,join(A,meet(B,join(C,meet(B,join(A,C)))))))) = meet(A,B). [para(2(a,1),14(a,2,2)),rewrite([8(5),22(13)])].
% 3.24/3.58 31 meet(A,join(B,meet(C,join(A,complement(B))))) = meet(A,join(B,meet(C,join(A,C)))). [para(3(a,1),14(a,1,2,2,2,2,2)),rewrite([18(2)]),flip(a)].
% 3.24/3.58 32 meet(A,join(B,meet(C,join(A,meet(B,D))))) = meet(A,join(B,meet(C,join(A,B)))). [para(6(a,1),14(a,1,2,2,2,2,2)),rewrite([7(1),27(5)]),flip(a)].
% 3.24/3.58 33 meet(A,meet(B,join(C,meet(D,join(A,meet(D,join(C,E))))))) = meet(A,meet(B,join(C,meet(D,join(A,E))))). [para(14(a,1),10(a,2,2)),rewrite([7(6),10(12,R),7(11)])].
% 3.24/3.58 34 meet(A,join(B,meet(C,join(A,meet(D,join(C,meet(D,join(B,E)))))))) = meet(A,join(B,meet(C,join(A,meet(D,join(C,E)))))). [para(14(a,1),14(a,1,2,2,2,2)),rewrite([14(8)]),flip(a)].
% 3.24/3.58 37 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(7(a,1),17(a,1)),rewrite([8(4)])].
% 3.24/3.58 42 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(19(a,1),14(a,1,2,2,2,2,2)),rewrite([7(1),32(5),19(6),7(5)])].
% 3.24/3.58 43 meet(A,join(B,meet(C,join(A,meet(B,D))))) = meet(A,join(B,meet(A,C))). [back_rewrite(32),rewrite([42(9)])].
% 3.24/3.58 44 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 3.24/3.58 46 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([44(5)])].
% 3.24/3.58 47 complement(one) = zero. [hyper(17,a,44,a,b,19,a)].
% 3.24/3.58 48 one != A | complement(A) = zero. [para(44(a,1),17(a,1)),rewrite([19(5)]),flip(b),xx(a)].
% 3.24/3.58 50 meet(A,B) != zero | join(A,meet(B,join(A,C))) != one | meet(B,join(A,C)) = complement(A). [para(22(a,1),17(a,1)),flip(c)].
% 3.24/3.58 51 complement(join(A,one)) = zero. [hyper(48,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 3.24/3.58 53 join(A,one) = one. [para(51(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 3.24/3.58 55 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([53(5)])].
% 3.24/3.58 57 meet(A,join(B,meet(C,join(A,C)))) = meet(A,join(B,C)). [para(53(a,1),14(a,1,2,2,2,2,2)),rewrite([18(2),53(6),18(6)])].
% 3.24/3.58 58 meet(A,join(B,meet(C,join(A,complement(B))))) = meet(A,join(B,C)). [back_rewrite(31),rewrite([57(9)])].
% 3.24/3.58 59 meet(A,join(B,meet(join(B,C),join(A,C)))) = meet(A,join(B,C)). [back_rewrite(26),rewrite([57(6),23(2)]),flip(a)].
% 3.24/3.58 89 complement(complement(A)) = A. [hyper(37,a,4,a,b,3,a)].
% 3.24/3.58 104 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(3(a,1),29(a,1,2,2,2,2,2)),rewrite([18(3),57(5),8(2)]),flip(a)].
% 3.24/3.58 105 meet(A,join(B,meet(A,B))) = meet(A,B). [para(6(a,1),29(a,1,2)),flip(a)].
% 3.24/3.58 109 meet(A,join(one,meet(A,B))) = A. [para(53(a,1),29(a,1,2,2,2,2,2)),rewrite([18(3),57(5),8(2),53(2),18(2)]),flip(a)].
% 3.24/3.58 119 meet(A,meet(B,join(one,meet(A,C)))) = meet(A,B). [para(109(a,1),10(a,2,2)),rewrite([7(4),7(6)])].
% 3.24/3.58 120 meet(A,join(one,meet(B,join(A,meet(B,C))))) = A. [para(109(a,1),14(a,1,2,2,2,2)),rewrite([57(5),8(2),53(2),18(2)]),flip(a)].
% 3.24/3.58 127 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(46(a,1),105(a,1,2,2)),rewrite([8(4),46(8)])].
% 3.24/3.58 131 meet(A,B) != zero | join(A,B) != one | complement(join(B,meet(A,B))) = A. [para(105(a,1),37(a,1)),rewrite([25(6)])].
% 3.24/3.58 133 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),127(a,1,2,2))].
% 3.24/3.58 138 meet(complement(A),join(zero,meet(A,B))) = zero. [para(89(a,1),127(a,1,2,2,2)),rewrite([7(3)])].
% 3.24/3.58 140 join(zero,complement(A)) = complement(A). [hyper(17,a,133,a,b,55,a),flip(a)].
% 3.24/3.58 146 meet(A,join(meet(B,join(A,C)),meet(B,join(A,meet(B,join(join(C,meet(A,D)),meet(B,join(A,C)))))))) = meet(A,B). [para(25(a,1),30(a,1,2,1,2)),rewrite([25(7)])].
% 3.24/3.58 157 join(complement(A),join(zero,meet(A,B))) != one | join(zero,meet(A,B)) = A. [para(138(a,1),17(a,1)),rewrite([89(12)]),flip(c),xx(a)].
% 3.24/3.58 158 meet(complement(A),meet(join(zero,meet(A,B)),join(C,complement(A)))) = zero. [para(138(a,1),22(a,2)),rewrite([8(6)])].
% 3.24/3.58 217 meet(A,join(one,meet(B,join(A,meet(C,join(B,meet(C,D))))))) = meet(A,join(one,meet(B,join(A,C)))). [para(109(a,1),34(a,1,2,2,2,2,2,2)),rewrite([57(5)]),flip(a)].
% 3.24/3.58 235 meet(meet(A,B),join(one,meet(A,B))) = meet(A,B). [para(2(a,1),120(a,1,2,2,2)),rewrite([20(4)])].
% 3.24/3.58 236 meet(A,join(one,meet(B,join(A,C)))) = A. [para(120(a,1),14(a,1,2,2,2,2)),rewrite([57(5),8(2),53(2),18(2),217(8)]),flip(a)].
% 3.24/3.58 282 meet(complement(meet(A,B)),join(zero,meet(A,B))) = zero. [para(235(a,1),138(a,1,2,2))].
% 3.24/3.58 286 join(zero,meet(A,B)) = meet(A,B). [para(282(a,1),17(a,1)),rewrite([12(9),8(8),140(8),3(7),89(9)]),flip(c),xx(a),xx(b)].
% 3.24/3.58 290 meet(one,complement(meet(A,B))) = complement(meet(A,B)). [para(282(a,1),109(a,1,2,2)),rewrite([19(5),7(4)])].
% 3.24/3.58 303 meet(complement(A),meet(meet(A,B),join(C,complement(A)))) = zero. [back_rewrite(158),rewrite([286(4)])].
% 3.24/3.58 304 join(complement(A),meet(A,B)) != one | meet(A,B) = A. [back_rewrite(157),rewrite([286(4),286(8)])].
% 3.24/3.58 334 meet(one,complement(A)) = complement(A). [para(1(a,1),290(a,1,2,1)),rewrite([1(4)])].
% 3.24/3.58 485 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(57(a,1),43(a,1)),rewrite([6(2)]),flip(a)].
% 3.24/3.58 488 meet(A,join(join(A,B),meet(A,C))) = A. [para(5(a,1),485(a,2)),rewrite([7(3),22(4)])].
% 3.24/3.58 498 meet(A,join(join(one,meet(A,B)),meet(A,C))) = A. [para(109(a,1),485(a,2)),rewrite([7(7),119(8)])].
% 3.24/3.58 509 meet(one,join(complement(A),meet(B,complement(A)))) = complement(A). [para(334(a,1),485(a,2)),rewrite([7(5),10(6,R),18(5)])].
% 3.24/3.58 526 meet(one,join(A,B)) = join(A,B). [para(488(a,1),236(a,1,2,2)),rewrite([8(3),53(3),7(3)])].
% 3.24/3.58 532 meet(complement(A),join(B,complement(A))) = complement(A). [para(303(a,1),488(a,1,2,2)),rewrite([8(3),8(5),12(5,R),19(4)])].
% 3.24/3.58 537 join(complement(A),meet(B,complement(A))) = complement(A). [back_rewrite(509),rewrite([526(6)])].
% 3.24/3.58 567 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(526(a,1),485(a,2)),rewrite([7(5),10(6,R),7(5),526(5),526(6)])].
% 3.24/3.58 649 join(one,meet(A,B)) = one. [para(498(a,1),236(a,1,2,2)),rewrite([8(5),53(5),7(5),5(5)]),flip(a)].
% 3.24/3.58 1066 meet(A,meet(B,join(join(A,C),complement(B)))) = meet(A,B). [para(104(a,1),33(a,1,2)),rewrite([8(2),8(6),12(6,R),8(5),22(8),104(6)]),flip(a)].
% 3.24/3.58 1098 meet(meet(A,B),join(join(A,C),complement(B))) = meet(A,B). [para(1066(a,1),10(a,1)),rewrite([7(6)]),flip(a)].
% 3.24/3.58 1160 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(1098(a,1),567(a,1,2)),rewrite([8(5),12(5),12(4),8(3),6(3),8(2),12(3),8(2),12(3,R),8(2)]),flip(a)].
% 3.24/3.58 1191 join(A,join(B,complement(join(A,B)))) = one. [para(1160(a,1),3(a,1))].
% 3.24/3.58 1192 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(6(a,1),1160(a,1,1)),flip(a)].
% 3.24/3.58 1229 join(A,join(B,join(C,complement(join(A,B))))) = one. [para(1191(a,1),12(a,2,2)),rewrite([8(4),12(4,R),8(3),53(7)])].
% 3.24/3.58 1264 join(A,join(B,join(C,complement(join(A,C))))) = one. [para(1229(a,1),8(a,1)),rewrite([8(2),8(6),12(6,R),8(5),12(5,R),8(4)]),flip(a)].
% 3.24/3.58 1285 join(A,complement(meet(A,B))) = one. [para(3(a,1),1192(a,1,2)),rewrite([53(2)]),flip(a)].
% 3.24/3.58 1300 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(1192(a,1),1264(a,1,2))].
% 3.24/3.58 1348 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [para(1285(a,1),303(a,1,2,2)),rewrite([7(4),10(4),7(3),10(4,R),7(3),7(6),10(6,R),7(5),10(5),7(4),18(4),7(3),10(5,R)])].
% 3.24/3.58 1349 join(A,join(B,complement(meet(C,join(A,B))))) = one. [para(1285(a,1),1160(a,1)),rewrite([7(3)]),flip(a)].
% 3.24/3.58 1356 join(A,join(B,complement(join(B,meet(A,C))))) = one. [para(1300(a,1),12(a,2)),rewrite([8(4)])].
% 3.24/3.58 1361 join(A,join(complement(A),complement(B))) = one. [para(303(a,1),1300(a,1,2,2,1,2)),rewrite([19(3),8(3)])].
% 3.24/3.58 1414 meet(A,meet(meet(B,C),complement(meet(A,C)))) = zero. [para(7(a,1),1348(a,1,2,1))].
% 3.24/3.58 1604 join(A,complement(join(meet(A,B),meet(A,C)))) = one. [para(1356(a,1),1192(a,1)),flip(a)].
% 3.24/3.58 1614 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(5(a,1),1414(a,1,2,1))].
% 3.24/3.58 1726 meet(A,complement(join(A,B))) = zero. [hyper(50,a,1614,a,b,649,a),rewrite([526(3),8(5),53(5),7(5),10(5,R),7(4),334(4),47(5)])].
% 3.24/3.58 1728 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(1614(a,1),10(a,1)),rewrite([7(6)]),flip(a)].
% 3.24/3.58 1745 meet(A,join(complement(A),complement(join(A,B)))) = zero. [para(1726(a,1),104(a,1,2,2)),rewrite([19(3),4(2),8(5)]),flip(a)].
% 3.24/3.58 1757 join(complement(A),complement(join(A,B))) = complement(A). [hyper(17,a,1745,a,b,1361,a),flip(a)].
% 3.24/3.58 1766 join(A,complement(join(B,complement(A)))) = A. [para(89(a,1),1757(a,1,1)),rewrite([8(2),89(6)])].
% 3.24/3.58 1772 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(1757(a,1),532(a,1,2)),rewrite([7(4)])].
% 3.24/3.58 1789 meet(A,complement(join(B,complement(A)))) = complement(join(B,complement(A))). [para(1766(a,1),532(a,1,2)),rewrite([7(4)])].
% 3.24/3.58 1798 join(A,complement(join(B,complement(meet(A,C))))) = A. [para(1766(a,1),1192(a,1,2)),rewrite([6(2)]),flip(a)].
% 3.24/3.58 1866 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(526(a,1),1728(a,1,1)),rewrite([8(4),12(4),8(3),12(4,R),8(3),526(5)])].
% 3.24/3.58 2077 meet(meet(A,B),complement(join(C,meet(A,B)))) = zero. [para(286(a,1),1866(a,1,1)),rewrite([8(4),12(5,R),8(4),286(4)])].
% 3.24/3.58 2280 meet(meet(A,B),join(meet(complement(join(C,meet(A,B))),join(D,meet(A,B))),meet(complement(join(C,meet(A,B))),join(meet(A,B),meet(complement(join(C,meet(A,B))),join(D,meet(complement(join(C,meet(A,B))),join(D,meet(A,B))))))))) = zero. [para(2077(a,1),30(a,2)),rewrite([8(6),8(19)])].
% 3.24/3.58 3476 meet(complement(A),join(B,complement(meet(A,C)))) = complement(A). [para(1798(a,1),1789(a,1,2,1)),rewrite([7(5),1798(10)])].
% 3.24/3.58 3481 meet(complement(A),complement(meet(A,B))) = complement(A). [para(2(a,1),3476(a,1,2))].
% 3.24/3.58 3513 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(3481(a,1),537(a,1,2)),rewrite([8(4)])].
% 3.24/3.58 3595 join(A,complement(meet(B,join(A,complement(B))))) = one. [para(3513(a,1),1349(a,1,2))].
% 3.24/3.58 4539 meet(meet(A,B),join(meet(C,join(D,meet(A,B))),meet(C,join(meet(A,B),meet(C,join(D,meet(C,join(D,meet(A,B))))))))) = meet(A,meet(B,C)). [para(1728(a,1),146(a,1,2,2,2,2,2,1,2)),rewrite([8(3),19(7),8(7),7(16),10(16),7(15),10(16,R),7(15)])].
% 3.24/3.58 4597 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [back_rewrite(2280),rewrite([4539(26)])].
% 3.24/3.58 4702 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(1772(a,1),4597(a,1,2))].
% 3.24/3.58 4746 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [hyper(131,a,4702,a,b,1604,a),rewrite([4702(13),8(8),140(8),89(7)])].
% 3.24/3.58 5123 join(meet(A,B),meet(B,complement(meet(A,B)))) = B. [para(7(a,1),4746(a,1,1)),rewrite([7(2)])].
% 3.24/3.58 5343 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(5(a,1),5123(a,1,1)),rewrite([5(3),7(3)])].
% 3.24/3.58 6125 join(A,meet(B,complement(A))) = join(A,B). [para(58(a,1),5343(a,1,2)),rewrite([5343(4),2(4)]),flip(a)].
% 3.24/3.58 6228 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(89(a,1),6125(a,1,2,2)),rewrite([7(2),8(5)])].
% 3.24/3.58 6300 join(A,complement(B)) != one | meet(B,A) = B. [back_rewrite(304),rewrite([6228(3)])].
% 3.24/3.58 6466 join(complement(A),meet(B,join(A,C))) = join(B,complement(A)). [para(22(a,1),6228(a,1,2)),rewrite([6228(3),8(6)]),flip(a)].
% 3.24/3.58 6721 meet(A,join(B,complement(A))) = meet(A,B). [hyper(6300,a,3595,a),rewrite([7(4),22(4),7(1)]),flip(a)].
% 3.24/3.58 6794 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,join(C,complement(A)))). [para(14(a,1),6721(a,2)),rewrite([8(7),12(7,R),8(6),6466(6)]),flip(a)].
% 3.24/3.58 6795 meet(A,join(B,meet(A,C))) = meet(A,join(B,join(C,complement(A)))). [para(6721(a,1),29(a,2,2,2)),rewrite([6794(10),8(4),12(4,R),2(3)]),flip(a)].
% 3.24/3.58 6800 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [para(59(a,1),6721(a,2)),rewrite([8(6),12(6,R),8(5),6466(5),1160(3),23(4)])].
% 3.24/3.58 6806 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [para(1604(a,1),6721(a,1,2)),rewrite([7(5),526(5),7(7),6795(7),12(7),8(6),12(7,R),8(6),6228(6),12(6,R),8(5),6800(7)])].
% 3.24/3.58 6807 $F # answer(prove_distributivity). [resolve(6806,a,16,a)].
% 3.24/3.58
% 3.24/3.58 % SZS output end Refutation
% 3.24/3.58 ============================== end of proof ==========================
% 3.24/3.58
% 3.24/3.58 ============================== STATISTICS ============================
% 3.24/3.58
% 3.24/3.58 Given=322. Generated=74411. Kept=6802. proofs=1.
% 3.24/3.58 Usable=230. Sos=4087. Demods=3136. Limbo=13, Disabled=2484. Hints=0.
% 3.24/3.58 Megabytes=11.95.
% 3.24/3.58 User_CPU=2.55, System_CPU=0.05, Wall_clock=3.
% 3.24/3.58
% 3.24/3.58 ============================== end of statistics =====================
% 3.24/3.58
% 3.24/3.58 ============================== end of search =========================
% 3.24/3.58
% 3.24/3.58 THEOREM PROVED
% 3.24/3.58 % SZS status Unsatisfiable
% 3.24/3.58
% 3.24/3.58 Exiting with 1 proof.
% 3.24/3.58
% 3.24/3.58 Process 13310 exit (max_proofs) Tue Jun 28 19:31:25 2022
% 3.24/3.58 Prover9 interrupted
%------------------------------------------------------------------------------